quantitative measurements of shrinkage and cracking during ...

QUANTITATIVE MEASUREMENTS OF SHRINKAGE ANDCRACKING DURING FREEZE-DRYING

OF AMORPHOUS CAKES

Der Naturwissenschaftlichen Fakultat

der Friedrich-Alexander-Universitat

Erlangen-Nurnberg

zur

Erlangung des Doktorgrades Dr. rer. nat

vorgelegt von

Sabine Ullrich

aus Aschaffenburg

Als Dissertation genehmigt

von der Naturwissenschaftlichen Fakultat

der Friedrich-Alexander-Universitat Erlangen-Nurnberg

Tag der mundlichen Prufung: 26.Juni 2014

Vorsitzender der Prufungsorgans: Prof. Dr. Johannes Barth

Gutachter/in: Prof. Dr. Geoffrey Lee

Prof. Dr. Hartwig Steckel

Fur meine Eltern und Sebastian.

Danke, dass ich immer auf euch zahlen kann.

ACKNOWLEDGEMENTS

The research work presented in this thesis has been performed between January 2010 and

March 2014 at the Division of Pharmaceutics, University of Erlangen-Nuremberg, Erlangen,

Germany.

First of all, Prof. Dr. Geoffrey Lee is gratefully acknowledged for giving me the opportunity to

work in the Division of Pharmaceutics, serving as my doctoral adviser, and for refereeing this

thesis. Many thanks for choosing the fascinating topic of this research, for the continuous

support throughout my work and for the tolerance to discuss and implement own ideas.

Prof. Dr. Steckel of the Department of Pharmaceutics and Biopharmaceutics at the Christian

Albrecht University of Kiel is gratefully acknowledged for co-refereeing this thesis.

Further I would like to thank Prof. Dr. Dr. Willi Kalender, Prof. Dr. Engelke, Dr. Svitlana

Gayetskyy, Dr. Oleg Museyko and Marek Karolczak from the Institute of Medical Physics for

their inestimable help with the µ-CT analysis and their development of the image evaluation

method.

Many thanks to all the staff at the Cauerstraße for making it a great pleasure for me to work

at that place. Very special thanks to Dr. Stefan Seyferth for always having an open door

for discussions, for the joint development of new ideas within my research work and for the

continuous support with all IT concerns or measurement devices within the department.

Petra Neubarth is gratefully acknowledged for her continual and competent support with all

kind of administrative issues. Thank you so much for receiving all my packages and for nice

chats. I would further like to thank Joseph Hubert for his invaluable and persevering support

concerning technical and mechanical questions, especially for his inestimable help to cut the

top shelf, to built the dark cell, and to take care of our ”Christ”. I would further gratefully thank

Luise Schedl for taking excellent SEM pictures of various lyophilizates and for the help and

conjoint time while supervising the student’s basic practical course. Thanks to Christiane

Blaha for the fast and reliable ordering of supplies and support of new equipment.

Thanks to Erasmus student Daria Rychlicka, my ”Wahlpflichtfach” students Theresa Franz,

Maraike Geier, and Alexandra Boersting. Your work has been a great help.

VI

Many thanks to my former colleagues Dr. Stefan Schneid, Dr. Georg Straller, Dr. Simone

Landwehr, Dr. Jakob Beirowski, and Dr. Susanne Hibler for giving me a warm welcome and

for your support. Special thanks to Dr. Georg Straller, who introduced me to the operating

of the ”Christ” and its tricky troubleshooting. You saved me plenty of time. Dr. Simone

Landwehr, thank your for out great time not only at the Department and for our enjoyable

conversations. Dr. Elke Lorenzen, Anne Mundstock, Felix Wolf, and Joachim Schafer,

thanks a lot for our joint attendance of the ”Fachapotheker” seminars and the wonderful and

unforgettable time we had together. In particular I would like to thank my favorite lab-mate

Felix Wolf for the great time we had in Erlangen, for the fruitful discussions and for sharing all

ups and downs through all the years at the department. I would like to thank Ulrike Stange

for our expert discussions, for introducing me to the Pore Master and for our lovely chats.

Matthias Erber, Anders Kunst, Julia Staudenecker, Sandra Wiedemann, Natalie Keil, Zixin

Huang, Alexander Grebner, Claudia Kunz, Jens Holtappels, Peter Startzel, I would like

to thank you for spicing up my time at the department. I enjoyed our funny time and

conversations during our new ”breakfast coffee”, lunch, coffee breaks and evenings. To the

girls, thanks for our enjoyable conversations and discussions during our lovely ”girly nights”.

Melinda Rupp, thank you for sharing my last months with me in the lab. I enjoyed our daily

”sweets break” very much. Claudia Kunz, thank your for making the last months at the

department unique. I enjoyed your friendship so much, I did not want to leave. Outside the

department I would like to thank Nele Bargmann for refereeing the Zusammenfassung and

for the wonderful time we had together.

Last but not the least important, I owe more than thanks to my parents Hanna and Klaus

who paved the way for my doctorate, to my brother Stefan, and Sebastian. Thank you so

much for your continuous support and encouragement during all the years, taking me as I

am and for being always on my side while I follow my path.

PARTS OF THIS THESIS HAVE ALREADY BEEN PRESENTED

I. : S. Ullrich, S. Seyferth and G.Lee, Technique to Determine Kinetics of Shrinkage

and Cracking of Amorphous Cakes during Freeze-Drying. Joint Meeting of the

Austrian and German Pharmaceutical Societies, Innsbruck (Austria), September

20-23, 2011. Poster presentation

II. S. Ullrich, S. Seyferth and G.Lee, Technique to Determine Kinetics of Shrink-

age and Cracking of Amorphous Cakes during Freeze-Drying, 8th World Meeting

on Pharmaceutics, Biopharmaceutics and Pharmaceutical Technology, Istanbul

(Turkey), March 19-22, 2012. Poster presentation

III. S. Ullrich, S. Seyferth and G.Lee, Formulation and Process Optimization to avoid

Shrinkage and Cracking during Freeze-Drying, 9th World Meeting on Pharma-

ceutics, Biopharmaceutics and Pharmaceutical Technology, Lisbon (Portugal), 31

March to April 3, 2014. Poster presentation

Table of contents

List of Abbreviations XIII

1 General Introduction 1

2 The Freeze-Drying Process 5

2.1 Freeze-Drying Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Process Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Primary Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.3 Secondary Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Heat and Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.3 Coupling between Heat and Mass Transfer . . . . . . . . . . . . . . 17

2.4 Monitoring Technology used for Freeze-Drying . . . . . . . . . . . . . . . . . 17

2.4.1 Invasive Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1.1 Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1.2 Resistance Thermal Detectors . . . . . . . . . . . . . . . . 19

2.4.1.3 Microbalance . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Non-invasive Measurements . . . . . . . . . . . . . . . . . . . . . . 21

2.4.2.1 Vacuum Gauges . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.2.2 Comparative Pressure Measurement . . . . . . . . . . . . 25

2.4.2.3 Dew Point Sensor . . . . . . . . . . . . . . . . . . . . . . 25

2.4.2.4 Pressure Rise Technology . . . . . . . . . . . . . . . . . . 26

2.4.2.5 Mass Spectrometry . . . . . . . . . . . . . . . . . . . . . . 27

Table of contents IX

3 Freeze-Drying of Amorphous Materials 29

3.1 The Amorphous State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Glass Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 Thermodynamic Approach considering Enthalpy and Free Volume . . 30

3.2.2 Thermodynamic Approach considering Entropy . . . . . . . . . . . . 31

3.2.3 The Kinetic Relaxation Approaches . . . . . . . . . . . . . . . . . . 32

3.2.4 Glass transition during Freeze-Drying . . . . . . . . . . . . . . . . . 33

3.2.5 Temperature Dependence of Viscosity and Relaxation Time . . . . . 34

3.2.6 Prediction of the Glass Transition Temperature . . . . . . . . . . . . . 36

3.3 Protein Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Product Appearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Fracture Mechanics of Solids 43

4.1 Mechanical Behavior of Solids . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Brittle Fracture and Ductile Fracture . . . . . . . . . . . . . . . . . . 47

4.2.2 The Energy-Balance Approach . . . . . . . . . . . . . . . . . . . . . 50

4.2.3 The Stress Intensity Approach . . . . . . . . . . . . . . . . . . . . . 53

4.3 Fracture of Glassy Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Materials and Methods 57

5.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.1 Amorphous Disaccharides . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.1.1 D-(+)-trehalose dihydrate . . . . . . . . . . . . . . . . . . . 57

5.1.1.2 D-(+)-sucrose . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.1.3 D-(+)-maltose . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.1.2 Bovine Serum Albumin (BSA) . . . . . . . . . . . . . . . . . . . . . 59

5.1.3 Overview of Excipients and Reagents . . . . . . . . . . . . . . . . . 59

5.1.4 Packaging Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.4.1 Freeze Dryer . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.4.2 Microbalance . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.5 Camera System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

X Table of contents

5.2 Freeze-Drying Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.1 Endpoint Detection of Shrinkage and Cracking . . . . . . . . . . . . 63

5.2.2 Determination of the Kinetics of Shrinkage and Cracking . . . . . . . 64

5.2.3 Freeze-drying Protocols . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3.1 Differential Scanning Calorimetry (DSC) . . . . . . . . . . . . . . . . 66

5.3.2 Mercury Porosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3.3 Scanning Electron Microscopy (SEM) . . . . . . . . . . . . . . . . . 67

5.3.4 Texture Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3.5 Contact Angle Measurements . . . . . . . . . . . . . . . . . . . . . 68

5.3.6 µ-CT-Imaging Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3.7 Ring Tensiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4 Image Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4.1 Image Evaluation of the Endpoint-Detection . . . . . . . . . . . . . . 71

5.4.2 Image Evaluation of the Kinetics . . . . . . . . . . . . . . . . . . . . 71

5.4.3 Image Evaluation of the µ-CT-Reconstructions . . . . . . . . . . . . . 72

6 Results 73

6.1 Endpoint Evaluation Method . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1.1 Development of the Image Evaluation Method . . . . . . . . . . . . . 73

6.1.1.1 Standardized Picture Taking . . . . . . . . . . . . . . . . . 73

6.1.1.2 Semi-Automatic Evaluation with Axio Vision . . . . . . . . . 76

6.1.1.3 Automatic Evaluation with Matlab . . . . . . . . . . . . . . 82

6.1.2 Statistical Comparison between Axio Vision and Matlab . . . . . . . . 85

6.1.3 Sample Selection and Edge Effect . . . . . . . . . . . . . . . . . . . 88

6.1.4 Shrinkage, Cracking and the Amount of Unfrozen Water, w′ . . . . . . 93

6.1.5 Impact of the Trehalose Concentration . . . . . . . . . . . . . . . . . 99

6.1.6 Impact of the Surface Chemistry on Shrinkage and Cracking . . . . . 106

6.1.7 Impact of the Fill Height and the Vial Diameter . . . . . . . . . . . . . 110

6.1.8 Impact of Hydrophobic Vial Coating . . . . . . . . . . . . . . . . . . 113

6.1.9 Impact of a Variation of the Freezing Step . . . . . . . . . . . . . . . 121

6.1.9.1 Standard Cooling Rate versus Slow Cooling Rate . . . . . . 122

Table of contents XI

6.1.9.2 Standard Cooling Rate versus Shock Freezing . . . . . . . 127

6.1.9.3 The Crack Pattern at Different Cooling Rates . . . . . . . . 129

6.1.10 Impact of the Freezing Protocol . . . . . . . . . . . . . . . . . . . . . 132

6.1.11 Impact of a Variation of the Freezing Step in Combination with the Use

of a Toplyo R© Vial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.2 Kinetic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.2.1 Development of Online Video Method during Freeze-Drying . . . . . . 142

6.2.1.1 Illumination of the Experiment Setup . . . . . . . . . . . . . 145

6.2.1.2 Selection of the Camera Setup . . . . . . . . . . . . . . . . 149

6.2.1.3 Heat Transfer on the Top Shelf . . . . . . . . . . . . . . . . 152

6.2.1.4 Influence of Vial Cutting on Shrinkage and Cracking . . . . 154

6.2.2 Development of a Kinetic Image Evaluation Method . . . . . . . . . . 156

6.2.2.1 Semi Automatic Picture Evaluation . . . . . . . . . . . . . . 156

6.2.2.2 Image Evaluation with Axio Vision . . . . . . . . . . . . . . 161

6.2.3 Kinetics of Shrinkage and Cracking of a 10% Trehalose Solution . . . 164

6.2.4 Kinetics of Different Trehalose Concentrations . . . . . . . . . . . . . 172

6.2.5 Impact of Ramp Rate to Secondary Drying . . . . . . . . . . . . . . 180

6.2.6 Impact of a Lower Primary Drying Temperature . . . . . . . . . . . . 185

6.2.7 Impact of Tween 80 or Glycerol . . . . . . . . . . . . . . . . . . . . . 190

6.2.8 Impact of a Protein . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.2.9 Kinetics of Different Disaccharides . . . . . . . . . . . . . . . . . . . 199

6.3 µ-CT Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.3.1 Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.3.2 Development of Adequate Measuring Conditions . . . . . . . . . . . 204

6.3.3 Image Evaluation of the µ-CT-Reconstructions . . . . . . . . . . . . . 205

6.3.4 Comparison between 2D-Analysis (Endpoint Evaluation Method) and

3D-Analysis (µ-CT) . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6.3.5 Comparison between the 3D-Structure of Samples obtained in a Reg-

ular and a Toplyo R© Vial . . . . . . . . . . . . . . . . . . . . . . . . . 213

7 Conclusions 217

XII Table of contents

8 Zusammenfassung 221

9 Appendix 225

List of Abbreviations

EXPRESSIONS

Symbol Meaning

API Active Pharmaceutical Ingredient

AEB Auto Exposure Bracketing

BSA Bovine Serum Albumin

BTM Barometric Temperature Measurement

CM Capacitance Manometer

CMC Critical Micelle Concentration

DSC Differential Scanning Calorimetry

EPFM Elastic-Plastic Fracture Mechanics

FDA Food and Drug Administration

GMP Good Manufacturing Practice

HDR High Dynamic Range Image

HP High Pressure Measurement

LED Light Emitting Diode

LEFM Linear-Elastic Fracture Mechanics

LP Low Pressure Measurement

XIV Table of contents

MTM Manometric Temperature Measurement

RGA Residual Gas Analysis

PDT Primary Drying Temperature

RTD Resistance Thermal Detector

SEM Scanning Electron Microscopy

TC Thermocouple

VOI Volume of Interest

CAPITAL LETTERS

Symbol Unit Meaning

A% [%] Fragment’s Area to the Area of the Whole Cake

AC [m2] Crack Area

AI [m2] Inner Area of the Vial

Af [m2] Area of a Cake Fragment

AF [m2] Area of the Whole Cake

Av [m2] Cross sectional Area of the Vial (outer diameter)

Ap [m2] Product Area (outer diameter)

Cp [J/K] Heat Capacity

df [-] Degree of Freedom

E [GPa] Young’s Modulus

mc [-] Mean Color Value of the Cake

Table of contents XV

H [J] Enthalpy

Hs [J] Heat/Enthalpy of Sublimation

Kc [J/s m2 K] Vial Heat Transfer Coefficient (Conduction)

Kr [J/s m2 K] Vial Heat Transfer Coefficient (Radiation)

Kg [J/s m2 K] Vial Heat Transfer Coefficient (Convection)

KIc [MPa ·m1/2] Stress Intensity Factor

Kv [J/s m2 K] Vial Heat Transfer Coefficient (Total)

Lice [m] Thickness of the Ice Layer (Total)

Pc [Pa] Chamber Pressure

Pcd [Pa] Vapor Pressure of Ice at the Surface of the Condenser

Pice [Pa] Equilibrium Vapor Pressure of Ice at the Sublimation Interface

Psat [Pa] Saturation Vapor Pressure

Pv [Pa] Partial Pressure of Water Vapor in the Head Space of the Vial

PY [-] Yielding Point

lm [m] Major Width of a Cake Fragment

R% [%] Fragment’s Width to the Radius of the Whole Cake

Rp [m2 Pa s/kg] Product Resistance

Rs [m2 Pa s/kg] Stopper Resistance

S [J/K] Entropy

T0 [K] Vogel Fulcher Temperature (see TK)

Tc [K] Collapse Temperature

Te [K] Eutectic Temperature

XVI Table of contents

Tg [K] Glass Transition Temperature

T ′g [K]

Glass Transition Temperature of the Maximally

Freeze Concentrated Solute

Tg(mix) [K] Estimated Glass Transition Temperature of the Formulation

TK [K] Kauzmann Temperature

Tf [K] Freezing Temperature

Tp [K] Product Temperature

Ts [K] Shelf Temperature

Vocc [m3] Occupied Volume

Vspec [m3] Specific Volume

Vf [m3] Free Volume

SMALL LETTERS

Symbol Unit Meaning

w′ [%]Content of non-frozen Water in the Maximally

Freeze Concentrated State

B IG GREEK LETTERS

Symbol Unit Meaning

Γ [mg/m2] Surface Excess Concentration

Table of contents XVII

SMALL GREEK LETTERS

Symbol Unit Meaning

e [-] Emissivity

k [kg m/s3 K] Thermal Conductivity

σb [J/K] Boltzmann Constant (1.3806504 · 10−23J/K)

σ [MPa] Stress

ǫ [-] Deformation

ǫB [-] Deformation at Breaking Point

τr [s] Relaxation Time

η [Pa s] Viscosity

1 General Introduction

Freeze-drying or lyophilization is still the method of choice to establish a stable biopharma-

ceutical product [1, 2] despite its complexity and cost. Approximately 50% of all biophar-

maceuticals during the last 20 years were stabilized with freeze-drying [3]. Nevertheless,

the lyophilization process can cause a diversity of potential difficulties during the freezing

and drying procedure such as pH change, formation of ice crystals and solute concentration

which may damage proteins. Therefore it is in most cases important to use stabilizers in a

formulation to keep labile proteins in their native state during the entire lyophilization pro-

cess. A number of carbohydrates, especially amorphous disaccharides, are used as such

stabilizers [4].

However, the application of these stabilizers or bulking agents may cause problems

with cake appearance (pharmaceutical elegance). The freeze-drying of fully amorphous

lyophilizates from protein drugs in combination with a bulking agent like trehalose or sucrose

usually leads to a product with optical defects known as shrinkage and cracking [5, 6, 7].

Shrinkage is a contraction of the lyo mass and cake detachment of the freeze-dried cake

from the inside walls of the glass vial. Consequently, the cake does not fill the entire interior

of the vial, but leaves a gap between the inner wall of the vial and the cake. In the case of

cracking the cake is lacerated in numerous places and the product shows fissures or cracks

inside the dry matrix. These two phenomena occur either alone or together [5].

Shrinkage is a macroscopic change in cake structure and therefore must be carefully dis-

tinguished from a loss of microstructure of the cake resulting in a collapse of the solute

framework [8]. This collapse is caused by the product temperature, Tp, exceeding the col-

lapse temperature, Tc, of an amorphous formulation. Tc is related to the glass transition

temperature of the maximally freeze-concentrated solute, T ′g, and collapse can occur either

during primary drying (Tc ≈ T ′g) or secondary drying, when Tc approaches the glass transi-

2 1 General Introduction

tion temperature, Tg. Cracking and shrinkage appear to be no consequence of exceeding Tc,

but are likely caused by tension or stress in the cake that lead to plastic flow or brittle fracture

of the lyophilizate mass during drying [5]. Cracks may be a result of removal of unfrozen

water by evaporative drying and leads to an accelerated rate of freeze-drying because of

enhanced water vapor transfer through cavities and fissures [8].

Shrinkage produces a serious heterogeneity with respect to the residual water content.

The rate of mass transfer is offered less resistance in the peripheral cake region in the result-

ing gap between cake and glass wall than in the central region. This may lead to a nonuni-

form drying behavior [9]. A heterogeneous water content through the cake can exacerbate

damage to proteins and lead to a shorter shelf life as well as a narrower range for storage

temperature [5, 10]. In addition, reconstitution may be hindered, so a particulate-free solu-

tion with satisfactory content uniformity cannot be assured [10, 11]. Consumer and physician

acceptance for a shrunken and cracked product is also questionable if not doubtful [12]. In

summary, the question of pharmaceutical elegance constitutes not only a visual problem, but

is a relevant product property of a lyo as already cited by the Food and Drug Administration

(FDA) [3, 13].

The research presented in this thesis is focused on studying freeze-drying introduced

shrinkage and cracking, on developing a quantification method for in situ measurement and

reducing or avoiding either or both. On the basis of the current state of knowledge a general

avoidance or reduction in shrinkage and cracking is tackled by different ways. Freeze-drying

cycles can be applied that - according to visual observation - lead to less shrinkage of a fully

amorphous cake. The few publications on this topic report the application of product temper-

atures that are well below Tc and give therefore long process durations, hardly acceptable for

a commercial application [5, 14]. The inclusion of an annealing step at the end of the freezing

phase may also counteract to some extent the development of cracking [15].

The mechanisms underlying these more or less successful measures to avoid shrinkage

and cracking have never been investigated. Either ”internal stresses” [15] or the formation of

”crystalline networks” [14, 16] were suspected to be accountable, but these are only vague

ideas. Above all, there is a lack of a basic outline of the cause and development of shrinkage

and cracking during the three phases of freeze-drying. Furthermore, the relationship between

the two separate phenomena is unclear: there may occur both, or just one and also neither.

3

It is also questionable whether the total amount of changes, i.e. shrinkage and cracking of

the cake, is dependent on the formulation. An apparent correlation between shrinkage and

the content of non-frozen water in the maximum freeze-concentrated state, w′, has been

reported on the basis of a single substance, sucrose [5]. The same authors postulate that

adhesion between the inside wall and the lyo mass may be relevant for shrinkage, but without

verifiable data. Even the time point of occurrence is uncertain: either after the removal of the

ice (i.e. first during the secondary drying step) or already during primary drying.

There are no quantitative measurements of the extent of shrinkage and cracking and their

kinetics determined in situ during the three phases of lyophilization. There is also no suitable

method for an accurate, quantitative determination of the degree of both processes in one

finished vial. The stresses or adhesion forces occurring in the lyo have also never been

investigated.These deformations of a freeze-dried product can substantially affect both the

process time and the energy consumption, owing to the reduced contact area between the

cake and the inside wall for thermal conduction.

The results of this work should therefore offer a better understanding of both the kinetics

and the incidence of shrinkage and cracking in dependence on process and formulation

parameters. The mechanisms that trigger these cake changes should be elucidated. The

central issue is to establish a method to quantify shrinkage and cracking both in the end

product and in situ. The results should provide the user of amorphous cakes during freeze-

drying with more knowledge for a targeted prevention or reduction in shrinkage and cracking.

2 The Freeze-Drying Process

Freeze-drying is a desiccation technique used to produce a solid form characterized by a

sponge-like appearance and a high specific surface area. Sensitive materials such as pro-

teins or aromatic ingredients can also be preserved by their immobilization during freezing

and the low process temperatures used [17, 18]. The advantages of lyophilization over other

drying techniques are numerous, for example rapid and complete reconstitution owing to the

large specific surface area, accurate and reproducible dosing, as well as the ability of sterile

manufacturing. However, there are some distinct disadvantages to the freeze-drying method.

The long process time and the associated high operating costs of vacuum and freezing equip-

ment. Though there are continuous freeze-dryers available, lyophilization is in most cases a

batch process that charges a limited amount of vials or trays processed in each run [18].

2.1 Freeze-Drying Equipment

To achieve the low temperatures and pressures required for the lyophilization process, spe-

cific equipment is necessary (Figure 2.1). The main parts are a drying chamber (2), a con-

denser chamber (5) and a vacuum pumping system (6) [3]. The drying chamber encloses the

shelves on which the containers (e.g. vials or trays) are placed. It also ensures attainment of

the necessary pressures and aseptic conditions [19]. The shelves (1) and (3) are hollow with

a cooling and heater circuit to control the required temperatures [20]. In some laboratory

scale freeze-dryers, the shelves are only heatable and the freezing step has to be carried

out externally. In some machines the top shelf represents an unusable shelf (1), a radiation

shield for the vials on the lower usable shelf [19]. A hydraulic system is usually attached to

move the shelves together for the stoppering procedure at the end of lyophilization.

The configuration of the drying chamber depends on the application (e.g. laboratory scale

6 2 The Freeze-Drying Process

(1)(2)

(3)

(4)

(5)

(6)

Figure 2.1: General layout of a Freeze-Dryer: (1): Top shelf, (2): Drying Chamber, (3): Usableshelves, (4): Condenser, (5): Condenser chamber, (6): Vacuum pumping system.Adapted from [19].

or food/plant products). A baseplate with a bell, cylindrical chambers or tunnels with circu-

lar cross-sections are also possible [21]. In the majority of cases, however, the door is of

stainless steel, acrylic glass or PlexiglasTM with the chamber walls made of stainless steel.

The drying chamber is linked to a condenser chamber via a valve. A pumping system is

used to produce the sub-atmospheric pressures required during the freeze-drying process

and to remove non-condensable gases [19]. The condenser is constructed having several

plates or loops which are suitable to hold low temperatures down to -70 C [19]. On its surface

the water vapor generated during drying is condensed to ice [22].

2.2 Process Steps

The freeze-drying process is classically split in three parts: freezing, primary drying and

secondary drying. During freezing most of the liquid phase, usually water, is converted to ice

[21, 22]. Primary drying is the step where the ice is removed by sublimation. During the last

2.2 Process Steps 7

step, secondary drying, the unfrozen part of the solvent is desorbed and eliminated [18].

2.2.1 Freezing

After the preparation and filtration of the formulation (composed of the drug and several

excipients) the product solution is filled into containers. These are mostly tubing or molded

glass vials, but others e.g. plastic vials, glass ampoules, syringes and blisters can also be

used. The containers are positioned on the shelves of the freeze-dryer and chilled typically

to about -40 C to execute the freezing step. The product solution is cooled only slightly

more slowly than the shelf and stays several degrees above the shelf temperature, Ts [22,

23]. Kasper et. al. [24] describe this freezing step as in the following. On crossing the

equilibrium freezing point of the solution it remains liquid without spontaneous freezing (A,

Figure 2.2). Ice crystallization (point B) usually starts at temperatures about 10-15 C below

A

B

CD

E

Figure 2.2: Freezing behavior: Product and shelf temperatures during shelf freezing with A:supercooling and cluster forming, B: ice crystallization, C-D: Freezing time, icecrystal growth, E: completion of freezing. Adapted from [24].

the equilibrium freezing point [25]. This can depend on the degree of vibrations experienced

in any particular machine. The range between the equilibrium freezing point and incipient ice


crystallization is called supercooling and is a meta-stable state. It can be considered as an

”activation energy” that is required for the nucleation procedure [24].

On decrease in temperature density fluctuations occur in the supercooled liquid water,

whereupon molecular clusters (nuclei) arranged similar to ice crystals are formed transiently.

This state is energetically more favorable at lower temperatures, and accordingly the forma-

tion, maintenance and growth of the clusters becomes more pronounced as the temperature

falls. At point B the clusters have reached a sufficient extent that the formation of ice crystals

starts. A crystallization procedure where only one ice cluster is formed that subsequently

grows is termed homogeneous nucleation and should occur at about -40 C for water [26].

Even when using sterile-filtered water it is unlikely that homogeneous nucleation can take

place. Clusters form at higher temperatures is caused by the formation of nuclei on ”im-

purities” in the solution such as foreign particles (heterogeneous nucleation). From point B

to point C an incipient ice network is formed as ice crystal growth proceeds. The product

solution’s temperature now rises because of the release of latent heat of fusion [26]. Sub-

sequently, the major freezing period from point C to point D takes place in which a large

proportion of the water is converted to ice. At point E the freezing of the sample is completed

and the temperature decreases further in near parallel to the shelf.

During ice formation (C-E) the non-frozen interstitial fluid between the growing ice crystals

becomes more concentrated (”freeze-concentration”) until it finally solidifies due to crystal-

lization of the residual water alongside the crystalline excipient [22, 26]. An eutectic mixture

is generated at the eutectic temperature, Te. If no crystallization of the excipient occurs, the

interstitial fluid remains amorphous. With increasing ice crystal growth the amorphous phase

becomes more concentrated until at T ′g its viscosity increases to >1014 Pa s and the ice crys-

tal growth stops [26]. At this point an amorphous glass is formed with a specific amount of

unfrozen water, w′ [3, 22]. Knowledge of Te and T ′g of a formulation is essential, as these

values determine the temperature during freezing and also the maximum possible product

temperature during primary drying in order to avoid loss of cake structure by deformation,

partial or total collapse and meltback [5, 26].

The ice formation process is complex because it depends on several factors like process

parameters, formulation characteristics, filling volume or depth, concentration of the ingredi-

ents, as well as the properties of the vial surface [24, 25]. Yet, freezing is the ”key” step of the

2.2 Process Steps 9

whole process as it determines the quantity, the shape and the dimensions of the ice crystals

and pores. A high degree of supercooling (low nucleation temperature) and a high nucleation

rate leads to numerous small crystals. A low degree of supercooling and a low nucleation

rate causes a lower number of large ice crystals [23]. The specific surface area of the final

product is therefore already fixed during freezing. Small ice crystals should lead to a high

product resistance to vapor flow, Rp, and therefore prolonged primary drying times [7, 27].

The duration of secondary drying should, however, be reduced, since small ice crystals offer

a large specific surface area and an easy desorption of unfrozen water from the pore surface

[27]. This, in particular, has to be considered during the lyophilization of amorphous materials

possessing a high amount of unfrozen water. The freezing step represents the desiccation

process, as the majority of water is phase-separated from the solute components in the form

of ice crystals [5].

2.2.2 Primary Drying

Primary drying is defined as the process of solvent removal by sublimation and is performed

after the complete solidification of the solution during freezing. The sublimation of ice, i.e.

water, is enabled since ice has a vapor pressure. The system pressure is reduced to below

that of the triple point (in the range of 4-40 Pa) and the shelf temperature is increased to

provide the necessary enthalpy of sublimation [22].

The product temperature, Tp, at the sublimation interface is a major process parameter, as

it determines primary drying time and influences product quality (stability, residual moisture,

reconstitution time) [12]. It depends on the formulation properties, shelf temperature and

chamber pressure, Pc [28]. A 5 C rise in product temperature reduces the primary drying

time by a factor of 2, since a higher product temperature accelerates sublimation [29]. Hence,

primary drying should be performed at the highest possible Tp to achieve a short process time

(primary drying is normally the longest step in the whole freeze-drying cycle). However, the

upper limit of Tp, termed the ”maximum allowable temperature” or ”critical temperature” [29]

has also to be considered. This relates to Te for crystalline solutes and to Tc or T ′g if the

solute does not crystallize. Exceeding it leads to a loss of structure since the porous cake

formed close to the sublimation front still contains high amounts of water. Furthermore, the

viscosity of an amorphous solid decreases as a function of T−T ′g [30]. As a consequence the


matrix undergoes viscous flow causing loss of microstructure with closure of pores. Thereby

the specific surface area is reduced and the moisture content remains high [30]. This may

cause adverse effects on protein stability during storage and reconstitution behavior [10]. The

target product temperature is therefore selected approximately 2 C lower than the critical

temperature to obtain a dry product with acceptable appearance [22].

The chamber pressure, Pc, impacts both heat and mass transfer (see chapter 2.3). The

gradient between Pc and Pice, the equilibrium vapor pressure of ice at the sublimation inter-

face, constitutes the driving force for sublimation. If Pc is kept well below Pice at the target

product temperature, a high sublimation rate is accomplished. However, very low chamber

pressures are technically difficult to maintain at a constant value. Product quality can also be

compromised by contamination with vaporized vial stopper components or pump oil. Heat

transfer to the product is also low. A suitable chamber pressure, Pc, at known target product

temperature, Tp, can be estimated via Equation 2.1 [31].

Pc = 0.29 · 10(0.019 ·Tp) (2.1)

As soon as Pc falls below Pice in the product, sublimation begins from the top of the frozen

cake and moves down to the vial base with progressing primary drying. The boundary be-

tween ice and dried product is the ice-vapor interface. It is thought not to remain planar during

primary drying, but rather curved, because the sublimation process runs faster in the region

near the vial wall, as depicted in Figure 2.3 [9]. The water vapor reaches the condenser and

Linear Actual

Dry

Frozen

Figure 2.3: Schema of suggested geometry of the ice-vapor interface during primary drying.Adapted from [9].

is condensed and frozen on the condenser coils or plates which are cooled to about -70 C.

At the former position of the ice crystals there are now pores or ”ice ghosts” when the sub-

limation process is finished. Hence, an open network of pores is formed which serves as

2.2 Process Steps 11

pathways for the water vapor created in subsequently secondary drying [22]. Since sublima-

tion consumes energy, the product is cooled and sublimation slows down. To maintain the

ongoing removal of ice the shelves are heated to compensate this enthalpy consumption. To-

wards the end of primary drying this demand for heat reduces and Tp rises to approximately

that of Ts [19].

2.2.3 Secondary Drying

At the end of primary drying, the porous cake still contains moisture in terms of unfrozen

water. For a crystalline solute the remaining water comprises surface-adsorbed water, hy-

dration water, or water of crystallization. Mass transfer is therefore determined by desorption

and vaporization. As the amount of water is limited by the available specific surface area and

therewith low, the product is almost dry at the end of primary drying and secondary drying

is short [26]. In contrast for an amorphous solute with a glassy matrix the content of w′ ac-

counts for up to 40%, which is dissolved in the glassy amorphous phase as a solid solution

[26, 32]. Since mass transfer proceeds by molecular diffusion within the glassy phase and

the content of water is large, this drying stage can be long.

The secondary drying process is not clearly delineated from primary drying. Instead, both

processes run parallel. Once the ice has been locally removed by sublimation, the residual

dissolved water starts to leave in this region [32]. Ts is increased to a level higher than that

during primary drying to accelerate desorption. If Tp rises above Tg, due to the progres-

sive drying, a risk of collapse is likely [31]. Hence the temperature ramp has to be carried

out slowly for amorphous materials. In contrast, for crystalline products there is no danger

of collapse and a high ramp rate to secondary drying can be performed. As the chamber

pressure has no influence on the desorption rate, a further reduction in Pc is not necessary

[9, 31, 32, 33]. For most freeze-dried active pharmaceutical ingredients (APIs) the stabil-

ity increases with lower moisture content and secondary drying should therefore produce a

moisture of less than 1% [9, 34]. For proteins it is especially important to develop adequate

drying conditions that compromise between high thermal stress and low moisture content.


2.3 Heat and Mass Transfer

2.3.1 Mass Transfer

During primary drying, the water vapor has to overcome several barriers (resistances) on

its way between sublimation front and condenser. These lie in the partially dried product,

the openings of the stopper and the gas phase in the chamber to condenser pathway as

shown in Figure 2.4 [29]. The resistance impairing the mass transfer most is that of the

Resistance

Chamber

Stopper

Product

Condenser, Pcd

Pc

Pv

Dried Product

Ice, Pice

Figure 2.4: Schema of resistances to mass transfer in primary drying. Pice: vapor pressureof ice at the sublimation interface, Pv: Partial pressure of water vapor in the headspace of the vial, Pc: Partial pressure of water vapor in the chamber, Pcd: vaporpressure of ice at the surface of the condenser. Adapted from [35].

dried layer, the so-called product resistance, Rp. It accounts for nearly 80% of the total

mass transfer resistance between sublimation front and condenser [35, 36]. This resistance

depends on the cross-section area of the product as well as the vial diameter, the thickness

of the product layer and the container wall used [29]. Accordingly, Rp is higher with higher

solute concentration and increases as primary drying proceeds and the thickness of the

dried product layer lengthens [22]. Another parameter affecting Rp is the morphology of the

dried cake the water vapor has to pass through. The amount, shape, interconnection, and

2.3 Heat and Mass Transfer 13

dimensions of the ice crystals and therefore the pore size of the dried cake all depend on the

freezing protocol [37].

A further mass transfer barrier is the openings of the stoppers, the only outlet for the water

vapor from the vial. Before freeze-drying the stoppers are positioned, but not pushed onto

the necks of the vials to leave an opening for the water vapor. The diameter of the stopper

openings is in the range of 0.2-0.4 cm, which means that the area for vapor flow is large

in comparison to that of 15-60µm of the pores [38]. Therefore stopper resistance, Rs, is

negligible in comparison to the resistance of the dried product, with the possible exception

of the freeze-drying of very dilute solutions [22, 36]. The chamber to condenser pathway

constitutes another resistance to mass flow, since the water vapor needs to pass through

this gas phase. The dimensions of this distance vary greatly from machine to machine, so

that the resistance arising during this pathway varies accordingly [38].

The mass transfer rate, dmdt

, is therefore related to the difference between Pice and Pc, and

the resistance to vapor flow from the frozen product to the drying chamber [31]:

dm

dt=

Pice − Pc

Rp +Rs

. (2.2)

The mass transfer rate increases directly with larger pressure gradient between the subli-

mation front and the chamber and decreases with higher resistance to vapor flow. As the

stopper resistance is insignificant, the primary drying rate depends in the first instance on Rp

as largely determined by the freezing step [37].

2.3.2 Heat Transfer

For the sublimation process some 660 cal/g [38, 39] is necessary to convert ice to water

vapor and is provided by the freeze-dryer shelves [38, 39]. This heat has to be transferred

under vacuum from the shelves to the sublimation front. During this process the heat has to

cross a number of barriers like the transport through the shelf to its surface, the gap between

the shelf surface and the vial base, as well as the base of the vial and the frozen product [36].

Pikal [35] identified the major barrier to heat transfer as the gas-filled gap between the surface

of the shelf and the base of the vial (Figure 2.5). Only about 5% of the total surface between

the shelf and the vial is directly in contact due to an uneven vial base [26]. This curved base


results from the vial production process and is more pronounced for molded vials, but even

tubing vials exhibit only a small direct contact interface to the shelf [40, 41, 42]. The product,

the thickness of the glass, and the transfer of heat through the shelf up to its surface have

no substantial influence on heat transfer in a modern freeze dryer [36, 38, 40]. The heat

exchange takes place mainly between the glass vials and the stainless steel shelf on which

the vial is loaded. The walls of the freeze-drying chamber and the shelf above the vials also

contribute to heat transfer [43]. As shown in Figure 2.5 there are three mechanisms for heat

exchange: convection, conduction and radiation [36, 43].

d

g

convection

shelf

conduction

water vapor

radiation

dry layer

sublimation front Tp < Tc

ice core

Figure 2.5: Mechanisms of heat transfer to the product. Adapted from [44].

Conduction is the direct exchange of energy between two solid materials by molecular

motion. At freeze-drying it takes place in the contact zones between the shelves and the vials,

and subsequently between the vial and the product. The rate of heat transfer is described by

Fourier’s law, Equation 2.3:dQ

dt= −kA · dT

dx(2.3)

where dQdt

is the rate of heat transfer, k is the thermal conductivity, A is the area normal to the

direction of heat flow and dTdx

is the temperature gradient [26]. The amount of heat transfer, Q,

as expressed in Equation 2.3, is therefore proportional to the temperature difference between

the warmer shelf and the colder vial. The contact area between the base of the vial and the

shelf is determined by the container type used, as described above [43]. The fraction of

2.3 Heat and Mass Transfer 15

the total heat transfer caused by conduction cannot be calculated, since the temperature

difference between the shelf surface and the product at the container base results from all

three contributions to heat transfer. The contact area for a vial type may be estimated with

print tests shown in Figure 2.6 [36]. In this example the 10 ml Thuringer Pharmaglas tubing

(a) (b)

Figure 2.6: Prints of a 10 ml Thuringer Pharmaglas tubing vial (a) and a 10 ml Schott Toplyo R©

tubing vial (b).

vial (a) has a higher contact area with the shelf than the 10 ml Schott Toplyo R© tubing vial (b).

Radiation takes place, for example, between the cold vial and the shelf, the overlying

shelf as well as the chamber door and its walls [38]. Thermal radiation requires no medium

for energy transport, as the energy is transmitted by electromagnetic waves from warmer

surfaces and is absorbed by colder surfaces. The amount of energy per time transmitted by

radiation is given in terms of the Stefan-Boltzmann equation [36]

dQr

dt= Av · e · σb · (T 4

2 − T 41 ), (2.4)

where dQr

dtis the radiation heat flow, Av is the cross sectional area of the vial, e is the effective

emissivity for exchange of radiation (in the range of 0 and 1), σb is the Boltzmann constant

and T 42 −T 4

1 is the difference in the absolute temperatures of the two surfaces to the power of

four. The temperature difference between both surfaces is therefore the most powerful factor.

The effective emissivity e varies for different surface materials used in the construction of

a freeze-dryer. For example, for acrylic glass doors which show a high emissivity (0.86). The

walls are made of polished stainless steel with a much lower effective emissivity of about 0.59

[45]. Thermal radiation does not contribute a major part to heat transfer because of the low

temperatures during freeze-drying [46]. It affects, however, the inter-vial homogeneity in heat

transfer rates depending on the position on the shelf, especially for scale-up. The so-called

”edge effect” impacts in first instance the vials in an outer position closer to the warm surfaces


of the chamber walls and door. This leads to a higher drying rate of these vials up to 15%

[36] to 50% [46]. These differences are a serious issue in process control, since the product

temperature is often monitored in center positioned vials with a lower product temperature.

Vials positioned closer to the condenser chamber could radiate energy to the condenser

and have therefore a lower sublimation rate. To attenuate heat transfer by radiation a tightly

arranged, hexagonal positioning of the vials on the shelf is recommended [47].

Convection takes mainly place in the air gap between shelf and vial base. In this cavity

energy is transferred from the shelf to the gas molecules which move upwards to contact

the vial base. Convection is a pressure-dependent process and the heat flow increases with

increasing gas pressure since a higher amount of energy can be transported [38]. Convection

is influenced by the vial geometry, as the width of the gap varies accordingly [35]. The

distance that an average gas molecule can pass between two collisions is termed the mean

free path, depending on the pressure [18]. If the mean free path is small compared with

specified distance (vials with a large gap), then collisions between gas molecules are more

likely than collisions between gas molecules and the vial base wall and heat transfer is limited

[26]. The heat flow is expressed as

dQ

dt= Av ·Kv · (Ts − Tp), (2.5)

where dQdt

is the heat flow from the shelf to the product in a given vial, and Kv is the vial

heat transfer coefficient [29, 36, 38]. Equation 2.5 assumes that the overlying shelf above

the vials is at the temperature Ts and considers the temperature differential between ice at

the vial base and the subliming ice [36]. Kv is composed of the three different contributions

to heat transfer [35]:

Kv = Kc +Kr +Kg. (2.6)

Kc is the fraction arising from direct conduction from shelf to vial via direct contact (gas-

independent), Kr is the contribution by radiative heat (gas-independent), and Kg is the

pressure-dependent gas conduction inside the gap between shelf surface and vial base

[36, 38]. Kv is furthermore defined as the ratio of the area (Av) normalized heat flow (dQdt

)

and Hs the heat of sublimation of ice (660 cal/g), to the temperature difference between Ts

2.4 Monitoring Technology used for Freeze-Drying 17

and Tp:

Kv =dQdt

·∆Hs

Av · (Ts − Tp). (2.7)

Kv is dependent on the type of vial and increases with higher Pc [29].

2.3.3 Coupling between Heat and Mass Transfer

The coupling between heat and mass transfer is depicted in Equation 2.8 in the usual way

and linked by ∆Hs:dQ

dt= ∆Hs ·

dm

dt. (2.8)

dQdt

is the heat flow, and dmdt

is the mass flow rate [38]. During primary drying in vials the main

part of this process step is carried out under steady state conditions. The heat input from

the shelf fluid is in equilibrium with the amount of heat removed by sublimation, and Tp does

not change. The insertion of Equations 2.2 and 2.5 into Equation 2.8 describes this balance

between heat input from the shelf (left side) and heat removed by sublimation (right side)

during the steady state, to give:

Av ·Kv · (Ts − Tp) = ∆Hs ·P0 − Pc

Rp +Rs

. (2.9)

2.4 Monitoring Technology used for Freeze-Drying

Tp is the major product parameter during a lyophilization process and needs to be maintained

below the critical temperature to give a product with the desirable properties [48]. Neverthe-

less, primary drying should be performed at the highest possible product temperature to

achieve process efficiency. Tp is determined by the relative rates of heat and mass transfer

which in turn depend on Ts and Pc. The monitoring technology for these process parameters

is described in the following section.


2.4.1 Invasive Measurements

2.4.1.1 Thermocouples

The monitoring of Tp during freeze-drying on the laboratory scale is carried out using thin wire

thermocouples (TC) [18]. A TC is build on two dissimilar metals (e. g. copper-constantan,

chromel-alumel ) brazed at the tip [26]. TCs can be applied over a wide temperature range

depending on the combined metals used. They usually show an accuracy of only ±1 K

[49]. TCs have the advantage of allowing temperature measurement at a precise location

within the product container [50]. Furthermore, they are small, simple, self-powered and in-

expensive [18]. The functionality works on the Seedbeck effect which describes the electrical

potential difference that occurs in an electrically-conducting material with a nonuniform tem-

perature distribution [51]. If two wires composed of dissimilar materials are joined at both

ends and the two junctions are at different temperatures, then a continuous electric current is

created around the circuit (Figure 2.7a). If there is only one junction between the two wires,

Metal A

Metal B

Metal A

Metal B

+

-

(a) (b)

Figure 2.7: The Seedbeck effect (a) and the Seebeck voltage (b). Adapted from [18].

as is the case with a TC, a voltage (Seebeck voltage) can be measured across both open

ends (Figure 2.7b). This voltage is linearly proportional to the temperature at the junction

for small changes in temperature. The Seebeck voltage can therefore be correlated to the

temperature [52]. TCs are placed through the stopper into the center of the vial with con-

tact between its temperature-sensitive tip and the vial base. This position regime is of great

importance for endpoint-detection of primary drying. Drying progress proceeds from the top

to the base of the vial and from its edge to center [9, 22]. Hence, the final sublimation of

ice takes place at the base center of the vial and is accompanied by a sharp increase in

Tp. Incorrect thermocouple placement could thereby give a too-early endpoint and impair the

product quality. To ensure correct TC fixing during loading or freezing, the TC wire should be


placed under slight tension.

The use of TCs is an invasive measurement. Thermocouples can produce heterogeneous

ice nucleation as the bare TC constitutes an ice nucleation site and reduces the degree

of supercooling. Hence, nucleation proceeds at higher temperatures than without a TC.

Accordingly, the frozen matrix in which the thermocouple is located has a different frozen

structure with larger ice crystals and consequently larger pores in the dried product layers.

This results in a lower resistance to mass transfer making vials with inserted thermocouples

dry faster [22, 48]. The vials containing thermocouples are not representative of the rest

of the batch. For primary drying endpoint detection an additional, so-called soak period of

10-30% is therefore added to the time point at which the thermocouple Tp approaches the

shelf temperature [53]. Thermocouples cannot be used with automatic loading systems and

are usually positioned in the front row close to the door to minimize the chance of sterility

compromise during their placement. These vials suffer higher heat transfer due to radiation

effects [46]. In addition, the positioning of the thermocouples wires, the loading of these

vials, and connection to the thermocouple port has to be carried out manually. A sterility risk

cannot be excluded.

2.4.1.2 Resistance Thermal Detectors

Resistance thermal detectors (RTDs, Pt100) can be used for the monitoring of temperature.

They are constructed from platinum due to its corrosion resistance as well as its relatively

high electrical resistance [18]. Standard platinum RTDs offer a resistance of 100Ω at 0 C.

They are chemical inert and show linear behavior, they resist corrosion, are easy to steril-

ize and offer a mechanical robustness. Furthermore, the electrical signal is stable over a

wide temperature range [50]. The principle of measurement is based on the temperature

dependence of the electrical resistances of metals. With increasing temperature the resis-

tance increases linearly. To determine the resistance a Wheatstone bridge is used. To avoid

temperature changes, the platinum element is separated from the bridge, as illustrated in

Figure 2.8. Since an electrical current is necessary for measurement of the temperature-

dependent resistance, more heat transfer is possible. In addition, the sensing tip possesses

a large mass leading to disadvantages like an imprecise location and a temperature profile

across the length of the tip. This is especially relevant with small product containers or low


+-

RTD

Figure 2.8: Wheatstone bridge: RTD.

fill volumes, where the RTD may extend above the solution and measure a mixture of gas

headspace and Tp. As temperature measurement with RTDs takes place in a single vial, the

errors of ice nucleation occur together with the consequences on morphology of the cake,

drying behavior and endpoint detection (see 2.4.1.1). In comparison to TCs, RTDs are expen-

sive, larger and require a power source [18]. The overall disadvantage during temperature

measurements with TCs or RTDs is their non-applicability with automatic loading systems

during manufacturing scale [54]. Wireless solutions (active transponders) are available to

avoid this problem, but they require battery capacity leading to a limited operation time and

risks during sterile production [55].

2.4.1.3 Microbalance

For continuous measurement of mass transfer by sublimation of ice a microbalance sys-

tem can be used. The drying rate and the endpoint of primary drying can be calculated via

weight loss. The sample weight of a vial is low and the differences in weight during drying are

therefore small. The balance also has to work accurately under a wide temperature range be-

tween -50 C and +40 C, as well as vacuum. The construction of a feasible microbalance is

therefore a major challenge. Different attempts have been made to establish a microbalance

system. Pikal et. al. [7] investigated the sublimation rate as a function of freezing rate, thick-

ness of the dried product, residual air pressure, temperature and solute concentration during

isothermal drying of a small sample suspended from a balance arm in a high-vacuum cold

stage. Four different classes of product resistance behavior and evaporation coefficients for

ice were identified. For the monitoring of secondary mass transfer Pikal et. al. [32] adapted

the size of the sample cell of the microbalance to achieve a much larger sample capacity.

By placing a thermocouple into the microbalance, some temperature compensation was also


possible.

More recent microbalances can also be applied with non-isothermal processes. Roth et.

al. [56] showed that such a microbalance is suitable for endpoint detection of primary drying

by continuous monitoring of the cumulative water loss and the momentary drying rate of

a product in a standard vial within the drying chamber. Furthermore, a microbalance is a

useful tool in the research field as Gieseler and Lee [47, 57, 58] showed. The effects of

vial packing density on the drying rate and primary drying time were determined between

different drying chamber designs and geometries [47]. Furthermore, the product resistance

of different materials was studied [57] and also differences in the drying profile between spray

freeze-dried powders in vials and regular freeze-dried samples were determined [58].

A limitation of such a weighing system is that an application during a sterile process is not

possible [59]. Furthermore, an automatic stoppering is not possible as the microbalance is

larger in the height than the vials. In addition, the vials surrounding the single test vial as

well as the monitored test vial itself are more exposed to radiation from the microbalance

because of their lack of a hexagonal packing arrangement [56]. This leads to accelerated

drying of these samples [48]. Monitoring of secondary drying rates is not possible because

of low differences in weight [60]. The microbalance is a useful tool for laboratory studies, but

not suitable for scale up [48].

2.4.2 Non-invasive Measurements

2.4.2.1 Vacuum Gauges

As well as the monitoring of Tp, the control of Pc is also used for process control. Since

the chamber pressure influences the product temperature, it determines directly the drying

behavior. The pressure differential between the chamber and the vapor pressure of ice at

the sublimation interface is affected by Pc. Thus, this process parameter can be monitored

and maintained at a desired set point during the whole freeze-drying cycle. Three different

types of measurement systems are available: Pirani gauges, capacitance manometers (CM),

and thermocouple vacuum gauges. Vacuum gauges are measuring systems that record

pressures below atmospheric, whereas pressure gauges determine pressures greater than

atmospheric [18].


With CMs the pressure is metered by the movement of a metal diaphragm (usually inconel)

as caused by collisions of gas molecules [48]. The relative displacement of the diaphragm

from its position of rest provides a pressure measurement constituted by the gas molecules.

The diaphragm has on one side an electrical capacitor that changes its capacitance with the

movement or displacement of the membrane [19]. Figure 2.9 shows the general construction

of the pressure sensor. It is composed of two chambers containing the diaphragm in the

Figure 2.9: Construction of a capacitance manometer [61].

center position [18]. The first is sealed and serves as a reference chamber evacuated and

maintained at low pressures of <0.0013 Pa [19]. The second is open to the vacuum system

and represents the measuring cell. Electrically-insulated plates are mounted as a part of

the electrical capacitor. The pressure difference between the chamber pressure and the ref-

erence cell determines the displacement of the diaphragm and the distance to the insulated

plates. The capacitance of the electrical capacitor varies therefore inversely with the distance

between the plate and the flexible diaphragm. The measurement of Pc is determined from

the resulting voltage. The CM is independent of the gas composition in the chamber, and

a controlled vacuum level remains identical during both primary and secondary drying [22].

CMs provide high accuracy and cover a wide pressure range. They can be used under GMP


conditions and steam sterilization is possible. The CM is therefore ”the method of choice” for

monitoring of Pc [48].

Pirani or thermocouple vacuum gauges work on the principle of thermal conductivity of

gases. Energy is transmitted from a warm metal filament to the gas phase. A thermocouple

vacuum gauge consists of a power supply heating a platinum wire (filament). Platinum is used

as it has a very low emissivity (0.03-0.1 [26]) and heat loss due to radiation can be neglected.

On this wire a TC is mounted (Figure 2.10). The temperature of the heated platinum filament

Figure 2.10: Construction of a thermocouple gauge [62].

changes with Pc due to its thermal conductivity (i. e. decreasing temperature with increasing

pressure). This temperature variation is recorded by the voltage reading of the TC and from

this the change in chamber pressure can be calculated [19].

The second gauge working on thermal conductivity is the Pirani gauge (Figure 2.11). In

contrast to a thermocouple vacuum gauge, a Pirani consists of two current-carrying platinum

filaments. One serves as a sensor which is enclosed by the vacuum system (sensor filament),

and the other constitutes the reference (reference filament) and is positioned in a separate

chamber evacuated to a pressure <13 mPa. As pictured in Figure 2.11, both filaments are

integrated in a Wheatstone bridge [19]. The resistance of the platinum filament is dependent

on the temperature and its increase leads to a rise in electrical resistance [19]. If the chamber

pressure around the sensor filament approaches the pressure of the reference chamber, the

resistance of the sensor filament equals the resistance of the reference filament and the

output voltage approaches zero. When the chamber pressure surpasses the pressure of the

reference chamber, the temperature and the resistance of the chamber filament decrease


Figure 2.11: Construction of a Pirani gauge [19].

and an imbalance of the bridge occurs (Rreference > Rsenor). Consequently, an output voltage

can be observed. Due to the consistency of the reference resistance, and the resistances

R(1) and R(2) of the Wheatstone bridge (Figure 2.11), the resulting voltage can be allocated

to the resistance change of the sensor filament. From this Pc can be calculated. Pirani and

thermocouple gauges have a lower accuracy than CMs but are cheaper, more stable, easily

calibrated and have a faster response time [18].

One problem can arise during the chamber pressure measurement with a thermocouple

vacuum gauge or a Pirani is potential oxidation or contamination of the filaments. The emis-

sivity of the surface now increases leading to energy loss by radiation [26]. Should the gauge

become coated by oil or organic material, then an insulating film is generated and the tem-

perature of the filament will tend to be higher resulting in a false low pressure signal [19].

Additionally, the linearity between temperature change and chamber pressure is limited to a

specific range [26].

The thermal conductivity of gases is governed by the gas composition. Calibration of ther-

mocouple vacuum gauges or Pirani gauges is usually performed using nitrogen. The gauges

indicate therefore false pressures in the presence of other gases, since they possess a higher


(e. g. water vapor) or lower (e. g. argon) thermal conductivity [19]. The partial pressure of

gases varies during freeze-drying in particular at the end of primary drying when the vapor

composition changes from almost exclusively water vapor to mainly air, i. e. nitrogen. The

measured value is therefore higher than the true pressure during primary drying due to the

presence of water vapor. At the end of this process step the value declines because of the

progressive reduction in water vapor [18]. This is a potential problem for scale up or transfers

if different vacuum gauges (Pirani/thermocouple vacuum gauge vs. CM) for chamber pres-

sure control are used. Since the Pirani and the thermocouple vacuum gauges show higher

values at the beginning of primary drying, the set point of pressure is overestimated. Using

this set point with a CM gauge, the pressure of water vapor is higher. The reason for this is

that CMs are not governed by the gas composition and show the true pressure values [18].

2.4.2.2 Comparative Pressure Measurement

To determine the endpoint of primary and secondary drying for the whole batch, a combi-

nation of Pirani and CM (see chapter 2.4.2.1) is used [22, 48]. During primary drying the

gaseous phase consists largely of water vapor from the sublimation process. When the rapid

production of water vapor declines at the end of primary drying, the partial pressure of wa-

ter decreases until the chamber gas is mostly composed of nitrogen. As the Pirani gauge

is calibrated against nitrogen, its pressure values are therefore higher at the beginning of

primary drying (because of the water vapor presence) than those of the CM. The thermal

conductivity of water vapor is ∼1.6-fold higher in comparison to nitrogen [53]. As the com-

position changes at the end of primary drying, the Pirani pressure signal drops to the CM

measurement value and the endpoint is indicated [48].

2.4.2.3 Dew Point Sensor

This method also relies on the changing gas composition in the freeze-drying chamber dur-

ing the cycle. The decreasing concentration of water vapor is measured by the electronic

moisture sensor with output as the dew point of water [22]. The dew point is the temperature

at which the equilibrium vapor pressure of ice achieves the partial pressure of water in the

chamber [48]. A thin aluminum oxide film changes its capacitance by means of water adsorp-

tion at any given partial pressure [53]. This capacitance is converted to a voltage signal that


reads as the dew point. From this data the endpoint can be estimated the drop of the dew

point signal [48]. The sensor is more sensitive than comparative pressure measurements

because it can determine the presence of residual ice in less than 0.1% of the vials [48]. Fur-

thermore, the electronic moisture sensor can be applied for endpoint detection during bulk

freeze-drying of very small containers, where, for example, a product temperature response

(described in 2.4.1.1) cannot be utilized [63]. The sensor has, however, to be isolated during

steam sterilization by both a valve and a sterilizing filter [48].

2.4.2.4 Pressure Rise Technology

The temperature of the moving sublimation front can be estimated with barometric temper-

ature measurement (BTM). Oetjen and Haseley [21] describe the basic principle as follows.

The drying chamber is isolated from the condenser chamber by closing the connection valve

which interrupts the flow of water vapor from the chamber to the condenser. The pressure

in the chamber rises until the saturation vapor pressure, Psat, is attained. This value is de-

pended on the temperature of the sublimation interface which can be estimated by the water

vapor/ temperature diagram. This technique was further developed by Milton et. al. [64] and

is denoted the manometric temperature measurement (MTM) using closed valve times of up

to 25 s and monitoring the pressure rise in the chamber over that time. As the ice tempera-

ture will increase because of the continuing heat flow, Milton et. al. developed a pressure vs.

time relation, the MTM equation (Equation 2.10)

P (t) = Pice − (Pice − P0) · exp

[−3.461 ·N ·Ap ·Ts

V · (Rp +Rs)· t]+

0.0465 ·Pice ·∆T ·[1− 0.811 · exp(−0.114

Lice

· t)]+X · t,

(2.10)

in which P (t) is the chamber pressure of the time during the experiment, P0 is the chamber

pressure measured before isolation valve closure, N is the total number of product vials, Ap

is the total product area, V is the chamber volume including the duct to the closed separa-

tion valve, Rp + Rs is the total area normalized resistance of product and stopper to water

vapor transport, ∆T is the temperature difference between the sublimation interface and the

product at the vial base (which is dependent on Lice, the thickness of the ice layer), and X is

a constant. This model was further improved by Tang [65, 66].


A direct determination of Pice and Rp is now possible. As the vapor pressure declines,

the end point of primary drying can be estimated by MTM [48]. The endpoint of secondary

drying is also detectable [65]. The temperature of the ice sublimation interface during primary

drying can also be deduced, as well as the drying rate [48], heat and mass transfer [65], and

the ice thickness [66]. The implementation of MTM offers several advantages. The product

temperature measurement is a non-invasive method and representative for the whole batch

[28]. Moreover, product contamination is unlikely because an operator intervention (e.g.

placement of sensors) is not necessary for product temperature measurement.

The measurement of Tp, however, is problematic as a minimum ice sublimation area is

required for an accurate measurement [48]. Moreover, temperature determination in different

vials is not possible, and only one temperature value can be measured in terms of a system

average which favors the coldest, interior vials [65]. Tp measurement by MTM is therefore

currently thought to be reliable to a value around -35 C to -45 C. These are only reliable

during the first 23

of primary drying due to heterogeneities in drying [48, 65]. As the sublima-

tion process is decelerated while the valve is closed, the self-cooling effect declines resulting

in a higher product temperature [48].

MTM is not the recommended method for concentrated amorphous formulations, since

water reabsorption within the dried layer takes place during the pressure rise. This leads

to a false value of vapor ice pressure and therewith all further calculations are erroneous

[28]. Nevertheless, MTM is a useful process-monitoring tool. This is reflected in the ”Smart

Freeze Drying” system that produces an optimized cycle program. During primary drying this

system monitors the drying process and varies the protocol by means of shelf temperature

and chamber pressure on the basis of user-predefined input variables, if necessary [48].

2.4.2.5 Mass Spectrometry

The principle of mass spectrometry (RGA) is the separation of the analyte components by

means of their mass-to-charge ratio [mq]. For this process the analyte is evaporated (if neces-

sary), ionized and subsequently accelerated by an electric field for the transfer to the analyzer

(e.g. a quadrupole consisting of four parallel arranged electrodes for the segmentation pro-

cess). After separation, the ion current is transmitted to the detector. Here, in dependence of

the concentration and the type of the gas component, a signal is generated, from which the


gas composition within the lyophilization chamber can be determined [48, 67]. The moisture

content of the product can be related to the partial water vapor pressure. On reaching the

desired residual moisture content the end of secondary drying has been achieved. RGA in-

strumentation is more sensitive than the comparative pressure sensors (see chapter 2.4.2.2)

[19]. Additional applications are also possible, like the detection of leaks in the drying cham-

ber or contamination from residues like vacuum pump oil, cleaning supplies or extractables

from stoppers or formulation components [19]. RGA instrumentation is, however, very ex-

pensive and is not a common technique.

3 Freeze-Drying of Amorphous Materials

3.1 The Amorphous State

The amorphous or glassy state has two main characteristics: the absence of equilibrium

phase changes and an isotropic behavior. These characteristics result from the inter-

particulate arrangement of the material, as illustrated in Figure 3.1. In the crystalline state

crystalline solid amorphous solid gas

heterogeneity of amorphous solid

Figure 3.1: Schematic representation of the structure of a crystalline solid, a gas and anamorphous solid with respect to their heterogeneities. Adapted from [68].

the particles are arranged continuously in a three-dimensional long-range order [69]. This

leads to a discrete phase transition. In the gas phase the molecules are random assembled.

The order of a glassy state, however, is intermediate showing a short-range order between

the long-range order of a crystalline system and the random assembly of the molecules in

the gaseous phase [69, 70]. The inter-atomic distances differ therefore in an amorphous

system which causes bonds with varying intensities. These heterogeneities lead to transient

30 3 Freeze-Drying of Amorphous Materials

phase transitions and different physical properties of amorphous materials in comparison

to their corresponding crystalline states. Some distinct regions (α and β, Figure 3.1) with

different densities, relaxation behavior and residual crystallinity can occur in amorphous ma-

terials [68]. Amorphous materials are thermodynamically unstable and tend to rearrange to

the crystalline state [71]. Common ways to obtain a pharmaceutical amorphous system are

supercooling of the melt, mechanical activation of a crystalline mass, and rapid precipitation

from solution (e. g. during freeze-drying or spray drying) [69].

3.2 Glass Transitions

The glass transition process can be described as using a thermodynamic approach that

considers the changes in enthalpy H and in free volume Vf , or in a thermodynamic approach

that refers to a change in entropy S and a description of a kinetic relaxation process.

3.2.1 Thermodynamic Approach considering Enthalpy and Free

Volume

Hancock and Zografi [69] described the differences between the formation of glassy and

crystalline materials by their changes in enthalpy, H , or in free volume Vf with temperature,

see Figure 3.2. The cooling of a crystalline system from the liquid state to a temperature

lower than the freezing temperature, Tf , leads to a first order phase transition to a thermo-

dynamically stable crystalline state with respect to non-crystalline forms. This exothermic

crystallization process causes a contraction of the system to a regular arrangement of the

molecules. During this process H and Vf decrease to lower values in comparison to a

supercooled liquid or glass. During a rapid cooling through the freezing temperature of a

glass-forming material in the liquid state no crystalline state is formed, since insufficient time

is available for an ordering process. A supercooled liquid is formed and no discontinuities in

H or Vf are observed on crossing Tf . During further cooling the molecular mobility of the

system is reduced [71]. At Tg the system is kinetically unable to stay in the equilibrium state.

Hence, a change to higher values of H and Vf in comparison to the crystalline state and the

formation of a non-equilibrium state occur. The material becomes fixed in the glassy state. In

this system the bonds between molecules are essentially the same compared to those of a

3.2 Glass Transitions 31

Figure 3.2: Schematic depiction of changes in enthalpy, H , or in free volume Vf as a functionof temperature. Adapted from [69].

liquid. Translational and rotational motions (high H) are reduced and vibrational motions (low

H) appear. During the glass forming process a step change in heat capacity, Cp, occurs:

Cp =

(δH

δT

)

p

. (3.1)

Tg is dependent on the cooling rate since a slower reduction in temperature (dashed line)

results in lower values for Vf and H , as shown in Figure 3.2. In this model, the glass transition

is a second order thermodynamic phase transition due to the discontinuity of H and Vf

at the transition point [71]. Inconsistent with this classification is the dependence of the

glass transition on the cooling rate, since a second order thermodynamic transition is rate

independent.

3.2.2 Thermodynamic Approach considering Entropy

The entropy S of an amorphous system at the equilibrium state can be related to Cp:

Cp = T (δS

δT)p. (3.2)


In a glass the heat capacity arises from vibrational contributions, whereas above Tg additional

configurational degrees of freedom exist. The values of heat capacity above Tg are higher

compared to the values of an amorphous system. A higher S of the system occurs in the

rubbery state than in the glassy state and the glass transition is characterized by a step

change in S [71]. The glass transition can be considered as a thermodynamic requirement

for a supercooled liquid to avoid a fall in the entropy of the supercooled-liquid below the

entropy of a crystalline system at some critical temperature (a violation of the third law of

thermodynamics) [71]. This critical temperature is termed the Kauzmann temperature, TK ,

(Figure 3.2) which defines the lowest possible Tg.

3.2.3 The Kinetic Relaxation Approaches

The glass transition can also be considered as a structural relaxation process, e. g. a reorga-

nization of hydrogen bonds in hydrogen-bonded fluids developed when the liquid is cooled.

The time necessary for this relaxation, the relaxation time τr, is dependent on the tempera-

ture (longer relaxation times with decreasing temperature) [71]. In this model, the velocities

of relaxations are compared to characterize Tg. Above Tg, reorganization processes of hy-

drogen bonds are fast within the observation time, tO (τr < tO). The system behaves like a

liquid and responds to changes in temperature in the timescale of the temperature change.

The system is therefore in equilibrium with the cooling process [71]. Below Tg, however, the

relaxation process is slow with respect to the observation time (τr > tO). Molecular mobility

is reduced and the material takes on the characteristics of a solid. Hence, Tg is defined as

the time point when τr ≈ tO.

A related model to describe the glass transition considers the free volume, Vf , and has

been suggested by Fox et. al. [72, 73] and developed by Turnbull and Cohen [74]. The

basis of this concept is the differentiation between the volume taken up by the molecules

of the constituents, Vocc, and a free volume, Vf , available for movements of the molecules.

Vf consists of voids of varying sizes and positions due to the random movements of the

molecules. It is assumed that diffusion of the molecules through the system is only possible

when Vf is above a critical value. During a temperature decrease both volumes contract since

the configurational structure of the constituents becomes more compact and movements are

retarded. Vf of a glassy system reaches a lower limit independent of further cooling, when


glass transition occurs. Afterwards, the molecules are densely packed, the internal mobility is

negligibly small, and no further contraction of Vf by a temperature reduction takes place. The

molecular mobility and the macroscopic fluidity of amorphous systems can be associated

with this relaxation behavior that describes many of the characteristic properties of glassy

materials [71].

3.2.4 Glass transition during Freeze-Drying

During freeze-drying the amorphous state is formed by a high freezing rate. Freeze-

concentration occurs until T ′g is reached. At T ′

g the viscosity increases greatly, the ice crystal

growth stops, and an amorphous glass is formed [26]. In the thermogram a slight change in

the temperature-time profile occurs (Figure 3.3). Nail and Gatlin [26] described the freezing

Figure 3.3: Temperature vs. time during freezing of amorphous solute [26].

behavior of amorphous materials on the basis of the state diagram shown in Figure 3.4. The

different states of an amorphous material are a solution state (upper left area), an ice plus

freeze-concentrated solute state (middle section) and a glassy state (lower right area). The

solution is bordered by two curves, the equilibrium freezing temperature of water (function

of weight fraction of solutes) and the solubility curve of the substance. The intersection of

the lines is the eutectic point indicating the crystallization (dashed vertical line) of interstitial

fluid. Instead of crystallizing at the eutectic point, the amorphous solute remains liquid and


Figure 3.4: Schematic state diagram of a non-crystallizing solute. Adapted from [75].

the system follows the equilibrium behavior of a liquid (”rubbery state”). With decreasing tem-

perature the viscosity increases due to ice crystal growth and freeze concentration, but the

dynamics of the system decrease. The freeze-concentrated solute is distinguished from the

glass by the solid line. This is the glass transition point of the amorphous solid as a function

of water content. It is an isoviscosity curve representing a viscosity of about 1014 Pa s [26].

When the freeze-concentrated liquid crosses this line a glass is formed.

3.2.5 Temperature Dependence of Viscosity and Relaxation Time

The Arrhenius law is not valid for amorphous systems to predict the temperature dependence

of the viscosity, η, or the relaxation time, τr. The viscosity of amorphous systems near Tg is in

the range of 1012-1014 Pa s. But above Tg these materials show temperature-dependent vis-

cosity values [71]. The magnitude of this temperature dependence varies between different

amorphous materials. Some show a weak temperature dependence and obey the Arrhe-

nius law over a certain temperature range, while others deviate strongly from this behavior.


Immediately above Tg, amorphous systems follow the Vogel-Tamman-Fulcher equation:

η = η0 · exp[

B

T − T0

],

τr = τ0 · exp[

B

T − T0

].

(3.3)

B is a constant and T0 is the Vogel-Fulcher temperature which can set equal to TK (see

chapter 3.2.2) [76, 77]. As described at Angell [76], this equation can be written in the form:

η = η0 · exp[D ·T0

T − T0

],

τr = τ0 · exp[D ·T0

T − T0

].

(3.4)

Systems obeying this relationship show a temperature dependent activation energy instead

of the constant activation energy of the Arrhenius relationship. The parameter D (fragility)

is a constant characteristic of each amorphous material and can be used to characterize

the sensitivity of its η and τr to changes in temperature. A changing value of D shows the

change of T0 relatively to Tg [76]Tg

T0

= 1 +D

39.14. (3.5)

With increasing D the difference between Tg and T0 therefore increases (i. e. larger ratio ofTg

T0

). From Equation 3.4 it is apparent that in the region immediately above Tg, when T ≈ Tg,

this larger difference means a smaller temperature dependence of η or τr. The activation

energy and therewith the deviation from Arrhenius behavior is smaller. Angell [76] denoted

materials with large values of D as strong glasses and those with small D-values (less than

10 [78]) as fragile glasses. Strong glasses build a network in the liquid state, obey the

Arrhenius relationship, and feature minimal molecular mobility changes at the glass transition.

The shift in heat capacity during the glass transition is therefore small. Fragile glasses offer

non-directional, non-covalent interactions, and show a distinct reorganization during the glass

transition. They differ from Arrhenius and a distinctive change in Cp can be observed [71].

D therefore indicates the acceleration of a structural relaxation or an increase in η when a

glass approaches and passes through Tg. Since amorphous systems are used as stabilizers

during freeze-drying, the classification into strong and fragile glasses may predict the ability

of an excipient for adequate stabilization. One of the stabilizing effects of an amorphous


system is glassy immobilization. This hypothesis assumes that a low degradation rate can

be correlated to a high η and a large τr. Hence, fragile glasses such as trehalose and

sucrose (sharp change in η, large τr) are the excipients of choice during freeze-drying and

subsequent storage [38, 79].

3.2.6 Prediction of the Glass Transition Temperature

The most common equation applied to freeze-drying is an adaption of the Gordon-Taylor

equation given in Equation 3.6 which was originally developed for polymer compositions [80]:

Tg(mix) =w1 ·Tg1 +K ·w2 ·Tg2

w1 +K ·w2

. (3.6)

Tg(mix) is the estimated glass transition temperature of the mixture, w1, w2 are weight frac-

tions of the components and Tg1, Tg2 are the glass transition temperatures of each compo-

nent. K is a constant and can be calculated from the densities ρ1, ρ2 of each component and

Tg1,Tg2 via [71, 81, 82]:

K =ρ1 ·Tg1

ρ2 ·Tg2

. (3.7)

If the densities of the components are equal, Equation 3.6 can be simplified to the Fox equa-

tion1

Tg(mix)

=w1

Tg1

+w2

Tg2

, (3.8)

and calculation of the influencing effect of water is possible [72]. Water lowers the glass tran-

sition of the formulation and is therefore a plasticizer [22, 83]. Equation 3.8 is said not to be

accurate for low molecular glass formers such as sugars since the densities will not be equal.

The effect of glycine on T ′g of aqueous sucrose systems, however, has been shown [84]. The

plasticizing effect may be explained by an increased mobility in terms of molecular rotation

by the addition of plasticizing excipients [85]. The most important and potent plasticizer is

water which is apparent in most of the lyos and has a low Tg of -135 C [81, 86]. Hence, even

a slight increase in water content reduces Tg(mix) greatly. The residual water content at the

end of the lyophilization has therefore to be considered to specify the storage temperature.

The influencing effect of some components on the glass transition can be a benefit, since low

glass transition temperatures can be raised by adding a further component with a high glass

3.3 Protein Stabilization 37

transition temperature to improve the drying conditions or storage stability [71].

3.3 Protein Stabilization

Freeze-drying of APIs, especially proteins, is almost always not possible without the addition

of excipients [1, 22, 87]. They account for a correct pH-range, isotonicity, stabilization, and

protection of the API during freeze-drying and on storage. Additives operate specifically (e.

g. antioxidants) or unspecifically like sugars. Unspecific stabilizers can be differentiated by

their effectiveness into cryoprotectants and lyoprotectants.

Cryoprotectants preserve proteins during the liquid state. Representatives of this group

are carbohydrates, especially disaccharides, amino acids and inorganic and organic salts

[87]. Arkawa et. al. [87] summarized the cryoprotective mechanism as an effect of ”prefer-

ential interaction”. In the liquid state, the protein prefers to interact with either the dissolved

excipient or water. In the presence of a cryoprotective agent the protein prefers to interact

with water (”preferential hydration”) and the excipient is excluded from the surface of the pro-

tein (”preferential exclusion”). This leads to an irregular distribution of the stabilizer with a

lower concentration in the area around the protein increasing with distance. The chemical

potentials of the protein and the additive are thereby increased leading to a thermodynam-

ically unfavorable situation. Denaturation would cause a greater contact area between the

protein and the solvent resulting in a more thermodynamically unfavorable state. The protein

remains therefore in its native structure. Since the change in the chemical potentials depends

on the concentration of the excipient, a relatively high amount is necessary for its sufficient

change. Since this stabilizing mechanism depends on the presence of water, a stabilizing

effect does not occur in the dehydration stage of the protein.

Lyoprotectants preserve proteins during both freezing and drying [17]. Two mechanisms

for the stabilizing effect have been suggested in literature, water replacement and glass for-

mation. Water replacement is a direct interaction between the excipient and the protein by

hydrogen bonds [88]. During drying dehydration of the protein occurs which usually leads to

an irreversible unfolding of the protein. A lyoprotectant replaces the dehydrated water and

saturates the free hydrogen binding sites developed during drying [89]. This mechanism re-

quires the amorphous state of the stabilizing agent because sufficient formation of hydrogen


bonds between a crystalline structure and the protein is not possible. It has been shown

that the protective effect of lyoprotectants is increased with a higher weight ratio of the ex-

cipient to the protein, to form the required monomolecular layer on the protein surface [88].

Furthermore, the extent of possible hydrogen bonds (increasing concentration of stabilizer)

correlates with the degree of structural protection. However, an upper concentration limit

of the stabilizer that can lead to its crystallization has to be considered [87]. An example

for such an upper concentration is a trehalose content of 400 mg/ml [89]. The geometry of

the stabilizer is also important because steric hindrance (e. g. dextran) prevents adequate

hydrogen bonds of the excipient with the protein [90].

A further lyoprotective mechanism is the formation of a highly viscous glass around the

protein during freezing. Molecular mobility and the rate of degradation pathways including

unfolding or aggregation are then slowed down [4, 91]. Some carbohydrates such as tre-

halose or sucrose are preferential used as stabilizers since they act both as cryoprotectants

and lyoprotectants. This is an exception because cryoprotectants will not automatically stabi-

lize the API during drying. The stresses the protein is exposed to as well as the mechanisms

of stabilization in the solid and liquid state are different [4, 87, 89]. Depending on the stabilizer

one, two or more excipients with a stabilizing effect have to be added.

3.4 Product Appearance

Freeze-dried products occasionally show undesired defects. Especially the lyophilization of

fully amorphous cakes can lead to a product with optical defects such as shrinkage, cracking,

and partial or total collapse [5, 54]. Products with optical defects are rejected based on lack

of pharmaceutical elegance [3]. Currently, no classification of different product appearances

exists. Some appearances frequently cited in literature are described in the following with

regard to their possible causes and remedies. To describe the optical defects of lyophilizates

an optimal cake structure has to be defined. The cake structure depends on the compo-

sition, the concentration and the volume of the freeze-drying formulation, the geometry of

the container and several equipment and process parameters that influence heat and mass

transfer [92]. An ”ideal” product, Figure 3.5a, should offer a highly porous and sponge-like

appearance with a volume similar to the previous frozen matrix [19]. Discoloration should

3.4 Product Appearance 39

be avoided and the cake should form a single entity. The cake should provide mechanical

strength to resist a disruption during handling and distribution [1].

b c d e

a f g

h i j kl

m

Freezing

Drying

Formulation

Figure 3.5: Scheme of product defection resulting from freezing, drying or formulation prop-erties: Optical cake structure (a), chimney (b), foam (c), crust or glaze (d), ringformation (e), shrinkage (f), cracking (g), total collapse (h), partial collapse (i), to-tal melt back (j), partial melt back (k), browning (l), poor self-supporting structure(m).

A chimney-like structure in the middle of the cake may be visible on the top surface of

the product, as depicted in Figure 3.5b. This phenomenon is a result of the freezing process.

During ice crystal growth from the bottom to the top, the product is separated into two phases,

a liquid phase in the upper area and a mushy phase in the lower area of the product. The

mushy phase is a mixture of solid and liquid phases. At the interface between them two

modes of convection appear, as illustrated in Figure 3.6. One is developed in the liquid

at the border to the mushy region in which the second form exists. On the basis of these

convections the chimney-like structure is formed [19].

The final product can show a dried foam on the upper surface area (Figure 3.5c) that leads

to a heterogeneous product. This may result in a denaturation of proteins. Its cause is a rapid

filling especially of protein formulations in vials. Foam on the surface is thereby produced and

dries in place during the lyophilization process. An impact of the freezing step is also possible


Liquid

Mush

Figure 3.6: Streamlines at the interface of liquid and ”mush” during freezing. Adapted from[19].

if the formulation contains dissolved gases at saturation in the interstitial region. These can

be transferred to the cake surface leading to production of a foam [19]. This optical defect can

be avoided by a slowing of the filling step or by purging the formulation with a low-solubility

gas.

A crust or glaze (Figure 3.5d) is characterized by formation of a less porous film on the

surface of the cake. When the ice expands during freezing the remaining liquid is displaced.

Since this forced movement of the liquid is limited by the base and the wall of the container, it

is pushed up to the product’s surface. There it accumulates and freezes to a film. The result

is a product with a heterogeneity in solid’s concentration and an accumulation of proteins at

the surface. This phenomenon appears in formulations with a high content of amorphous

excipients, in containers with small diameters, or at high solute concentrations [7, 18]. The

thin solid film is a greater resistance to mass transfer and may affect the transport of water

vapor from the product [93]. This phenomenon can be reduced by changing of the freezing-

rate, adding of a small amount of ethanol in the formulation, or a selecting other containers.

As depicted in Figure 3.5e the cake can show horizontal layering. The components are

separated from each other during freezing by different freezing behavior of the formulation or

by varying freezing conditions.

A further undesired product appearance is shrinkage, where the cake volume is smaller

than the frozen matrix, as illustrated in Figure 3.5f. During lyophilization the lyo mass con-

tracts and the cake detaches from the inside wall of the vial. The result is a gap between the

vial and the cake. In contrast to microscopic collapse, shrinkage is a macroscopic change in

3.4 Product Appearance 41

cake structure [5]. With cracking (Figure 3.5g) the cake is lacerated in numerous places and

the product shows fissures or cracks inside the dry matrix. The cake usually does not form a

single entity. Cracking and shrinkage can occur either alone or together. During handling and

storage parts of the non-coherent cake may detach from the product in the case of cracking

or the whole cake moves in the vial when shrinkage occurs.

Should Tc be exceeded during primary or secondary drying, different degrees of cake

structure loss can occur ranging from total to partial collapse (Figure 3.5h and 3.5i). By

exceeding Tc at the drying interphase, there is a decrease in the viscosity of the amor-

phous matrix. As a consequence the interstitial concentrate possesses insufficient viscosity

to preserve its own structure without the additional support of the ice crystals. In regions

of sublimating ice the viscous liquid flows into the cavities and the porosity of the cake de-

creases. This process forms a layer that reduces evaporative cooling facilitating a further

increase in Tp. Depending on the magnitude of this process, a collapse with a complete loss

of microstructure is distinguished from a partial collapse where only a certain region of the

cake is affected. Partial collapse is a result of minimally exceeding Tc, for instance during an

improperly designed cycle or in the edge vials of the batch with an increased heat transfer.

Partial collapse occurs in most cases at the base center of the cake. The consequences

of collapse can be a heterogeneity in inter-vial moisture values, longer reconstitution times,

in-process degradation, or a higher residual moisture content [12]. To prevent collapse it is

necessary to determine Tc of the formulation to develop an appropriate process cycle as well

as to monitor Tp during lyophilization.

The freeze-dried product can show melt back (Figure 3.5j) or partial melt back (Figure

3.5k). A lyophilizate with total melt back possesses a ring of redissolved materials in its

lower region. At partial melt back only a small region at the base of the vial is affected.

Melt back occurs during an early start of secondary drying [92]. If the sublimation process

is incomplete, a frozen matrix at the vial base still exists. During the rise of Ts this frozen

matrix melts in a small region (partial melt back) or at the whole base area (total melt back).

As a consequence, the self support of the interstitial region is reduced and a melting of the

product occurs in certain regions [19]. Melt back is cosmetically unacceptable and is termed

”one of the major concerns (...) with regard to cake appearance by the FDA‘” [13]. It can

cause aggregation of the constituents. Due to the lower surface area the reconstitution time


can be increased. Undissolved substances may lead to a loss of potency. Changes in the

physical form of the drug substance as well as inhomogeneous moisture content are related

to melt back. This may lead to an increased instability and product degradation [13]. To avoid

meltback the end of primary drying has properly to be determined, as described above (see

chapter 2.4).

Browning (Figure 3.5l) is a discoloration of the cake, in most cases from white to yellow or

brown. It occurs in a formulation containing a reducing sugar and a protein or a peptide by

the Maillard reaction. To avoid browning the formulation can be optimized and more gentle

drying conditions can be used.

A lyophilizate can possess a poor self-supporting structure (Figure 3.5m). A solute content

lower than 2% and a high filling volume cause a fine cake structure that provides not enough

strength to withstand the stresses developed during lyophilization or handling. The risk of

physical disruption of the cake into a powder is therefore increased which leads to a possible

loss of the product and the API from the container [19]. If the powder reaches the area be-

tween the stopper and the neck, then stoppering is not possible which may cause insufficient

product stability. An increase in solute concentration or the addition of further excipients is

recommended.

4 Fracture Mechanics of Solids

4.1 Mechanical Behavior of Solids

The mechanical behavior of a material refers to its response to forces [94]. If a load is applied,

a material may deform or break [95]. Under a small stress the deformation of the material

can be elastic and the body will return to its original shape when the load is removed. This

material’s behavior is based on a disturbance of the interatomic equilibrium distances due to

the applied load. This produces a change in the inter-atomic distances and an increase in

the energy state of the system. Restoring forces appear as the atomic union works toward

a return to the original shape of the material. Energy is released and the system returns to

its original energy state. The deformation process is therefore reversible [96]. In the case of

a plastic material behavior on load removal, only a portion of the energy is released and the

body will not revert to its original shape. The deformation is therefore non-reversible [96, 97].

The material behavior can be ascertained by stress-strain tests if the load is static or

changes only slowly with time and is applied uniformly. The forces that act on the area of body

are described as stress. The amount of deformation of a material is described by the strain.

During a stress-strain test the deformation of the specimen (e. g. elongation, compression,

shear deformation, torsion deformation), usually to fracture, is measured as a function of a

gradually increasing load (e. g. nominal tension, compression, shear or torsion). In a tensile

test the output is load or force against the elongation of a specimen [94]. To take geometrical

factors into account, load and elongation are normalized to the parameters stress, σ, and

strain, ǫ. The si unit of stress is MPa (1 MPa =106 N/m2). Strain is dimensionless, but [m/m]

44 4 Fracture Mechanics of Solids

or [%] are often used. It holds for a tensile load:

σ =F

A0

,

ǫ =∆l

l0,

(4.1)

where F is the applied tensile load [N], A0 is the original cross-sectional area before any load

is applied [m2], l0 is the original length before load application [m] and ∆l is the deformation

elongation [m] [94]. Materials are typically not pure elastic or plastic, but rather linear elastic

or nonlinear elastic, elastic-plastic as well as visco-elastic. For a linear elastic material the

stress and strain are proportional to each other and the stress-strain relationship for tension

or compression stress is given by Hooke’s law:

σ = E · ǫ, (4.2)

where E is the Young’s modulus. The si unit of E is GPa (1 GPa =109 N/m2) [96]. E

corresponds to the slope of the stress-strain plot and describes the stiffness of a material or

its resistance to elastic deformation [94]. A stress-strain plot for a linear elastic material is

illustrated in Figure 4.1(a). On release of the load before breakage at point B, the stress-strain

(a) (b)

Figure 4.1: Schematic tensile stress-strain diagram showing (a) linear elastic deformationand (b) nonlinear elastic deformation. σ: stress, ǫ: strain, B: occurrence of break-ing, σB: stress at breaking point, ǫB: deformation at breaking point. Adapted from[94, 97].

curve is reversed and the material returns to its original shape. The area under the curve

represents the absorbed energy. It is in the case of material fracture the energy necessary

4.1 Mechanical Behavior of Solids 45

for the fracture of the material. If the stress-strain curve is not linear (Figure 4.1(b)), E has to

be determined for each specific stress level and the material possesses a nonlinear elastic

behavior [94].

Elastic-plastic material behavior, schematically shown for a tensile stress-strain testing in

Figure 4.2, is characterized by an incipient nonlinear or linear elastic behavior. With increas-

ing stress a transition from reversible elastic to irreversible plastic deformation occurs. The

onset of plastic deformation on microscopic level is termed ”yielding point” (PY , Figure 4.2)

[94]. Above this point the stress increases until at point M the maximum stress is reached.

The stress corresponding to point M is termed ”tensile strength” and displays the maximum

stress a material can withstand without breakage. An application and maintenance of this

stress leads to a fracture of the material at point B [96]. By release of the load before reach-

ing point M, however, the material does not return to its original form. Accordingly, the stress-

strain curve for the unloading process deviates from that of the loading process. Based on

plastic deformation, only a minor elastic recovery (e.g. Figure 4.2 1 → 2) occurs. On the

Figure 4.2: Schematic tensile stress-strain diagram showing elastic-plastic behavior. σ:stress, ǫ: strain, B: occurrence of breaking, σB: stress at breaking point, ǫB:deformation at breaking point, PY : Yielding Point. Adapted from [94].

microscopic level plastic deformation causes the breakage of atomic bonds with the original

neighbors. Since a high amount of atomic movement relative to one another occur, bonds

with new neighbors can now be formed. A return to the original atomic arrangement on load

release is therefore not possible [96].


Viscous behavior is characterized by a non-instantaneous deformation on stress. Hence,

the deformation in response to an applied stress changes with time. This deformation is

neither reversible nor completely recovered after stress release. Amorphous polymers, for

instance, show visco-elastic behavior. This material behavior, depicted in Figure 4.3 for ten-

sile stress, is dependent on temperature, loading rate, and time [97]. A slow and long-lasting

load application (or high temperature condition) leads to progressive elongation and predom-

inantly plastic deformation. A fast and short-time load application (or low temperature condi-

tion), however, leads to a high amount of elastic deformation [97]. The time and temperature

dependence of the material can be quantified with a stress relaxation measurement. During

this experiment a specimen is strained rapidly (e. g. in tension) to a low strain level. The

stress which is necessary to maintain this strain is then measured at a constant temperature.

The time-dependent relaxation modulus, Er(t), is determined by

Er(t) =σ(t)

ǫ0, (4.3)

where σ(t) is the measured time-dependent stress and ǫ0 is the constant strain [94]. The

time and temperature dependence of Er is illustrated in Figure 4.4.

decrease of loading rateincrease in temperature

increase of loading ratedecrease of temperature

Figure 4.3: Schematic tensile stress-strain diagram showing visco-elastic behavior. σ: stress,ǫ: strain. Adapted from [97].

The magnitude of Er decreases with time, owing to molecular relaxation in the specimen.

The curves also run at lower Er value with increasing temperature.

4.2 Fracture Mechanics 47

T2

Log

Er(t

)

Log time

T1

T1<T2

Figure 4.4: Schematic plot of logarithm of relaxation modulus versus logarithm of time.Adapted from [94].

4.2 Fracture Mechanics

4.2.1 Brittle Fracture and Ductile Fracture

Fracture is the separation of a body into at least two pieces as a response to an imposed

stress and at temperatures well below the melting point of the material. To fracture, a split

of inter-atomic bonds at the fracture cross-section is necessary [96]. The possible fracture

modes are ductile and brittle fracture based on the ductility of the material, which is the ability

of a material to undergo plastic deformation (see Figure 4.5). Upon stress, a brittle material

breaks without substantial plastic deformation and a low amount of energy is absorbed before

its fracture. This is termed ”brittle fracture” [94].

A ductile material, however, undergoes extensive plastic deformation with high energy

absorption before fracture. This is referred to as ”ductile fracture” [96]. Ductility is a function

of the strain rate, the stress rate and temperature and is quantified by percent elongation or

percent reduction in cross-sectional area [94].

A fracture process involves crack formation and subsequent crack propagation in response

to an applied stress [94]. With a ductile fracture, extensive plastic deformation occurs at the

tip of the crack (Figure 4.6a) and crack propagation proceeds slowly. The fracture is stable

since no further extension occurs without further applied stress. A brittle fracture occurs


Figure 4.5: Schematic representations of tensile stress-strain behavior for brittle and ductilematerials loaded to fracture. Adapted from [94].

suddenly (Figure 4.6c) and with rapid crack propagation [98]. This fracture is termed unstable

since a crack propagates spontaneously without any further stress application [94]. Ductile

materials are generally tougher than brittle materials as more strain energy is required to

induce a ductile fracture than a brittle fracture [94, 97, 98]. In the case of a highly ductile

a b c

Figure 4.6: Schematic representation of fracture modes (tensile stress) and surface charac-teristics of cylindrical specimen. a: highly ductile fracture, b: moderately ductilefracture, c: brittle fracture. Adapted from [94].

material (Figure 4.6a), plastic deformation occurs after initial elastic deformation when the

yield stress is exceeded. A uniformly-proceeding plastic elongation in combination with a

reduction of the cross section then takes place. Further deformation proceeds predominantly


at the neck, where finally the fracture occurs [96]. The most common mode is a fracture with

only a moderate amount of necking (Figure 4.6b). In this case small cavities occur in the

cross section area (Figure 4.7b). With continuing deformation an expansion and fusion of

these cavities takes place forming an elliptical crack normal to stress direction. This crack

grow along its major axis with further fusion (Figure 4.7c). In the area around the crack

a fracture then occurs (Figure 4.7d). The final fracture is formed by shear deformation at

an angle of about 45 to the direction of the tensile stress (Figure 4.7e) [96]. The area of

fracture usually shows an irregular and fibrous appearance. A brittle fracture is shown in

a b c d e

Figure 4.7: Schematic representations of a fracture process of ductile materials. Adaptedfrom [94].

Figure 4.6c. The type of brittle fracture is termed ”intergranular” if the fracture runs along

the grain boundaries (Figure 4.8a). A ”transgranular” fracture (Figure 4.8b) runs through the

grains [94]. The direction of the crack is normal to the direction of the applied tensile stress

a b

Figure 4.8: Schematic cross-section profile showing crack propagation. a: intergranular, b:transgranular. Adapted from [94].

and exhibits a flat fracture surface, as illustrated in Figure 4.6c.


4.2.2 The Energy-Balance Approach

A fracture can be initiated or extended if the applied stress exceeds a critical value. Since

atomic bonds must be broken for crack formation, the fracture strength of a material should

be in the range of the atomic binding energy. But the measured fracture strength for most

brittle material is much lower than the fracture strength predicted on the basis of atomic

binding energies [96]. An explanation is the presence of cracks and flaws at the boundary or

within the material. These defects propagate at a maximum stress, σm, that is lower than the

force of the atomic bonds [96]. This maximum stress, σm, can be approximated by modeling

the crack as an elliptical hole through a plate surface positioned normal to the applied stress

(Figure 4.9a):

σm = 2 · σ0 ·√

a

ρt; (4.4)

σ0 is the magnitude of the nominal applied stress, a is the length of a surface crack or half

the length of a crack in the interior. The radius of the curvature of the crack tip is ρt. Equation

4.4 holds for macroscopic internal defects such as voids, sharp corners, and notches in large

structures. Those macroscopic defects as well as microscopic discontinuities are denoted

as stress raisers [94]. At the tip of such a defect the applied stress becomes concentrated,

as demonstrated in Figure 4.9b. Stress concentration means that the stress along the line

X − X ′ increases to its maximum value, σm, as the flaw’s tip is approached. Inglis [99]

calculated in 1913 the pattern of stress concentration around an elliptical hole. His work

was the basis for Griffith to employ an energy-balance approach to define a criterion for

crack propagation [100]. Crack propagation in a completely elastic material proceeds if more

potential energy is released than the energy necessary for the formation of further crack

surfaces. As a result of stress concentration at a surface crack with length a, two triangular

regions each of length a and height h adjacent to the crack are relaxed, as illustrated in

Figure 4.10. According to Griffith the strain energy, U , of these two regions is now released

by crack growth and is given by:

U = − σ2

2E· π · a2, (4.5)

where σ is the nominal tensile stress, and E is Young’s modulus of the elastic solid. The

strain energy released on cracking is consumed partly during the fracture process since two

new surfaces are formed [101]. For the surface energy, S, associated with a crack of length


x

x

x′

x′2a

a

X X ′

σ0

σ0

ρt

a b

σm

σ0

Str

ess

Position along X −X ′

Figure 4.9: (a) Geometry of surface and internal cracks, (b) schematic stress profile alongthe line X − X ′ in a to demonstrate stress concentration at the tip of a crack.Adapted from [94].

a

h

σ

σ

Figure 4.10: Idealization of unloaded region near crack flanks. Adapted from [101].

a holds:

S = 2 · a · γ, (4.6)

where γ [J/m2] is the specific surface energy and the factor 2 accounts for two surfaces. The

energy required for crack propagation, W , is now the sum of the energy absorbed to create


the new surfaces, S, and the strain energy released by relaxation of the regions adjacent to

the crack, U . In Figure 4.11 the energy curves of S, W , and U are plotted against the crack

length, a. S increases linearly with crack length (Equation 4.6) whereas U increases as the

af

−U

Crack lengthW

S

Ene

rgy

Figure 4.11: Fracture energy balance. Adapted from [101].

square power of crack length (Equation 4.5). After the intersection of W and U the value of

W does not further increase with greater crack length and the crack will therefore become

self-propagating. From this point on the energy release is greater than the energy required

for crack propagation. At the intersection point of W and U it follows that dW/da = 0. Hence,

a critical crack length, af , can be defined by setting the derivative of W to zero (and a = af ):

d(U + S)

da=

dW

da= 2 · γ − σf

2

E· π · af = 0. (4.7)

σf is therefore the stress associated with an imminent fracture. Solving Equation 4.7 for af

gives [94]

af =2 ·E · γπ · σ2

f

. (4.8)

At crack lengths < af any crack propagation requires energy, whereas at crack length > af

energy is released by crack propagation. Equation 4.8 holds for a specimen that is assumed

to be thick relative to the crack length (plane-strain condition). In this case no strain relax-

ation in thickness direction exists. For a thin specimen having full relaxation in the thickness


direction (plane-stress condition) Equation 4.8 should be modified to:

af =2 ·E · γ

[1− ν2] · π · σ2f

, (4.9)

where ν is the Poisson’s ratio which takes the strain in the thickness direction into account.

Griffith’s work delt with brittle materials. His theory has been modified by Orowan in the

1950s to take the ductility of materials into account [95]. Orowan proposed that even at a

brittle fracture some energy is consumed by plastic deformation that is much greater than γ

and which occurs in the region around the crack [101]. The highest amount of the released

strain energy is therefore absorbed by the energy consumption of plastic flow near the crack

tip, instead of by the creation of new surfaces. Orowan modified Equation 4.8 to:

σf =

√E ·Gc

π · af, (4.10)

where Gc includes the plastic work and replaces 2γ [95].

4.2.3 The Stress Intensity Approach

The formation or propagation of a crack is influenced by the strength and the ductility of

the material and by environmental conditions such as temperature as well as the type and

magnitude of the load [102]. Three fracture modes (I-III) can be defined by the type of loading

with respect to crack orientation, as illustrated in Figure 4.12. Mode I describes a crack that

I II III

Figure 4.12: Fracture modes. I: Opening or tensile mode, II: sliding mode, III: tearing mode[98].

is a result of a nominal tensile stress, σ. With mode II the crack results from a shear stress


normal to the tip of the crack, whereas with mode III the crack is a result of a shear stress

parallel to the tip of the crack [98]. The basis of the stress intensity approach is the occurrence

of stress concentration at the tip of a crack or flaw, as pictured above in Figure 4.9b [102].

To predict the stress field near the tip of a crack, a stress intensity factor, K, is defined. It

can be calculated for a brittle material in dependence of the fracture mode I, II or III. For the

example of a central crack of length 2a in an infinite plate:

KI = Y · σ ·√π · a,

KII = Y · τ ·√π · a, with τ = τxy,

KIII = Y · τ ·√π · a, with τ = τyz,

(4.11)

where the subscript of K denotes the crack opening mode and σ and τ are the stress around

the crack (σ for normal stress and τ for shear stress). The subscript of τ describes the

direction of the shear stress as illustrated in Figure 4.13. Y is a dimensionless factor that

includes the crack and specimen geometries and sizes [94, 102]. For a central crack of

length 2a in an infinite plate it can be set to unity. For an edge crack of a length a in a semi-

infinite plate it is set to 1.12 [103]. K allows a single-parameter description of the processes

aaaax

x

y

y

z

σ0

σ0

(a) (b) (c)

τ

τ

τ

τ

Figure 4.13: Scheme of the directions of σ and τ at (a) Mode I, (b) Mode II and (c) Mode III.

near the crack, i.e. the deformations and stresses are described independent of loading or

the geometries of the specimen and the crack [100]. In literature there are expressions for K

for a large number of different loading and crack geometries.

In Irwin’s fracture analysis values of K are compared with a threshold value, the critical

stress intensity factor, which depends on the fracture mode and is termed KIc, KIIc, or KIIIc

4.3 Fracture of Glassy Materials 55

[101]. Each critical stress intensity factor represents the fracture toughness of the material.

It measures the material’s resistance to brittle fracture containing a crack. KIc is valid for

stress application according to mode I and the governing mode of brittle fracture [101]. In the

case of mode I for a central crack of length 2a in an infinite plate KIc is therefore given by

σf =KIc√π · a. (4.12)

Since KIc depends on the specimen thickness, it is determined for a specimen whose thick-

ness is much greater than the dimensions of the crack. For this specimen geometry only

plane-strain occurs and KIc is a material property [94]. To measure KIc there are standard

test methods developed, for example, by ASTM International [104]. KIc values are also avail-

able in literature [105]. A brittle fracture occurs if the stress intensity factor equals or exceeds

KIc. By using KIc it is possible to calculate a critical crack length at given stress, or a critical

stress at given crack length. Comparison of Equations 4.10 and 4.12 shows the interrelation

between the energy balance approach and the stress intensity approach (a = af ):

σf =KIc√π · a =

√E ·Gc

π · a → K2Ic = E ·Gc. (4.13)

4.3 Fracture of Glassy Materials

Defects of solid materials can be dislocations which are localized lattice distortions [94].

Those lead to a change in the bonding state like different atomic distances in parts of the

lattice. Accordingly tensile stresses or attractive bond forces and compression stresses or

repellent bond forces occur. Those forces promote displacements of atomic rows by rupture

and reformation of atomic bonds [96]. Solid materials may also possess point defects like

vacancies and interstitials, where an atom or a ion is missing in the ordered structure or

is crowded into an interstitial site. If the solid material is composed of long chains with

polymers, for instance, the chain ends or branches in the polymer are considered to be a

point defect, because they are chemically dissimilar to normal chain units and vacancies

can be associated to them [94]. Localized plastic deformation can lead to the formation of

small and interconnected microvoids wherein the molecular chains of the polymer become

oriented and form fibrillar bridges between those microvoids. Upon sufficient load these


bridges elongate and break that causes the microvoids to grow and coalescence and cracks

begin to form (crazing). The basic concept of defects in solids is therefore a deviation of the

system’s long range order or the existence of definite chains. Since a long-range order or

definite chains do not exist in glassy materials this concept cannot be implemented to this

material group.

The material behavior of a glassy system is dependent on its temperature. At low tem-

peratures the glassy material is rigid and plastic deformations are not possible since the

molecules are fixed in their positions. In the glass transition region a deformation is time-

dependent and not totally recoverable by the release of an applied load. The material shows

visco-elastic behavior. At temperature above the glass transition, the material transits to a

rubbery state and finally to a viscous fluid. Since at temperatures below Tg plastic deforma-

tion processes are not possible, a stress concentration can therefore not be relaxed by micro

plastic deformation of a crack’s tip by rounding out notches or stress rearrangements. Hence,

glasses show a brittle material behavior [96]. Possible causes and propagates of stress in

glassy materials can be microcracks, internal pores and moisture [94].

5 Materials and Methods

5.1 Materials

5.1.1 Amorphous Disaccharides

5.1.1.1 D-(+)-trehalose dihydrate

D-(+)-trehalose dihydrate (α,α-trehalose dihydrate) is a non-reducing disaccharide formed

by a 1,1-glucoside bond between two α-glucose molecules [106]. Its chemical structure is

given in Figure 5.1. D-(+)-trehalose dihydrate forms supersaturated liquids and an amor-

phous glass during freezing [20]. It can be found in numerous species such as plants, algae,

bacteria, and insects. These organisms can survive complete dehydration and exist in a state

of anhydrobiosis. This ability can be correlated with the large amount of trehalose present

in this organisms serving as a cryoprotectant [71]. The chemical and physical properties of

trehalose can be found in Table 5.1

Figure 5.1: Structure of D-(+)-trehalose dihydrate [107].

5.1.1.2 D-(+)-sucrose

D-(+)-sucrose is a non-reducing sugar linked via the anomeric carbons of glucose and fruc-

tose [111]. Its chemical structure is illustrated in Figure 5.2. During freezing sucrose forms

58 5 Materials and Methods

Chemical and physical properties Value

Molecular Weight 342.30g/molMelting Point 97-99CWater Solubility 0.689g/ml at 20CTg 350KT ′g 243.5K

Table 5.1: Chemical and Physical properties of D-(+)-trehalose [108, 109, 110].

a supersaturated liquid and an amorphous glass. Sucrose serves in many organisms as a

cryoprotectant as described for D-(+)-trehalose [71]. Some chemical and physical properties

are summarized in Table 5.2

Figure 5.2: Structure of D-(+)-sucrose [107].


Molecular Weight 342.30g/molMelting Point 185.5CWater Solubility 1.970mg/ml at 15CTg 330KT ′g 241K

Table 5.2: Chemical and Physical properties of D-(+)-sucrose [110, 111, 112].

5.1.1.3 D-(+)-maltose

D-(+)-maltose is a disaccharide formed by two glucose molecules linked via an α(1 → 4)

bond. It is a sweetening agent and a fermentable intermediate in brewing [113]. Its chemical

5.1 Materials 59

structure is given in 5.3. Some chemical and physical properties of D-(+)-maltose are given

in Table 5.3

Figure 5.3: Structure of D-(+)-maltose [114].


Molecular Weight 342.30g/molMelting Point 119-121CWater Solubility 1.080g/mL at 20CTg 316KT ′g 243.5K

Table 5.3: Chemical and Physical properties of D-(+)-maltose [110, 113, 115].

5.1.2 Bovine Serum Albumin (BSA)

BSA is a single polypeptide chain consisting of about 583 amino acid residues and no car-

bohydrates. It has a molecular weight of ∼66,000 Da. The sequence has 17 disulfide bonds,

resulting in 9 loops (see Figure 5.4) [116]. It belongs to the class of albumins which ac-

counts for 56% of the proteins in human plasma. They serve as a carrier for small molecules,

are involved in the protein-buffer system for pH-maintenance in blood and play a role in the

regulation of the water distribution between the plasma and the extra cellular fluid. Serum

albumins are a major factor in pharmacokinetics since they bind APIs and influence therefore

their body distribution [117].

5.1.3 Overview of Excipients and Reagents

All excipients used for the preparation of the freeze-dried formulations during this work are

summarized in Table 5.4. The aqueous solutions for freeze-drying were prepared with double

distilled water from an all-glass apparatus (Destamat Bi 18 T, Heraeus) and filtered through


Figure 5.4: X-ray structure of BSA at 2.25 A resolution [118].

0.2µm filters (Sartorius RC, Sartorius Stedim Biotech GmbH, Goettingen, Germany) before

use. An overview of further substances used in this work is given in Table 5.5.

Substance Lot Number Supplier

Bovine serum albumin 051M1875V Sigma-Aldrich, Steinheim, GermanyGlycerol ≥99,5%D-(+)-Maltose monohydrate 020M1588V Sigma-Aldrich, Steinheim, GermanyPolysorbate 80 72334517 Caesar & Loretz GmbH, Hilden,

GermanyD-(+)-Sucrose 096K0026 Sigma-Aldrich, Steinheim, GermanyD-(+)-Trehalose dihydrat 099K7351 Sigma-Aldrich, Steinheim, GermanyTris pufferan 06042843 Carl Roth GmbH & Co. KG,

Karlsruhe, Germany

Table 5.4: Substances used in this work in alphabetical order.

Reagents and further substances Supplier

Nitrogen (gaseous) Linde, Munich, GermanyNitrogen (liquid) Linde, Munich, Germany

Table 5.5: Reagents and further substances used in this work in alphabetical order.

5.1 Materials 61

5.1.4 Packaging Equipment

Table 5.6 gives an overview of the packaging materials used in this work.

Equipment Description (Item Number), Supplier

Vials 2.0 ml, 2R,Toplyo (1229432), Schott, Muhlheim, Germany10.0 ml, 10R, Toplyo (1229431), Schott, Muhlheim, Germany3.0 ml 2R, ”regular vial” (VC002-13c), Schott, Muhlheim, Germany10.0 ml 10R, ”regular vial” (13041450), Thuringer Pharmaglas & Co. KG,Neuhaus am Rennweg, Germany

Stoppers 13 mm Freeze-drying stoppers, gray silicone B (FDW13) AdelphiHealthcare Packaging, Haywards Heath, West Sussex, UnitedKingdom20 mm Rubber Stopper, RfS (Ready for Sterilization),gray bromobutyl (V9172 FM460), Helvoet Pharma, Karlsbad,Germany

Seals 20 mm Flip-Off (5921-2831), WEST Pharmaceutical Services,Lionville, PA, USA13 mm Flip-Off (FOT13W), Adelphi Healthcare Packaging,Haywards Heath, West Sussex, United Kingdom

Table 5.6: Substances used in this work in alphabetical order.

5.1.4.1 Freeze Dryer

A Martin Christ Delta 1-24 KD freeze-dryer with three usable shelves (0.36 m diameter,

a shelf area of 0.31 m2) and a plastic cover was used for the freeze-drying experiments.

The freeze-dryer was equipped with thermocouples linked to a data logging unit (Omega,

OM-SQ2010). To observe the product temperature thin thermocouples (T-type, PTFE, 36,

Item-number 5SRTC-TT-Tl-36) were used. For the monitoring of the shelf temperature self-

adhesive thermocouples (Omega, SA1-TI-1M-SC) were fixed on the shelf and connected

with the data logging unit.

5.1.4.2 Microbalance

The microbalance (Martin Christ, CWS-40, 2nd edition) is designed to work under extreme

conditions (vacuum, low temperature, high temperature differences) during the lyophilization

process with an accuracy of measurement of ±0.005 g and a weighing range of 0.05 g -

50.0 g. The measuring principle is based on electromagnetic power compensation. Because


of its small size it is possible to place it on a shelf during drying. The balance weighs a single

commercial vial (2R-10R) fixed by a clamped ring on the lifting arm, as pictured in Figure

5.5a. At preprogrammed time intervals the lifting arm lifts the vial for weighing (as illustrated

Figure 5.5: Christ microbalance CWS-40 in the lowered (a) and lifted (b) position.

in Figure 5.5b). Afterward the vial is lowered back on the shelf and released. This procedure

lasts approximately 10 s [56]. The total measuring time accounts for approximately 5 min,

so the duration of interruption of heat transfer across the contact area between the shelf

and the vial bottom caused by weighing is only <2% of the primary drying time. The data

obtained is monitored online via a computer software (WZ-KO 40-6, MTC-HUB), which is

relatively robust to changes in temperature and vacuum as a internal temperature compen-

sation mechanism is integrated. The obtained data is transferred to spreadsheet software.

5.1.5 Camera System

A camera system (Canon EOS 60D, Canon, Krefeld, Germany) with a macro lens (Canon

macro lens EF 100 mm f2.8 USM, Canon, Krefeld, Germany) and a Siocore 48-LED macro

ring light (Siolex GmbH, Lubeck, Germany) was mounted via a tripod (Manfrotto 055XPROB,

Manfrotto Distribution, Cologne, Germany) to the freeze-drying unit. The camera system is

linked to computer software (EOS Utilities 2.9, Canon, Krefeld, Germany) to enable automatic

control. The camera settings used are summarized in Table 5.7. A Canon Digital Ixus 801S

(Canon, Krefeld, Germany) with a Canon zoom lens 3xIS and 8 megapixels was also used.

The manual modus and the macro module were enabled, the flash was turned off, and the

ISO speed was set to 80.

5.2 Freeze-Drying Methods 63

Function Settings

Zone mode AVFocus MF -0.31mAperture 16Drive mode Single shootingShutter speed automaticallyExposure compensation 0Metering mode Spot meteringISO 800Image record quality RAW onlyAmbience MonochromeWhite balance Daylight

Table 5.7: Settings of EOS 60D for the freeze-drying kinetics.

5.2 Freeze-Drying Methods

5.2.1 Endpoint Detection of Shrinkage and Cracking

For the endpoint detection of shrinkage and cracking the fill solution was placed in vials that

were then semi-closed with stoppers on the neck of the vials. The vials were placed in a

hexagonal arrangement on the shelves of the freeze-dryer. At least two vials with thermo-

couples in a center position and one shelf thermocouple were placed on each shelf for tem-

perature monitoring every 10 s. The freeze-drying cycles described (see chapter 5.2.3) were

used unless otherwise stated. After completion of the secondary drying step the lyophilizer

was ventilated with nitrogen gas. The vials were stoppered, sealed and stored in a -80 C re-

frigerator (Heraeus Instruments, Germany). For the quantitative evaluation of shrinkage and

cracking the vials were horizontally cut with a Proxon FBS 240/E (see Figure 5.6) and a dia-

mond grinding wheel to visualize the whole cake and the inner wall of the vial. Subsequently

the vial was placed in a dark cell (Figure 5.7) to ensure uniform illumination conditions and

distances to the camera. This was positioned in the circular cavity of the closed cell. An

image was taken of every freeze-dried cake.


(a) (b)

Figure 5.6: (a): Equipment to horizontally cut the vials, (b) close-up view of the grindingwheel.

Figure 5.7: Dark cell for standardized image taking.

5.2.2 Determination of the Kinetics of Shrinkage and Cracking

To determine the kinetics of shrinkage and cracking during a freeze-drying run some vials

were cut horizontally below the neck (sample vials) as illustrated in Figure 5.8. No stop-

pers were used for these sample vials. All vials were filled with the respective fill solution

and freeze-dried on the second shelf from the top in the Martin Christ Delta 1-24 KD in a

hexagonal arrangement around the microbalance and around seven sample vials in a center

position.

A vial with a cut neck was mounted in the lifting arm of the microbalance to obtain the mo-

mentary water loss during primary drying. The freeze-drier was equipped with thermocouples

connected to the data logging system to monitor the product temperature of a sample vial

5.2 Freeze-Drying Methods 65

Figure 5.8: Horizontal cut of a vial (3.0 ml, 2R, Schott). Left: complete vial, right: horizontallycut vial.

and the shelf temperature. The unusable top shelf was perforated circularly directly above

the cut vials, as illustrated in Figure 5.9. This ensured a radiation shield, but still enabled

Figure 5.9: Circular perforation of the top shelf.

observation of the sample vials by the camera placed vertically above them. Every 10 min

an image (Raw-file, .CR2) was taken. The freeze-drying cycles described in Table 5.8 (see

chapter 5.2.3) were used unless otherwise stated.

5.2.3 Freeze-drying Protocols

The freeze-drying cycles used in this work are summarized in Table 5.8. Vacuum was ap-

plied after freezing (0.04 mbar) and hold during primary and secondary drying. If a two-step

freezing process was included, the freezing protocol was adapted to a ramp at 1 C/min to

5 C hold for 30 min, a ramp at 1 C/min to -5 C hold for 60 min, and a ramp at 0.4 C/min


to -40 C hold for 60 min. An annealing step was performed at -15 C for 8 h with a ramp at

1 C/min. The endpoint of primary drying was determined when the product temperature had

Process name Freezing Ramp to 1 D 1D Ramp to 2 D[C/min] [C/min] [C] [C/min]

1 0.4 0.11 -20 0.152 0.4 0.17 -20 0.153 0.4 0.17 -20 0.734 0.4 0.17 -20 0.245 0.4 0.17 -25 0.156 0.4* 0.17 -20 0.157 0.4*,** 0.17 -20 .015

Table 5.8: Description of the freeze-drying protocols. *A two-step freezing was included; **Anannealing step was included.

reached the shelf temperature. A soak period of 30% was added to this timepoint.

5.3 Analytical Methods

5.3.1 Differential Scanning Calorimetry (DSC)

Thermal transitions of lyophilized cakes and fill solutions were analyzed with a DSC822e

(Mettler Toledo, Gießen, Germany). To purge and dry the measuring cell nitrogen gas was

used. Solid samples of approximately 50 mg (AT 261 DeltaRange, Mettler Toledo) were

sealed in 40µl aluminum pans at room temperature at 0.1% relative humidity within a dry-

air purged glove box. For Tg determination each solid sample was heated and cooled at

5 C/min. To eliminate interference from enthalpic relaxation and to ensure the reversibility

of each run, a second heating scan was performed and used for evaluation [71]. For the

determination of T ′g 30µl of the fill solution was sealed in a 40µl aluminum pan, cooled down

to -80 C at 1 C/min, hold for 5 min and then reheated at 3 C/min to 5 C. The values of

Tg and T ′g as the inflection point of the transitions were calculated with the Mettler STARe

Software.

5.3 Analytical Methods 67

5.3.2 Mercury Porosimetry

The pore distribution of the freeze-dried samples was determined with a Poremaster R© 60

GT, manufactured by Quantachrome GmbH & Co. KG. A short sample cell with an inner

diameter of 2 mm (P/N 74012) with a stem volume of 0.5 cm3 was used. This analytical

technique is based on the intrusion of mercury at pressure into the pores of the sample.

The pore size is determined as a function of the external pressure necessary to force the

liquid into a pore against the opposing surface tension of the liquid. For cylindrical pores the

Washburn equation is valid:

2 · π · r · l · γ · cosΘ = P ·∆V, (5.1)

where r is the radius and l is the length of the pore, γ is the liquid’s surface tension, P is the

pressure and V the volume. The term cosΘ is introduced since the capillary pressure that

inhibits the mercury from pore intrusion acts through the contact angle θ.

Samples of approximately 100 mg of the freeze-dried cake were weighed into a sample

container and placed in the sample cell. This was positioned with its housing in the low

pressure station to perform a low pressure measurement (LP). LP was performed up to a

final pressure of 50 psi. After completion of the analysis the station was re-evacuated and

refilled in preparation for a high pressure analysis (HP). Afterward the sample was transferred

to the HP cavity and the high pressure measurement was performed up to a final pressure of

60000 psi.

5.3.3 Scanning Electron Microscopy (SEM)

The inner and outer microscopic structures of the freeze-dried cakes were investigated with

scanning electron microscopy (SEM). The lyophilizates were carefully taken out of the vial

and broken into smaller pieces. These had the original crack edges in the case of a cracked

sample to characterize the structure from the cracks and the inner structure of the cake.

The pieces were mounted on an aluminum stub G301 (Plano GmbH,Wetzlar, Germany),

Plano), gold-sputtered at 20 mA/5 kV (Hummer JR Techniques, ANATECH, Union City, CA,

USA) and examined on an Amray 1810 T Scanning Electron Microscope (Amray, Bedford,

Massachusetts) at 20 kV with different magnifications.


5.3.4 Texture Analyzer

The hardness of the lyophilizates was measured with a TA.XT.Plus (Stable MicroSystems,

Surrey, United Kingdom) equipped with a 5 kg load cell. A cylindrical, 5 mm-diameter probe

was used. The zero-calibration of the probe was performed with an empty vial. The sample

vial was positioned on the measuring bench and the probe was penetrated vertically in the

middle with a speed of 6 mm/s. The hardness was defined as the measured peak force after

1 mm penetration. The hardness of five lyophilizates of each formulation was determined.

5.3.5 Contact Angle Measurements

To investigate the wetting behavior of the D-(+)-trehalose dihydrate solutions an OCA 20

contact angle measuring device (Dataphysics, Filderstadt, Germany) was used. A contact

angle is the angle that is formed between the solid-liquid and liquid-vapor interface of a

liquid drop on a solid surface. For the experiments a small drop of each formulation was

positioned on a microscope slide (Thermo Scientific, Menzel-Glaser, Menzel GmbH & Co

KG, Braunschweig, Germany) at room temperature in front of the camera (”sessile drop”

method). The drop was focused and zoomed in by the camera to obtain a large field of

view. An image was taken and the SCA 20 software (Dataphysics, Filderstadt, Germany)

was used to evaluate the contact angle. The basis and the shape of the drop were therefore

manually defined and the contact angle was automatically calculated by the software. To

obtain the contact angle of a solution on a Toplyo R© vial, its bottom area was used instead of

a microscope slide.

5.3.6 µ-CT-Imaging Analysis

Micro Computed Tomography (µ-CT) analysis offers a three-dimensional method to exam-

ine non-destructively the inner structure, the path of the cracks, the volume of the cracks,

and the volume of the whole cake structure. The high resolution scanner Forbild R© devel-

oped at the Institute of Medical Physics (Erlangen, Germany) consists of a microfocus X-ray

tube, a two-dimensional, low area noise detector (flat detector) and a rotating sample holder,

as illustrated in Figure 5.10 [119]. The freeze-dried cake was left in the 2R-vial and stabi-

lized by styrofoam to prevent cake movement due to its shrinkage. The use of styrofoam is

5.3 Analytical Methods 69

Figure 5.10: µ-CT-Scanner developed at the Institute of Medical Physics, Erlangen, Germany[119].

interference-free since it shows nearly the same X-ray absorption as air. For this fixation the

vial was opened and a piece of styrofoam was clamped between the cake and the stopper.

To obtain a 3D-Image of the lyophilized cake two steps were necessary (Figure 5.11). The

first consisted of data acquisition by the X-ray scanning process (1) to receive several records

so-called ”projections” (2) of the sample. In the second step those projections were combined

to a 3D-data set (3), the stack. This stack-building process is termed ”reconstruction”. For

X-ray tube

Flat detectorSample

StopperBalk-like styrofoam stilit

(2) Projections (3) Reconstruction(1) Scanning

Figure 5.11: µ-CT-analysis flow chart.

the scanning process the sample was placed on the sample holder (rotation table) upside

down to allow the X-ray beam to penetrate the whole sample. The X-rays were absorbed by

the solid material, but not by the air within the pores. A power of 10 W and a high voltage


of 40 kV were used for the scans sufficient for carbohydrates with a low weakening behav-

ior. A mechanical shutter (0.5 mm aluminum-plate) was fixed to limit exposure (photons not

affecting the measurement result were retained). The distance between tube-to-object and

tube-to-detector were adjusted to the sample size and its position was fixed. All scanner ele-

ments were controlled by computer software and a volumetric scanning was carried out by a

single rotation of the sample around its y-axis. During this rotation the sample was scanned

horizontally by the X-ray beam from 2880 directions, evenly distributed in a 360 circle. The

radiogram was recorded by the flat detector. This measurement setup is deviant from the

typical gantry rotation measuring method where the X-ray tube and the detector rotate and

the sample holder is fixed. The duration for one scan was 2 h. The flat detector has an active

area with a width of 1536 pixel and a height of 864 pixel so that a maximum of 864 2D-slices

of the sample volume could be recorded during the whole scan.

During the subsequent µ-reconstruction process the single projections were combined to

obtain the density distribution of the sample in a 3D data set. The volume of the samples

scanned had the dimensions of 400-500 slices and a range of 1250x1250-1400x1400 pixels

for every slice. A spatial resolution of 10µm was achieved. One voxel (three-dimensional

pixel) had the size of 10x10x10µm3. The stacks of the lyophilizates were analyzed as de-

scribed in 5.4.3 to obtain the 3D cake volume and the 3D crack volume. The measurement of

principle is as follows: The X-ray beam that penetrates the sample consists of photons with

an energy in the range of 0keV up to 40keV. During penetration the sample interacts with the

photons. In dependence of the photons energy (the higher energy of a photon the higher

the penetration power and therewith a higher achieved depth in the sample) and the material

behavior of the sample, the photons were either absorbed or no absorption takes place. In

the case of absorption the photons were removed from the beam and the detector registers

a lower number of photons as well as a lower photon energy in comparison to a beam with-

out photon removal by absorption. If no interaction occurs the beam falls unhindered on the

detector. As a consequence brightness (intensity) differences in levels of gray can be seen

in the projection.

5.4 Image Evaluation 71

5.3.7 Ring Tensiometry

With the Kruss Digital Tensiometer K 10 ST (Kruss GmbH, Hamburg, Germany) the equilib-

rium interfacial tension was measured. A platinum/iridium ring, annealed after each measure-

ment was used. 20 ml of aqueous solutions were investigated at 25±0.5 C. Each solution

was equilibrated for 180 min before measurement.

5.4 Image Evaluation

5.4.1 Image Evaluation of the Endpoint-Detection

For endpoint detection the images of the freeze-dried cake upper surface were evaluated.

The inner area of the vial, AI , was determined with the circle tool and the top face area of

the whole cake, AF , with the ”contour tool” of Axio Vision software (release 4.8.2, Carl Zeiss

Vision GmbH, Aalen, Germany). In the case of a circular cake surface the crack area was

determined with a Matlab script (MathWorks R©, Inc., Ismaning, Germany). For an irregular

cake surface the crack area was determined with the ”auto measure” module of Axio Vision

(Carl Zeiss Vision GmbH, Aalen, Germany). A standardized measuring program was created

containing defaults for image processing such as brightness, contrast and filters as well as

segmentation conditions. The shrinkage of the freeze-dried cake was calculated as

Shrinkage[%] = 100%− AF · 100%AI

. (5.2)

The cracking of the cake was defined in % of the crack area AC to AF .

5.4.2 Image Evaluation of the Kinetics

The brightness of each image (RAW-file (.CR2) obtained during the freeze-drying cycle was

initially normalized against each of the other images regarding its brightness by Digital Photo

Professional (Canon, Krefeld, Germany) and converted to the Tagged Image File format

(.TIF). For the image evaluation with Avio Vision software (release 4.8.2, Carl Zeiss Vision

GmbH, Aalen, Germany) the ”auto measure” module (Carl Zeiss Vision GmbH, Aalen, Ger-

many) was used. The measuring program was adapted for each image to account for fluc-


tuations in contrast and any reflections of the lyophilization equipment (shelf, microbalance).

Shrinkage and cracking were calculated, as described in 5.4.1.

5.4.3 Image Evaluation of the µ-CT-Reconstructions

The volumes of the samples received by the µ-CT-analysis were analyzed with MIAF-

software (developed at the Institute of Medical Physics in Erlangen) at the Institute of Medical

Physics in Erlangen. The volumes of the whole cake and of the cracks were determined for

each slice of the stack. The overall cracking of the freeze-dried cake in % of the whole

cracking volume to the whole cake volume was calculated, as described in 5.4.1.

6 Results

6.1 Endpoint Evaluation Method

The development of the complex system developed in this work is first given, before consid-

ering the application to various freeze-drying experiments.

6.1.1 Development of the Image Evaluation Method

6.1.1.1 Standardized Picture Taking

To quantify the amount of shrinkage and cracking of the lyophilizate a focused image is

required showing the whole cake and the complete inside wall of the vial in two dimensions.

Pictures taken through the neck of the vial are shown Figure 6.1a. The neck of the vial

obstructs the view of the cake’s complete outline and of the inside wall of the vial. Another

problem is incorrect focus of the cake (Figure 6.1b). Figure 6.1c shows the influence of

uncontrolled exposure to light on the laboratory bench. In this case lateral exposure to light

a b c

Figure 6.1: Images of freeze-dried D-(+)-trehalose dihydrate with a: obstructed view, b: in-correct focus, c: uncontrolled exposure to light.

occurs in the upper cake region. The cracks in this region appear therefore brighter compared

74 6 Results

to cracks in the lower region. The image also shows a heterogeneous cake surface structure

as a result of the nonuniform exposure to light. A further difficulty is that the images are not

taken perfectly normal to the cake surface. The cracks in the lower area appear therefore

wider than those in the upper area. This leads to an imprecise evaluation of cracking.

To keep conditions as constant as possible during image taking and to enable automatic

image evaluation a consistent and reproducible method is developed. This method should

ensure a constant distance between camera lens and cake surface, a fixed position of the

camera normal to the cake surface, a constant and even exposure to light, exclusion of any

interfering light, an unobstructed view of the cake surface and the inner wall of the vial, as

well as a high and consistent contrast between the cracks and the cake structure.

To enable an unobstructed view the vial is horizontally cut (Figure 6.2) with a Proxon

FBS 240/E and a diamond grinding wheel at a constant distance from the cake surface. As

Figure 6.2: Horizontal cut of a vial (3.0 ml, 2R, Schott). Left: complete vial, right: horizontallycut vial.

illustrated in Figure 6.3a, an unobstructed view of the inside wall of the vial and the whole

cake surface is now possible. To achieve a high contrast between the cake and the glass

wall, the vial is placed on its side and images are taken with background light. To prevent

excessive brightness from the background light a shutter is used. This is a rectangular black

colored paper with a circular cut-out for the vial positioned around the vial on the level of the

cake top surface. A higher contrast, exclusion of interfering light and an even exposure to

light is now possible (Figure 6.3b). To increase the sharp focus of the cake, an additional

front light is used (Figure 6.3c). Attempts with a warmer background light (Figure 6.3d),

or together with an additional front light (Figure 6.3e) do not bring any improvement. To

optimize the exclusion of interfering light, the side of the vial at the cake surface is masked

6.1 Endpoint Evaluation Method 75

a b c d

e f g h

Figure 6.3: Images of lyophilizates of the development of the standardized picture taking. a:only shutter, b: shutter and background light, c: shutter, background light, addi-tional front light, d: shutter, warm background light, e: shutter, warm backgroundlight, additional front light, f: shutter, warm background light, mask, g: LED back-ground light, front light, h: LED Background light, shutter, taken in the dark cell.

with a lightproof adhesive tape to ensure exposure only to light from the bottom of the vial

(Figure 6.3f). This leads to a strong darkening effect without any decrease in sharpness and

contrast. The best contrast is achieved by the use of background light emitting diodes (LED)

in combination with front light (Figure 6.3g).

a b c d

Figure 6.4: Images of lyophilizates of the development of the standardized picture taking.a: without modification b: shutter and warm background light, c: shutter, LEDbackground light, additional front light, d: LED Background light, shutter, taken inthe dark cell.

It is also necessary to achieve a high contrast between cake and any cracks present at

its surface. Figure 6.4b in comparison to Figure 6.4a shows that background light results in

76 6 Results

a high contrast between the cake structure and the cracks. The use of background LED in

combination with front light (Figure 6.4c) results in a more uniform lightness of the cake struc-

ture. However, the light intensity is too small since cracks located in the outer cake regions

appear smaller or have vanished. The front light causes reflections on the cake surface that

have similar brightness levels to the cracks in the image. This would hinder automatic image

evaluation. Hence, additional front light is not used, despite the best contrast between the

cake and the glass vial being achieved.

To ensure a constant distance and a fixed normal angle between camera and cake surface,

a dark cell is developed (Figure 6.5a). It is built on a wooden base as a wood housing fixed

with hinges for simple sample placing. The middle of the housing lid is cut out for the lens

of the camera. On the wooden base, directly below the camera cavity in the housing, a

cylindrical metal tube is fixed with five LED circularly arranged around its base to ensure a

uniform and constant illumination (Figure 6.5b). A translucent plastic cover is fixed on the top

of the metal tube by a foam ring acting as a sample holder. A high and consistent contrast

(a) (b)

Figure 6.5: (a) Scheme of the dark cell, (b) source of light.

between the cracks and the cake surface can be achieved with the five LED, see Figures

6.3h and 6.4d. Since the housing lid is closed when a picture is taken, no interfering light

occurs and standardized lighting conditions are given for all samples.

6.1.1.2 Semi-Automatic Evaluation with Axio Vision

To evaluate shrinkage and cracking a consistent and, if possible, automatic evaluation

method should be developed. Since an image shows reliably only the top surface of the


cake, the evaluation is limited to a 2D analysis. The basis of the image analysis is the eval-

uation of the number of pixels belonging to the crack area, AC , for cracking, the number of

pixels of the top surface of the whole cake, AF , and the number of pixels of the inner area of

the glass vial cross-section, AI , for shrinkage.

For the determination of AI the ”circle measure” tool of Axio Vision is used. Marks left by

the cake on the inner wall of the vial are used as a reference point (Figure 6.6). Axio Vision

calculates the radius of the defined circle in pixels to allow calculation of AI . AF is evaluated

Figure 6.6: Evaluation of AI (white line) and AF (black line) of a sample with a circular cakestructure.

for a circular cake in the same way (Figure 6.6). In the case of a non-circular cake profile

(Figure 6.7a, black line compared to white line) the ”contour measure” tool is used. A manual

border is drawn along the cake’s contour (Figure 6.7a, white line) and the cake area in pixel2

is calculated by the software. For the sample shown in Figure 6.7a an area of 962432 pixel2

(= 22% shrinkage) is obtained for AF with the ”contour measure” tool. If the cake area of this

sample is evaluated with the ”circle measure” tool a value of only 19% shrinkage is obtained,

illustrating the importance of measuring contour correctly. In this example the cake shows

only a small deviation from a circular shape, but a large measuring error is made by using

the ”circle measure” tool.

In Figure 6.7a the cake detachment from the vial wall is complete. In the majority of cases

parts of the cake remained attached to the vial wall, as illustrated in Figure 6.7b (bottom

of the image). In Figure 6.8a the cake is lacerated into seven regions. This necessitates

78 6 Results

(a) (b)

Figure 6.7: (a): Non-circular cake structure, (b) Incomplete cake detachment.

a standardized method to define whether the fragment that remains attached to the glass

wall is either allocated to AF or can be neglected. A threshold is defined as the percentage

of a fragment’s width to the radius of the whole cake as determined from 30 images. A

fragment is defined as a piece of the cake that has no connection to the intact cake structure.

Figure 6.8b shows a cake with two apparent fragments, 1 and 2. The regions marked with

black rectangles show, however, that the fragments are connected to the intact cake and are

therefore not considered as fragments. For each image the area of the cake fragments, Af ,

and their major width, lm, is determined, see Figure 6.8a. Six fragments are identified, each

(a) (b)

Figure 6.8: (a): Evaluation of a threshold value (b): Definition of fragments.


numbered in black. Each fragment is completely detached from the intact cake structure,

numbered 7 in white. The lm of each fragment, its area, Af , and the area of the intact

cake, AF , without any fragments, are evaluated for each image, given in Table 6.1 for Figure

6.8a. AF , marked with the thick white line, is determined as 786159.5 pixel2. To obtain the

percentage of the fragment’s major width to the radius of the whole cake, R%, the radius of

a circle with the same area as AF is determined (500.24 pixel2 for Figure 6.8a). For every

fragment its percentage area to AF , A%, and R% is determined, see Table 6.1.

Fragment Major width of Fragment area Af Percentage Percentagenumber the fragment lm [Pixel 2] width, R% area, A%

1 234.88 72972.50 46.95% 9.28%2 131.47 38671.00 26.28% 4.91%3 63.80 20097.50 12.75% 2.55%4 41.59 7562.50 8.31% 0.96%5 121.17 36370.50 24.22% 4.63%6 97.62 34992.00 19.51% 4.45%7 786159.50

Table 6.1: Values of the fragments of Figure 6.8a.

The results of this fragment analysis (n=37) determine whether a fragment belongs to AF

or is neglected. The mean value of lm of the fragments for the example in Figure 6.9 is 3

Figure 6.9: Evaluation of narrow fragments.

pixel (n=37). These fragments in this image are very small and barely detectable. This area

of 3 pixel is therefore selected as the threshold value. Since the mean value of the radius

of AI for the 30 images is 650 pixel, fragments with a width of 3 pixel account for 12233.94

80 6 Results

pixel2. The mean value of AF of the 30 images is 961465.46 pixel2, leaving A% as 1.27%,

the lower threshold for fragment detection.

Af and lm as well as A% and R% are evaluated for all 30 images and their A% values are

compared with the threshold value. Among the fragments included in AF by the threshold,

the smallest R% is 7.40%. Hence, the threshold for R% for fragments whether to be included

or not is set to 7%. On the basis of this threshold all fragments of the image given in Figure

6.8a have to be included in the calculation of AF since the percentage width of each fragment

is greater than the threshold value of 7%. The applicable region of AF is therefore given by

the black line in Figure 6.8a. This also shows the treatment of the fragments. The whole

fragment is included and the border between fragment and cake is generated perpendicular

to the glass wall at the end of each fragment.

For the evaluation of AC the Axio Vision’s ”auto-measure” module is used. The region of

interest is defined so as to minimize the size of the image (Figure 6.10a). Then the module is

started using a measuring program suitable for all images. AC cannot, however, be defined

correctly, as illustrated by the unsatisfactory result for outlining cracks in Figure 6.10b. Due

to the background light all images show brighter values at the edge of the cake compared

to those in the middle. A threshold that satisfactory captures and outlines the cracks in the

middle of the cake falsely includes pixels of the cake structure in the cake’s edge regions

as well. Furthermore, the image shows bright regions in the cake’s middle due to its porous

structure, which are incorrectly included (numerous red dots in Figure 6.10b). The bright

regions outside the cake structure that arise from the background light are included to the

crack area as well.

To solve this problem the contour evaluated by the determination of AF (Figure 6.10c,

green line) is used, since along this line separate regions are defined by the threshold pro-

cess. In the regions marked with a rectangle in Figure 6.10d where the cracks run to the

edge, a manual separation between crack and outer bright regions with the ”separator” tool

is necessary. In all other edge regions the separation is carried out automatically along the

contour, so that the outer area is manually deleted, as shown in Figure 6.10e. The rectangles

in this figure show small regions that are not deleted in this separation step since they are

not connected to the large outer area. As these small regions are clearly located outside

the cake structure, they must be deleted manually. The outlined crack area shown in Fig-


a b c d

e f

f

g h

i j

Figure 6.10: Development of the crack area image evaluation. a: Region of interest, b: Seg-mented crack area without image processing, c: Application of the contour orcircle of the AF determination, d: Regions of manual segmentation, e: Imagewithout the major outer cake region, but with small not separated regions markedwith rectangles, f: Optimal selection of brightness, contrast, and gamma, g: AC

separation with brightness, contrast and gamma adaption, h: Gaussian correc-tion of the image, i: shading correction, j: segmentation of AC .

ure 6.10e includes regions of cake structure in the middle of the cake. Image processing

operations are therefore still necessary for an accurate separation of AC . Those operations

are performed by the ”auto measure” module and a standardized method is developed for all

images.

The optimal selection of the brightness, the contrast, and the color gamma of the image

has first to be defined. A brightness of -0.59, a contrast of 2.35 and a gamma value of 0.92,

shown in Figure 6.10f, give good results in the evaluation of AC from this image, as illustrated

in Figure 6.10g. Since small regions inside the intact cake structure are still included to AC

(Figure 6.10g), a further optimization is necessary by the application of a Gaussian correction

82 6 Results

given in Figure 6.10h. The Gaussian filter used is a linear technique working via convolution.

During convolution the value of any given pixel in the output image is given by the weighted

sum of neighboring pixel values in the input image [120]. The neighborhood is normally

a rectangle of given size (e. g. 3x3, 5x5) and the pixel itself can be included or excluded.

The Gaussian filter reduces noise in the images and has therefore a smoothing effect. The

decisive factor of this filter is the variance, σ, which controls the degree of smoothing. A large

value of σ leads to a large smoothing of the image [120]. For the evaluation of AC the σ value

is intuitively set to 20. The ”auto measure” module furthermore contains a shading correction

to balance an uneven brightness gradient. A satisfactory balance is possible by a shading

correction of 4, as illustrated in Figure 6.10i. With all these corrections the evaluation of AC

is possible, as shown in Figure 6.10j. This is the best result achieved.

6.1.1.3 Automatic Evaluation with Matlab

For a complete automatic evaluation of AC a Matlab program is used. An image is loaded in

the form of a (i,j)-matrix in which each entry represents one pixel of an image. The values of

i and j give the information of the location of each pixel, where i = rows and j = columns. In

a gray-scale image each entry contains the intensity of the pixel in the image. There are two

classes for the representation of the number that gives the brightness of the pixels. In the

”double” data type the intensities are given as a floating number between 0 and 1, at which

the value 0 corresponds to black and the value of 1 corresponds to white. In the ”uint8” class

an integer between 0 and 255 is used, where the value of 0 corresponds to black and 255 to

white. Since many mathematical functions can only be applied to the double data class, the

image has to be converted in Matlab to ”double”. In a color image (RGB-image) the intensity

of each pixel is given by three channels, a red, a green and a blue one. It is therefore given

by three matrices where each matrix corresponds to one of the three colors and contains the

information of the composition of each pixel. In Matlab every pixel can therefore be identified

by using a (i,j,z) matrix, where z contains the information of the red component (z = 1), of

the green component (z = 2) and the blue component (z = 3).

After the conversion to ”double” the pixels belonging to the cake are defined to neglect

pixels located outside the cake area. This lets the program run faster due to the lower data

volume. To identify the pixels of the image belonging to the cake area, AF , Axio Vision is


used. AF is defined by the ”circle measure” tool, as described in 6.1.1.2. The coordinates

of the midpoint of this circle and its radius are identified and used in Matlab for a reference

point given by the coordinates (mx/my).

In a first step every pixel with an x-value and a y-value not obeying the following equation

is excluded for a rough definition of the cake area of interest:

mx− radius < x < mx+ radius

my − radius < y < mx+ radius(6.1)

The reference point is the midpoint of a square whose half-height equals the radius of the

cake. The image section included for the evaluation during this step is shown in Figure 6.11.

By using the Pythagoras’ theorem the squared distance of each pixel to the reference point

(a) (b)

Figure 6.11: (a): Sample Image, (b) Image section included for the evaluation.

is calculated and compared with the squared radius. If the sum of both squared distances

(x-direction and y-direction) exceeds the squared radius, the pixel is located outside of the

circular cake area and its value is set to ”-1”. With an ”if/else” function the pixels belonging

only to AF can now be selected. For further operations on each pixel value an averaged value

of the three z-channels (red, green, blue) is used. Figure 6.12 shows the red (a), the green

(b), and the blue (c) channel in a 3D shaded surface plot from the z components (color data),

with the height z as a single-valued function defined over a rectangular grid. The color of z is

proportional to the surface height. To enable automatic image evaluation, a flexible threshold

is necessary to account for differences between all images. The threshold is therefore linked

84 6 Results

(a) (b)

(c)

Figure 6.12: (a): Red component, (b) Green component, (c) Blue component.

to the mean color value of the cake, mc, and is calculated by the mean value of all pixel

values with a value 6= 1. To account for the brighter pixel values at the edge of the cake

a polyfit function is included. All pixels of each row belonging to the cake area (6=1) are

written in a row vector and the numbers of entries are counted. With the ”polyfit” function

a fitting polynomial of fourth order is produced and used to fit every row with the ”polyval”

function. From each fitted value, the mean color value of the cake area is subtracted. This

fitting procedure (polyfit, polyval) is performed for the columns of the cake area as well.

At this stage all pixel values (6= 1) are compared with the threshold value, taken as

1.15 ·mc. A pixel value >1.15 ·mc is defined as belonging to the crack; a pixel value <mc

as a pixel of the cake. The cracking in % is calculated from the sum of the crack pixels and

the sum of the cake pixels already calculated for mc. An example of a separated cake area

is given in Figure 6.13. With the Matlab program automatic rapid evaluation of the AC of


Figure 6.13: Separated crack area in red, cake area in yellow.

numerous images without any operator intervention is possible. An evaluation of shrinkage,

however, is not possible and must be performed manually with Axio Vision. Moreover, the

evaluation of sample images with a non-circular cake structure must also be done with Axio

Vision because of the uneven cake shape and the fragment problem described in 6.1.1.2.

6.1.2 Statistical Comparison between Axio Vision and Matlab

D-(+)-trehalose dihydrate (hereafter referred to ”trehalose”) solutions in four different concen-

trations (7.5%, 10%, 20% and 30%) were freeze-dried with cycle 1 (see chapter 5.2.3) and

images of each cake taken, as described in 6.1.1.1. All images were evaluated with Axio

Vision and in the case of a circular cake structure with Matlab. Since the values of % crack-

ing obtained with both programs come from the same image, the samples are ”paired” and

a dependent t-test may be performed [121]. For each evaluation method and at each con-

centration a Chi2-test is performed to verify a normal distribution with a significance level, α,

of 0.05%. The null hypothesis is proposed that the cracking values are normally distributed

with the expectancy value of µ and the variance of σ. The alternative hypothesis is that the

cracking values are not normally distributed with the expectancy value of µ and the variance

of σ.

86 6 Results

For the Chi2-test the mean value, µ, the standard deviation, s, and the sample size, n are

calculated. The % cracking values are divided into classes and the actual frequencies of

each class, fa, are calculated. The basis of the test is a comparison of the actual and the

expected frequencies of each class. For the calculation of the expected frequency of each

class, fe, the z-values of each class are calculated via:

z =xu − µ

s, (6.2)

where xu is the upper limit of each class. The φ(z)-values of each class are obtained from

the distribution function, F (z), of the standardized normal distribution by the value of z [121].

The φ(z) value constitutes the area under the standardized normal distribution curve from 0

to z. The difference of φ(z) of each class to its prior class is calculated and multiplied with

the sample size, n, to obtain the expected frequency of the class, fe.

Figure 6.14 shows for each evaluation method and each trehalose concentration the fre-

quencies of each cracking class. The black columns give the actual cracking frequencies,

fa, and the gray columns the calculated expected values, fe. To compare fe with fa of each

class, the standardized residue, fs, of each classes is calculated by:

fs =(fa − fe)

2

fe. (6.3)

The sum of fs gives the test statistic, χ2, which is compared with the critical value of the

Chi2-distribution, χ2c. This critical value is obtained from the table of the Chi2-distribution and

the degree of freedom, df (given by the number of classes minus 3) [121]. Table 6.2 gives

an overview of the values obtained. It shows for all test groups that χ2 is smaller than χ2c,

and the proposed null hypothesis can be accepted. The cracking values of each test group

are therefore normally distributed and a dependent t-test for paired samples (α =0.05) may

be performed.

The null hypothesis is that the cracking values obtained by the evaluation with Axio Vision

equal those obtained with Matlab. The alternative hypothesis is that there is a difference be-

tween the cracking values obtained by the different evaluation programs. For the dependent

t-test for paired samples the differences between all pairs are calculated. From this data the

number of pairs, n, the mean value, XD, and the standard deviation, SD, are calculated. The


0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 >80

2

4

6

8

10

12

14

16 Observed Expected

Freq

uenc

y A

xioV

isio

n 7,

5%

Classes cracking [%]

(a)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 >80

2

4

6

8

10

12

14


Freq

uenc

y M

atla

b 7,

5%


(b)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 >110

2

4

6

8

10

12

Observed Expected

Freq

uenc

y A

xioV

isio

n 10

%


(c)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 >110

2

4

6

8

10


Freq

uenc

y M

atla

b 10

%Classes cracking [%]

(d)

0-9,5 9,5-10 10-10,5 10,5-11 11-11,5 11,5-12 12-12,5 12,5-13 13-13,5 13,5-14 14-14,5 >14,50

2

4

6

8

10

12

14


Freq

uenc

y A

xioV

isio

n 20

%


(e)

0-9,5 9,5-10 10-10,5 10,5-11 11-11,5 11,5-12 12-12,5 12,5-13 13-13,5 13,5-14 14-14,5 >14,50

2

4

6

8

10

12

Observed Expected

Freq

uenc

y M

atla

b 20

%


(f)

0-9,5 9,5-10 10-10,5 10,5-11 11-11,5 11,5-12 12-12,5 12,5-13 13-13,5 13,5-14 14-14,5 >14,50

2

4

6

8

10

12


Freq

uenc

y A

xioV

isio

n 30

%


(g)

0-9,5 9,5-10 10-10,5 10,5-11 11-11,5 11,5-12 12-12,5 12,5-13 13-13,5 13,5-14 14-14,5 >14,502468

101214161820 Observed

Expected

Freq

uenc

y M

atla

b 30

%


(h)

Figure 6.14: Observed and expected cracking values for each class and the following testgroups: 7.5% trehalose (w/v) evaluated with Axio Vision (a) and with Matlab (b),10% trehalose (w/v) evaluated with Axio Vision (c) and with Matlab (d), 20%trehalose (w/v) evaluated with Axio Vision (e) and with Matlab (f), 30% trehalose(w/v) evaluated with Axio Vision (g) and with Matlab (h).

88 6 Results

Test Group n µ s σ χ2 χ2c

7.5% AV 44 2.70 1.76 3.09 10.3133 12.59167.5% ML 44 2.74 1.71 2.92 12.0131 12.591610% AV 41 6.18 1.99 3.96 6.2147 16.919010% ML 41 6.12 1.96 3.84 3.9262 16.919020% AV 55 11.64 1.09 1.19 9.3711 16.919020% ML 55 11.67 1.09 1.19 5.7306 16.919030% AV 64 12.19 0.96 0.92 2.8469 16.919030% ML 64 12.23 0.85 0.72 10.5754 16.9190

Table 6.2: Results of the χ2-test. AV: Evaluation with Axio Vision, ML: Evaluation with Matlab.

test value, t, is calculated via:

t =XDsD√n

. (6.4)

t is than compared to the value of the t-distribution, tc, with a significance level of 2α/2 and a

degree of freedom, df , of n−1 obtained from the table of the T-distribution [121]. The results

of the dependent t-test for paired samples are given in Table 6.3. It shows for all test groups

Test Group XD SD n t tc

7.5 0.04 0.22 44 1.2464 2.018110 0.06 0.25 41 1.6572 2.021120 0.02 0.36 55 0.4986 2.004930 0.04 0.51 64 0.5907 1.9983

Table 6.3: Results of the dependent t-test for paired samples with the test groups 7.5% tre-halose (w/v), 10% trehalose (w/v), 20% trehalose (w/v), 30% trehalose (w/v).

that t is smaller than tc, and the proposed null hypothesis can be accepted. The evaluation

with Matlab equals therefore that of Axio Vision. Figure 6.15 shows a comparison between

the cracking values obtained with each evaluation method. Judged visually there is also no

difference between the two methods. This result in Figure 6.15 will be discussed later.

6.1.3 Sample Selection and Edge Effect

For endpoint evaluation the vials are positioned in a hexagonal arrangement (Figure 6.16)

on the shelf of the freeze-drier contained within a hexagonal metal ring. The influence of an

edge effect on shrinkage and cracking is unknown. The vials at the outer positions that show

a different cake appearance in comparison to center vials need therefore to be investigated


5 10 15 20 25 30

2

4

6

8

10

12

14

Cra

ckin

g [%

]

Concentration of trehalose (w/v)

Axio Vision Matlab

Figure 6.15: Mean values of cracking obtained with Axio Vision (square) and Matlab (circle).The coordinates for cracking are the mean average ± standard error of all valuesobtained.

3456789

10

21

Figure 6.16: Arrangement of the vials in a hexagonal position. The numbers 1-10 mark therows of the arrangement.

and, if needed, excluded from further experiments.

To analyze the edge effect on shrinkage and cracking the batch is classified in rows num-

90 6 Results

bered with 1 to 10 from the outside to the inside, as illustrated in Figure 6.16. All vials are

marked with the corresponding row number and freeze-dried with cycle 1 (see chapter 5.2.3).

After the freeze-drying process is complete images of every vial are taken and evaluated with

regard to shrinkage and cracking. To compare the values of shrinkage and cracking the t-

test for independent samples is performed. Since the number of vials is less at higher row

number, the rows located in the center are combined to one test group, as shown in Figure

6.16. The number of vials in this row is the sample size n. For this test homogeneity of

both variances is provided and an F-test is performed. This requires calculation of the stan-

dard deviations, s1 and s2, and the variances of both test groups, σ1 and σ2, with regard to

shrinkage and cracking. The test statistic, F , is given by:

F =σ1

σ2

. (6.5)

The critical values, Fc, are obtained from the table of the F-distribution with df of n1 − 1 and

n2 − 1 and a significance level, α, of 0.01 [122]. The null hypothesis is that the variances

of the test groups, σ1, σ2 are homogeneous. The alternative hypothesis is that they are

not homogeneous. Tables 9.1 and 9.2 (both in Appendix, see chapter 9) give an overview

of the calculated values and the critical values for cracking and shrinkage, respectively. The

F-values that indicate rows with inhomogeneous variances are printed in bold text. For homo-

geneous variances, σ1, σ2, the standard deviation of the sample distribution of sample-mean

differences, sm−m is calculated as:

sm−m =

√s21n1

+s22n2

, (6.6)

where s1, s2 are the standard deviations of each test group and n1, n2 are the group sizes.

Then the test statistic, t, can be calculated via:

t =

√n1 ·n2

n1 + n2

· µ1 − µ2

sm−m

, (6.7)

where µ1, µ2 are the mean values of the test groups. The null hypothesis is that the mean

values of the test groups, µ1, µ2 are equal. The alternative hypothesis is that µ1, µ2 are

not equal. The critical values, tc, are obtained from the table of the t-distribution with df


of n1 + n2 − 2 and α of 0.01 [121]. The results of the t-test for independent samples and

homogeneous variances for cracking and shrinkage are given in Table 9.3 and Table 9.4

(both in Appendix, see chapter 9), respectively. The vales of t and tc belonging to rows with

differences in the mean values are printed in bold text. The rows for shrinkage show only

inhomogeneous variances (see Table 9.1 and Table 9.2, both in Appendix, see chapter 9).

For these rows the t-test for independent samples with inhomogeneous variances, σ1, σ2, is

performed. In this case the test statistic, t, is calculated as:

t =µ1 − µ2

sm−m

. (6.8)

The critical values, tc, are obtained from the table of the t-distribution with df and α of 0.01

[121]. df is calculated via:

df =1

c2

n1−1+ (1−c)2

n2−1

, with c =

s21

n1

s21

n1

+s22

n2

. (6.9)

An overview of the results of this t-test is given in Table 9.5 (see Appendix in chapter 9).

Table 9.6 (see Appendix in chapter 9) summarizes the uniformity of the values of shrinkage

and cracking depending on position of the vials, as obtained by the t-test for independent

samples.

The behavior of shrinkage is seen to be more independent of the position of the vials than

is the behavior of cracking. The results indicate a trend to more inhomogeneous cracking or

shrinkage behavior at the edge of the shelf compared to a center position. This trend is more

pronounced with cracking. Up to row four inhomogeneity is found in cracking. To ensure a

sample selection with high uniformity of shrinkage and cracking and no influence of the edge

effect, the vials positioned at rows one to four are therefore excluded from evaluation. Only

the vials from row 5 up to row 10 are included.

To investigate the edge effect on shrinkage and cracking, the vials of row 1-4 and of row

5-10 are combined into two groups. The mean values, µ, the standard deviations, s, and the

group sizes, n are given in Table 6.4. For the t-test for independent samples the F-test is

performed to investigate the homogeneity of the variances, σ1 and σ2. The null hypothesis

is that the variances of the test groups, σ1, σ2 are homogeneous. The alternative hypothesis

is that they are not homogeneous (α =0.01). Table 6.5 gives an overview of the calculated

92 6 Results

Concentration µ1−4 µ5−10 s1−4 s5−10 n1−4 n5−10

Cracking 7.5% 2.74 2.65 1.87 1.65 25 19Cracking 10% 6.39 6.25 2.02 2.01 30 11Cracking 20% 11.72 11.49 1.17 0.93 37 18Cracking 30% 12.13 12.30 0.97 0.95 39 25

Shrinkage 7.5% 13.71 12.64 5.49 3.39 25 19Shrinkage 10% 16.97 17.19 5.31 5.92 30 11Shrinkage 20% 7.41 6.97 0.80 0.63 37 18Shrinkage 30% 7.58 7.49 1.20 1.25 39 25

Table 6.4: Mean values, µ, the standard deviations, s, of shrinkage and cracking and thegroup sizes, n of the vials with 7.5%-30% trehalose concentration belonging torow 1-4, and 5-10.

values and the critical values for cracking and shrinkage. The critical values, Fc, are obtained

from the table of the F-distribution with df of n1 − 1 and n2 − 1 and a α of 0.01 [122]. The

F-values that indicate rows with inhomogeneous variances are printed in bold text. Since

Concentration s1 s2 σ1 σ2 F Fc

Cracking 7.5% 1.87 1.65 3.49 2.72 1.28 3.04Cracking 10% 2.02 2.01 4.09 4.05 1.01 3.94Cracking 20% 1.17 0.93 1.36 0.86 1.58 2.63Cracking 30% 0.95 0.97 0.90 0.95 0.96 2.96

Shrinkage 7.5% 3.39 5.49 11.50 30.19 0.38 2.81Shrinkage 10% 5.92 5.31 35.04 28.15 1.24 2.90Shrinkage 20% 0.80 0.63 0.63 0.40 1.58 2.63Shrinkage 30% 1.25 1.20 1.56 1.44 1.09 2.96

Table 6.5: Results of the F-test for the cracking and shrinkage values of 7.5% trehalose (w/v),10% trehalose (w/v), 20% trehalose (w/v), 30% trehalose (w/v). Test groups foreach concentration are the combination of rows 1-4 and 5-10. F-values that indi-cate rows with inhomogeneous variances are printed in bold text.

the variances of each test group are homogeneous, the t-test for independent samples and

homogeneous variances is performed for all samples. The null hypothesis is that the mean

values of the test groups, µ1, µ2, are equal. The alternative hypothesis is that the mean

values of the test groups, µ1, µ2 are not equal (α =0.01). The critical values, tc, are obtained

from the table of the t-distribution with df of n1 + n2 − 2 and a α of 0.01 [121]. The results of

the t-test for independent samples and homogeneous variances for cracking and shrinkage

are given in Table 6.6. The vales of t and tc belonging to rows with differences in the mean


values are printed in bold text. Table 6.6 shows that a difference between the mean values

Concentration s1 s2 sm−m µ1 µ2 t df tc

Cracking 7.5% 1,87 1,65 0,53 2,74 2,65 0,5559 42 2,6981Cracking 10% 2,02 2,01 0,71 6,39 6,25 0,5591 39 2,7079Cracking 20% 1,17 0,93 0,29 11,72 11,49 2,7482 53 2,6718Cracking 30% 0,95 0,97 0,25 12,30 12,13 2,6987 62 2,6575

Shrinkage 7.5% 3,39 5,49 1,35 12,64 13,71 2,6068 42 2,6981Shrinkage 10% 5,92 5,31 2,03 17,19 16,97 0,3076 39 2,7079Shrinkage 20% 0,80 0,63 0,20 7,41 6,97 7,6323 53 2,6718Shrinkage 30% 1,25 1,20 0,32 7,49 7,58 1,1409 62 2,6575

Table 6.6: Results of the t-test for the shrinkage values of 7.5% trehalose (w/v), 10% tre-halose (w/v), 20% trehalose (w/v), 30% trehalose (w/v) with homogeneous vari-ances. Conc.= trehalose concentration (w/v). Rows with differences in the meanvalues are printed in bold text.

of the outer rows (1-4) and the center rows (5-10) can be found with 20% and 30% trehalose

(w/v) for cracking and with 20% trehalose (w/v) for shrinkage. A clear influence of an edge

effect is therefore not found at all trehalose concentrations. Table 6.6 shows no tendency to

any influence of an edge effect on either cracking or shrinkage.

6.1.4 Shrinkage, Cracking and the Amount of Unfrozen Water, w′

The endpoint evaluation method is used to investigate any apparent correlation between the

content of non-frozen water in the maximum freeze-concentrated state, w′, of an amorphous

cake and shrinkage, as has been suggested by Rambhatla et. al. [5]. These authors used 5%

sucrose solutions (w/v) and measured the geometric shrinkage of the cake after lyophiliza-

tion from its average diameter and height. They found a value of shrinkage of 17.3% at

a low primary drying temperature (-38 C) and a slow ramp rate towards secondary drying

(0.1 C/min). Tg was at no time exceeded by the product temperature, Tp, during secondary

drying. When using an aggressive cycle (-25 C, 2.5 C/min), Tp exceeded Tg during sec-

ondary drying, but a cake shrinkage of only 19.5% was measured. The authors reasoned

that secondary drying conditions have only a second-order effect. They suggested a correla-

tion between w′ and shrinkage, since sucrose contains about 18% water at T ′g. They hypoth-

esized that w′ occupies volume which must be preserved as void space during secondary

drying or shrinkage will occur. This shrinkage would then lead to a decrease in volume of the

94 6 Results

sucrose phase by the same volume occupied by w′.

The disaccharides trehalose, D-(+)-Maltose, and D-(+)-Sucrose that have different w′ were

freeze-dried with cycle 1 (see chapter 5.2.3). A wide concentration range (7.5% (w/v), 10%

(w/v), 20% (w/v) and 30% (w/v)) was used. To confirm the T ′g values found in the literature,

DSC measurements were first carried out with a 7.5% aqueous solution (w/v) of each dis-

accharide. The thermograms in the region of the inflection point are shown in Figure 6.17.

Table 6.7 gives an overview of the disaccharides used and their corresponding w′ and T ′g

-80 -70 -60 -50 -40 -30 -20 -10 0 10-6,0

-5,5

-5,0

-4,5

-4,0

-3,5

-3,0

endo

Hea

t Flo

w [m

W]

Temperature [°C]

D-(+)-Sucrose D-(+)-Trehalose D-(+)-Maltose

exo

Figure 6.17: DSC scans in the region of the inflection point of D-(+)-Maltose (circle), trehalose(triangle), and D-(+)-Sucrose (square).

values reported from Slade and Levine [83], and also the mean value of T ′g determined by

the current DSC measurements. The measured values for T ′g are about 2.5 C lower than

those reported by Slade and Levine [123]. The deviation may be explained by the use of

different measurement methods. The value of the glass transition depends on the heating

and cooling rate.

Above Tg the system behaves like a liquid and responds to changes in temperature in the

timescale of the temperature change and is therefore in equilibrium with the cooling process.

At Tg, the system is kinetically unable to stay in the equilibrium state, since its molecular


Disaccharide w′[83] T ′g[83] Mean value of T ′

g (midpoint)

trehalose 16.7% -28,65C -30.99CD-(+)-Maltose 20.0% -28,65C -31.59CD-(+)-Sucrose 35.9% -31,15C -33.81C

Table 6.7: Overview of the disaccharides used and the corresponding w′ and T ′g obtained

from Slade and Levine [83].

mobility is reduced, and it is therefore not able to respond to the changes in temperature in

the timescale of the temperature change. At lower cooling rates, the timescale for relaxation

is higher and the systems stays in the equilibrium state till lower temperatures compared to

a faster cooling rate. Hence, a lower value of the glass transition temperature is measured

[71].

The exact cooling rate used for the determination of the glass transition temperature is not

given at Slade and Levine [123], only the information that a slow cooling rate was used. The

differences between the measured data and the values of T ′g reported by these authors are

likely caused by different cooling rates.

Lyophilization was performed in the hexagonal vial packaging according to Figure 6.16.

After its completion images were taken of every vial in rows 4-10 and evaluated for shrinkage

and cracking.

D-(+)-sucrose has the highest w′ and should show the highest amount of shrinkage, fol-

lowed by D-(+)-maltose and trehalose. Figure 6.18 shows the mean values of shrinkage

for each disaccharide at each concentration. With increasing concentration less shrinkage

occurs. The values for % shrinkage with a 7.5% disaccharide concentration are some three

times higher than at 30% disaccharide concentration for D-(+)-sucrose (circle), D-(+)-maltose

(triangle) and more than sevenfold higher for trehalose (square). The highest amount of

shrinkage is found for D-(+)-sucrose which possesses the highest value of w′. The lowest

amount of shrinkage is observed for trehalose that has the lowest w′. These results appear

to confirm the assumption suggested by Rambhatla et. al. [5] of a direct causal correlation

between shrinkage and w′, but needed to be considered in more detail.

Rambhatla et. al. [5] correlated the value of shrinkage to the value of w′. Table 6.8 gives

an overview of w′ and the values of shrinkage obtained in the current work from the 7.5%

disaccharide samples. Rambhatla et. al. [5] compared their degree of shrinkage with a w′

96 6 Results

5 10 15 20 25 30

0

5

10

15

20

25

30

Shr

inka

ge [%

]

Concentration [%] (w/v)

Sucrose Maltose Trehalose

Figure 6.18: Shrinkage values of freeze-dried D-(+)-sucrose (circle), D-(+)-maltose (triangle),and trehalose (square) solutions with 7.5% (w/v), 10% (w/v), 20% (w/v), and30% (w/v) disaccharide concentration. The coordinates for shrinkage are themean average ± standard error of all values obtained (trehalose: 7.5%: n=32,10%: n=33, 20%: n=30, 30%: n=26; D-(+)-sucrose: 7.5%: n=20, 10%: n=17,20%: n=24, 30%: n=19; D-(+)-maltose: 7.5%: n=19, 10%: n=23, 20%: n=13,30%: n=14).

Disaccharide w′ Shrinkage

7.5% trehalose 16.7% 16.43%7.5% D-(+)-maltose 20.0% 18.69%7.5% D-(+)-sucrose 35.9% 23.57%

Table 6.8: Values of shrinkage obtained from the 7.5% disaccharide samples in comparisonto the corresponding values of w′ reported by Slade and Levine [123].

value for sucrose of approximately 18%, but Slade and Levine [123] determined 35.9% for

w′. The literature contains conflicting values for w′ and T ′g, as shown in Table 6.9. Miller

et. al. [124] and Craig et. al. [71] explain these different values as a probable result of the

measuring method since these may use the same heating and cooling rate, but the different

solutions measured have different characteristic time scales. Since Slade and Levine [123]

used a method that accounted for the dependence on the solution composition, the values of


w′ (printed in bold text in Table 6.9) are obtained by these authors. Hence, a value of 35.9%

of unfrozen water for sucrose instead of about 18% reported by Rambhatla [5] seems to be

more likely.

Disaccharide w′ Tg′ Reference

Trehalose 16.7% -28.65 C [123]18.8% -22.20 C [124]18.4% -35.00 C [125]

Maltose 20.0% -28.65 C [123]23.0% -31.00 C [126]

Sucrose 17.0% -31.50 C [127]18.8% -39.15 C [128]20.0% -36.15 C [127]21.0% -48.15 C [127]35.9% -31.15 C [82, 123]

Table 6.9: Values of w′ and T ′g of trehalose, D-(+)-maltose, and D-(+)-sucrose reported by

various authors.

Trehalose follows the correlation between the values of w′ and T ′g and D-(+)-maltose shows

with 20.0% w′ and 18.69% (shrinkage) almost similar values. But a large deviation between

w′ (35.9%) and the degree of shrinkage (23.57%) is observed for D-(+)-sucrose. Ramb-

hatla et. al. suggested that additional free volume in the cake is generated as a result of the

desorption of the unfrozen water. D-(+)-sucrose may transform the excess free volume not

only to cake shrinkage, but also to free volume in the cake. This does not occur with D-(+)-

maltose and trehalose, where possibly the complete excess free volume is transformed to

cake shrinkage.

Another explanation is that the cake cracks during the desorption of the unfrozen water.

The amount of cracking for D-(+)-sucrose should then be greater than that for D-(+)-maltose

and trehalose. This would explain the difference between the high amount of w′ but the

low degree of shrinkage. Figure 6.19 illustrates the amount of cracking observed for D-(+)-

sucrose, D-(+)-maltose, and trehalose for solutions with 7.5% (w/v), 10% (w/v), 20% (w/v),

and 30% (w/v) disaccharide concentration. The highest amount of cracking is not found for

D-(+)-sucrose, but rather for trehalose. The excess free volume is therefore evidently not

transformed in cracking.

Shrinkage increases in the order: trehalose > D-(+)-maltose > D-(+)-sucrose. Cracking

98 6 Results

5 10 15 20 25 30

0

5

10

15

20

25

30

Cra

ckin

g [%

]

Concentration [%] (w/v)

Trehalose Sucrose Maltose

Figure 6.19: Cracking values of freeze-dried D-(+)-sucrose (circle), D-(+)-maltose (triangle),and trehalose (square) solutions with 7.5% (w/v), 10% (w/v), 20% (w/v), and30% (w/v) disaccharide concentration. The coordinates for cracking are themean average ± standard error of all values obtained (trehalose: 7.5%: n=32,10%: n=33, 20%: n=30, 30%: n=26; D-(+)-sucrose: 7.5%: n=20, 10%: n=17,20%: n=24, 30%: n=19; D-(+)-maltose: 7.5%: n=19, 10%: n=23, 20%: n=13,30%: n=14).

increases in the order: D-(+)-maltose > D-(+)-sucrose > trehalose. The order of shrinkage

is neither equal nor opposite to that of shrinkage. A correlation between the amount of w′

and the degree of cracking is not therefore observed.

Figure 6.19 also illustrates that the degree of cracking depends on the disaccharide con-

centration, as already observed for shrinkage. With increasing disaccharide concentration

the values for cracking increase while those for shrinkage decrease. At low concentrations

D-(+)-sucrose and D-(+)-maltose show very little cracking, but trehalose shows up to 7%

cracking at 10% disaccharide concentration. As concentration increases the behavior of D-

(+)-sucrose and trehalose runs parallel, but D-(+)-maltose behaves differently and remains

at a low level.


6.1.5 Impact of the Trehalose Concentration

A 2R vial was used and filled with trehalose solutions at concentrations of 5%, 7.5%, 15%,

20%, and 30% to a fill height of 2.5 mm. The semi-stoppered vials were freeze-dried in a

hexagonal vial packaging with cycle 1 (see chapter 5.2.3). After lyophilization images of

each vial were taken in rows 4-10 and evaluated for shrinkage and cracking. The measured

values of cracking at each concentration are given in Figure 6.20.

5 10 15 20 25 300

5

10

15

20 Shrinkage [%] Cracking [%]

Trehalose concentration [%]

Cra

ckin

g [%

]

0

5

10

15

20

Shr

inka

ge [%

]

Figure 6.20: Cracking (black circle) and shrinkage (black square) values of freeze-dried tre-halose solutions with 5% (w/v), 7.5% (w/v), 10% (w/v), 15% (w/v), 20% (w/v),and 30% (w/v) trehalose concentration. The coordinates for cracking are themean average ± standard error of all values obtained (trehalose: 5%: n=4,7.5%: n=32, 10%: n=33, 15%: n=19, 20%: n=30, 30%: n=26).

The curve for cracking lies at 5%, 7.5% and 10% trehalose concentrations at lower values

compared to shrinkage. At a concentration between 10% and 15% both curves cross and

with higher trehalose concentrations the values of cracking exceed those of shrinkage. In-

creased values of cracking and decreased values of shrinkage are seen with higher trehalose

concentration.

100 6 Results

Figure 6.21 shows representative sample images at each trehalose concentration. The

a b c

d e f

Figure 6.21: Sample images of lyophilizates with a: 5% (w/v), b: 7.5% (w/v), c: 10% (w/v), d:15% (w/v), e: 20% (w/v), and f: 30% (w/v) trehalose.

cakes show narrow, long cracks at 5% trehalose that propagate from the outside of the cake

to its center, as shown in Figure 6.21a. The crack width is greater at the edge of the cake

compared to its center. With this crack pattern the cake surface is mostly separated into two

parts.

For samples at 7.5% trehalose the cracks run together in the center of the cake and split

its surface generally into four to five pieces, illustrated in Figure 6.21b. As already seen for

the samples at 5% trehalose, the crack width of the samples is greater at the cake’s edge

than in the central region.

At 10% trehalose (Figure 6.21c) the cracks run through the whole cake surface from the

edge to the center. The cakes show a multiple cracked surface which is separated into four

to six pieces, typically with a center piece. This center piece in Figure 6.22a is shown for

a quartered cake and in Figure 6.22b for a cake that is split into six regions. These crack

patterns suggest that samples with four or five pieces are intermediate stages of a cake

with six pieces. The quartered cake in Figure 6.22a suggests a split into five pieces as a


a b

Figure 6.22: Sample images of lyophilizates with 10% trehalose (w/v). The path of the cracksseparated the cake surface in a: four and b: six pieces.

crack propagates from the right towards the cake’s edge, but not completely to its edge. The

development of a fifth surface piece is therefore initiated, but not finished. The sixth piece of

cake may also be developed based on the crack pattern of a cake with five cake pieces, since

a further crack runs through the center piece (Figure 6.22b). Such a split is also initiated on

the left side of the center piece of the cake shown in Figure 6.22a.

Samples containing 15% trehalose (Figure 6.21d) show a greater amount of cracks which

separate the cake into at least nine pieces. The size of the pieces differs strongly from

one cake to another, much more than for samples at lower trehalose concentrations. This

observation suggests that fragments are additionally separated by further crack growth. A

center piece which is observed for samples at 10% trehalose is not clearly found.

Cakes that contain 20% and 30% trehalose (Figure 6.21e, f) possess a crack pattern

similar to each other but different to samples with less trehalose. Both show fine cracks in

the outer region of the cake with no connection to the cake’s edge. The crack width increases

inwards and at least ten surface pieces can be identified. The sizes of the pieces are similar

to each other and are likely caused by further crack growth through original connected areas

of the cake.

The lyophilizates can also be analyzed for mechanical strength when compressed in the

texture analyzer. The typical stress-strain curves are shown in Figure 6.23. The lyophilizates

show the typical irregular, oscillating (”jagged”) strain during the compression of a brittle

solid foam described at Peleg [129] and Harnkarnsujarit [130]. The deformation leads to

major and minor failure-events by the breaking of the pore walls within the highly porous

cake. A fracture-controlled crushing process takes place. The stress decreases sharply after

102 6 Results

-0,5 0,0 0,5 1,0 1,5

0

10

20

30

40

50

60

Forc

e [N

]

Displacement [mm]

0

10

20

30

40

50

60

0

10

20

30

40

50

60

0

10

20

30

40

50

60

0

10

20

30

40

50

60

30% 20% 15% 10% 7,5% 5%

0

10

20

30

40

50

60

Figure 6.23: Compressive force-displacement curves of freeze-dried trehalose cakes in theconcentration range 5% - 30%.


each fracture-event, when a critical stress level is reached and causes the stress fluctuations

by pore (cell) wall breakage [131]. The mechanical properties are therefore dependent on

the cell wall material and the size distribution of the cells. The brittleness of these cellular

structures can be quantified by the degree of the jaggedness obtained by the apparent fractal

dimension, F , of the curve [129].

The fractal dimensions of the curves listed in Table 6.10 were determined with the ”box

count” tool of Image J software. It can be seen that F and hence the brittleness of the

Trehalose concentration (w/v) Fractal Dimension, F Hardness [N]

5% 1.575 0.417.5% 1.555 2.8710% 1.532 6.0715% 1.442 7.9720% 1.382 25.430% 1.352 44.3

Table 6.10: Fractal dimensions and harness of the lyophilizates at different trehalose concen-trations (w/v).

lyophilizates decrease with trehalose concentration. Table 6.10 furthermore contains the

hardness of the lyophilizates defined as the measured peak force after 1 mm penetration. The

hardness increases with trehalose concentration. This is apparent from Figure 6.23 since

a higher compressive force is necessary to deform the freeze-dried cakes with increasing

trehalose concentration and the curves run at higher values. This correlates with the cell size

of the lyophilizates shown in Figure 6.24 at different trehalose concentrations. The cell sizes

of the lyophilizates increase visually in the order: 7.5% < 10% < 30%. This observation is

confirmed by mercury porosimetry illustrated in Figure 6.25. Larger cells are found at higher

trehalose concentrations.

The cell structure influences the mechanical properties of a freeze-dried cake. Freeze-

dried cakes of trehalose generally produce hexagonal prism shaped cells of various sizes.

Devi and Williams [131] described such cellular materials as ”bodies with vertices joined by

edges, which surround faces that enclose cells” and classified the cell structure in ”open

celled” and ”close-celled” foam structures. They also found the predominantly closed cake

cells (with no thickening in the cell edges) and with an outlet passageway for water seen

here, Figure 6.24.

104 6 Results

(a) (b) (c)

Figure 6.24: SEM of freeze-dried trehalose solutions at (a) 7.5%, (b) 10%, and (c) 30% (w/v));all at 3000x magnification.

Figure 6.25: Pore size distribution of different trehalose concentrations obtained by mercuryporosimetry.

To estimate the amount of cracking of a cellular foam structure the tensile fracture tough-

ness for a closed cell without thickening of the cell edges can be used.

KIc = B

(ρ

ρS

)2

σf

√πl, (6.10)


where KIc is the critical stress intensity factor, B is a structure geometry [dimensionless

constant], ρ is the density of the foam, ρS is the true density of the pure solid, σf is the

modulus of rupture of cell-wall material, and l is the cell length [132]. Equation 6.11 shows

the connection between the densities ρ, ρS and the cell-wall thickness, t, and l:

(ρ

ρS

)≈

(t

l

)2

. (6.11)

KIc increases at greater density and a lower porosity of the foam, as well as with smaller

pores and thicker cell walls. Harnkarnsujarit et. al. [130], Kim et. al. [133], and Kazmina and

Semukhin [134] also correlated the cell wall size to the mechanical strength of the porous

system and found a higher strength at smaller cell sizes. The influence of the cell size on

the mechanical properties of porous glass and ceramics was investigated by Hasselman and

Fulrath [135]. These authors investigated the micro mechanical stress concentrations in two-

phase brittle-matrix ceramic composites containing a homogeneous, uniform, and pore-free

matrix material as one phase and spherical pores as the other phase. They found the same

dependence of the material’s strength on the degree of porosity.

They further found if the size of the cell is substantially larger than the size of a Griffith flaw

(case I) then the stress concentration approach (KIc) can be applied and the structure fails

when the maximum stress concentration exceeds the strength of the material. These authors

described cases where the flaw size approaches the cell size (case II) and where the cell size

is much smaller than the flaw size (case III). Amorphous freeze-dried samples contain two

phases, the amorphous framework as one phase and ice or vapor as the second phase.

Freeze-dried samples usually show a high porosity and a large pore volume in comparison

to the matrix volume. A possible flaw in the freeze-dried matrix has therefore to be smaller

than cell. Case I can now be applied to freeze-dried systems.

Bertolotti and Fulrath [136] investigated the strength of porous glass and also found a

precipitous decrease in strength with increasing pore sizes or porosity. These author explain

how differences in elastic properties of the components lead to stress inhomogeneities and

a decrease in strength of brittle materials.

Since freeze-dried cakes with a high trehalose concentration possess larger cells, they

should show a lower strength and a lower KIc. Adhesion of the cake to the inside wall of the

vial leads to tensile forces in the cake, since a contraction of the lyo mass may is hindered.

106 6 Results

The larger cells found at higher trehalose concentrations cause therefore a lower KIc and a

higher amount of cracking is developed during drying [5].

6.1.6 Impact of the Surface Chemistry on Shrinkage and Cracking

Rambhatla et. al. [5] suggested that poor adhesion of the dried product to the glass wall

leads to a more uniform cake shrinkage, whereas great adhesion produces fracture of the

product and the development of cracks. To investigate this correlation the wetting behavior

of different trehalose concentrations (5%, 7,5%, 10%, 15%, 20%, 30%) was investigated

with the OCA 20 contact angle measuring device. If a cutout base of a 2R vial is used, its

curvature prohibits a centered positioning of the drop (Figure 6.26a). A precise definition of

(a) (b)

Figure 6.26: Images of aqueous solutions with 15% trehalose on a) a 2R vial base and b) amicroscope slide taken with an OCA 20 contact angle measuring device.

the boundary between the vial base and the drop is therefore difficult and the variability of the

measured data is high (mean average ± standard error >1.4, Figure 6.27). A microscope

slide was therefore used and a sample image obtained is given in Figure 6.26b. A distinct

drop shape is now evident and wetting is much greater. The contact angles for the different

trehalose solutions on the vial base are therefore larger (Figure 6.27, black square) than on

the slide (Figure 6.27, black circle). The wetting behavior between the trehalose solutions

and the microscope slide is therefore better than between the trehalose solutions and the

vial base.


The cutout vial base is made of neutral glass with the hydrolytic class 1, and the micro-

scope slide consists of soda-lime glass with the hydrolytic class 3 [137, 138]. The amount

and the type of atoms and ions in each glass type differs (see Table 6.11) which may be re-

sponsible for some part of the different wetting behavior. Difference in cleanliness may also

play a role. As Figure 6.27 shows, the contact angles decrease with increasing trehalose

Chemical composition Cutout vial base Microscope slide

SiO2 75% 72.2%Al2O3 5% 1.2%Na2O 7% 14.3%CaO 1.5% 6.70%B2O3 10.5% -K2O - 1.20%MgO - 4.30%Fe2O3 - 0.03%SO3 - 0.30%

Table 6.11: Chemical Composition of the vial base and the microscope slide [137, 139].

concentration, i. e. the wetting improves. The surface tension of 5% trehalose is in the range

of that of water (72.8 mN/m) and is increased with higher trehalose concentration (Figure

6.28). This behavior has already be seen by Kaushik and Bhat [140]. Trehalose in negatively

adsorbed at the water/air interface. The surface excess concentration of the solute over that

in bulk solution, Γ, can be calculated by:

Γ = − 1

RT

(dγ

dlnc

), (6.12)

where c is the solute concentration in the bulk phase of the aqueous solution, R is the univer-

sal gas constant, T is the temperature, and γ is the interfacial tension. Figure 6.29 illustrates

that Γ is negative at all trehalose concentrations and the value converges to an upper limit of

approximately -0.0050 mg/m2 for a saturated solution (=68.9%) of trehalose [141]. The con-

centration of trehalose inside the liquid phase compared to the concentration at the boundary

surface to the vapor decreases, i.e. the difference becomes smaller.

The relation between the contact angle and the surface tension of a drop on a planar solid

108 6 Results

5 10 15 20 25 30

5

35

40

45

Con

tact

ang

le [°

]


Vial base Microscope slide

Figure 6.27: Effect of the trehalose (w/v) concentration on the contact angle [] between a vialbase (square) or an microscope slide (circle) and the aqueous solution of tre-halose. The coordinates for the contact angle are the mean average ± standarderror of all values obtained (n=5).

surface is given by the Young’s equation:

γSG = γSL + γLG · cosΘ, (6.13)

where γSG, γSL, and γLG are the interfacial tensions between the the solid and the vapor, the

solid and the liquid, and the liquid and the vapor, respectively. Θ is the contact angle []. As

γLG increases in Figure 6.28, the Θ also decreases in Figure 6.27. The solid/gas interfacial

tension has to be independent of the trehalose concentration. From Equation 6.13 it is there-

fore apparent that the increasing value of γLG and the decreasing value of Θ with increasing

trehalose concentration indicate a decreasing value of γSL. Trehalose decreases therefore

the value γSL likely by an adsorption to the surface of the microscope slide. This behav-

ior is favored by the decreasing excess concentration at the glass/liquid interface found at

higher trehalose concentrations (Figure 6.29). Increasing trehalose concentration improves

therefore the wetting behavior of the inner vial wall by the solution.


5 10 15 20 25 30

73,2

73,3

73,4

73,5

73,6

73,7

73,8

73,9

Sur

face

tens

ion

[mN

/m]


Figure 6.28: Effect of the trehalose (w/v) concentration on the surface tension [mN/m] of anaqueous solution. The coordinates for the surface tension are the mean average± standard error of all values obtained (n=6).

This experiment was intend to correlate the adhesion of the product to the wall of the vial

to the amount of shrinkage. Should Γ at the liquid/solid interface be positive, then an adhe-

sive effect of the solid trehalose cake produced during primary drying to the inner vial wall

is possible. During drying shrinkage occurs to balance the tensions that are built up [142].

If the adhesion between the dried cake and the glass vial is high, then any shrinkage of

the lyophilizate mass to relax these tensions in the cake will be hindered. When the tensions

exceed the cohesion within the cake, the lyophilizate mass will now fracture or crack for relax-

ation. This explains the low amount of shrinkage and the high values of cracking of samples

with 20% and 30% trehalose. If the tensions that occur during drying are greater than the

adhesion of the cake to the wall of the vial, but are lower than the cohesive forces, then

shrinkage occurs. This behavior appears at samples with a trehalose concentration lower

than 20%. The simultaneous occurrence of shrinkage and cracking with 5-20% trehalose,

indicate that adhesion and cohesion are of similar strength.

110 6 Results

5 10 15 20 25 30-0,0080

-0,0075

-0,0070

-0,0065

-0,0060

-0,0055

-0,0050S

urfa

ce e

xcce

ss [m

g/m

²]


Figure 6.29: Surface excess concentration, Γ, as a function of solution concentration of tre-halose solutions.

6.1.7 Impact of the Fill Height and the Vial Diameter

Solutions were filled in 2R and 10R vials with a fill height of 2.5 mm or 5 mm and are

lyophilized with cycle 1 (see chapter 5.2.3) in the hexagonal positioning of the vials. Figure

6.30 shows the cracking values obtained for each trehalose concentration prepared in both

vial sizes at both fill heights. The curves for cracking have similar shape over all trehalose

concentrations. Cracking decreases in the order 10R 5 mm > 10R 2.5 mm > 2R 2.5 mm >

2R 5 mm. Cracking is therefore more pronounced in vials with a larger diameter. Cracking

increases to a greater extent in 2R vials than in 10R vials with rising trehalose concentration.

The result is a similar degree of cracking at trehalose concentration ≥ 20%. With 2R vials

the smaller fill height causes higher cracking values compared to the higher fill height, but at

10R vials no impact of the fill height on cracking is observed.

Figure 6.31 illustrates the shrinkage values obtained for each trehalose concentration pre-

pared in both vial sizes and at both fill heights. The curves for shrinkage have similar shape

over all trehalose concentrations. Shrinkage decreases in the order 2R 5 mm > 2R 2.5 mm


0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

20

22 10R 5mm 10R 2.5mm 2R 2.5mm 2R 5mm


Cra

ckin

g [%

]

Figure 6.30: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration in 2R(square) and 10R (circle) vials with a fill height of 2.5 mm (white) and 5 mm(black). The coordinates for cracking are the mean average ± standard error ofall values obtained (see Appendix 9).

> 10R 5 mm > 10R 2.5 mm. A smaller vial diameter causes therefore a higher amount of

shrinkage. Figure 6.31 also shows that a higher fill height causes a higher amount of shrink-

age only at low trehalose concentrations.

The amount of shrinkage may be correlated to the contact area between product and the

lateral inside wall of the vial to which the product can adhere to. This contact area changes

for different vial sizes and fill heights and influences the extent of shrinkage and cracking.

The 2R vials have an inner diameter, D, of 12.4 mm ± 0.03 mm (n=10), and the 10R vials

22 mm ± 0.08 mm (n=10). The calculated lateral contact areas, Alc, for the corresponding

fill heights, h, and vial diameter, D can be calculated by:

Alc = πDh, (6.14)

and are given in Table 6.12. The wall contact area to the cake or frozen formulation is

112 6 Results

0 5 10 15 20 25 30

2

4

6

8

10

12

14

16

18

20

22 2R 5mm 2R 2.5mm 10R 5mm 10R 2.5mm


Shr

inka

ge [%

]

Figure 6.31: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration in 2R(square) and 10R (circle) vials with a fill height of 2.5 mm (white) and 5 mm(black). The coordinates for shrinkage are the mean average ± standard errorof all values obtained (see Appendix 9).

2.5 mm 5 mm

2R 97 mm2 195 mm2

10R 173 mm2 346 mm2

Table 6.12: Lateral contact areas in dependence of the fill heights in a 2R and a 10R vial.

therefore 1.8 times larger in a 10R vial than in a 2R vial. If the area of the vial’s glass at

which the cake or frozen formulation can adhere to is larger, than may the interaction of the

product to the glass be more pronounced. The detachment of the cake from the inside wall

of the vial to relax stress may therefore be easier in a 2R vial with a smaller Alc than in a

10R vial with a larger Alc. Shrinkage is therefore more pronounced in a vial with a smaller

diameter.

In a 10R vial this stronger adhesion results in the higher amount of cracking, as the drying

tensions must be released this way. This observation confirms the relation between a low


adhesion of the product to the glass vial and a low amount of cracking because of a high

amount of shrinkage.

The wall contact area to the cake or frozen formulation is according to Table 6.12 for each

vial size at a fill height of 5 mm 2.0 times larger compared to a fill height of 2.5 mm. A similar

relation of Alc between different D at the same h (1.8) and different h at the same D (2.0)

is therefore found. Hence, a similar influence of the fill height on shrinkage is expectable.

Shrinkage should then be more pronounced at a smaller fill height in both vial sizes due to

the smaller values of Alc. However, a higher amount of shrinkage is found at the larger fill

height for low trehalose concentrations. Adhesion to the vial wall is therefore not the only

influencing factor of shrinkage. The size of the cake across the diameter is therefore more

important for the extent of shrinkage than the height of the cake.

It has to be pointed out that the evaluation of shrinkage is based on the change of the

cake’s area and not on a change across the diameter of the cake. This aspect needs there-

fore to be considered.

6.1.8 Impact of Hydrophobic Vial Coating

Figures 6.32 and 6.33 illustrate the shrinkage values found for different trehalose concen-

trations with a fill height of 2.5 mm or 5 mm, respectively, prepared in Toplyo R© vials versus

regular vials. A greater amount of shrinkage is found for all concentrations in Toplyo R© vials

compared to regular vials at the same fill height and vial size. The manufacturer claims a

decreased adhesion of the product to the inside wall of the vials [143, 144]. Contact angle

measurements of aqueous trehalose solutions at different concentrations (Figure 6.34) con-

firm much reduced wetting of the Toplyo R© vials. The contact angles are 2.4fold higher than

those found for a regular vial base.

The different drop shape that is formed by a 30% trehalose solution (w/v) on a Toplyo R© vial

base (a) and a regular vial base (b) is shown in Figure 6.35. The drop forms a more hemi-

spherically structure on a Toplyo R© vial base (a) than on a regular vial base (b). The inside

of the Toplyo R© vial is coated with a hydrophobic, transparent Si-O-C-H layer (40-100 nm).

The more hemispherical drop on the Toplyo R© vial base is therefore caused by this layer. The

drop reduces its contact area to the hydrophobic glass surface and a higher contact angle is

formed.

114 6 Results

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24 2R 2.5mm Toplyo 2R 2.5mm 10R 2.5mm Toplyo 10R 2.5mm


Shr

inka

ge [%

]

Figure 6.32: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration witha fill height of 2.5 mm in 2R (circle) and 10R (square) vials prepared in regularvials (black) and Toplyo R© vials (white). The coordinates for shrinkage are themean average ± standard error of all values obtained (see Appendix 9).

As already discussed above (see chapter 6.1.6), Γ appears to be positive at the liquid/solid

interface. An adhesive effect of the solid trehalose cake produced during primary drying to

the inner vial wall is therefore possible. The higher contact angles indicate that an adhesive

effect is reduced in Toplyo R© vials compared to regular vials. Shrinkage of the freeze-dried

cake to relax the drying tensions will then be favored in a Toplyo R© vial compared to a regular

vial. The result is a higher amount of shrinkage found for samples freeze-dried in Toplyo R©

vials.

Figures 6.32 and 6.33 show that the shape of the curves for shrinkage are different. The

values of shrinkage decrease at higher trehalose concentration to the same extent for both

10R vials (regular and Toplyo R©). For the 2R vials, however, the values of shrinkage decrease

less in Toplyo R© vials than in regular vials as trehalose concentration increases. The differ-

ences in shrinkage between the Toplyo R© vials and the regular vials are always smaller in

2R vials than in 10R vials. This can be explained by the lateral contact area Alc. As shown


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24 2R 5mm Toplyo 2R 5mm 10R 5mm Toplyo 10R 5mm


Shr

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]

Figure 6.33: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 5 mm in 2R (circle) and 10R (square) vials prepared in regular vials(black) and Toplyo R© vials (white). The coordinates for shrinkage are the meanaverage ± standard error of all values obtained (see Appendix 9).

in Table 6.12, Alc is larger in a 10R vial greater than in a 2R vial for both fill heights. The

area available for adhesion is greater in a vial with a larger vial diameter. The reduction in

adhesion achieved in Toplyo R© vials is then stronger in a 10R vial than in a 2R vial. This effect

is more pronounced at higher trehalose concentrations due to a higher adhesion of a more

dense cake structure and causes the parallel run of the curves for the 10R vials. Because

of the lower contact area in 2R vials, the influence of adhesion is less pronounced at higher

trehalose concentrations and the concentration dependence is more distinct.

The values obtained for cracking in regular vials and Toplyo R© vials are plotted against the

different trehalose solutions for both fill heights and vial sizes in Figures 6.36 and 6.37.

For all concentrations, fill heights and vial sizes a lower amount of cracking is found in the

Toplyo R© vials. The amount of cracking is reduced to below 2% in the concentration range

≤ 15%. This reduction is particularly pronounced for the samples prepared in 10R vials at

both fill heights. The use of 10R Toplyo R© instead of regular 10R vials leads to a reduction in

116 6 Results

5 10 15 20 25 30

40

80

90C

onta

ct a

ngle

[°]


Toplyo vial base Vial base

Figure 6.34: Effect of the trehalose (w/v) concentration on the contact angle [] between aToplyo R© vial base (square) or a regular vial base (circle) and the aqueous solu-tion of trehalose. The coordinates for the contact angle are the mean average± standard error of all values obtained (n=7).

(a) (b)

Figure 6.35: Sample images of aqueous solutions with 30% trehalose on a) a Toplyo R© vialbase and b) a regular vial base taken with an OCA 20 contact angle measuringdevice.


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20 10R 2.5mm 2R 2.5mm 2R 2.5mm Toplyo 10R 2.5mm Toplyo


Cra

ckin

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]

Figure 6.36: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration witha fill height of 2.5 mm in 2R (circle) and 10R (square) vials prepared in regularvials (black) and Toplyo R© vials (white). The coordinates for cracking are themean average ± standard error of all values obtained (see Appendix 9).

cracking from about 11%-12% to 0%-1.5%. At 2R vials, however, only a reduction from 2%-

9% to nearly 0% is observed. The large reduction in cracking by the use of Toplyo R© vials is

caused by greater shrinkage that releases the drying tensions. Cracking is then reduced. As

shrinkage is more pronounced in 10R than in 2R vials, a higher reduction in cracking takes

place.

Figures 6.38 and 6.39 show representative sample images of all trehalose concentrations

and compare the crack patterns that arise in regular 2R vials (left) and 2R Toplyo R© vials

(right). The Toplyo R© 2R vials illustrate the lower amount of cracking as well as the higher

amount of shrinkage compared to regular 2R vials. The sample images of the Toplyo R© vials

at concentrations between 5% and 15% (Figure 6.38(b), (d), (f) and 6.39(b)) show a more-

or-less intact cake structure with at most some fine cracks that propagate from the outside of

the cake to its center. The reduction of cracking with Toplyo R© vials is obvious, especially at

trehalose concentrations higher than 7.5%, where distinct cracks are found.

118 6 Results

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Cra

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]

Figure 6.37: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 5 mm in 2R (circle) and 10R (square) vials prepared in regular vials(black) and Toplyo R© vials (white). The coordinates for cracking are the meanaverage ± standard error of all values obtained (see Appendix 9).

For the images of 20% and 30% trehalose (Figure 6.39(c)-(f)) a different crack configura-

tion is observed for the sample images of the Toplyo R© vials in comparison to those taken

from regular vials. The samples with 20% trehalose in Toplyo R© vials (Figure 6.39(d)) are

similar to that obtained for 7.5% in regular vials (Figure 6.38(c)). The cakes show the typical

amount of 3-5 pieces, the crack width at the edge is larger than in the center of the cake, and

the cracks run together into the cakes’s center. Samples with 30% trehalose in Toplyo R© vials

(Figure 6.39(f)) show a crack pattern similar to that of cakes obtained from regular vials at

10% (Figure 6.38(e)) trehalose. A multiple cracked surface with a center piece is found. In

contrast, samples of regular vials with 20% or 30% trehalose show fine, narrow cracks in the

outer region of the cake and wide cracks in its inside surface with no connection to the cake’s

edge.

The hydrophobic coating of the Toplyo R© vials and the strength of adhesion of the product to

the vial influences therefore the crack pattern at each concentration. The relaxation process


(a) (b)

(c) (d)

(e) (f)

Figure 6.38: Sample images of lyophilizates with a fill height of 2.5 mm and 5% (a,b) , 7.5%(c,d), 10% (e,f) (w/v) trehalose. Left: regular 2R vial, right: Toplyo R© 2R vial.

120 6 Results

(a) (b)

(c) (d)

(e) (f)

Figure 6.39: Sample images of lyophilizates with 2.5 mm and 15% (a,b), 20% (c,d) and 30%(e,f) (w/v) trehalose. Left: regular 2R vial, right: Toplyo R© 2R vial.


of the cake at a particular concentration is altered by the different adhesion behavior and

confirms a connection between the extent of shrinkage and cracking. Figures 6.38 and 6.39

show that a more intact cake structure is found for samples prepared in a Toplyo R© vial, as well

as less fragments that stick to the inside of the glass vial. These advantages of Toplyo R© vials

as noted by Dietrich et. al. [145] are shown quantitatively in the current work. The ”optimized

geometry” of the vial may also hinder the adherence [143, 144].

6.1.9 Impact of a Variation of the Freezing Step

Solutions at different trehalose concentrations were filled into 2R and 10R vials with a fill

height of 2.5 mm or 5 mm and lyophilized with cycle 1 (see chapter 5.2.3). The standard

shelf cooling rate of 0.4 C/min was varied to a slower rate of 0.2 C/min. For a high cooling

rate (”shock freezing”) liquid nitrogen (LN2) was used filled in a metal tray with immersion

of the samples, as illustrated in Figure 6.40. The frozen samples were then transferred to

the pre-cooled shelf (-40 C) of the freeze-drier, arranged in the hexagonal positioning and

surrounded by frozen dummy vials. The subsequent steps of cycle 1 were performed after

an equilibration time (at -40 C) of at least 2 h.

Figure 6.40: Freezing of the samples with liquid nitrogen.

122 6 Results

6.1.9.1 Standard Cooling Rate versus Slow Cooling Rate

The values for shrinkage obtained for different cooling rates, different vial sizes and different

fill heights are illustrated in the Figures 6.41 - 6.44. It can be seen that a higher amount

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Shr

inka

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Figure 6.41: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm in 10R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle). The coordinates for shrinkage are the mean average ± standarderror of all values obtained (see Appendix 9).

of shrinkage is found with the slow cooling rate in comparison with the standard cycle. The

application of a slower cooling rate promotes cake detachment from the inside walls of the

vial.

A slow cooling rate can lead to a higher degree of supercooling, to a faster subsequent

solution freezing rate, and to a high number of small ice crystals [24]. At the same trehalose

concentration, smaller ice crystals have a higher specific surface area within the whole sam-

ple. At the boundary between product and glass this may lead to a smaller contact area

between trehalose and the glass and to less adhesion. An easier detachment of the cake

from the inside wall of the vial is promoted and more shrinkage occurs. However, as Figure


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Shr

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Figure 6.42: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 5 mm in 10R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle). The coordinates for shrinkage are the mean average ± standarderror of all values obtained (see Appendix 9).

6.45 illustrates, similar pore sizes for both slow and standard cooling rates are observed.

Another possible reason may be the more homogeneous cake structure illustrated in Fig-

ure 6.45(a) in comparison to the heterogeneous cake structure obtained for the standard

cooling rate (Figure 6.45(b)). A more uniform cake structure could give the cake a better

coherence and an easier detachment of the cake from the vial wall causing more shrinkage.

Figures 6.46 - 6.49 show for all trehalose concentrations that the slow cooling rate

(0.2 C/min) causes a lower amount of cracking in both vial sizes at both fill heights com-

pared to the standard cooling rate. This reduction in cracking is especially pronounced for

samples in 10R vials with the smaller fill height (Figure 6.48) where for all concentrations

nearly 0% cracking is achieved. The same strong reduction is observed in 2R vials with the

higher fill height up to 20% trehalose (Figure 6.47). Such low cracking values are only seen

at the lowest trehalose concentration with the 2R vial/2.5 mm (Figure 6.46) or with 10R/5 mm

124 6 Results

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hrin

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[%]


2R 2.5mm Slow cooling rate 2R 2.5mm Standard cooling rate 2R 2.5mm Shock freezing

(a)

Figure 6.43: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm in 2R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle). The coordinates for shrinkage are the mean average ± standarderror of all values obtained (see Appendix 9).

(Figure 6.49).

The more uniform cake structure found for samples with the slow cooling rate (see Figure

6.45) is a possible explanation for the lower amount of cracking obtained for these samples.

The heterogeneous regions of the cake structure formed by standard cooling rate constitute

a defect in the material’s structure. Small pores adjacent to larger pores are similar to a

localized lattice distortion that leads to a higher stress in this region and promotes cracking.

In a uniform cake structure the drying tensions are evenly distributed over the whole structure

and stress hotspots are less likely.

The mechanical properties of porous materials are influenced by the homogeneity of their

pore distribution [134]. An increase in the material’s strength is achieved by a homogeneous

and integrated solid network [146, 147]. Inhomogeneity of the pore structure leads to differ-


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2R 5mm Standard cooling rate 2R 5mm Slow cooling rate 2R 5mm Shock freezing

Figure 6.44: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 5 mm in 2R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle). The coordinates for shrinkage are the mean average ± standarderror of all values obtained (see Appendix 9).

(a) (b)

Figure 6.45: SEM of a freeze-dried trehalose solution (10% (w/v)). (a): slow cooling rate, (b):standard cooling rate, both at 3000x magnification.

126 6 Results

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Cra

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Figure 6.46: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm in 2R vials obtained from samples with the standard (blacksquare), a slow (white circle) cooling rate and by shock freezing (black circle).The coordinates for cracking are the mean average ± standard error of all valuesobtained (see Appendix 9).

ences in the density distribution that cause regional differences in material behavior within

a sample [148]. Some regions have therefore low strength and a fracture of the sample in

this region is favored. A high amount of cracking may therefore be caused by nonuniform

pore structure. The large reduction in cracking by the use of a slower cooling rate could be

caused by a more homogeneous pore structure. However, more important than this may be

the greater amount of shrinkage of these samples, as already observed. Drying tensions are

released by shrinkage and then less cracking occurs as the tensile fracture toughness is not

exceeded. The more homogeneous pore structure found at these samples may only favor

this behavior.


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2R 5mm Shock freezing 2R 5mm Standard cooling rate 2R 5mm Slow cooling rate

Figure 6.47: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration witha fill height of 5 mm in 2R vials obtained from samples with the standard (blacksquare), a slow (white circle) cooling rate and by shock freezing (black circle).The coordinates for cracking are the mean average ± standard error of all valuesobtained (see Appendix 9).

6.1.9.2 Standard Cooling Rate versus Shock Freezing

Figures 6.41 - 6.44 show for samples frozen with liquid nitrogen (”shock freezing”) no clear

pattern of shrinkage compared to samples obtained by the standard cooling rate. Even the

concentration dependence of shrinkage (higher shrinkage values for low trehalose) is only

observed for a fill height of 2.5 mm in both vial sizes and is not as pronounced as seen

before. But a lower amount of cracking is found for the shock frozen samples (Figures 6.46

- 6.49). It has to be pointed out that this tendency is not found in 2R/5 mm (Figure 6.47) at

concentrations ≤ 10% trehalose.

Figure 6.50 illustrates the pore structure of freeze-dried samples obtained by the standard

freezing rate (a) and shock freezing (b)-(d). The pores of the freeze-dried cake obtained by

shock freezing are narrow, long and lamellar with a degree of vertical orientation at the base

and the sides of the cake. The spherulitic, non-orientated pores produced with the standard

128 6 Results

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10R 2.5mm Standard cooling rate 10R 2.5mm Shock freezing 10R 2.5mm Slow cooling rate

Figure 6.48: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm in 10R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle).The coordinates for cracking are the mean average ± standarderror of all values obtained (see Appendix 9).

cooling rate are only found in the middle of the cake.

A fine pore structure caused by shock freezing has already been found at Webb et. al.

[15], Searles et. al. [23, 149], and Dawson and Hockley [150]. It leads to a low degree of

supercooling and to a directional freezing due to the extreme temperature gradients along

the vial bottom and its sides [23]. This directional freezing takes place when a small portion

of the volume is supercooled to the point of ice nucleation. The fronts between nucleation

and freezing then move in the direction of the non-nucleated liquid (from the surfaces of

the vial inwards (Figure 6.50(c),(d)) and are temporal and spatially close together [23]. The

pores run therefore along the direction of freezing and the pore channels are oriented in a

plane normal to the ice front propagation. This lamellar structure is formed by the anisotropic

growth of ice (hexagonal crystal form of ice) and can exhibit a high mechanical strength. Its

strength depends on the nature of the material, increases with smaller channels and shows


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Figure 6.49: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 5 mm in 10R vials obtained from samples with the standard coolingrate (black square), a slow cooling rate (white circle) and by shock freezing(black circle). The coordinates for cracking are the mean average ± standarderror of all values obtained (see Appendix 9).

a strongly anisotropic response the more the pores are unidirectionally orientated [151].

The lamellar structure at the edge of the cake obtained by shock freezing may therefore

influence the strength of the cake. A connection then exists between a stronger porous struc-

ture and a lower amount of cracking. As previous results show, a lower amount of cracking

is caused by a higher amount of shrinkage because of stress release by contraction of the

lyophilizate mass from the vial wall. This relation as well as the concentration dependence is

not seen clearly with the shock frozen samples. This point will be discussed later.

6.1.9.3 The Crack Pattern at Different Cooling Rates

The crack pattern and the cake appearance for different vial sizes, fill heights and cooling

rates is shown in Figure 6.51 for lyophilizates with 20% trehalose. The images show the

different cake appearances of samples frozen with liquid nitrogen in comparison to the shelf-

130 6 Results

(a) (b)

(c) (d)

Figure 6.50: SEM of a freeze-dried trehalose solution (10% (w/v)). (a): standard cooling rate(b): shock freezing, (c): shock freezing (lamellar structure at the wall of the vial),(d): shock freezing (lamellar structure at the wall and the bottom of the vial), allat 3000x magnification.

frozen samples with either standard or slow cooling rate. Shelf-frozen samples show, if cracks

are present, the typical crack pattern with fine and narrow cracks in the outer region of the

cake and an inwardly increasing crack width. The lower amount of cracking found at the slow

cooling rate compared to the standard cooling rate can also be seen. The strongest decrease

in cracking found at samples in 2R/5 mm and in 10R/2.5 mm is also visible.

For shock frozen samples in 2R/2.5 mm, a crack pattern similar to that of shelf frozen

samples at low trehalose concentrations is found. At all other shock frozen samples, however,

a different crack pattern is observed. In a 2R vial at 5 mm the cracks run lunate. In the 10R

vial at the low fill height the crack pattern is only similar to that of the self-frozen samples in


2R 2.5 mm 2R 5 mm 10R 2.5 mm 10R 5 mm

Standard

Slow

Shock

CR

CR

Freezing

Figure 6.51: Sample images for 20% trehalose for different vial sizes, fill heights and coolingrates (CR).

the center cake region. The edge of the cake, however, is more intact compared to the cake

obtained by the standard cooling rate at the same fill height and the same vial size. In a 10R

vial at the high fill height sometimes star-like cracks are observed.

The edges of the cakes frozen with liquid nitrogen are less affected by cracks compared to

the samples frozen on the shelf. The edges of the cracks are more sharp. The detachment of

the lyophilizate mass from the vial is less complete with the samples that were shock frozen.

The crack patterns indicate therefore the different cracking and shrinkage behavior of these

samples. One possible cause is the different pore structure in the outer cake regions which is

formed by directional freezing. The lamellar arrangement of long pores with a small diameter

in the outer cake region would have a higher mechanical strength and can resist the drying

tensions to a greater extent than inside the cake structure. A different stress relaxation in

the sample over the cake’s diameter might occur. It is for this reason that the correlation

between shrinkage and cracking as well as the concentration dependency found for shelf-

132 6 Results

frozen samples is not seen with shock frozen samples.

6.1.10 Impact of the Freezing Protocol

Solutions with different trehalose concentrations were filled into 2R and 10R vials with a fill

height of 2.5 mm or 5 mm and freeze-dried in a hexagonal positioning of the vials with cycle

1 (see chapter 5.2.3). A two-step freezing process in combination with an annealing step

(”2stepA”) was implemented in the freezing phase.

The results of shrinkage for different vial sizes, fill heights and trehalose concentrations

are given in Figures 6.52 and 6.53. For all concentrations, all fill heights and all vial sizes a

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2R 2.5mm 2stepA 2R 5mm 2stepA 2R 5mm 2R 2.5mm

Figure 6.52: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (square) and 5 mm (circle) in 2R vials obtained from sam-ples with the standard cycle (black) and a two-step freezing cycle with includedannealing (2stepA, white). The coordinates for shrinkage are the mean average± standard error of all values obtained (see Appendix 9).

higher amount of shrinkage is found with 2stepA in comparison to samples freeze-dried with

the standard cycle. Exceptions are the mean shrinkage values found in the 2R vial with a fill

height of 5 mm at low trehalose concentrations and in 10R vials at 30% trehalose for both fill


0 10 20 30

2

4

6

8

10

12

14

16

18

20

22

24 10R 5mm 2stepA 10R 2.5mm 2stepA 10R 5mm 10R 2.5mm

Shr

inka

ge [%

]


Figure 6.53: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (square) and 5 mm (circle) in 10R vials obtained from sam-ples with the standard cycle (black) and a two-step freezing cycle with includedannealing (2stepA, white). The coordinates for shrinkage are the mean average± standard error of all values obtained (see Appendix 9).

heights. The use of the 2stepA cycle promotes therefore cake detachment from the inside

walls of the vial. This may be explained by the processes in the product that occur during ice

nucleation and annealing.

With the standard cycle different degrees of supercooling (about ± 3 C from the mean)

take place during freezing and cause variability in the porosity and the product appearance

of the lyophilizates (inter-vial heterogeneity) [92]. Intra-vial heterogeneity may also appear

which is influenced by the distribution of the solutes across the vial during freezing. The

distribution of solutes is determined in a vial with limited amount of water by the different

rates of ice nucleation and ice crystal growth [25]. During freezing with the standard cycle

the ice crystal growth is more rapid than the ice nucleation. Large ice crystal are therefore

formed and create heterogeneity in solute distribution [19]. It is also observed that the single-

step freezing used in the standard cycle causes vertical heterogeneity in the sample with a

134 6 Results

coarse-grained irregularity in the middle (concentrated core). This is formed in the freezing

stage which also causes heterogeneity in solute distribution [25, 19]. Such a coarse-grained

irregularity is also found for the standard cycle in this experiment, as illustrated in Figure

6.54(a).

(a) (b)

(c)

Figure 6.54: SEM of a freeze-dried trehalose solution 10% (w/v). (a): standard cycle (b)+(c):two-step freezing in combination with annealing, all at 3000x magnification.

To improve intra- and inter-vial homogeneity of ice crystallization a two-step freezing is

recommended by Tang and Pikal [31]. The vials should be equilibrated for about 15-30 min on

the shelves at 5 C. Afterward Ts is linearly decreased to -5 to -10 C and hold for 30-60 min.

This step is termed ”supercooling holding” and leads to a more homogeneous supercooling

state within the whole fill volume. By further decrease in Ts ice formation proceeds with a

greater rate of ice nucleation than of ice crystal growth. The ice formation occurs therefore

nearly instantaneous and is relatively homogeneous in the whole sample. A uniform intra-vial

distribution of solutes is achieved. This nucleation type causes many small ice crystals and

prevents vertical heterogeneity [25, 152].

Liu et. al. [25] reported that two-step freezing in conjunction with annealing results in high


intra-vial cake uniformity. Annealing is a hold step at a specified subfreezing temperature for a

defined period and is routinely performed after freezing [153]. Its purpose is an improvement

in the inter-vial heterogeneity [31]. Annealing has a rigorous effect on the ice nuclei size

distribution. Annealing above T ′g causes melting of ice. Smaller ice crystals melt faster and

preferentially than larger ones, and very small ice crystals may melt completely. Furthermore,

the size of larger ice crystals increases by Ostwald ripening (recrystallization) as the water

migrates to larger ice crystals. This reduces the differences in ice crystal sizes between all

samples and the particle size distribution narrows. Since on further re-cooling the larger ice

crystals serve as nucleation sites, the small ice crystals do not reappear [149, 153].

Figures 6.54(b) and 6.54(c) show a sample of a freeze-dried cake received by the appli-

cation of two-step freezing with an additional annealing step. A more uniform pore structure

without vertical heterogeneity is visibly found. The pore sizes of the annealed samples frozen

with the two-step protocol sizes are visibly similar to those obtained by the standard cycle in

the coarse-grained region. This may be caused by melting and recrystallization during the

annealing step [25, 149, 153]. A possible reason for the higher amount of shrinkage is there-

fore the more homogeneous cake structure. Such a relation was also found for the slow

cooling rate (see chapter 6.1.9.1). A more uniform cake structure provides better coherence

and an easier detachment of the cake from the vial wall.

It also can be seen that the differences in shrinkage at trehalose concentrations ≥ 15%

are greater in 2R vials than in 10R vials. Furthermore less shrinkage is developed in 10R

vials compared to 2R vials for the 2stepA cycle at each concentration. A possible reason

may be the smaller contact area found in 2R vials than in 10R vials (see Table 6.12) which

favors shrinkage.

Figures 6.55 and 6.56 depict the values of cracking obtained by this process cycle with

different vial sizes and different fill heights.

It is apparent for all concentrations, fill heights and vial sizes that a lower amount of crack-

ing is achieved by the inclusion of 2stepA compared to the standard cycle. The homogeneous

cell structure obtained by the 2stepA protocol (see Figure 6.54) causes homogeneity in the

density distribution, a uniform material behavior within the whole sample and an increased

material strength [146, 147, 148]. Fracture caused by differences in the material strength

and density distribution may thereby be reduced. This behavior was already observed with

136 6 Results

0 10 20 30

0

2

4

6

8

10

12

14

16

Cra

ckin

g [%

]


2R 2.5mm 2R 5mm 2R 2.5mm 2stepA 2R 5mm 2stepA

Figure 6.55: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (square) and 5 mm (circle) in 2R vials obtained from sam-ples with the standard cycle (black) and a two-step freezing cycle with includedannealing (2stepA, white). The coordinates for cracking are the mean average± standard error of all values obtained (see Appendix 9).

samples freeze-dried at the slow cooling rate (see chapter 6.1.9.1). This cracking behavior

may also by explained by the greater amount of shrinkage found, as already observed for the

slow cooling rate (see chapter 6.1.9.1). Drying tensions are released by shrinkage and then

less cracking occurs since the tensile fracture limit is not exceeded. The more homogeneous

pore structure found at these samples may only favor this behavior.

6.1.11 Impact of a Variation of the Freezing Step in Combination with

the Use of a Toplyo R© Vial

Both 2stepA and the use of Toplyo R© vials lead individually to less cracking and more shrink-

age. A combination of both is now used to investigate any further influence on cake behavior.

Solutions were filled into 2R and 10R Toplyo R© vials with a fill height of 2.5 mm or 5 mm and


0 10 20 30

0

2

4

6

8

10

12

14

16

10R 5mm 10R 2.5mm 10R 2.5mm 2stepA 10R 5mm 2stepA

Cra

ckin

g [%

]


Figure 6.56: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (square) and 5 mm (circle) in 10R vials obtained from sam-ples with the standard cycle (black) and a two-step freezing cycle with includedannealing (2stepA, white). The coordinates for cracking are the mean average± standard error of all values obtained (see Appendix 9).

were freeze-dried with cycle 1 with 2stepA in hexagonal positioning of the vials. Figures

6.57 and 6.58 show the values of shrinkage obtained for 2stepA in regular vials and Toplyo R©

vials. For all fill heights, vial sizes and trehalose concentrations a higher amount of shrink-

age is observed. The only exception is found in 2R vial with a fill height of 5 mm as no clear

difference is seen for the trehalose concentrations ≤ 15%.

The higher amount of shrinkage in a Toplyo R© vial compared to regular vials at these freez-

ing conditions can be explained by the hydrophobic layer of the Toplyo R© vial. A possible

reduction in adhesion of the cake to the inside glass may occur and shrinkage is then fa-

vored. Thus, the drying tensions must be released by shrinkage. Figure 6.59 compares the

pore structure of lyophilizates obtained in Toplyo R© vials (a)+(b) and regular vials (c)+(d) by

the usage of 2stepA. The pore structure of the cakes in a Toplyo R© vial show visibly the same

uniform, predominantly cell-closed pore structure as the lyophilizate freeze-dried in regular

138 6 Results

0 10 20 306

8

10

12

14

16

18

20

22

24S

hrin

kage

[%]


2R 2.5mm Topylo2stepA 2R 5mm Topylo2stepA 2R 5mm 2stepA 2R 2.5mm 2stepA

Figure 6.57: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (diamond) and 5 mm (square) in 2R vials obtained by a two-step freezing protocol with included annealing in regular vials (2stepA, white)and Toplyo R© vials (Toplyo2stepA, black) . The coordinates for shrinkage are themean average ± standard error of all values obtained (see Appendix 9).

vials. Over the whole fill height no regions with different pore structures are found. This ho-

mogeneous pore structure causes a better coherence and promotes an easy detachment of

the cake from the vial. Hence, more shrinkage is observed at the same cycle in a Toplyo R©

vial than in a regular vial.

From Figures 6.57 and 6.58 it is apparent that the differences in shrinkage between the

regular and Toplyo R© vials are more pronounced in 10R vials than in 2R vials. This was

already found in the comparison between regular vials and Toplyo R© vials at the standard

freeze-drying cycle. It confirms the greater influence of the hydrophobic layer at a higher

Alc. In addition, the differences are more pronounced at both vial sizes at higher trehalose

concentrations. This was also found in 2R vials at the comparison between regular vials

and Toplyo R© vials with the standard cycle. Adhesion may be greater at higher trehalose

concentrations and the influence of the hydrophobic layer is then more pronounced.


0 10 20 302

4

6

8

10

12

14

16

18

20

22

24 10R 2.5mm Topylo2stepA 10R 5mm Topylo2stepA 10R 5mm 2stepA 10R 2.5mm 2stepA

Shr

inka

ge [%

]


Figure 6.58: Shrinkage values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration witha fill height of 2.5 mm (diamond) and 5 mm (square) in 10R vials obtained bya two-step freezing protocol with included annealing in regular vials (2stepA,white) and Toplyo R© vials (Toplyo2stepA, black) . The coordinates for shrinkageare the mean average ± standard error of all values obtained (see Appendix 9).

Figures 6.60 and 6.61 compare the cracking values obtained by Toplyo R© and regular vials.

The usage of Toplyo R© vials with the implementation of 2stepA leads to a further reduction

in cracking to < 0.5% in 2R vials for all concentrations. This reduction is in particular large

for trehalose concentrations higher than 15% where for the regular vials cracking of about

6.1% (20% trehalose (w/v)) or 10.0% (30% trehalose (w/v)) for the fill height of 2.5 mm and

3.4% (20% trehalose (w/v)) and 6.4% (30% trehalose (w/v)) for the fill height of 5 mm is

found. The same tendency is found for 10R Toplyo R© vials and both fill heights. For 20%

and 30% trehalose a reduction from 9% to <2% in Toplyo R© is reached. The concentration

dependence of cracking is therefore strongly reduced in Toplyo R© vials with a 2stepA freezing

protocol.

As the homogeneous pore structure is found in regular vials and also in Toplyo R© vials

(see Figure 6.59), the reduction in cracking is explained by the increased strength of the

140 6 Results

(a) (b)

(c) (d)

Figure 6.59: SEM of a freeze-dried trehalose solution 10% (w/v) obtained by two-step freez-ing in combination with annealing. (a)+(b): Toplyo R© vial, (c)+(d): regular vial,both freeze-dried with the 2stepA cycle, both at 3000x magnification.

lyophilizate. As already found (see chapter 6.1.9.1), the higher amount of shrinkage is more

crucial for reduced of cracking, as drying tensions must be released in this way. The tensile

fracture limit is then not exceeded. The more homogeneous pore structure found with these

samples may only favor this behavior.

Figure 6.62 illustrates some representative sample images of the lyophilizates. For sam-

ples at 15% trehalose or less (Figure 6.62 (a), (d)), the change in the cake appearance is

not as pronounced as for samples with a higher trehalose concentration. The images show

therefore no substantial difference.

A comparison of the images (b), (c) with (e), (f) in Figure 6.62 shows the large reduction

in cracking by change of container. Whereas wide cracks in the cake structure are found in

regular vials (b), (c), the cakes obtained with Toplyo R© vials (e), (f) show a whole entity with

only hair-line cracks. At samples with 30% trehalose in Toplyo R© vials (f) cracking occurs only

in the outer regions of the cake and an intact middle region is found. This middle region is

6.2 Kinetic Method 141

0 10 20 30

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2

4

6

8

10

12

14 2R 2.5mm 2stepA 2R 5mm 2stepA 2R 5mm Topylo2stepA 2R 2.5mm Toplyo2stepA

Cra

ckin

g [%

]


Figure 6.60: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration with afill height of 2.5 mm (diamond) and 5 mm (square) in 2R vials obtained by a two-step freezing protocol with included annealing in regular vials (2stepA, white)and Toplyo R© vials (Toplyo2stepA, black) . The coordinates for cracking are themean average ± standard error of all values obtained (see Appendix 9).

not very pronounced in the regular vial (c). This shows the importance of greater relaxation

of the cake structure during drying by shrinkage in Toplyo R© vials, and by cracking in regular

vials. The link between shrinkage and cracking is therefore also confirmed by the patterns of

cracking and shrinkage. A related behavior is observed for samples of 20% trehalose (Figure

6.62 (b)+(e)).

6.2 Kinetic Method

The development of the complex system developed in this work is first given, before consid-

ering the application to various freeze-drying experiments.

142 6 Results

0 10 20 30

0

2

4

6

8

10

12

14C

rack

ing

[%]


10R 2.5mm 2stepA 10R 5mm 2stepA 10R 5mm Topylo2stepA 10R 2.5mm Topylo2stepA

Figure 6.61: Cracking values of freeze-dried trehalose solutions with 5% (w/v), 7.5% (w/v),10% (w/v), 15% (w/v), 20% (w/v), and 30% (w/v) trehalose concentration witha fill height of 2.5 mm (diamond) and 5 mm (square) in 10R vials obtained bya two-step freezing protocol with included annealing in regular vials (2stepA,white) and Toplyo R© vials (Toplyo2stepA, black) . The coordinates for crackingare the mean average ± standard error of all values obtained (see Appendix 9).

6.2.1 Development of Online Video Method during Freeze-Drying

Some aspects of the endpoint detection method can be transferred to the kinetic method,

for example the cut vial without a stopper and a fixed camera mounting normal to the cake

surface. The influence of the use of a cut and unstoppered vial instead of a stoppered and

unmodified vial will be discussed later.

For camera fixation the center leg of the tripod is moved to a horizontal position to enable

positioning of the lens directly above the vial. The cut vial is placed on the top shelf to enable

an unobstructed view through the transparent PlexiglasTM cover of the freeze-drier. The cam-

era is linked to computer software (EOS Utilities) to enable automatic control. Sublimation

rate is measured during primary drying using a microbalance technique.

To keep the process conditions as far as possible equivalent to the endpoint evaluation

method, several dummy vials (stoppered, unmodified) containing the product formulation are


(a) (b) (c)

(d) (e) (f)

Figure 6.62: Sample images of lyophilizates freeze-dried in 2R vials with a fill height of 5 mmwith a two-step freezing and an annealing step in regular vials with (a): 15%,(b): 20%, and (c): 30% trehalose ((w/v), upper row) or in Toplyo R© vials with (d):15%, (e): 20%, and (f): 30% trehalose (w/v, lower row).

arranged in a hexagonal positioning around the microbalance and the sample vials. This

experimental setup is shown in Figure 6.63.

Atypical heat transfer is experienced by the weighing vial held in the microbalance. It is

exposed to the warmer surfaces of the front of the microbalance [29, 60, 46]. The weighing

vial is therefore not chosen for photography but only to estimate sublimation rate. A radiation

shield (Figure 6.63) is placed around the microbalance to protect the weighing vial against

mechanical interference. The weighing vial is cut like the sample vial.

The lifting system of the microbalance is constructed to lift the vial via a ring clamped

around its neck. A modified technique is therefore required for a cut vial without a neck. A O-

ring is clamped around the cut vial. As the position of the O-ring is lower than the cut-off neck,

the lifting arm needs to be adapted to the height of its sample holder. An extension (Figure

144 6 Results

Cut vial

Dummy vials

Sample vial

Microbalance

Radiation shield

Figure 6.63: Experimental setup of the vials in a hexagonal position around the microbalanceand the sample vial.

6.64(a)) was developed to lower the regular lifting arm and sample holder (Figure 6.64(b)).

The adapted lifting technique is illustrated in Figure 6.64(c)+(d). The six vials surrounding

the sample vials are cut similarly to the sample vial, since their necks obscure the view of the

sample vial. This group of cut vials is placed in a center position between the microbalance

and the edge vials to ensure uniform heat transfer (Figure 6.63).

To correlate the product temperature to shrinkage and cracking a TC is placed in one of

the cut sample vials. TC placement direct in the sample vial for photography is not possible

as heterogeneous ice nucleation might occur [22, 48]. This would influence the extent of

shrinkage and cracking.

The placement of the TC in a cut vial is illustrated in Figure 6.65(a), (b). To position the tip

of the TC in the center of the cut vial it is placed with its end at the outside wall of the vial.

This is fixed in a loop with adhesive tape to keep this position during subsequent operations.

The tip of the TC is then carefully bent with tweezers to the center base of the vial until it


(a) (b)

(c) (d)

Figure 6.64: Adaption of the lifting arm for the weighting of a cut vial. (a): lifting arm withextension, (b): regular lifting arm, (c) cut vial with o-ring in the lowered position,(d) cut vial with o-ring in the lifted position.

stays in the correct central position, as illustrated in Figure 6.65(a), (b).

6.2.1.1 Illumination of the Experiment Setup

To ensure constant and even light-exposure all windows of the laboratory are shaded during

the whole measurement. To prevent uncontrolled lateral exposure to light the freeze-drier’s

cover is blacked-out on its sides. This leads to a strong darkening of the images that requires

an adequate illumination.

Figure 6.66 illustrates that the inside wall of the vial and the outline of the cake can be

defined in all pictures. The contrast problem between cake structure and cracks as solved

by background light in the endpoint method cannot be transferred to the kinetic setup, since

146 6 Results

(a) (b)

Figure 6.65: Thermocouple placement in a cut vial.

the samples are placed on the shelf during freeze-drying. A uniform appearance of the cake

structure is, however, vital for crack detection as well as automatic image evaluation. Figure

6.66(a) shows the image taken with a large LED mounted next to the camera for highlight

exposure. Bright and wide reflections occur on the cake surface with circular reflections that

illuminate the cracks in some regions. Shadows are found which come from the upper edge

of the vial wall caused by the lateral mounting of the light source. This darkening makes the

cracks appear darker in some areas and further impairs non-uniform crack and cake structure

appearance. Automatic image evaluation would not be possible.

Figure 6.66(b) illustrates the changes in the image caused by a different positioning of the

large LED placed above the camera to minimize exposure to light. This improved arrange-

ment attenuates the distinct reflections of Figure 6.66(a), but some in the upper right and

lower left regions still exist. The shadows observed in the upper left and lower right regions

of the image maybe caused by camera mounting. These cause a non-uniform cake appear-

ance and automatic image evaluation as well as a manual image evaluation would not be

possible.

In Figure 6.66(c) the laboratory ceiling lighting in combination with a large LED is used to

achieve uniform illumination of the lyophilizate. The LED is fixed at a larger distance com-

pared to (b) above the camera to attenuate its reflections on the cake. With this uniform

illumination no shadows and only a small reflection in the lower right region appear on the


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6.66: Images of lyophilizates during the development of the kinetic method. Illumina-tion by (a): LED mounted next to the camera, (b): LED mounted above the cam-era, (c): the ceiling lighting of the laboratory in combination with LED, (d): theceiling lighting of the laboratory in combination with LED and an energy-savinglamp (warm white), (e): the ceiling lighting of the laboratory in combination anenergy-saving lamp (white), (f): the ceiling lighting of the laboratory, only, (g):the ceiling lighting of the laboratory with covered reflection source, (h) the ceil-ing lighting of the laboratory with a polarizing filter, (i) the ceiling lighting of thelaboratory with a ring light extension for the camera.

148 6 Results

lyophilizate. The contrast between cracks in the edge region of the cake and the cake struc-

ture, however, is very low and a crack detection in these regions is not possible.

A combination of the ceiling lighting of the laboratory, a large LED, and a white energy-

saving lamp is illustrated in Figure 6.66(d). This arrangement leads to strong reflections in

the lower right area and a poor illumination in the upper left region of the cake. Accurate

crack detection is not possible, since pixels belonging to cracks have the same brightness

as those belonging to the cake structure. Use of the strong LED is therefore unfeasible for

the illumination of a lyophilizate in the freeze-drier. Its illumination power is too strong and

causes large reflections.

If a white energy-saver lamp is used in combination with the ceiling lighting, its effect on

the image of the cake is shown in Figure 6.66(e). A uniform cake structure, less reflections

compared to (b), (c) and (d), as well as good contrast between cracks located at the edge of

the cake and the cake structure are found. The picture, however, has poor quality and also

increased noise due to insufficient lighting. Automatic crack detection is not possible.

If only laboratory ceiling lighting is used to prevent reflections, the result is as in Figure

6.66(f). This result shows that the reflections come not only from the strong LED but also

from the laboratory ceiling lighting. Reflections similar to (b) can be seen in the right and

lower left regions. The cracks located in the upper region of the cake are hardly visible,

worse than in the experimental setup of (b).

The cause of the reflections from outside the freeze-drier is further investigated. The

metal mounting of the cover or the metal housing of the microbalance’s connector could

be the sources of reflections. These regions are therefore covered with paper towels. Some

possible sources of reflections are also located inside the freeze-drier and cannot be avoided,

such as the shelves, the dummy vials and the microbalance. The consequences of this

modification is shown in Figure 6.66(g), where the laboratory ceiling lighting is only used. A

uniform illumination of the lyophilizate is found with only some punctual reflections close to

the lower middle of the cake. No shadows are observed. With this adaption uniformity of the

cake structure is achieved. The separation of cracks from the cake structure, however, is not

possible in the outer regions of the cake due the low contrast between the pixels of the cake

structure and of the cracks.

To counter the reflections caused by reflective surfaces inside the freeze-drier, a circular


polarizing filter is placed in front of the camera macro lens. Since reflections are only partially

linearly-polarized, a linear polarizer gives a better balance of light in the image. The rotational

orientation of the filter is adjusted until the best effect is achieved. A circular polarizer is

composed of a linear polarizer and a quarter-wave plate to polarize the waves first linearly

and second circularly before they enter the camera. The effect of a polarizing filter in this

experimental setup without any coverage of reflective areas is illustrated in Figure 6.66(h).

Less reflections are found since only a small area with punctual reflection is observed on

the left side of the lyophilizate. Those are detrimental to automatic image evaluation since

they are caused by the lyophilizate itself and appear only in regions without cracks. The cake

structure appears nearly uniform and only a smaller area with brighter pixels compared to the

other pixels of the cake structure is found in the right region of the lyophilizate. The cracks

appear nearly uniform, and even small fissures in the outer cake region can be recognized.

The quality of the image, however, is poor and possesses increased noise due to insufficient

lighting which makes automatic image evaluation difficult.

The best results are obtained by the use of a macro ring light placed directly in front of

the macro lens via an adapter ring. An image taken with this adjustment is shown in Figure

6.66(i). The ring light is produced by 48 LED and guarantees a shadow-free illumination.

With this accessory averaged image sharpness, good contrast and uniform illumination is

possible. Small fissures at the edge of the cake can be recognized and the cake structure

appears uniform. The outline of the cake as well as the inside walls of the vial for shrinkage

are clearly detectable. This source of light was therefore chosen for the experimental setup.

6.2.1.2 Selection of the Camera Setup

The vertical position of the cake surface as well as the surface itself changes during the

freeze-drying process. The use of automatic focus led to images with different focused and

non-focused regions, making manual focus necessary. The closest focusing distance is se-

lected as 0.31 m, since the distance between the cake surface and the camera is always

smaller than this value. The focus is set in the region between the middle and the edge of

the lyophilizate due to its curved surface during the whole drying process and is adapted,

if needed. The camera’s zone mode is set to ”AV” (Aperture Value). This mode is termed

”aperture priority” at which the aperture can by selected manually and the shutter speed is

150 6 Results

automatically set by the camera to obtain the standard exposure suiting the subject bright-

ness. The best aperture was found at the value 16. This leads to a relatively small aperture

hole that accentuates the foreground, but the background is also within an acceptable focus.

This setup is suitable for unfavorable lighting conditions, since it enables a sharp image due

to a short shutter speed.

In this mode the ISO value can be chosen manually. This is the sensitivity of the camera’s

sensor to light. A high ISO value is used for darker objects and is set in this experimental

setup to 800. For this value an acceptable picture with a low noise level and a good image

quality is obtained.

Despite equal camera settings (values of aperture, ISO) and constant illumination, fluctu-

ations in the image brightness between all images of a freeze-drying run are observed. The

differences are very small and can hardly be seen by the observer. Nevertheless different

brightness values occur for the cracks in all images making an automatic evaluation difficult.

The high dynamic range image, HDR, technique is therefore used to balance brightness

fluctuations and to obtain details which are usually lost in bright and dark areas. HDR are

created by bracketing, at which several pictures are taken with different exposures, an un-

derexposure, a normal exposure and an overexposure. The camera is able to execute auto

exposure bracketing, AEB. The AEB amount is set to -0.3, 0.7, 1.7. Since it is not possible

to control the camera with enabled AEB automatically, a macro was written which starts and

stops the AEB at predefined time intervals to obtain AEB during the whole freeze-drying cy-

cle. The bracketing of one time point is illustrated in Figure 6.67(a)-(c). The HDR are then

produced with Digital Photo Professional software. The HDR corresponding to the bracket-

ing of Figure 6.67(a)-(c) is shown in Figure 6.67(d). It exhibits increased image sharpness,

fewer reflections or shadows, and uniformity of cake structure. Figure 6.67(e)+(f) clarifies the

improvement caused by the HDR technique. In the HDR (Figure 6.67(f)) the cracks appear

clearer, the contrast between the cake structure and the cracks is increased, and the sharp-

ness is considerably higher. The HDR offers a better depth effect as well as clearer edges

of the cracks. It yields details which are usually lost in bright and dark areas by common

photography. However, granulation of the image is found which may impair the results of au-

tomatic image evaluation. Furthermore, the fluctuations in the image brightness between all

HDR are not prevented by this technique. A possible reason may be the flickering of the LED


(a) (b) (c)

(d) (e) (f)

Figure 6.67: Bracketing of lyophilizates with an AEB amount of (a): -0.3, (b): 0.7, (c): 1.7.(d): Produced HDR image. Detailed view of the cracks obtained by the image of(e): -0.3 AEB and (f): HDR.

which may lead to variations in the illumination of the lyophilizate. The use of HDR technique

does not therefore improve automatic image evaluation. This is discussed later.

To solve the problem of brightness fluctuations the image format is changed from JPEG to

RAW. A camera RAW image file contains data from the image sensor of the digital camera

which is only minimally processed. The advantage of a RAW over a JPEG file is that precise

adjustments can be made before the file is converted to TIFF or JPEG. The RAW constitutes

the digital negative of an image and possesses a higher image quality like a better brightness

resolution and more shades of colors than the final image format.

As the image color is non-relevant for the evaluation of shrinkage and cracking,

monochrome RAW-images are taken. The RAW files are then loaded in Digital Photo Profes-

sional and the brightness of each picture is adjusted to obtain more similar brightness values

to prevent brightness fluctuations. Subsequently the RAW files are converted to TIFF.

152 6 Results

6.2.1.3 Heat Transfer on the Top Shelf

The cut vials were first positioned on the top shelf during the kinetic technique. No top

radiation shield is therefore used which is expected to influence drying. Figure 6.68 shows

the temperature profile of the top shelf and the product obtained during a freeze-drying cycle.

An increasing Ts is found during primary drying. The flow of the coolant through the top shelf

0 200 400 600 800 1000 1200 1400-50

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-30

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0

10

20

30 Shelf Temperature, TS

Product Temperature, TP

Drying Time [min]

Tem

pera

ture

[°C

]

Figure 6.68: Temperature profile of the the top shelf (Ts) and the product (Tp).

is not constant which causes temperature fluctuations. From the time point at which Tp

reaches Ts, Tp usually is in the range of 3 C - 5 C above Ts [154]. In this experiment a

difference of about -7 C is found between Ts and Tp. This may be a result of increased

heat transfer to the product. The absence of the radiation shield above the vials influences

therefore heat transfer considerably. The design of the experiment was therefore improved

in that the top shelf is perforated at the position directly above the cut sample vials to enable

camera observation on a lower shelf. The maintenance of the heating and cooling circuit in

the top shelf is still required for an adequate radiation shield. The perforation is therefore


carried out on a position of the shelf where only one coil of the heating and cooling circuit is

affected. This coil is then bypassed by a metal ring sealed in the perforation, as illustrated

above in Figure 5.9 to enable an intact circuit.

A further reason for the elevated heat transfer may be a high emissivity of the unit’s cover.

Acrylic glass shows a higher emissivity (0.86) compared to polished stainless steel (0.59) or

aluminum (0.77) [155]. The interior lateral walls of the cover were therefore masked with an

adhesive aluminum tape. The effects of these changes on Tp are depicted in Figure 6.69.

The usage of a regular shelf instead of the top shelf brings a constant shelf temperature

200 400 600 800 1000 1200 1400-50

-40

-30

-20

-10

0

10

20

30 Shelf Temperature, TS

Product Temperature, TP

Drying Time [min]

Tem

pera

ture

[°C

]

Figure 6.69: Temperature profile of the product (Tp) and the shelf (Ts) with the perforated topshelf as radiation shield and the masking of the cover by an adhesive aluminumtape.

during primary drying. The ramp to secondary drying is also more accurate. The difference

between Tp and Ts at the end of primary drying is reduced to only 4 C and is now in the

typical range of 3 C-5 C [154].

154 6 Results

6.2.1.4 Influence of Vial Cutting on Shrinkage and Cracking

An influence of the cut of the vial or the presence of a stopper on shrinkage and cracking

cannot be excluded [35]. A group of 7 cut vials (2R) as well as a group of seven vials

without a stopper (2R) were therefore positioned between dummy vials and freeze-dried

with cycle 2 (see chapter 5.2.3). The values of cracking and shrinkage obtained by the

endpoint evaluation method after lyophilization are illustrated in Figures 6.70 and 6.71. The

0 10 20 30

0

2

4

6

8

Cra

ckin

g [%

]


Cracking [%] Cracking without a stopper [%] Cracking cut vial [%]

Figure 6.70: Cracking values of freeze-dried trehalose solutions with 10% (w/v) trehaloseconcentration, a fill height of 2.5 mm in 2R vials with stopper (black square),2R vials without a stopper (white diamond), and cut 2R vials (black star). Thecoordinates for cracking are the mean average ± standard error of all valuesobtained (n=7) for the cut or unstoppered vials, n=20 for the stoppered vials.

absence of the stopper has no influence on the extent of cracking and shrinkage. The stopper

resistance to mass transfer is negligible in comparison to the resistance of the dried product,

since the area for vapor flow through the stopper is large in comparison to that of the pores

[22, 36, 38]. A change in the mass transfer rate is therefore unlikely and an influence of the

mass transfer rate on cracking or shrinkage is not observed.

Figure 6.71 shows smaller shrinkage for all concentrations in cut 2R vials compared to


0 10 20 300

5

10

15

20

25

Shr

inka

ge [%

]


Shrinkage [%] Shrinkage without a stopper [%] Shrinkage cut vial [%]

Figure 6.71: Shrinkage values of freeze-dried trehalose solutions with 10% (w/v) trehaloseconcentration, a fill height of 2.5 mm in 2R vials with stopper (black square),2R vials without a stopper (white diamond), and cut 2R vials (black star). Thecoordinates for shrinkage are the mean average ± standard error of all valuesobtained (n=7) for the cut or unstoppered vials, n=20 for the stoppered vials.

intact 2R vials either with or without a stopper. The vapor flow though the dried product is

the determinative quantity for mass transfer as the area for vapor flow through the stopper

openings (0.2-0.4 cm) or through the vial neck (diameter = 0.7 cm) is large compared to that

of the cake pores (15-60µm) [38, 144]. The resistances of the neck of the vial and the

stopper openings are therefore negligible in comparison to the pore resistance.

Within the lyophilizate, the drying rate near the vial wall is higher because of greater heat

transfer near the vial edge than in the middle of the vial [9]. When shrinkage occurs, the

mass transfer in these regions occurs in the gap now present between the product and the

vial wall. The resistance to mass transfer near the vial wall is therefore reduced [9, 156]. The

product resistance in these regions is therefore not determinative for mass transfer and the

absence of the vial neck or a stopper may now play a role. Faster drying near the vial wall

may increase the compressive resistance of the cake since the plasticizing effect of water is

156 6 Results

reduced [157, 158, 159]. As a result a lower amount of shrinkage may occur.

The vial cut leads to a lower amount of cracking for concentrations > 10% trehalose com-

pared to samples in intact vials with or without a stopper. Again, the faster drying at the edge

of the cake may result in increased compressive resistance of samples having a reduced

plasticizing effect of water [157, 158, 159]. The cake can therefore withstand the drying ten-

sions in a greater extent and less cracking occurs at trehalose concentrations >10%. As

cracking is not pronounced at lower trehalose concentrations, preferential drying at the edge

would be less pronounced. This would explain why no differences ≤10% trehalose are found

for cracking.

6.2.2 Development of a Kinetic Image Evaluation Method

6.2.2.1 Semi Automatic Picture Evaluation

Several demands are placed on a semi-automatic image evaluation. It needs to have high

accuracy to register small distinctions between successive images taken during drying, as

illustrated in Figure 6.72(a)-(c). It must detect the hair-like fissures that appear at the begin-

ning of drying (Figure 6.72(a)). Any method is exacerbated by the poor contrast between the

cracks and the cake structure that appears especially at the edge of the cake since no back-

ground light is used. Figure 6.72(c) compared to (d) shows the differences that appear on the

basis of different lighting conditions. A high contrast is given between the cake structure and

the cracks, and even hair-like fissures can clearly be seen in the right region of (d) (marked

with black rectangles in (e)). These hairless fissures are not found in (c). The wide crack at

the bottom of the image in (d) (marked with a black rectangle in (f)) appears white with poor

contrast to the cake structure.

The threshold value needs to be defined anew, since the cracks appear as light regions

in the endpoint evaluation method (d), but as dark regions during the kinetics due to the

absence of background light (f). Figure 6.73(a) shows the result of the endpoint evaluation

method of the image of Figure 6.72(c) with the typical threshold of >1.15 ·mc. Values greater

than the 1.15fold of mc which are assigned to the crack area in the endpoint evaluation

method, are now the bright pixels of the reflections on the cake. The Matlab program assigns

the reflections as cracks (black in Figure 6.73(a)). The cake structure without reflections


(a) (b) (c)

(d) (e) (f)

Figure 6.72: Images taken of the same sample containing 10% trehalose (w/v) during freeze-drying after (a) 856 min primary drying, (b) 924 min primary drying, and (c)600 min secondary drying, as well as (d) after 600 min secondary drying in theendpoint evaluation dark cell; (e) image of (d) with marked regions with smallfissures, (e) image of (c) with the marked region of a crack with a poor contrast.

and the cracks are then defined as the cake area (gray in Figure 6.73(a)). A change of

the threshold to <1.15 ·mc will therefore only change the classification of the areas, since

the gray area will appear black, and the black area will appear gray, as illustrated in Figure

6.73(b). Parts of the cracks are now detectable as such, but most of the cake surface is also

captured. A clear distinction of a crack with this threshold is therefore not possible. It does

not separate clearly the brightness values of the crack from the brightness values of the cake

structure. Other threshold values need to be tested.

Figure 6.74 shows the results of the endpoint evaluation method for the image from Figure

6.72(c) with different thresholds. With increasing threshold the crack area (black) increases.

The image shows, however, lower brightness values at the edge of the cake and on its

left compared to the values in the cake’s middle. The increasing threshold values capture

158 6 Results

(a) (b)

Figure 6.73: Result of the endpoint evaluation method for the image from Figure 6.72(c) withthe typical threshold of >1.15 ·mc (a), where black marks the crack area andthe gray area around the black area marks the cake area, and a threshold of>1.15 ·mc (b), where gray marks the crack area and the black area around thegray area marks the cake area.

(a) (b) (c)

Figure 6.74: Results of the endpoint evaluation method for the image of 6.72(c) with a thresh-old of (a) <0.89 ·mc, (b) <0.99 ·mc, and (c) <1.10 ·mc.

therefore more pixels that belong to the cake structure. A correct separation of the crack

area is also not possible. Image processing steps are therefore required.

To cope with the illumination problems in this experimental setup, the HDR technique is

used to enable semi-automatic image evaluation. Figure 6.75 shows the HDR used for the


development of an semi-automatic image evaluation and also the results of the image eval-

uation. The use of the HDR technique leads to a more uniform appearance of the cake

(a)

(b) (c) (d)

Figure 6.75: HDR image (a), results of the image evaluation with the endpoint evaluationmethod and a threshold of <0.98 ·mc (b), <0.985 ·mc (c), and <0.99 ·mc(d).

structure in the image shown in Figure 6.75(a), as already observed. A greater portion of

the crack can now be distinguished from the cake structure. However, the elevation of the

threshold from <0.98 ·mc (b) to <0.985 ·mc (c), and further to <0.99 ·mc (d) causes worse

separation of the crack area, since a greater portion of the area belonging to the cake struc-

ture is included to the crack area. A threshold that captures the correct crack area without

inclusion of the cake structure area can therefore not be defined. A clear improvement of the

image evaluation method is not given by the HDR technique.

Similar image-processing problems have been found to occur during the automatic vi-

sual rating of the surface conditions of pavements. Segmentation of surface cracks in a

pavement involves an image neutralization before segmentation [160]. During this process

the images are normalized to remove non-uniformity in background brightness (Kaseko and

160 6 Results

Ritchie [160], here the cake structure brightness) across the image and to increase the gray

level contrast between the background and the cracks. Kaseko and Ritchie [160] adjusted

the gray level of each pixel in proportion to the ratio of a standardized background bright-

ness level to the mean background brightness. The latter was obtained from a series of

pixels along the column containing the pixel. This normalization technique is now used in the

current study.

The standardized background brightness level is mc. For the mean background brightness,

Mjs, the mean gray scale value of each column of pixels, MJ is calculated. Across the

columns the values of Mj are smoothed via a moving average and the mean background

brightness value, Mjs, of each column is calculated. The gray level of each pixel in a column

is then adjusted by the ratio mc/Mjs. This procedure is also performed for each line. The

results of this image normalization are shown in Figure 6.76. The comparison between (a)

(a) (b)

(c) (d) (e)

Figure 6.76: Sample image (a), normalized image (b), results of the image evaluation methodand a threshold of <0.85 ·mc (c), <0.95 ·mc (d), and <1.00 ·mc(e).

and (b) shows that the normalization of the image leads to a uniform background and an


increased contrast between the cracks and the cake structure. The segmentation of the

cracks, however, is still not possible. An increase in the threshold value captures a greater

part of the crack area, but also a greater part of the cake area in terms of little spots over the

whole cake area (Figures 6.76(c)-(e)). A high accuracy is thereby not achieved for the small

distinctions between successive images taken during drying. This is also the case to detect

the hair-like fissures that appear at the beginning of drying.

To avoid the acquisition of those little spots, the crack area is evaluated by ”region growing”.

By this technique the crack area grows iteratively around a seed point located in the crack

area. All unallocated neighboring pixels of this seed point are compared to a threshold value.

As a constant threshold is used, this method leads to strong fluctuations between successive

images of each run based on different intensity values. The threshold value is therefore

automatically adapted to the intensity values of each image by their intensity distribution. As

an almost bimodal intensity distribution is obtained for each image, its minimum was used for

the threshold value. This, however, brings no further improvement.

By another attempt the crack area obtained for each image is transferred to the proximate

image. Hence, only the boundaries around the prior crack area are tested by region growing.

This, however, leads to an oversized crack area, since errors in the counting process are

transferred to the next image and accumulate.

It is therefore not possible to develop a semi-automatic evaluation method for the evalua-

tion of the crack area in each image. The contrast between the crack area and the area of

the cake structure is not strong enough to detect the small changes that occur in successive

images.

6.2.2.2 Image Evaluation with Axio Vision

The images obtained by the kinetic method were evaluated in Axio Vision with the Auto-

Measure module, as described for the endpoint evaluation method. For satisfactory crack

detection several image processing steps are necessary. A sample image is given in Figure

6.77(a) taken at the end of the freeze-drying process. The crack area captured without

any image processing is given in Figure 6.77(b). The captured areas outside the cake are

deleted, as described for the endpoint evaluation method. Large areas located in the cake

structure are wrongly assigned to the crack area. This necessitates image processing steps.

162 6 Results

(a) (b) (c)

Figure 6.77: Sample image (a), image evaluation of (a) without image processing (b), imageevaluation of (a) with image processing (c).

For this image processing the brightness (≈ -0.5), the contrast (≈ 1.0), and the gamma

value (≈ 1.0) are adapted for each image and a Gaussian filter with σ = 1927 is used. A

satisfactory shading correction to balance the uneven brightness gradient is given by 6866.

With these corrections a correct segmentation of the crack area is possible, as illustrated in

Figure 6.77(c).

Only small changes are found between successive images and the hair-like cracks at the

beginning of the process are barely detectable. The crack pattern of each sample must

therefore be defined before processing. The last image of each run is therefore evaluated

first to define all fine cracks that appear during drying, as shown in Figure 6.78(a). This

(a) (b) (c)

Figure 6.78: Evaluated image at the end of the freeze-drying run (a), evaluated image of thetime point at the end of primary drying (b), evaluated image at the time pointafter 795 min primary drying (c).


final crack pattern is then compared with the crack pattern of each image to enable manual

deletion of those pixels automatically assigned to the crack area but not found in the final

crack pattern. With this evaluation step non-uniform gray levels of each picture are balanced.

Pixels that are wrongly segmented to the cake area on the basis of lighting fluctuations are

found and can be deleted. A manual adaption of the crack area of regions that were wrongly

defined to the cake area is also possible.

Figure 6.78(b) and (c) show the evaluated crack areas at time points during freeze-drying.

It is possible to distinguish the crack area from the cake structure in all images. The increas-

ing cracking values are found with increasing primary drying time ((c) < (b) < (a)). Some

small regions in the cake structure appear not to be cracked during drying but can be as-

signed to the crack area of the final crack pattern, as shown in Figure 6.79(a). Figure 6.79(b)

(a) (b)

Figure 6.79: (a) Evaluated image at the time point after 795 min primary drying. (b) Evaluatedimage at the time point after 570 min primary drying. The rectangles mark pixelsthat are wrongly be defined to the cake structure without the comparison withthe crack pattern.

shows that small, hair-like fissures at the beginning of crack propagation can correctly be de-

fined by a comparison of these regions with the final crack pattern. These regions would be

lost in any other evaluation. The evaluation method developed here achieves high accuracy

to register small distinctions between successive images taken during drying. It also allows

the correct detection of hair-like fissures.

164 6 Results

6.2.3 Kinetics of Shrinkage and Cracking of a 10% Trehalose Solution

Figure 6.80 shows the kinetics of shrinkage and cracking in % of a 10% trehalose solution

(w/v) freeze-dried with cycle 2 (see chapter 5.2.3). Also shown are the temperatures of the

product (Tp) and of the shelf (Ts) obtained by the TC measurements, as well as the cumulative

water loss measured with the microbalance and the drying rate. The process time is given in

% of the total primary or secondary drying times.

The development of shrinkage and cracking during primary drying can be divided into three

periods. The first proceeds during 15% and 55%, the second during 55% - 75% and the third

during 75% - 100% of primary drying. The first period is characterized by the initiation of

shrinkage and cracking. Cracking occurs first at about 15% and shrinkage at about 20% of

primary drying. A slight increase in both can be observed during this period which is more

pronounced with cracking. Shrinkage reaches a plateau at about 1% after 35% of primary

drying. From the temperature and drying profile it is apparent that in this phase Tp rises and

Ts has reached the set temperature. The sublimation process has started and cumulative

water loss has reached nearly its first maximum at the start of this period. The sublimation

process is almost finished at the end of this period.

In the second period (55% - 75% of primary drying) a further rise in shrinkage and cracking

is observed. This is more pronounced with cracking and proceeds faster than during the first

period. Tp rises sharply. At the beginning of this phase the cumulative water loss has reached

a constant value and the drying rate drops (≈ 60% primary drying). Tp also meets and

exceeds Ts (≈ 75% primary drying). This indicates the completion of sublimation. During

the third period cracking and shrinkage increase further, but to a lesser extent compared

to the previous period. At the end of primary drying 2.41% shrinkage and 3.37% cracking

has developed. During secondary drying the further increase in shrinkage and cracking run

parallel until the end of lyophilization. Here, 4.30% cracking and 3.25% shrinkage are finally

found.

The increase in shrinkage and cracking is gradual. This is in particular the case during

primary drying. This progression can be clarified by the first derivatives of shrinkage and

cracking (Figure 6.81). The phases of high shrinkage and cracking are evident in this figure.

There are three during primary drying and two during secondary drying. This maximum

extent of shrinkage is reached at the middle point of secondary drying (Figure 6.80). The


20 40 60 80

0

2

4

6

8

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20 40 60 80

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]

Shr

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]

20 40 60 80-50

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20

Pro

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Tem

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[°C

]

20 40 60 80-50

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She

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C]

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600

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oss

[mg]

20 40 60 80

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0

2

4

6

8

10

12

14

Dry

ing

Rat

e [m

g/%

]

Figure 6.80: Kinetics of cracking and shrinkage in % in correlation to Tp (solid line), Ts

(dashed line), the drying rate (solid line), and the cumulative water loss (dashedline) during primary and secondary drying. The coordinates for cracking andshrinkage are the mean average ± standard errors of all values obtained (n=3).Total duration of primary drying = 17 h, total duration of secondary drying = 5 h.

166 6 Results

0 20 40 60 80

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0 20 40 60 80 100

1st D

eriv

ativ

e [%

/%]

1st Derivative of Cracking 1st Derivative of Shrinkage



Figure 6.81: First derivatives of cracking (black) and shrinkage (gray).

maximum extent for cracking is not as pronounced at this time point. Those maxima may

result from the approach of Ts and Tp to the secondary drying temperature.

Figure 6.81 also shows the connection between shrinkage and cracking, as the maxima

proceed nearly simultaneously. In the first period (15%-55% primary drying time) cracking

starts first and then shrinkage follows. Thereafter shrinkage and cracking continue simulta-

neously. The increase in shrinkage lasts longer than the increase in cracking. Furthermore

it can be seen that in the first period (15%-55% primary drying time) and in the last two peri-

ods (secondary drying time) shrinkage better releases drying tensions, as greater values are

found. In the last two periods of primary drying (55%-100% primary drying time), however,

the first derivative of cracking is greater than that of shrinkage.

The highest values of the first derivatives are observed for cracking. This indicates that

the release of drying tensions by cracking is a fast process. This can be explained by the

mechanism of cracking. To induce a fracture, high drying stress is necessary. If this stress

exceeds the strength of the lyophilizate (i.e. KIc) the bonds within the lyophilizate in the

region of the stress concentration break. This results in high stress release. With shrinkage


the bonds remain and only a contraction of the lyophilizate mass takes place. No threshold

value such as KIc is necessary for stress release and therefore the highest maxima for the

first derivative are smaller than with cracking. Hence, relaxation by shrinkage takes longer

and its duration is greater.

The drying stress may be caused by the sharp increase in Tp observed in the second

period where cracking relaxes the drying tensions. This suggests that the slow relaxation by

shrinkage is not enough, and the drying tensions caused by the sharp increase in Tp exceed

the tensile fracture limit of the system and cause cracking.

In the periods between the maxima both shrinkage and cracking proceed at a relative con-

stant extent (plateau in the first derivative). Figure 6.81 shows that a more consistent increase

in shrinkage takes place during the whole lyophilization process compared to cracking. That

indicates, as already suggested during the endpoint evaluation method, that shrinkage is the

basic process to release drying tensions. Figure 6.82 shows representative sample images

of a lyophilizate at different time points. The images are obtained by a freeze-drying run

where finally 2.47% cracking and 2.02% shrinkage are found. Figure 6.82(a) shows the cake

at 15% primary drying time (at the start of the first period). A first crack is observed (0.0009%

cracking, Figure 6.82(b)), but no shrinkage. Magnification (black rectangle) is shown in Fig-

ure 6.82(b). A very thin crack can be seen which runs from the lower left of the cake to its

upper right. The first maximum in the first derivative of cracking can therefore be related to

the first crack initiation (see Figure 6.81).

This crack propagates and elongates within the next 25% of primary drying (see Figure

6.82(c)). In addition hairlike cracks appear that run nearly perpendicular to the original crack

in the cake regions located upper and lower to the original crack. Not only crack propagation

but also the development of new cracks takes place during the first period. This increase

in cracking is related to the slight increase in the first derivative of cracking in the period

between 20% and 40% of primary drying. The complete extent of cracking is evaluated as

0.03% at this time point. Shrinkage now starts at the upper and the left edge of the cake,

as a gap between the cake and the vial is observed. This is displayed in the first maximum

of the first derivative of shrinkage in the first period. The momentary amount of shrinkage is

0.21%.

Figure 6.82(d) shows the cake after 70% of primary drying when the maxima in the first

168 6 Results

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6.82: Sample images of a lyophilizate at 10% trehalose at (a): 15%, (b): Enlargementand of image (a) of the region marked with an rectangle in image (a) with imageprocessing, (c): 40%, (d): 70%, (e): 75%, (f): 100% primary drying and (g):40%, (h): 85% and (i): 100% secondary drying.

derivative of cracking and shrinkage have been reached. This is the time point at which about

50% of the final extent of cracking is developed and the previous sharp increase in cracking

is finished. A value of cracking of 1.90% is found, with additional cracks found to (c) being

evident. These run perpendicular to the vertical crack in the upper cake region. Hence, a


maximum of the first derivative of cracking indicates again the formation of new cracks (see

Figure 6.81). Additional shrinkage is observed in the upper region of the cake and displays

the maximum in the first derivative of shrinkage. It accounts overall for 0.64%. The other

cake regions either adhere to the inside wall of the glass vial or no further detachment is

observed.

Figures 6.82 (e)-(i) illustrate that the final crack pattern is achieved after 70% of primary

drying. From now on only crack expansion takes place. The elongation of the cracks as well

as the development of new cracks is finished. A comparison of (e) with (i) shows that the

increase in cracking is developed by a crack expansion of the wide crack that proceeds from

left to right of the cake. This crack expansion is pronounced between (e) and (f) (75%-100%

or primary drying) as well as between (g) and (h) (40-85% of secondary drying). This is where

the maxima in the first derivative of cracking are found (see Figure 6.81). The maximum of

the first derivative of cracking indicates therefore also a crack expansion.

From (c) to (d) shrinkage proceeds only at the upper region of the cake. The further de-

tachment of the cake in the left region starts at (e). In this time interval (70%-75% of primary

drying) the second maximum in shrinkage is observed. Shrinkage proceeds thereafter from

these initial points to left and right (c)-(i), being more pronounced in the upper region of the

cake. No further initiation points are observed. After 10% of secondary drying (g)-(i) the first

derivative of shrinkage is always higher compared to that of cracking. Hence, shrinkage is

from now on the dominant mechanism to relax the drying tensions.

In the subjacent and adjacent regions around the initial points of shrinkage tensions occur

which may be caused by cake detachment and promote further shrinkage. As drying pro-

ceeds from the top of the cake to its bottom, a gradual development of shrinkage in the same

direction is likely.

Mujat et. al. [2] found that changes in cake structure due to a rise of temperature proceed

from the top of the product to its bottom in the direction of the movement of the drying front.

Figure 6.83 illustrates these cake structure changes obtained at different Tp with proceeding

drying time. The rectangles mark the regions of cake detachment from the vial. A gradual

detachment of the cake from the wall of the vial in the same direction is observed. This

confirms the suggestion in the current work of a development of shrinkage in the direction of

the drying front. Tensions in the subjacent regions of the initial point caused by shrinkage are

170 6 Results

(a) (b) (c)

Figure 6.83: Structural collapse of a 5% sucrose solution obtained by optical coherence to-mography at a Tp of (a):-29.3 C, (b): -27.7 C, and (c): -25.7 C; adapted from[2].

therefore likely. This can be seen in the lower regions of each rectangle, where a changeover

between detached and not detached product layer is observed. Whereas a wide gap is

observed in the upper regions, this gap becomes more narrow in the direction to the bottom

of the cake. The cake shrinkage has therefore an impact on subjacent regions and may favor

further cake shrinkage. Since shrinkage proceeds from the top to the bottom of the cake,

this process may be delayed by the movement of the sublimation front. Shrinkage is likely

caused by desorption processes after completed sublimation [5, 8, 9].

These tensions may not only act on subjacent regions (y-direction), but also on the regions

adjacent to the initial point in the same product layer (x-direction). Further detachment that

starts from an initial point and moves in x-direction to the left and the right of this initial point,

as it occurs between 6.82(c) and (d) in the upper region and (e)-(i) in the left region, is then

the result. A further detachment in the area of the initial shrinkage is therefore more likely

than an initiation in other cake regions, as found in this experiment.

In Figure 6.82(d) the original crack runs nearly to the edge of the cake and then moves

upwards until it reaches the vial wall in the region where no further detachment from the

glass is observed. It has already been suggested that shrinkage and cracking are closely

interlinked and interact. This can be confirmed by the observation of this cake region, since

no shrinkage to the right beyond this point is observed. The drying tensions in the region are

therefore likely released by cracking instead of shrinkage, and no further shrinkage appears.

At this intersection incomplete detachment of the cake from the glass is observed. This


may promote the development of the horizontal crack in this region and confirms the relation

between strong adhesion of the product to the glass and cracking. This is also observed in

the lower and upper left region of the cake. A strong adhesion is also observed in this areas.

This explains the development of the horizontal crack and its initiation in the lower region, as

well as the development of the horizontal crack in the upper left region of the cake. At these

regions shrinkage is also disrupted.

A relation between shrinkage and cracking is also observed in the upper cake region. On

the basis of the large shrinkage in this area a relaxation of the cake structure occurs and an

initiation of cracking is unlikely. This results in the more intact cake structure in the upper

region of the cake and may have stopped the elongation of the vertical crack. Cracks are

initiated by an adhesion of the product to the inside wall of the vial, as already found during

the endpoint evaluation method. Shrinkage and cracking proceed simultaneously as in some

regions shrinkage is pronounced and more or less no cracking occurs. In other regions

cracking is pronounced due to the adhesion of the product the the glass and no shrinkage

occurs.

The initiation of cracking depends therefore on the extent of adhesion of the product to

the inside wall of the vial, as suggested during the endpoint evaluation method. This state

of stress produced by adhesion or detachment of the cake to the glass is developed during

the sublimation process. The crack pattern and the initial points of shrinkage are produced

during the first ≈ 70% of primary drying where sublimation takes place (see Figures 6.80 and

6.82). In this period the drying of the cake takes place from the top to its bottom and further

shrinkage and cracking is caused by movement of the sublimation front. The state of stress

is therefore transferred to subjacent and adjacent regions as drying proceeds. A detachment

of the cake in the region of the initial points is therefore favored. Any crack development,

elongation or expansion is also transferred to the dried regions above the drying layer and

are therefore visible at the surface of the product.

Further crack expansion may occur after the sublimation process is finished and the drying

front has reached the base of the vial. This is due to the continuing adhesion of the cake to

the wall and tensions that occur due to secondary drying processes. It has to be pointed out

that a contraction of the lyophilizate mass may also occur in the regions where the bonds

within the cake are broken. The crack expansion that is caused by this contraction is then

172 6 Results

falsely assigned to the amount of cracking, although it is caused by shrinkage. As shrinkage

better releases drying tensions, this is likely and the maxima of the first derivative of cracking

found after the sublimation process is finished may be caused by this process. In this period

only secondary drying processes occur and shrinkage is related to secondary drying effects,

so this is likely.

6.2.4 Kinetics of Different Trehalose Concentrations

Figure 6.84 shows the results obtained for different trehalose concentrations. Table 6.13

gives a summary of the final extents of shrinkage and cracking. It is apparent that cracking is

Trehalose concentration Cracking Shrinkage

5% 0.00% 12.4%10% 4.30% 3.25%30% 6.91% 1.97%

Table 6.13: Values of shrinkage and cracking at different trehalose concentrations found bythe kinetic method.

not observed at 5% trehalose, where only shrinkage occurs. The extent of cracking increases

in the order 5% < 10% < 30%. Shrinkage decreases in the order 5% > 10% > 30% and

behaves therefore in the opposite direction to cracking. This concentration dependence of

shrinkage and cracking was already observed with the endpoint evaluation method for all

shelf-frozen samples.

A gradual kinetic increase in shrinkage and, if present, cracking for 5% and 30% trehalose

similar to that of 10% trehalose (see chapter 6.2.3) is seen. With 5% trehalose shrinkage

is initiated at 48% of primary drying. A sharp increase in shrinkage is observed, faster than

for 10% trehalose, that proceeds until 92% of primary drying. With 30% trehalose cracking

occurs simultaneously with shrinkage at 45% of primary drying. Cracking increases slower

compared to 10% trehalose until 82% of primary drying. Thereafter it increases faster until at

93% of primary drying a plateau phase is reached. With 30% trehalose shrinkage reaches

a plateau at 52% of primary drying with 0.13% shrinkage. This plateau remains until at 62%

primary drying two small rises in shrinkage are seen. At the end of primary drying cracking

decreases in the order: 10% trehalose > 30% trehalose > 5% trehalose and shrinkage

decreases in the order: 5% trehalose > 10% trehalose >30% trehalose.


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]

20 40 60 80-50-45-40-35-30-25-20-15-10-505

1015202530

Pro

duct

Tem

pera

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[°C

]

20 40 60 80

20 40 60 80

-50-45-40-35-30-25-20-15-10-5051015202530

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ulat

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Wat

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oss

[mg]

20 40 60 80


-101234567891011121314

Dry

ing

Rat

e [m

g/%

]

Figure 6.84: Kinetics of cracking and shrinkage in % at 5% (red), 10% (black) and 30% (blue)trehalose in correlation to Tp (solid line), Ts (dashed line), the drying rate (solidline), and the cumulative water loss (dashed line) during primary and secondarydrying. The coordinates for cracking and shrinkage are the mean average ±standard errors of all values obtained. Total duration of primary drying = 17 h,total duration of secondary drying = 5 h.

174 6 Results

During secondary drying cracking increases at 30% trehalose faster than at 10% trehalose.

This is more pronounced between 50% and 70% of secondary drying, where the extent of

cracking with 30% trehalose exceeds that with 10% trehalose. At the end of secondary

drying an increase in cracking similar to that with 10% trehalose is observed. Shrinkage with

30% trehalose proceeds similar to 10% trehalose as the curves are coincident due to the

large mean average ± standard errors of 10% trehalose. It reaches its final extent at 91%

of secondary drying. Shrinkage increases with 5% trehalose rapidly during the first half of

secondary drying, but not as fast as during the second period of primary drying. The rise

in shrinkage slows down at about 50% of secondary drying and shrinkage increases until at

85% of secondary drying its final extent is reached.

The kinetic progress of shrinkage and cracking with 30% trehalose is illustrated in Figure

6.85 by their first derivatives. The simultaneous periods of large increase in shrinkage and

0 20 40 60 80 100

0

2

4

6

8

10

0 20 40 60 80 100

1st D

eriv

ativ

e [%

/%]

Primary Drying Time [%] Secondary Drying Time [%]

1st Derivative of Cracking 1st Derivative of Shrinkage

Figure 6.85: First derivative of cracking (black) and shrinkage (gray) at 30% trehalose (w/v).

cracking found with 10% trehalose (see Figure 6.81) are not seen here for 30% trehalose.

Cracking and shrinkage now occur more or less alternately. Two periods of cracking are

found, the first between 60% - 90% of primary drying and the second during the whole of


secondary drying. The first period can be correlated to the rise in cracking during primary

drying after the sublimation process is finished and Tp rises (≥ 60% primary drying). As

already observed for 10% trehalose, there is an increase in cracking correlated with a rapid

increase in Tp. The second is flat and long and fluctuates about a value of 0.7%/%. It is

caused by the relatively constant increase in cracking during secondary drying. The slight

maximum between 50% and 70% of secondary drying is the reflection of the faster increase

in cracking observed during this time interval.

Two periods of shrinkage are found. One at 40% - 55% of primary drying and the second

between 80% - 100% of primary and 0% - 30% of secondary drying. The first period can

be related to the initiation of shrinkage and is less pronounced. In the second period two

maxima are seen. These can be related to the two step-rises in shrinkage in the second

half of primary drying. The reduction in the second maxima is related to the slow-down in

the development of shrinkage at the end of primary drying. The subsequent constant level

of the first derivative of shrinkage at 2% - 20% secondary drying time is related to the linear

increase in shrinkage during the first period of secondary drying.

The profiles of the first derivatives are opposite to those with 10% trehalose (see Figure

6.81). With 10% trehalose shrinkage is the dominant mechanism to release drying tensions,

and cracking occurs auxiliary during the sharp rise in Tp. With 30% trehalose, however,

cracking is the dominant mechanism. This can be seen by the long periods where the first

derivative of shrinkage has the value of 0 (55% - 80% primary, 30% - 100% secondary drying

time). Shrinkage occurs mainly at the end of primary drying and when Tp rises at the start of

secondary drying. This is also evident in the final extents of shrinkage and cracking, as higher

cracking values and lower shrinkage values are obtained with 30% trehalose compared to

10% trehalose.

Figure 6.86 shows representative sample images of 30% trehalose obtained at different

time points of drying. After 15% of primary drying time (Figure 6.86(a)) neither shrinkage nor

cracking are seen. Figure 6.86(b) depicts the image of the cake at the time point of the first

occurrence of cracking. The first hair-like crack in the cake is shown in the magnification of

Figure 6.86(b) marked with the black rectangle (Figure 6.86(c), 60% of primary drying)). A

narrow crack can be seen that runs from the left of the image to its right. This crack initiation

is reflected in the onset of the first maximum of the first derivative of cracking with 30%

176 6 Results

(a) (b) (c)

(d) (e) (f)

Figure 6.86: Sample images of a lyophilizate at 30% trehalose at (a): 15%, (b): 60%, (c)Enlargement and of image (b) of the region marked with an rectangle in im-age (b) with image processing, (d): 90%, (e): 100% primary drying, (f): 100%secondary drying.

trehalose (see Figure 6.85). In Figure 6.86(b) also two initial points of shrinkage are found in

the upper left and lower right cake regions (better visible in (d)), which were initiated at 45%

of primary drying. This is also reflected in the first period of the first derivative of shrinkage

(40% - 55% of primary drying time, Figure 6.85).

After ≈ 90% of primary drying the final crack pattern is reached (d). The development

of this crack pattern is reflected in the maximum of the first derivative of cracking between

60% and 90% of primary drying. Between 90% and 100% of primary drying ((d) compared

to (e)) the largest portion of shrinkage is developed. This is related to the second phase of

the first derivative of shrinkage shown in Figure 6.85 and the sharp increase in shrinkage at

the end of primary drying (Figure 6.84). During secondary drying (e) compared to (f)) crack

expansion takes place. This is reflected in the second period of the first derivative of cracking.


A small rise in shrinkage is seen in the upper and lower regions of the cake. These occurred

during the early phase of secondary drying (see Figure 6.84).

A more or less intact cake structure in the lower right region of the cake is observed (see

Figure 6.86). Here, shrinkage is pronounced and drying tensions are released by this. The

tensile fracture limit is therefore not exceeded and no cracking occurs in this cake region.

In the left and right regions of the cake, however, shrinkage is not observed. This may

possibly be caused by adhesion of the cake to the inside wall of the vial at this high trehalose

concentration. In the outer cake regions small, hair-like cracks can be seen. These cracks

may be a result of the adhesive forces between the cake and the inside wall of the vial being

greater than the cohesive forces within the cake. These tensions cause tensile fracture limit to

be exceeded and lead to a fracture of the lyophilizate in the outer cake regions. This process

can be seen by the comparison of the regions concerned in Figures 6.86(b) and (d). Further

expansion of the cracks in the middle of the cake may now be enabled by this fracture in the

outer regions near the glass. Contraction of the lyophilizate mass is possible, as no counter

force in terms of adhesion acts. This is in particular the case at the lower left cake fragment.

It has visibly no contact either to the inside wall of the vial. This is due to shrinkage in its

lower region or to the cake/glass because of the small, hairlike cracks in its edge region, as

well as the cracks that separate the fragment from the cake in the upper and left regions. This

contraction of the lyophilizate mass is then falsely assigned to cracking instead of shrinkage.

The crack expansion appears predominantly during secondary drying. Pikal [9] suggested

that shrinkage is developed during primary drying due to desorption of the unfrozen water.

MacKenzie [8] also correlated the development of shrinkage to molecular rearrangements

caused by the desorption of externally bound water and a reduction in internally bound water.

Shrinkage is therefore likely caused by desorption of unfrozen water that occurs both during

primary and secondary drying. An expansion of the cracks during secondary drying by the

mechanism of shrinkage is therefore likely.

As observed with 10% trehalose, shrinkage proceeds from its initial points in the upper

left and lower right cake regions. No further initial points are observed. This confirms the

suggestion that tensions caused by the movement of the sublimation front are transferred to

subjacent and adjacent regions and cause the progress of shrinkage from the initial points to

their left and right.

178 6 Results

Figure 6.87 shows the first derivatives of shrinkage and cracking obtained with 5% tre-

halose. Two periods of an increase in the first derivative of shrinkage are observed, the first

0 20 40 60 80

0,0

0,5

1,0

1,5

2,0

2,5

0 20 40 60 80 100

1st D

eriv

ativ

e [%

/%]

Primary Drying time [%] Secondary Drying Time [%]

1st derivative of Cracking 1st derivative of Shrinkage

Figure 6.87: First derivative of cracking (black) and shrinkage (gray) at 5% trehalose (w/v).

between 45% and 95% of the primary and the second between 0% and 90% of the sec-

ondary drying time. In the first period four maxima are seen that represent the step-changes

of shrinkage during primary drying. These are not that visible in Figure 6.84. From the tem-

perature and drying profile (see Figure 6.84) it is apparent that after 50% of primary drying

Tp and shrinkage rises fast with 5% trehalose. A correlation between shrinkage and the in-

crease in Tp at the end of sublimation is therefore likely. The absence of cracking with 5%

trehalose explains the greater increase in shrinkage compared to 10% and 30% trehalose,

as drying tensions that occur by the rise of Tp are released this way. The sublimation process

is almost finished at the time point of the rise in Tp, as the cumulative water loss has nearly

reached its maximum and the drying rate decreases sharply (see Figure 6.84). Only 3.13%

of shrinkage is developed with 5% trehalose during primary drying when the sublimation

takes place (≈ 60% of primary drying). Most of shrinkage is therefore developed after the

completion of sublimation (this is discussed later). The plateau phase of the second period


of the first derivative of shrinkage (see Figure 6.87) shows the linear increase in shrinkage

during the first half of secondary drying.

Figure 6.88 shows that no cracking occurs at samples with 5% trehalose during all of

freeze-drying. The initiation of shrinkage is observed after 48% of primary drying, as il-

(a) (b) (c)

(d) (e) (f)

Figure 6.88: Sample images of a lyophilizate at 5% trehalose at (a): 40%, (b): 48%, (c) 64%,(d): 88%, (e): 100% primary drying, (f): 100% secondary drying.

lustrated in Figure 6.88(a) compared to (b). It can be seen that already a complete cake

detachment from the inside wall of the vial is developed, whereas with 10% trehalose and

30% trehalose only a partial detachment is observed even at the end of lyophilization (see

Figures 6.82 and 6.86). This may be caused by low adhesion between the cake and the

inside wall of the vial that enables an easy detachment simultaneously at all cake edges from

the inside wall of the vial. This initiation of shrinkage and the complete detachment is evident

in the sharp onset of the first maximum of the first derivative of shrinkage in Figure 6.87. Fig-

ures 6.88(c) - (f) show the further increase in shrinkage. A consistent contraction of the lyo

mass on all sides of the cake takes place. This also supports the suggestion that no (further)

180 6 Results

cracking occurs when no counter force in terms of adhesion of the cake to the inside wall of

the glass is present. A free contraction of the lyophilizate mass is then possible and drying

tensions are released by this mechanism instead of cracking.

Only 25% of the final extent of shrinkage is developed during the sublimation phase. This

confirms the relation between shrinkage and secondary drying and is supported by the ob-

servation that shrinkage occurs first after 20% of primary drying. From the cumulative water

loss and the drying rate it is apparent that sublimation is already in progress and the upper

product layers must be almost dry. If shrinkage were related to primary drying processes, its

initiation would proceed parallel with sublimation and an earlier initiation would be the result.

The delayed first occurrence of shrinkage indicates therefore that shrinkage is related to sec-

ondary drying processes that already occur in the dried product layer during primary drying.

This is also observed with 10% and 30% trehalose, as most of the shrinkage (60.38% and

93.40%) is developed after sublimation is finished.

6.2.5 Impact of Ramp Rate to Secondary Drying

The slow ramp rate (0.15 C/min) to secondary drying of cycle 2 (see chapter 5.2.3) was

varied to a fast ramp rate (0.73 C/min, cycle 3) and an intermediate ramp rate (0.24 C/min,

cycle 4). Solutions containing 10% trehalose were lyophilized with each cycle. Figure 6.89

shows the kinetics of shrinkage and cracking in % obtained by the different ramp rates to

secondary drying, as well as Tp, Ts, the drying rate, and the cumulative water loss. The

kinetics for cracking during primary drying are similar and the curves are coincident at all

ramp rates. Only the tendency to a slower increase in cracking is seen for the fast ramp rate

compared to the slow ramp rate. The curves for shrinkage during primary drying coincide for

the fast and the intermediate ramp rate. The curve of the slow ramp rate increases slower

and at a lower extent.

During secondary drying also no differences in cracking can be observed. Only the ten-

dency to lower cracking values can be seen for the fast ramp rate compared to the slow

ramp rate. In the first 5% of secondary drying the curve for shrinkage for the fast ramp rate

rises rapidly to values more similar to those obtained for the intermediate ramp rate. Then

the curves for shrinkage during secondary drying of the fast and the intermediate ramp rate

are coincident. They run during secondary drying always at higher values compared to the


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0

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Rat

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]

Figure 6.89: Kinetics of cracking and shrinkage in % at a slow (black, 0.15 C/min), an inter-mediate (blue, 0.24 C/min) and a fast (red, 0.73 C/min) ramp rate in correlationto Tp (solid line), Ts (dashed line), the drying rate (solid line), and the cumulativewater loss (dashed line) during primary and secondary drying. The coordinatesfor cracking and shrinkage are the mean average ± standard errors of all valuesobtained (n=3). Total duration of primary drying for all conditions = 17 h, totalduration of secondary drying: 10 h for the slow, 8 h for the intermediate, 6 h forthe fast ramp rate.

182 6 Results

slow ramp rate. Figure 6.90 shows the first derivatives of shrinkage and cracking of all sam-

ples. The same phases of a rise in shrinkage and cracking are observed. For cracking these

0 20 40 60 80

0

1

2

3

4

5

0 20 40 60 80 100

1st D

eriv

ativ

e [%

/%]

Primary Drying time [%]

1st Derivative of Cracking (fast RR) 1st Derivative of Cracking (slow RR) 1st Derivative of Cracking (intermediate RR)

Secondary Drying time [%]

(a)

0 20 40 60 80 100

0

1

2

3

4

5

0 20 40 60 80 100

1st D

eriv

ativ

e [%

/%]

Primary Drying time [%] Secondary Drying time [%]

1st Derivative of Shrinkage (fast RR) 1st Derivative of Shrinkage (slow RR) 1st Derivative of Shrinkage (intermediate RR)

(b)

Figure 6.90: First derivative of cracking (a) and shrinkage (b) at a slow (black, 0.15 C/min),an intermediate (blue, 0.24 C/min) and a fast (red, 0.73 C/min) ramp rate (RR)to secondary drying.

phases are seen at 10% - 30% and 40% - 90% of primary drying. Cracking increases at a


similar extent for all samples during primary drying. For shrinkage the phases are found at

20% - 40%, 45% - 90%, and 90% - 100% of primary drying. Shrinkage increases at a higher

extent at the intermediate and the fast ramp rate compared to the slow ramp rate. During

secondary drying cracking is developed in all samples during the first 60% of secondary dry-

ing. The maxima of the first derivative of shrinkage for the fast/intermediate ramp rate are

reached at earlier time points at the very beginning of secondary drying and reach higher

values compared to the slow ramp rate. This is not as pronounced in the comparison of the

slow and the intermediate ramp rate. The decline in the last period of the first derivative of

shrinkage during primary drying is also found at the beginning of secondary drying.

Table 6.14 gives a summary of the final extents of shrinkage and cracking. The large mean

Ramp Rate Cracking Shrinkage

slow (0.15 C/min) 4.30% (2.41) 3.25% (2.31)intermediate (0.24 C/min) 3.11% (2.14) 8,72% (2.28)fast (0.73 C/min) 1.73% (0.16) 8.30% (1.01)

Table 6.14: Values of shrinkage and cracking and their mean average ± standard errors of allvalues obtained (n=3) given in brackets found by the kinetic method at differentramp rates.

average ± standard error indicate that no influence of the ramp rate on the extent of crack-

ing is observed. Only a slight tendency to a decrease in cracking with a larger duration of

the ramp rate to secondary drying is observed, which is caused by the greater amount of

shrinkage. The differences found in the kinetics of shrinkage between the fast/intermediate

and the slow ramp rate are also found in the final amounts of shrinkage. This is seen de-

spite the mean average ± standard error, as the values for shrinkage are greater for the

fast/intermediate ramp rate compared to the slow ramp rate. As Figure 6.91(a) shows,

shrinkage at the slow ramp rate is only found at some points after primary drying. At the

intermediate (d) and fast (g) ramp rates, however, shrinkage is found to a greater extent and

an almost complete cake detachment is observed. During the first 40% of primary drying

the lyo mass contracts to a greater extent at the intermediate and fast ramp rate as shown in

Figures 6.91(e), (h), compared to (b). The greater amount of shrinkage and the lower amount

of cracking for the fast/intermediate ramp rate compared to the slow ramp rate found at the

end of secondary drying can be seen in the comparison of Figures 6.91(c), (f), (i).

A ramp rate to secondary drying greater than 0.15 C/min promotes therefore shrink-

184 6 Results

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6.91: Sample images of a lyophilizate at 10% trehalose at the end of primary drying(a), (d), (g), after 40% (b), (e), (h) and 100% (c), (f), (i) of secondary drying.First line = slow ramp rate, second line = intermediate ramp rate, third line = fastramp rate.

age. This result is in agreement with the ramp rates to secondary drying of 0.1 C/min or

0.15 C/min recommended by Rambhatla et. al. [5], Nail and Gatlin [26], and Tang and Pikal

[31] for amorphous products.

Since amorphous products contain a high residual moisture content of up to 40% in the


early stage of secondary drying and thus a low Tg, a great potential for collapse exists at this

stage. A slow ramp rate to secondary drying, however, does not run that close to Tg during

secondary drying and prevents therefore a collapse of the lyophilizate [5, 26, 31]. Rambhatla

et. al. [5] suggested based on the work of Liapis et. al. [161] that shrinkage may be a result

of approaching to Tp in early secondary drying.

As Figure 6.89 shows, Tp of the samples freeze-dried with the intermediate/fast ramp rate

rises more rapidly compared to Tp of the slow ramp rate. An approach to or even exceeding

of Tg is therefore more likely during secondary drying at the intermediate/fast ramp rate.

Especially at the beginning of secondary drying the difference between Tp and Tg might be

smaller at the fast/intermediate ramp rate compared to the slow ramp rate. If the difference

between Tp and Tg is decreased, the mechanical strength of the amorphous glass is weaker.

A compression of the lyophilizate mass is therefore more likely causing a higher amount of

shrinkage. The fast approaching of Tp and Tg during the early stage of secondary drying

causes therefore the sharp increase in shrinkage observed for the fast/intermediate ramp

rate. This relation between a greater shrinkage and a smaller difference between Tg and Tp

was already observed at Rambhatla et. al. [5].

However, Figure 6.91 shows that a more complete cake detachment is already developed

during primary drying. Hence, tensions caused by adhesion of the cake to the inside wall of

the vial are lower at samples freeze-dried with a fast/intermediate ramp rate. Shrinkage is

then favored and promotes the differences found between the slow and the intermediate/fast

ramp rate. From the comparison of Figures 6.91(a) - (c), however, it can be seen that crack

expansion likely caused by shrinkage is not as pronounced as the cake shrinkage at the

intermediate (d) - (f) and the fast (g) - (i) ramp rates. The influence caused by the different

adhesion behavior developed during primary drying must therefore be low.

6.2.6 Impact of a Lower Primary Drying Temperature

The primary drying temperature, PDT, of cycle 2 (-20 C, see chapter 5.2.3) was varied to

-25 C (cycle 5). Solutions containing 10% trehalose were lyophilized with each cycle. A

lower PDT leads to a lower end amount of cracking and to a higher end amount of shrinkage,

see Table 6.15. The kinetics of shrinkage and cracking obtained by a different PDT are shown

in Figure 6.92. Cracking is initiated at the lower PDT at 41% of primary drying, whereas at the

186 6 Results

Ramp Rate Cracking Shrinkage

-20 C PDT 4.30% (2.41) 3.25% (2.31)-25 C PDT 0.77% (0.13) 12.0% (0.42)

Table 6.15: Values of shrinkage and cracking and their mean average ± standard errors of allvalues obtained (n=3), given in brackets, found by the kinetic method at differentprimary drying temperatures (PDT).

standard PDT cracking is initiated earlier (20% of primary drying). The curves for cracking

during primary and secondary drying have similar shapes. The greatest increase in cracking

is observed with both between 40% and 70% of primary drying. But the amounts of cracking

developed during primary drying differ strongly, as after 25% of primary drying the amount of

cracking is always smaller at the lower PDT.

The curves for shrinkage during the first 45% of primary drying are similar at the different

PDTs. After 45% of primary drying sublimation slows down. The curves of the drying rate

drop and the curves of the cumulative water loss approach their maximum. Shrinkage in-

creases to a higher extent at the lower PDT and has always higher values. After ≈ 60% of

primary drying, when sublimation is finished, Tp rises in both samples more sharply than at

prior time points. The differences in shrinkage are more pronounced after 60% of primary

drying as a further acceleration of the increase in shrinkage for the lower PDT is observed.

The rapid increase in shrinkage for the lower PDT is decelerated after 68% of primary drying.

The curves for shrinkage during secondary drying have the same shape, but run at higher

values for the lower PDT. These differences in shrinkage are developed during primary dry-

ing and are therefore related to the lower PDT.

Figure 6.93 shows the first derivatives of shrinkage at both PDTs. The development of

shrinkage rises fast between 40% and 70% of primary drying at the low PDT. The values

of the first derivative of shrinkage are more than 4-fold higher at the maxima compared to

the standard PDT in this phase. The highest increase in shrinkage is observed during 60% -

70% of primary drying when the sublimation is completed.

According to Figures 6.92 and 6.93 a lower PDT promotes detachment of the product from

the inside wall of the vial. The drying tensions are then released by shrinkage and the tensile

fracture limit is not exceeded. Hence, a lower amount of cracking results. This process is

observed during the whole of primary drying: the reduction in cracking is first caused by a


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Figure 6.92: Kinetics of cracking and shrinkage (in % to their final amounts) at -20 C (black)and -25 C (gray) primary drying temperature (PDT) in correlation to Tp (solidline), Ts (dashed line), the drying rate (solid line), and the cumulative water loss(dashed line) during primary and secondary drying. The coordinates for crackingand shrinkage are the mean average ± standard errors of all values obtained(n=3). Total duration of primary drying: 17 h for the PDT of -20 C and 24 h forthe PDT of -25 C , total duration of secondary drying = 10 h for all conditions.

188 6 Results

0 20 40 60 80 100

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eriv

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/%]

Primary Drying time [%] Secondary Drying time [%]

1st Derivative of Shrinkage (standard PDT) 1st Derivative of Shrinkage (low PDT)

Figure 6.93: First derivative of shrinkage at the standard (black, -20 C) and the lower (gray,-25 C) PDT.

prior initiation of shrinkage. With increasing values of shrinkage caused by the lower PDT a

reduction in cracking is observed. During 20% - 75% of primary drying cracking increases

from 0.1% up to 2.75% at the standard PDT. At the lower PDT an increase from 0% up

to only 0.26% is observed. Shrinkage, however, increases in this time interval at the lower

PDT from 0.50% up to 9.16% and at the standard PDT from 0% only up to 1.90%. This

development is also visible in the cake appearance shown in Figure 6.94 and confirms that a

high amount of shrinkage causes a low amount of cracking, as already found at the endpoint

evaluation method. Figure 6.94(b) compared to (d) shows that at the lower PDT a complete

detachment of the cake from the inside wall of the glass occurs. This is not observed at the

standard PDT ((a) compared to (c)), where only initial points of shrinkage are observed. With

both samples the final crack pattern is achieved after 70% of primary drying. As observed in

the kinetics, nearly no further cracking is developed thereafter. This is also visible in Figure

6.94(f) compared to (h).

Easier detachment of the cake from the inside walls of the vial at a lower PDT may be

a result of the slower drying process caused by the lower PDT. This slower process is not

visible in Figure 6.92, as the durations of primary and secondary drying are normalized for

comparison. The time point at which Tp reaches Ts is reached after ≈ 1150 min with the lower


(a) (b)

(c) (d)

(e) (f)

(g) (h)

Figure 6.94: Sample images of a lyophilizate at 10% trehalose at 15% (a): standard PDT,(b): low PDT, 40% (c): standard PDT, (d): low PDT; 70% (e): standard PDT, (f):low PDT and 100% primary drying (g): standard PDT, (h): low PDT.

190 6 Results

PDT and after ≈ 925 min with the standard PDT. The increase in Tp after the sublimation

process is finished is therefore slower at a lower PDT and the rise in drying tensions related

to this temperature rise is reduced. The lyophilizate has more time for release of drying

tensions. As already observed with 10% trehalose (see chapter 6.2.3) shrinkage is a slow

process compared to cracking. As sufficient time is available at a lower PDT for relaxation

of the cake by shrinkage, shrinkage occurs. The tensile fracture limit is then not exceeded

as drying tensions are released by shrinkage and no cracking occurs. At the standard PDT,

however, the increase in Tp proceeds faster and also the increase in drying tensions. The

increase in drying tensions is then too fast for sufficient shrinkage. The tensile fracture limit

is exceeded and cracking occurs.

6.2.7 Impact of Tween 80 or Glycerol

Tween and glycerol were added to a 10% aqueous trehalose solution. For tween a concen-

tration of 0.03% was chosen, which is higher than the critical micelle concentration, CMC,

(= 0.0014 g/100 ml) [162]. Glycerol has a very low glass transition temperature (-92 C) and

the lowering of T ′g needed to be investigated to define suitable drying conditions [123]. DSC

measurements were performed with different amounts of glycerol in a 10% aqueous tre-

halose solution to determine the T ′g of each formulation (see Table 6.16). With increasing

Glycerol [%] T ′g

1% -37.6C2.5% -44.6C5%% -54.6C

Table 6.16: Overview of values of T ′g of aqueous solutions with 10% trehalose and different

portions of glycerol obtained by DSC measurements.

glycerol concentration T ′g is decreased and glycerol acts as a plasticizer, as already found

for example at Buera et. al. [163] and Gontard et. al. [164]. A decrease in T ′g of trehalose

by glycerol was already noted by Cicerone and Soles [165]. Since formulations containing

2.5% and 5% glycerol show low values of T ′g which are not suitable for freeze-drying, a glyc-

erol concentration of 1% was chosen. Solutions were prepared and freeze-dried with cycle 2

(see chapter 5.2.3). The primary drying temperature was adapted for the samples containing

glycerol to -30 C (instead of -20 C) to assure a similar difference between Tp and T ′g for all


formulations. The effect of the different additives on the kinetics of shrinkage and cracking is

shown in Figure 6.95 and Table 6.17.

Pure trehalose Trehalose/tween Trehalose/glycerol

Cracking 1D 3.37% 0.00% 0.00%Cracking 2D 4.30% 0.00% 0.00%Shrinkage 1D 2.41% 11.19% 8.85%Shrinkage 2D 3.25% 12.83% 13.48%

Table 6.17: Values of shrinkage and cracking for samples with pure trehalose, and with amixture of trehalose and tween or trehalose and glycerol, respectively at the endof primary (1D) and secondary drying (2D).

With both additives no cracking is observed and the curves are coincident. Shrinkage is

first developed after about 20% of primary drying in all formulations and increases gradually

during primary drying. For trehalose/tween three steps are seen, the first at 20% - 40%, the

second at 40% - 80%, and the last at 80% - 100% of primary drying. For trehalose/glycerol

also three steps are observed, the first at 20% - 35%, the second at 35% - 65%, and the

last at 65% - 100%. After 25% of primary drying the curve of shrinkage during primary

drying runs always at higher values for trehalose/tween compared to trehalose/glycerol and

pure trehalose. After 40% of primary drying also shrinkage of trehalose/glycerol increases

faster than pure trehalose. Shrinkage develops therefore in the order: pure trehalose <

trehalose/glycerol < trehalose/tween. After 80% of primary drying a stagnation of shrink-

age is observed with both additives, whereas an increase in shrinkage is still found for pure

trehalose. At the end of primary drying the values of shrinkage increase in the order pure

trehalose < trehalose/glycerol < trehalose/tween.

During secondary drying of all formulations an increase in shrinkage during the ramp to

secondary drying is found (≤ 50% of secondary drying). This is more pronounced with

trehalose/glycerol. At 50% of secondary drying the curves for trehalose/glycerol and tre-

halose/tween cross and trehalose/glycerol increases faster and to higher values compared

to trehalose/tween. For trehalose/tween the final amount of shrinkage (12.83%) is reached

after 64% and for trehalose/glycerol (13.48%) at ≈ 68% of secondary drying. The curves

for trehalose/tween and trehalose/glycerol run always at higher values compared to pure

trehalose.

From the drying and temperature profile (sharp rise in Tp, decline of the drying rate and

192 6 Results

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Figure 6.95: Kinetics of cracking and shrinkage in % of samples with 10% trehalose freeze-dried without any additive (black), with the additive of tween (blue) and the addi-tive of glycerol (red) in correlation to Tp (solid line), Ts (dashed line), the dryingrate (solid line), and the cumulative water loss (dashed line) during primary andsecondary drying. The coordinates for cracking and shrinkage are the mean av-erage ± standard errors of all values obtained (n=3). Total duration of primarydrying: 18 h for trehalose/tween and 23 h for trehalose/glycerol, total duration ofsecondary drying = 10 h for all formulations.


constant value of the cumulative water loss) it can be seen that sublimation is finished af-

ter 48% of primary drying at trehalose/tween, and after 58% at pure trehalose and tre-

halose/glycerol. Only < 40% of the final amount of shrinkage is developed during the subli-

mation process. This confirms that shrinkage is caused by secondary drying processes. An

influence of the rise in Tp caused by the completion of sublimation on the increase in drying

tensions and shrinkage is likely. According to the time point of the rise in Tp, the time points

of a rise in shrinkage should proceed in the order: trehalose/tween < trehalose/glycerol <

pure trehalose. This is observed in this experiment. The distinct delay of the rise in shrinkage

of pure trehalose may be caused by the simultaneously rise in cracking. For trehalose/tween

and trehalose/glycerol no cracking is observed and the drying tensions are released only by

shrinkage.

The addition of tween or glycerol to a 10% aqueous trehalose solution favors detachment

of the cake from the inside wall of the vial. Tween is a surfactant and will be positively

adsorbed at the air/water interface and decreases the adhesion of the product to the inside

wall of the vial. Should Γ at the liquid/solid interface be positive for trehalose, then the

adhesive effect of the solid trehalose cake to the inner vial wall will be reduced by the tween.

A detachment of the cake from the inside wall of the vial and a release of drying tensions by

shrinkage is then more likely. Glycerol is commonly used as an additive for an improvement

of protein stabilization during lyophilization [166, 167]. It is a non-volatile and is left within the

lyophilizate during freeze-drying [167]. It may therefore also decrease the adhesion of the

cake to the inside wall of the vial and promotes detachment of the cake as it remains liquid.

The tensile fracture limit is not exceeded and no cracking occurs.

Figure 6.96(a), (d), (g) shows that no shrinkage and no cracking is observed at the start of

primary drying. Figures 6.96 (b), (e), and (h) show that shrinkage at the end of primary drying

decreases in the order: trehalose/tween (e) > trehalose/glycerol (h) > pure trehalose (b). A

complete detachment of the cake from the inside wall of the vial is caused by the additives

during primary drying (Figure 6.96(a), (d), (g) compared to (b), (e), (h)). The influence of

the additives on adhesion is more pronounced with tween compared to glycerol, as a larger

amount of shrinkage is observed for tween/trehalose. The positive adsorption of tween to

the inside glass lowers therefore the adhesion of the product to the inside wall of the vial to a

greater extent than the liquid glycerol.

194 6 Results

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6.96: Sample images of the lyophilizates with 10% trehalose without additive at (a):0% , (b) 100% primary drying, (c) 100% secondary drying; with 10% trehaloseand 0.03% tween at (d): 0%, (e): 100% primary drying, (f) 100% secondarydrying; with 10% trehalose and 1% glycerol at (g) 0%, (h): 100% primary drying,(i) 100% secondary drying.

Cracking is observed only with samples of pure trehalose at the end of primary and sec-

ondary drying, whereas no cracking appears at samples with an additive ((a) - (c) compared

to (d) - (i)). This is caused by the adhesion of the pure trehalose to the inside wall of the


vial. Based of this adhesion the drying tensions cannot be released by a contraction of the

lyophilizate mass. The stress rises until the tensile fracture limit is exceeded. As a result

fracture occurs and a lower amount of shrinkage is observed as drying tensions are released

by cracking.

At the end of secondary drying (right column of Figure 6.96) shrinkage increases in the

order: pure trehalose < trehalose/tween < trehalose/glycerol. The lyophilizates with an

additive show an intact cake structure with no cake fragments left on the inside wall of the

cake. This results from easy detachment during primary drying. After primary drying the

freeze-drier shelf is visible in the gap between cake and inside wall of the vial. Complete

lateral detachment of the product from the glass has therefore developed. Any influence of

the adhesion of the product to the inside wall of the glass is therefore not relevant during

secondary drying. Only adhesion of the product to the vial base may play a role. As the

images of Figures 6.96(f), (i) show, an enlargement of the gap between cake and glass is

observed and the influence of adhesion of the product to the base of the vial should be less

pronounced.

An influence of Tp on the drying tensions during secondary drying is likely, as the in-

crease in shrinkage stops during secondary drying when Tp reaches Ts. The increase in

Tp, however, is similar for all formulations. The drying tensions and an increase in shrink-

age related to this temperature rise must be similar. Shrinkage, however, increases faster

with trehalose/glycerol than with pure trehalose or trehalose/tween. With trehalose this lower

increase may be explained by the increase in cracking that releases the drying tensions.

Shrinkage, however, increases to a different extent with the formulations containing an addi-

tive and no cracking is observed. The contraction of the lyophilizate mass during secondary

drying is therefore related to the strength of the lyophilizate to withstand the drying tensions.

This strength must be stronger with trehalose/tween. As glycerol acts as an plasticizer the dif-

ference between Tp and Tg should be smaller at the same Tp for trehalose/glycerol compared

to pure trehalose or trehalose/tween [163, 164, 165]. As already observed at Rambhatla et.

al. [5] and at the current study with different ramp rates (see chapter 6.2.5), a relation be-

tween a smaller difference (Tp - Tg) causes a higher amount of shrinkage due to a weaker

amorphous glass. A compression of the lyophilizate is therefore easier, as is evident in a

higher amount of shrinkage.

196 6 Results

6.2.8 Impact of a Protein

Solutions with 10% trehalose either with or without BSA (1/3 BSA, 2/3 trehalose) in a buffer

solution containing tris (pH = 7.4) were freeze-dried with cycle 7 (see chapter 5.2.3). The

kinetics of shrinkage and cracking obtained and their values after primary and secondary dry-

ing are shown in Figure 6.97 and Table 6.18. No cracking is observed in both samples. The

absence of cracking caused by the 2stepA cycle is therefore not influenced by the addition of

BSA. Shrinkage occurs earlier with samples containing BSA (36% of primary drying) com-

End of 1D End of 2D

Cracking BSA 0.00% 0.00%Shrinkage BSA 4.54% 7.53%Cracking without BSA 0.00% 0.00%Shrinkage without BSA 7.12% 9,46%

Table 6.18: Values of shrinkage and cracking for samples with BSA and without BSA at theend of primary (1D) and secondary drying (2D).

pared to the formulations without the protein (47% of primary drying). In the period of 47% -

62% of primary drying the curves for shrinkage overlap because of the large mean average ±

standard errors found for the sample containing BSA. However, shrinkage rises more rapidly

for the formulation without BSA. The values of shrinkage are thereafter always higher during

primary drying than those obtained with BSA. This sharp increase in shrinkage is in particu-

lar the case between 55% - 80% of primary drying. In this period shrinkage increases from

1.05% up to 6.25%. This increase accounts for almost three-quarters of the shrinkage devel-

oped during primary drying. In the same period shrinkage increases with samples containing

BSA from 1.55% up to 3.40% (only 41% of the shrinkage developed during primary drying).

For the samples with BSA, the rise in shrinkage proceeds more gradually and consistently

as 3-4 similar steps are observed. These occur between the initiation of shrinkage at 36%

of primary drying until 89% where a plateau phase is reached that remains until the end of

primary drying. No plateau phase is observed with samples without BSA, but a deceleration

of shrinkage is observed after 70% of primary drying.

During the first half of secondary drying shrinkage increases with both formulations. After

50% of secondary drying both reach their final extents of 7.12% with, and 9.46% without

BSA. Figure 6.98 shows the lower amount of shrinkage developed during primary drying in


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Figure 6.97: Kinetics of cracking and shrinkage in % of samples with 10% trehalose freeze-dried with a two-step freezing and included annealing step (2stepA) without theaddition of BSA (black) and with the addition of BSA (gray) in correlation to Tp

(solid line), Ts (dashed line), the drying rate (solid line), and the cumulative wa-ter loss (dashed line) during primary and secondary drying. The coordinatesfor cracking and shrinkage are the mean average ± standard errors of all val-ues obtained (n=3). Total duration of primary drying = 17 h, total duration ofsecondary drying = 10 h.

198 6 Results

samples with BSA (a), (b) compared to samples without BSA (d), (e). With both samples

(a) (b) (c)

(d) (e) (f)

Figure 6.98: Sample images of the lyophilizates with 10% trehalose with BSA (a): 0% , (b)100% primary drying, (c) 100% secondary drying and without BSA at (d): 0%,(e): 100% primary drying, (f) 100% secondary drying.

incomplete detachment of the cake from the inside wall of the vial is found. With samples

containing BSA this is found in the upper region, and with samples without BSA in the right

region of the image. During secondary drying a higher amount of shrinkage occurs with the

samples having no BSA ((c) compared to (f)). With both samples no cracking occurs.

The drying rate drops at 45% of primary drying for samples without BSA and at 58% of

primary drying for samples with BSA, and the cumulative water loss reaches a constant

value. This indicates the completion of sublimation (see Figure 6.97). Thereafter a sharp

rise in Tp is observed. The sharp rise in shrinkage is therefore caused by secondary drying

processes. The initiation of shrinkage can be related to the first rise in Tp, as a prior rise

in Tp and a prior initiation of shrinkage is observed for samples containing BSA compared

to samples without BSA. Two step-rises in Tp are observed with BSA, causing the more

gradual increases in shrinkage. The higher solid content in samples with BSA caused by the


protein itself and the buffer salts may influence the compressibility of the lyophilizate and less

shrinkage is therefore observed.

Since during secondary drying no cracking is observed, cracking cannot be the reason

for the differences in shrinkage. These are developed during the ramp to secondary drying

(< 50% of secondary drying). During this phase Tp rises more rapidly with samples not

containing BSA and the difference (Tp - Tg) should be smaller. The weakness of the cake is

therefore increased and a higher amount of shrinkage is observed.

6.2.9 Kinetics of Different Disaccharides

The kinetics for 10% trehalose, D-(+)-sucrose and D-(+)-maltose obtained with cycle 2 (see

chapter 5.2.3) are shown in Figure 6.99. A summary of the final extents of shrinkage and

cracking is given in Table 6.19. Shrinkage decreases in the order: D-(+)-sucrose > D-

Trehalose D-(+)-sucrose D-(+)-maltose

Cracking 1D 3.37% 0.00% 0.00%Cracking 2D 4.30% 0.00% 0.00%Shrinkage 1D 2.41% 7.71% 7.30%Shrinkage 2D 3.25% 10.09% 8.35%

Table 6.19: Values of shrinkage and cracking for samples with trehalose, D-(+)-sucrose andD-(+)-maltose at the end of primary (1D) and secondary drying (2D).

(+)-maltose > trehalose. The same order was already found with the endpoint evaluation

method. The causal correlation between shrinkage and w′ is seen again (see chapter 6.1.4).

The values of shrinkage obtained by the endpoint method are higher (14.37% for trehalose,

20.37% for D-(+)-sucrose and 17.58% for D-(+)-maltose). No cracking is observed for D-

(+)-sucrose and D-(+)-maltose with the kinetic method. With the endpoint evaluation method

also no cracking occurs for D-(+)-maltose and only 0.12% for D-(+)-sucrose. The differences

may be caused by the vial cutting (see chapter 6.2.1.4).

As Figure 6.99 also shows, no cracking is observed for D-(+)-sucrose and D-(+)-maltose.

Shrinkage starts for all disaccharides after ≈ 20% of primary drying and increases until 55%

of primary drying. After this time point D-(+)-maltose and D-(+)-sucrose rise faster compared

to trehalose. This is initiated earlier at D-(+)-maltose (55% of primary drying) compared to

D-(+)-sucrose (≈ 60% of primary drying). Both reach after 90% of primary drying a plateau

200 6 Results

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-101234567891011121314

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Figure 6.99: Kinetics of cracking and shrinkage in % of samples with 10% trehalose (black),10% D-(+)-sucrose (blue) and 10% D-(+)-maltose (red) freeze-dried without thestandard cycle in correlation to Ts, Tp, the drying rate and the cumulative waterloss during primary and secondary drying. The coordinates for cracking andshrinkage are the mean average ± standard errors of all values obtained (n=3).Total duration of primary drying = 17 h, total duration of secondary drying = 10 h.


with a similar amount of shrinkage of about 7-8%.

Most of the shrinkage for all disaccharide (≈ 60%) is developed between 50% - 75% of

primary drying. This rapid curve progression can be correlated to the rise in Tp after the

completion of sublimation, as already found. This indicates again a greater influence of sec-

ondary drying processes on shrinkage. During the first 60% of secondary drying shrinkage is

developed faster in the order D-(+)-sucrose > D-(+)-maltose > trehalose. The rise in shrink-

age is not as pronounced with trehalose and the curves for D-(+)-maltose and D-(+)-sucrose

are always at higher values during secondary drying. Figure 6.100 shows representative

sample images of lyophilizates with trehalose (a)-(c), D-(+)-maltose (d)-(f), or D-(+)-sucrose

(g)-(i) at different time points. As (a), (d), and (g) show, no shrinkage and no cracking is

observed at the start of primary drying. According to Table 6.19 it can be seen that similar

values are obtained at the end of primary drying for D-(+)-maltose (e) and D-(+)-sucrose (h).

For trehalose less shrinkage is observed (b). The lyophilizate of trehalose also shows incom-

plete cake detachment (b), whereas D-(+)-maltose (e) and D-(+)-sucrose (h) show complete

cake detachment from the inside wall of the vial. At the end of secondary drying shrinkage

increases in the order: trehalose (c) < D-(+)-maltose (f) < D-(+)-sucrose (i). It is further

apparent that cracking is only observed for lyophilizates containing trehalose.

The differences in shrinkage between D-(+)-sucrose, D-(+)-maltose and trehalose are

caused, as already discussed in 6.1.4, by the different contents of non-frozen water in the

maximum freeze-concentrated state, w′. This correlation was already suggested by Ramb-

hatla et. al. [5]. These authors suggested that additional free volume in the cake is generated

as a result of the desorption of w′ during secondary drying. This additional free volume

can then be transformed to shrinkage. As w′ decreases in the order: D-(+)-sucrose > D-

(+)-maltose > trehalose, additional free volume is generated in the cake during secondary

drying in the same order. More shrinkage occurs therefore with D-(+)-sucrose followed by

D-(+)-maltose and trehalose.

The differences in shrinkage should be more pronounced when sublimation is finished and

desorption processes occur. This is observed in the current study, as > 52% of shrinkage is

developed when the sublimation process is finished. As the desorption of w′ takes place in

the dried layer (simultaneously to sublimation processes in lower product layers) this extent is

likely underestimated and may explain the differences in shrinkage that occur during primary

202 6 Results

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 6.100: Sample images of the lyophilizates with 10% trehalose (a): 0% , (b) 100%primary drying, (c) 100% secondary drying; with 10% D-(+)-maltose at (d): 0%,(e): 100% primary drying, (f) 100% secondary drying; with 10% D-(+)-sucroseat (g) 0%, (h): 100% primary drying, (i) 100% secondary drying.

drying. Most of the desorption of w′ takes place during secondary drying, especially when

Tp rises (< 50% of secondary drying). According to Figure 6.99 shrinkage increases in this

phase in the order: D-(+)-sucrose > D-(+)-maltose > trehalose. During this phase propor-

tionally a higher extent of w′ can be desorbed from D-(+)-sucrose followed by D-(+)-maltose

6.3 µ-CT Analysis 203

and trehalose, according to their values of w′. The free volume generated by the desorption

process increases in the same order and explains the different extents of shrinkage found.

The lower extent of shrinkage with trehalose is a result of cracking, as drying tensions are

released by fracture. This reduces the increase in shrinkage during secondary drying.

6.3 µ-CT Analysis

6.3.1 Sample Selection

The length of a sample has no impact on µ-CT, but its diameter influences the achievable

resolution - smaller diameter enables higher resolution. The sample has to be smaller than

10-20 mm in order to fit into the measurement angle of the of the X-ray beam [168]. Samples

prepared in a 2R vial were therefore selected for the µ-CT scans to assure a high resolution

and to allow an analysis of the whole cake.

Even with this small sample diameter, brightness artifacts appear in the µ-CT images

caused by ”beam hardening”. The low X-ray energy photons are most strongly absorbed in

the sample material and removed from the beam (the beam becomes harder [168]). Only

the remaining higher energy photons penetrate the inner part of the object. These photons

are then less strongly absorbed in the sample depth than were the lower energy photons

in the surface layer (absorption coefficient is photon energy dependent and decreases with

increasing energy). This causes the outer layer to show an apparently higher absorption

efficiency than the inner layers of the sample. Since CT images show absorption coefficient

values coded as pixel brightness, the outer regions of a sample seem brighter (absorb more

efficiently) than the inner parts (which appear darker). This effect is further impaired by the

use of the glass vial, as glass possesses a high ability to weaken the X-ray beam. As the

beam must first penetrate the glass, most of the photons with lower energy are absorbed by

the glass and removed from the beam. The sample itself is then penetrated by fewer photons

and image noise is high. The absorption process of the photons by the sample is a statistical

process, so scanning the same region several times leads not to exactly the same absorption

result. This is further impaired by the removal of high number of low-energy photons caused

by beam hardening of the glass. Fluctuations in photon absorption occur therefore, which in

turn shows up as statistical noise (brightness variations) in in reconstructed images. It was

204 6 Results

clearly necessary to leave the cake in the glass vial during the µ-CT analysis to evaluate

shrinkage.

6.3.2 Development of Adequate Measuring Conditions

The samples were initially analyzed at a measuring duration of 1 h and 1440 projections.

One slice out of the stack of slices obtained is illustrated in Figure 6.101(a). Due to the short

(a) (b)

(c)

Figure 6.101: Sample images of a freeze-dried cake of 30% trehalose (w/v) obtained by µ-CT at a scanning time of (a): 1 h and (b): 2 h; (c): enlargement of the middleregion of (b), where ”ring artifacts” are well recognizable. Only one slice ofeach sample is shown.

scanning time, high noise appears in the images which makes the contrast between gas

phase and cake structure barely visible. An evaluation of shrinkage and cracking is therefore

not possible in this case.


A longer scanning time of 2 h and an increase in the number of projections to 2880 im-

proves photon statistics. A decrease in tube high-voltage or an increase in power are not

possible due to the specifications of the scanner. One slice of the stack of slices obtained by

the longer scanning time is illustrated in Figure 6.101(b). A reduced noise is obtained. Even

at the lower edge region of the cake a slight shrinkage is visible. The contrast between cake

structure and gas phase is improved and sharper crack edges are seen.

Artifacts termed ”ring artifacts” (see Figure 6.101c) now appear in the images [168]. At

a long scanning time instabilities such as heating of the detector or the tube occur. These

lead to fluctuations in the scanning results between earlier and later projections. During the

tomographic reconstruction process from these projections the fluctuations become apparent

and ring artifacts occur. An even longer scanning time for further image improvement (noise

reduction), although possible, would lead to stronger artifacts, so the scanning time of 2 h

was used for the µ-CT-analysis as a compromise.

6.3.3 Image Evaluation of the µ-CT-Reconstructions

The 3D images obtained by the µCT-scanner (Vorbild; Institute of Medical Physics, Erlangen)

were evaluated with MIAF software (Institute of Medical Physics, Erlangen). The basis for

the evaluation is the differences in the intensity values of the voxels. Initially, the volume

of the glass vial was segmented. Since the intensity values of the glass differ significantly

from those of the lyophilizate or the cracks, this segmentation step was performed by simple

”volume growing”. In this process the regional connectivity among neighboring voxels in the

x-, y-, and z-directions of the sample is used [169]. A range of intensity values for the glass

(minimal and maximal value) was evaluated from the histogram, and a seed location in the

region of the glass was defined. The neighbors of this seed location were assigned to the

glass volume if their intensity values were within the defined intensity range. The further

voxels belonging to the glass volume were then iteratively assigned. On each iteration, the

voxels located in proximity to voxels previously assigned to the glass volume were tested.

They were added to the glass volume, if their intensity value is within the defined intensity

range, making the volume grow. This operation is therefore termed ”volume growing”. The

captured glass volume of an image of a sample cake (Figure 6.102(a)) is shown in red in

Figure 6.102(b). In a second step, the complete cake volume was evaluated. Note, however,

206 6 Results

(a)

(b) (c)

Figure 6.102: (a) Sample images of a freeze-dried cake with 30% trehalose obtained by µ-CT analysis. (left): xy-direction, (right) yz-direction of the volume; (b) Capturedvolume of the glass (red; xy-direction); (c) VOIs of the cake volume (blue, cyan,yellow, xy-direction).

that voxels at the cake’s edge expose brighter values compared to those in its middle, as

illustrated in Figure 6.102. This effect is caused by beam hardening (and is discussed later).

The cake was therefore partitioned into three volumes of interest (VOI, Figure 6.102(c)) to

account for the different intensity levels: the interior part (yellow colored in Figure 6.102(c)),

the outer border where the highest intensity values are observed (the dark blue VOI), and a

shell in-between (the cyan VOI).

The definition of the dark blue VOI consisted in identifying all voxels from the total volume

(glass and its interior) that laid within a certain distance from the inner surface of the glass

VOI. For the cyan VOI, the same procedure was used: all voxels within a predefined distance


from the inner boundary surface of the previously computed blue VOI formed the cyan VOI.

The rest of the glass interior defined the yellow VOI. The certain distance for the definition of

the three VOIs was defined empirically. The cake volume in each VOI was then segmented

by comparing the intensities of every voxels in it with a predefined value (this global threshold

was chosen empirically and individually for each of three VOIs). The cake volume was then

calculated by the sum of the cake volumes obtained in each VOI.

By this point, segmentation of the cake volume did not include the part of the volume

contained in the cracks. To obtain the cake volume that includes the volume of the cracks,

the following procedure was applied. First, a new segmentation volume was constructed by

combining all voxels of the previously segmented cake with all voxels that laid within a certain

small distance from the interior and exterior cake surface (boundary between cake volume

and vapor). The distance was chosen to be slightly larger than the empirically estimated

width of the largest crack to ensure an ascertainment of the whole crack volume. By this step

all cracks were ”filled” with intensity values of the cake. Note that this operation is known as

”morphological dilatation” [170]. However, beside the voxels that belong to the crack volume,

also voxels that laid within the small distance from the top of the cake surface were captured.

The cake volume with all cracks filled is falsely ”swollen” with regard to its height.

The converse operation, termed ”morphological erosion” was therefore performed to ac-

count for the ”swollen” part: all voxels of the segmented ‘swollen cake’ volume within a certain

distance from its boundary (between cake and vapor) were removed [170]. As result, the cake

will loose its ‘swollen’ part, but the cracks remain filled. The cracks are not concerned by this

operation, as boundaries between cake surface and vapor are no longer present within the

cake (as the cracks are ”filled” with the intensity values of the cake). This sequence of mor-

phological operations (dilatation and erosion) applied is known as ”morphological closing”,

since it closes gaps or fills holes. The complete cake volume (cake volume with filled cracks)

obtained is shown in Figure 6.103(a). The crack volume (Figure 6.103(b)) is then obtained

by subtracting the original cake volume (without the ”filled” cracks) from that obtained by

morphological closing (with filled cracks and without swollen part).

Several problems occurred during this image evaluation. At samples with 7.5% or 10%

trehalose the cake segmentation was difficult due to a very low contrast caused by the low

densities of the samples and a manual improvement was necessary. Evaluation of shrinkage

208 6 Results

(a) (b)

Figure 6.103: (a) Segmentation of the cake volume (green), (b) Segmentation of the crackvolume.

by analysis of µCT-images was furthermore not possible. The difference in intensity values

between vapor and cake at the edge of the cake nearby the glass wall were too small due to

beam hardening and the influence of the high intensity values of the glass (discussed later).

Only cracking is therefore considered in the following.

6.3.4 Comparison between 2D-Analysis (Endpoint Evaluation Method)

and 3D-Analysis (µ-CT)

Lyophilizates were already analyzed by µ-CT in order to investigate the total pore volume of

sucrose or mannitol lyophilizates [171] or the porosity and the pore size distribution, for in-

stance, of porous gelatin hydrogels obtained by freeze-drying [172]. In this work a resolution

of 10µm was achieved and the size of one voxel was 10x10x10µm3. This resolution is in

agreement with the spatial resolution of 9µm or 10µm found at Stange et. al. [171] and Van

Vlierberghe et. al. [172]. In this work µ-CT was used to investigate differences in the amount

of cracking on the top surface only (endpoint evaluation method, 2-dimensional picture) and

in the inside of a lyophilizate (µ-CT, 3D-analysis). The two analysis lead to different images

of the samples, as shown in Figure 6.104(a) - (c) (2D-analysis) compared to (d) - (f) (3D-

analysis). Figures 6.104(d)-(f) show the first slice of the cake (counted from top to bottom).


(a) 2D-analysis (7.5%) (b) 2D-analysis (10%) (c) 2D-analysis (20%)

(d) 3D-analysis, slice 156, (7.5%) (e) 3D-analysis, slice 156, (10%) (f) 3D-analysis, slice 118, (20%)

Figure 6.104: Images of samples with 7.5%, 10% and 20% trehalose obtained by 2D-analysisand 3D-analysis.

As horizontal slices of the sample are obtained by the µ-CT analysis, the slices in the up-

per and lower regions of the cake show ring-like structures. A white interior appears (glass)

caused by the curvature of the vial base (6.105a). On the top of the cake a black interior

(vapor) can be seen that arises from the curved top surface of the lyophilizate (caused by the

meniscus of the formulation, Figure 6.105b). Hence, an interior slice of the sample volume

is used to enable a comparison of the complete crack patterns. The image of a cake con-

taining 7.5% trehalose obtained by the 2D-analysis (Figure 6.104(a)) shows a wide crack in

its upper region, while the image of the 3D-analysis (6.104(d)) exhibits a more narrow crack

in this area. The cracks in the left and lower area found in the image of the 2D-analysis (a)

are not visible in the 3D-analysis (d). This shows that the background light of the 2D-analysis

causes the cracks to appear larger and wider than they actually are. The background light

is scattered and more diffuse light hits the lens of the camera. This causes blurred crack

edges and different crack patterns. The background light furthermore increases the contrast

between the cracks and the cake structure. This can be seen in the fine cracks found in the

210 6 Results

(a) Lower region of the sample,cross-section in the region of theglass vault of the vial (white),slice 45

(b) Upper region of the sample,cross section in the region of themeniscus of the sample (black),slice 251

Figure 6.105: Pictures of the 7.5% trehalose sample by 3D-analysis in the lower region of thesample (a) and the upper region of the sample (b).

left and lower regions of Figure 6.104(a), which cannot be seen in (d) by the 3D-analysis.

In Figure 6.104(d) no cracks are visible in the border area between cake and glass. This

effect arises in the edge region by a strong weakening-material (e.g. metal, glass) and is

well known as metal artifacts in medicine [168]. The intensity values are strongly distorted in

the transition area by beam hardening and the intensity values get blurred. The cracks are

therefore barely visible in this region.

The images of 10% and 20% trehalose (Figure 6.104(b), (c) compared to (d), (f)) show

similar crack patterns. Only the fine cracks in the border region between cake and glass

wall cannot be seen in the image of the 3D analysis. This is also caused by beam hardening.

Another reason for the differences between both methods may be the trehalose concentration

of the sample. Cracks with similar width that are not visible with 7.5% trehalose (left and lower

region of (d)) are visible at 10% (left region in (e)) or 20% trehalose. With increasing trehalose

concentration the density of the samples increases and more photons are absorbed by the

cake structure. This results in a lower statistical noise and the contrast between the cake

structure and cracks is higher. Even fine cracks in the middle of the cake can therefore be

distinguished from the cake structure at 20% trehalose.

The differences caused by the usage of different methods of analysis are reflected in

the lower cracking values found for the 3D analysis at each trehalose concentration (Fig-

ure 6.106). The major reason for the differences is the use of background light for the 2D


5 10 15 20 25 300

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18 2D: Axio Vision 3D: Micro-CT

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Figure 6.106: Cracking of samples obtained by cycle 1 (see chapter 5.2.3) for 7.5%, 10% and20% trehalose (w/v). The results obtained by the 2D analysis (black square)and the 3D analysis (white circle) are shown.

analysis, as discussed above. With the 2D-analysis the cracks appear smaller and more nar-

row as the contrast between the cracks and the cake structure is low. Cracks at the border

region between cake and glass wall are not detectable. This causes a lower amount and a

underestimation of cracking.

With the 2D analysis only the cracks on the cake’s surface are captured and evaluated.

With the 3D analysis all cracks within the sample are considered. Figure 6.107 shows the

xz- and yz -directions of the volume of the samples with 7.5%, 10% and 20% trehalose. It

can be seen that for 7.5% and 10% trehalose (Figure 6.107(a) - (d)) the cracks run vertical.

As Figure 6.107(c) shows, not all cracks run from the top to the base of the vial. Some

cracks run also funnel shaped (d) with a wider diameter at the surface. Both cases cause the

overestimation in cracking in the 2D-analysis (see Figure 6.106).

Figure 6.107(e) - (g) illustrates that the cracks run diagonal for 20% and 30% trehalose.

Some cracks are wider in the middle of the cake than at its bottom or surface. Some run

together or start in the middle of the cake (e), (g). These crack patterns cause an underesti-

mation of cracking with the 2D-analysis. As Figure 6.106 shows, higher cracking values are

found with the 2D analysis for 20% and 30% trehalose. The overestimation of cracking by

the use of background light may therefore outweigh the underestimation of cracking caused

by the different crack patterns within the sample compared to its surface.

212 6 Results

(a) yz-view of the volume, 7.5% trehalose (b) xz-view of the volume, 7.5% trehalose

(c) yz-view of the volume, 10% trehalose (d) xz-view of the volume, 10% trehalose

(e) yz-view of the volume, 20% trehalose (f) xz-view of the volume, 20% trehalose

(g) yz-view of the volume, 30% trehalose (h) xz-view of the volume, 30% trehalose

Figure 6.107: Volumes of the samples with 7.5%, 10%, 20% and 30% trehalose by 3D-analysis in yz-direction and xz-direction, respectively.

With all samples the surface curvature is not considered in the 2D analysis. Because of the

concave surface, cracks are captured in a diagonal position. This causes an optical enlarge-

ment of the cracks. From Figure 6.107 it is apparent that this curvature is more pronounced

at higher trehalose concentrations. This optical enlargement causes higher cracking values

in the 2D analysis. It explains further the higher cracking values obtained by the 2D-analysis

although the crack patterns indicate an underestimation of cracking by the 3D-analysis.

Despite the differences in the methods of analysis, a consistently higher amount of crack-

ing is obtained with increasing trehalose concentration (see Figure 6.106). This confirms the


concentration dependency of cracking already found at the endpoint evaluation method. A

2D-analysis of the surface of the lyophilizate is therefore sufficient for the endpoint evaluation

of cracking.

6.3.5 Comparison between the 3D-Structure of Samples obtained in a

Regular and a Toplyo R© Vial

Figure 6.108 compares the lyophilizates obtained by the 2stepA cycle in a regular vial (a) or

by the standard cycle in a Toplyo R© vial (b) with 30% trehalose. It exemplifies the different

surface curvature developed in a Toplyo R© vial and a regular vial. Whereas a flat lyophilizate

with a relative constant thickness is obtained in a Toplyo R© vial (a), the curved surface which

is already observed above (see chapter 6.3.4) is obtained in a regular vial (b). This different

surface geometry is produced by the hydrophobic vial coating and the greater contact angles

between the formulation and this layer in a Toplyo R© vial compared to a regular vial. As the

volume and the shape of the fill volume is preserved in the freezing step, the lyophilizate gives

the same surface shape as before lyophilization. The different structure of the lyophilizate in

a Toplyo R© vial can also be seen in the cake volume of the lyophilizate in (c) compared to a

regular vial (d). A sharper increase in cake volume at the top (slice 0-100) and a sharper

decrease at the bottom of the lyophilizate (slices > 270) is observed in a Toplyo R© vial. The

optimized container geometry of the Toplyo R© vial is reflected in this sharper decrease in cake

volume at the bottom of the cake. The constant value of the cake volume found in the middle

of the cake is more pronounced, as a more even distribution of the fill volume in the vial is

developed in a Toplyo R© vial.

From Figure 6.108(e) and (f) it is apparent that a homogeneous distribution of cracking is

found in the lyophilizate of a Toplyo R© vial (constant value of cracking in slices 160-270, (e)).

This is not observed with a lyophilizate in a regular vial obtained by the 2stepA cycle (f).

Figure 6.109 and 6.110 show the volumes of a 7.5% or 10% trehalose, respectively in a

Toplyo R© vial (standard cycle) and a regular vial (2stepA cycle). For 7.5% and 10% only

0.34% and 0.65% cracking, respectively, is found and the cracks are barely visible in the

images. A comparison of the crack patterns is therefore not possible. The flat cake geometry

found in a Toplyo R© vial and the curved cake geometry obtained in a regular vial, however, is

also visible.

214 6 Results

(a) (b)

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(f)

Figure 6.108: xz-view of the µ-CT volumes of the sample in (a) a Toplyo R© vial (standardcycle) and (b) in a regular vial (2stepA). Cake volume [Voxel] in a Toplyo vial(standard cycle) (c) and in a regular vial (2stepA cycle) (d). Cracking in % in aToplyo vial (standard cycle, (e)) and in a regular vial (2stepA cycle, (f)) as themean value of every 10 image slices of the µ-CT stack for 30% trehalose; lightgray: top and bottom area of the cake, dark gray: cylindrical part of the cake.

Figure 6.111 illustrates the values of cracking obtained by the 2D and the 3D analysis

under different conditions. As already found in the endpoint evaluation method, the usage of

Toplyo R© vials (see chapter 6.1.8) or the application of a two-step freezing phase with included

annealing (see chapter 6.1.10) leads to a strong reduction in cracking. This can be confirmed


(a) xz-view of the volume, 7.5% trehalose Toplyo (b) yz-view of the volume, 7.5% trehalose Toplyo

(c) xz-view of the volume, 7.5% trehalose 2stepA (d) yz-view of the volume, 7.5% trehalose 2stepA

Figure 6.109: Volumes of the samples with 7.5% trehalose by 3D-analysis in yz-direction andxz-direction.

(a) xz-view of the volume, 10% trehalose Toplyo (b) yz-view of the volume, 10% trehalose Toplyo

(c) xz-view of the volume, 10% trehalose 2stepA (d) yz-view of the volume, 10% trehalose 2stepA

Figure 6.110: Volumes of the samples with 10% trehalose by 3D-analysis in yz-direction andxz-direction.

by the 3D analysis as similar values for each condition are found with both methods. These

are smaller than those obtained with the standard cycle in a regular vial. The comparison of

Figures 6.107 - 6.110 also shows the reduction in cracking for all trehalose concentrations.

This is in particular pronounced for 7.5% and 10% trehalose in a Toplyo R© vial or by the

application of 2stepA in a regular vial and this confirms the strong reduction in cracking even

within the whole cake by these methods. The similar values of cracking for the 2D and the 3D

analysis for the lyophilizates obtained in Toplyo R© vials and by the 2stepA cycle (see Figure

6.111) indicate that the crack patterns of the cake surfaces are more similar to these within

the cake compared to samples obtained in regular vials with the standard cycle. This is also

seen in the images in Figure 6.107 - 6.110. The diameter of the cracks is similar within the

216 6 Results

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(a)

Figure 6.111: Comparison of the cracking values [%] obtained by a 2D analysis (endpointevaluation, circle) with the 3D analysis of lyophilizates obtained in a Toplyo R©

vial with the standard cycle (black) , or in a regular vial with the standard cycle(white), as well as with the 2stepA cycle (gray). The coordinates for crackingare the mean average ± standard error of all values obtained by the endpointevaluation method (n=20).

cake from the surface to the base of the vial and only some hair-like cracks start in the middle

of the cake to its bottom. This indicates a more homogeneous stress distribution inside the

sample. Possible causes may be easier and more homogeneous detachment of the cake

from the inside wall of the vial in a Toplyo R© vial or the higher mechanical strength caused

by the homogeneous cake structure obtained by 2stepA. The usage of Toplyo R© vials or the

application of 2stepA is therefore the method of choice to optimize cake appearance.

7 Conclusions

In this thesis the influence of the formulation or the process on shrinkage and cracking was

studied. Methods were developed to quantify the amount of both at the end of the lyophiliza-

tion process (”endpoint evaluation method”) as well as in situ during drying (”kinetic method”).

The endpoint evaluation method was used to investigate an apparent correlation between

the content of non-frozen water in the maximum freeze-concentrated state, w′, of an amor-

phous cake and shrinkage, as has been suggested by Rambhatla et. al. [5]. Model disac-

charides were D-(+)-trehalose dihydrate, D-(+)- maltose and D-(+)-sucrose having different

amounts of w′. The results obtained confirm the assumption of a causal correlation between

shrinkage and w′. No influence on cracking was observed. A direct correlation between the

value of w′ and the amount of shrinkage which was also suggested by Rambhatla et. al. [5]

could not be shown.

The extents of shrinkage and cracking at different trehalose concentration were investi-

gated. A concentration dependency was found. With increasing trehalose concentration the

amount of cracking increases and the amount of shrinkage decreases. This concentration

dependency was found with all shelf-frozen lyophilizates, also with the kinetic method. Mea-

surements with a texture analyzer show decreasing brittleness and increasing hardness of

the lyophilizate with increase trehalose concentration. SEM-pictures and the results of mer-

cury porosimetry gave increasing cell sizes (pore sizes) with increasing trehalose concen-

tration. More cracking is developed at higher trehalose concentrations because the tensile

fracture toughness decreases with increasing cell sizes.

The surface tension and wetting results obtained based on Young’s equation indicate a

positive adsorption of trehalose to the surface of the glass, despite its negative Γ at the

water/air interface. An adhesive effect of the trehalose cake produced during primary drying

to the inner vial wall is therefore possible. If this adhesion is high, then shrinkage of the

218 7 Conclusions

lyophilizate mass to relax drying tensions in the cake will be hindered and lead to cracking.

The extents of shrinkage and cracking determine each other. Increasing shrinkage re-

leases drying tensions and as a result the amount of cracking is reduced. The tensile fracture

toughness is then not exceeded. This is shown with the endpoint evaluation method devel-

oped in this work. It was used with different disaccharides, varying trehalose concentration,

change in vial diameter and the use of Toplyo R© vials. Additionally the effects of slow cooling

rate, as well as by the usage of a two step freezing step in combination with annealing were

examined.

A kinetic method was also developed to illustrate quantitatively the development of shrink-

age and cracking during freeze-drying. The first occurrence of shrinkage was after 20% of

primary drying, at that time point when the primary drying shelf temperature was reached.

The highest extent of shrinkage and cracking was developed after the completion of sublima-

tion. The development of shrinkage and cracking was then pronounced during the first half

of secondary drying, where the rise in product temperature takes place. The extent of shrink-

age is predominantly determined by processes of secondary drying, as has been suggested

before by Pikal [9] and MacKenzie [8]. The current work gives the first quantitative evidence.

The results obtained by the kinetic method show that if shrinkage is possible, then this is

the dominant mechanism to relax drying tensions. Cracking then predominantly occurs in the

phase after the completion of local sublimation when local Tp rises during primary drying and

drying tensions are high. Inadequate relaxation of drying tensions by shrinkage is the cause,

resulting in exceeding of the tensile fracture toughness and fracture of the lyophilizate. If

complete detachment of the cake from the vial wall takes place, then relaxation of the drying

tensions by cracking does not occur. With a higher adhesion of the product to the inside

wall of the vial (for instance at 30% trehalose w/v), cracking is the dominant mechanism to

release drying tensions. After completion of local sublimation, when Tp rises during primary

drying, partial shrinkage is possible.

Detachment of the cake from the inside wall of the vial proceeds from initial loci that then

proceed. Initiated cracking may also be transferred to subjacent regions. The images showed

that during secondary drying only crack expansion takes place. The crack patterns indicate

that this expansion is caused by shrinkage of island cake regions.

Based on µ-CT (3D analysis) slightly lower values are found for cracking compared with

219

the endpoint evaluation method (2D analysis). These differences result from the usage of

background light that visually enlarged the cracks and blurred the crack edges by cracks lo-

cated in deeper product layers. The curvature of the cake is furthermore not considered at the

endpoint evaluation method, which also causes enlargement of the cracks. Both methods,

however, led to similar results and a 2D-analysis of cracking at the endpoint of lyophilization

seems therefore to be sufficient. It could be confirmed by the 3D analysis that the usage

of Toplyo R© vials of the inclusion of a two step freezing with additional annealing leads to a

strong reduction in cracking. These methods should therefore be used for an optimization of

cake appearance.

Further work should be done in particular regarding a quantification of drying tensions

within the cake. A resistance strain gauge would have to be wetted by the freeze-drying

formulation and the frozen or dried cake must adhere to it. The use of a special coated strain

gauge, which enables evaluation of drying tensions could be one approach. For correct

embedding it should be considered that the drying tensions mainly occur in the direction of

the diameter of the sample based on whether shrinkage occurs or the cake adheres to the

inside wall of the vial. Another idea could be to spray a fine grid with ice color on the top

surface of the cake at the end of freezing to measure the strain quantitatively in analogy with

the ”Optical Full-Field Strain Measurement” well known in the field of mechanics. With this

method a quantitative measurement of shrinkage with regard to the height of the sample

would also be possible.

8 Zusammenfassung

Im Rahmen dieser Arbeit wurde der Einfluss von verschiedenen Formulierungen und und

Prozesseigenschaften auf den Rissanteil einer amorphen Lyophilisatmatrix (”Cracking “) oder

deren Schrumpfen (”Shrinkage “) untersucht. Es wurden Quantifizierungsmethoden einer-

seits in situ wahrend der Trocknung (”Kinetik-Methode “), und andererseits im Endprodukt

(”Endprodukt-Methode “) entwickelt.

Die Endprodukt-Methode fand Verwendung fur die Untersuchung einer von Rambhatla

et. al. [5] postulierten Korrelation zwischen dem Anteil an unausfrierbarem Wasser eines

amorphen Lyophilisates, der am Glasubergang vorliegt (”unfrozen water “, w′), und dem

Ausmaß an Shrinkage. Als Modelldisaccharide wurden D-(+)-Maltose und D-(+)-Saccharose

neben D-(+)-Trehalose-Dihydrat verwendet, welche unterschiedliche Anteile an w′ enthalten.

Die Ergebnisse zeigen, dass mit zunehmendem Anteil an w′ auch das Ausmaß an Shrinkage

zunimmt. Bezuglich Cracking ist kein erkennbarer Einfluss beobachtbar. Eine Korrelation

zwischen den absoluten Werten des Schrumpfens und dem Anteil an w′, die Rambhatla et.

al. [5] zudem vorschlug, konnte nicht gezeigt werden.

Außerdem wurden der Rissanteil und der geschrumpfte Anteil in Lyophilisaten ver-

schiedener Trehalose-Konzentrationen untersucht. Eine Konzentrationsabhangigkeit kon-

nte nachgewießen werden, bei der mit zunehmender Trehalose-Konzentration ein großerer

Rissanteil und ein geringeres Schrumpfen der Lyophilisatmasse auftrat. Diese Konzentra-

tionsabhangigkeit zeigt sich bei allen Gefriertrocknungskuchen, die mittels Stellflachen im

Gefriertrockner eingefroren werden (auch unter der Verwendung der Kinetik-Methode). Mes-

sungen mit einem Texturprufgerat zeigten, dass die Sprodigkeit des Lyophilisates mit steigen-

der Konzentration abnimmt und die Harte zunimmt. Aufnahmen mit dem Rasterelektro-

nenmikroskop und Messungen mittels Quecksilber-Porosimetrie ergaben, dass mit steigen-

der Trehalose-Konzentration die Zellgroße (Porengroße) wachst. Bei Lyophilisaten hoherer

222 8 Zusammenfassung

Trehalose-Konzentrationen kommt es unter geringeren Trocknungsspannungen zu Rissen,

da die Zugzahigkeit eines Lyophilisates mit steigender Porengroße sinkt.

Des Weiteren wurde der Einfluss der Oberflachenchemie des Vials auf das Schrumpfen

der Kuchenmatrix und deren Rissanteil erforscht. Die Ergebnisse lassen anhand der

Young’schen Gleichung vermuten, dass Trehalose positiv an der Glasoberflache adsor-

biert wird, obwohl Trehalose einen negativen Oberflachenexzess an der Grenzflache

zwischen Wasser und Luft besitzt. Daraus lasst sich eine mogliche Adhasion des

Trehalose-Lyophilisates an der Vial-Innenwand wahrend der Trocknung annehmen. Ist diese

Adhasionkraft stark, wird das Schrumpfen der Lyophilisatmasse wahrend des Trocknens

beeintrachtigt und es kommt zu einer Rissbildung.

Das Ausmaß an Shrinkage und Cracking beeinflussen sich gegenseitig. Bei einem ver-

mehrten Auftreten von Shrinkage werden Spannungen abgebaut und es tritt weniger Crack-

ing auf. Die Zugzahigkeit des Lyophilisatzes wird dann nicht uberschritten. Dieser Zusam-

menhang wurde bei der Endprodukt-Methode gezeigt, die im Rahmen dieser Arbeit entwick-

elt wurde. Mit dieser Methode wurden verschiedene Disaccharide, Trehalose-Losungen ver-

schiedener Konzentrationen, Veranderungen des Vialdurchmessers und Toplyo R©-Vials un-

tersucht. Außerdem wurden der Einfluß einer geringere Kuhlrate wahrend des Einfrierens

und die Verwendung eines zweistufigen Einfrierschritts mit zusatzlichem Annealing ermittelt.

Es konnte eine Kinetik-Methode entwickelt werden, um die Entwicklung des Schrumpfens

der Kuchenmatrix und der Rissbildung wahrend der Gefriertrocknung quantitativ zu verfol-

gen. Ein Schrumpfen der Kuchenmatrix tritt zuerst nach 20% der Primartrocknungszeit auf,

an dem Zeitpunkt, an dem die Stellflache die Primartrocknungstemperatur erreicht hat. Der

großte Anteil an Shrinkage und Cracking wahrend der Primartrocknung entsteht nach Ab-

schluss der Sublimation. In der ersten Halfte der Sekundartrocknung, in der die Temper-

aturanhebung stattfindet, wird der großte Anteil an Kuchenveranderungen in dieser Phase

gebildet. Vorwiegend bestimmen Sekundartrocknungsvorgange das Ausmaß an Shrinkage.

Dies wurde bereits bei Pikal [9] und MacKenzie [8] vorgeschlagen. Die vorliegende Arbeit

gibt den ersten quantitativen Nachweise dafur.

Es konnte gezeigt werden, dass, wenn ein Schrumpfen der Lyophilisatmatrix moglich

ist, dies der dominante Mechanismus ist, um Spannungen innerhalb des Lyophilisates

abzubauen. Eine Rissbildung tritt dann vorwiegend auf, wenn lokal die Sublimation

223

abgeschlossen ist und dort die Produkttemperatur zunimmt. Ursache hierfur konnte sein,

dass eine Relaxation der Trocknungsspannungen durch ein Schrumpfen der Lyophilisatma-

trix in dieser Phase nicht ausreicht und die Zugzahigkeit des Kuchens uberschritten wird. Als

Folge kommt es zum Reißen der Produktmatrix. Hat zu diesem Zeitpunkt bereits eine kom-

plette Ablosung des Kuchens von der Vialinnenwand stattgefunden, dann ist eine Relaxation

der Trocknungsspannungen durch Rissbildung nicht moglich. Die Ergebnisse zeigen weit-

erhin, dass erst bei starkerer Adhasion des Kuchens an der Vialinnenwand (30% Trehalose

w/v) die Rissbildung der dominante Mechanismus ist, um Spannungen abzubauen. Eine

partielles Schrumpfen der Lyophilisatmasse ist ebenfalls dann moglich, wenn lokal die Subli-

mation abgeschlossen ist und die Produkttemperatur wahrend der Primartrocknung ansteigt.

Die Ablosung des Kuchens von der Vialinnenwand geht von Startpunkten aus und breitet

sich von diesen weiter nach rechts und links aus. Begonnenes Risswachstum wird ebenso

auf angrenzende Regionen ubertragen. Die Bildaufnahmen der Lyophilisate wahrend der

Trocknung zeigen, dass es wahrend der Sekundartrocknung nur zu einer Rissausweitung

kommt. Das Rissmuster lasst allerdings vermuten, dass dieser Vorgang an Stellen, an denen

Kuchenstucke kontaktlos vorliegen, einem Schrumpfen der Kuchenmatrix zuzuordnen ist.

Bei einer Micro-CT Analyse (3D-Analyse) der Lyophilisate wurden etwas niedrigere Werte

fur den Rissanteil gefunden als bei der 2D-Analyse (Endprodukt-Methode). Dieser Unter-

schied kommt von der Verwendung von Gegenlicht, welches die Risse optisch vergroßert

und Rissrander aufgrund von tiefer liegenden Rissen undeutlich macht. Bei der 2D-Analyse

wurde außerdem die Krummung der Oberflache des Kuchens nicht berucksichtigt, die eben-

falls zu einer Vergroßerung der Risse fuhrt. Dennoch liefern beide Methoden vergleichbare

Ergebnisse und eine 2D-Quantifizierung des Rissanteils scheint im Endprodukt ausreichend

zu sein. Mit Hilfe der 3D-Analyse kann bestatigt werden, dass die Verwendung von Toplyo R©-

Vials bzw. eines zweistufigen Einfrierschritts mit integriertem Annealing zu einer starken Re-

duktion des Rissanteils fuhrt. Zu Optimierung des Produktaußeren sind daher beide Metho-

den heranzuziehen.

Zukunftige Untersuchungen sollten eine Quantifizierung der Trocknungsspannungen

ermoglichen. Ein Dehnungsmesstreifen musste von der flussigen Formulierung ausre-

ichend benetzt werden, und der gefrorene Kuchen bzw. das Lyophilisat musste an diesem

haften. Ein moglicher Losungsansatz konnte die Verwendung von speziell beschichteten

224 8 Zusammenfassung

Dehnungsmessstreifen sein. Fur eine korrekte Einbettung des Dehnungsmessstreifens sollte

allerdings beachtet werden, dass die Trocknungsspannungen vorwiegend in y-Richtung der

Probe auftreten, basierend auf einem Schrumpfen oder einem Anhaften des Lyophilisates

an der Vialinnenwand. Ein andere Ansatz ware das Aufspuhen eines feinen Netzes auf die

Oberflache des Lyophilisates nach Abschluß des Einfriervorgangs mit Eisfarbe. Damit konnte

die Deformation des Kuchens quantitativ in Analogie zur Optischen Dehnungsmessung der

technischen Mechanik bestimmt werden. Eine quantitative Messung der Hohenanderung

des Lyophilisates ware so ebenfalls moglich.

9 Appendix

Conc. Row s1 s2 σ1 σ2 F Fc

7.5% 1+2 1.85 0.78 0.6084 3.4225 0.18 6.372+3 1.85 1.70 3.4225 2.9800 1.18 8.473+4 3.91 1.70 2.8900 15.288 0.19 13.744+5 3.91 1.36 15.2881 1.8496 8.27 13.745+6/7 2.08 1.36 1.8496 4.3264 0.43 8.106/7+8/9/10 2.08 1.50 4.3264 2.2500 1.92 8.02

10% 1+2 2.30 1.57 5.2900 2.4649 2.15 6.622+3 2.48 1.57 2.4649 6.1504 0.40 7.853+4 2.48 0.96 6.1504 0.9216 6.67 11.394+5 1.17 0.96 0.9216 1.3689 0.67 12.065+6/7 2.20 1.17 1.3689 4.8400 0.28 28.716/7+8/9/10 3.09 2.20 4.8400 9.5481 0.51 21.20

20% 1+2 1.07 0.97 1.1449 0.9409 1.22 4.632+3 1.14 0.97 1.2996 0.9409 1.38 5.473+4 1.59 1.14 2.5281 1.2996 1.95 6.634+5 1.59 1.24 2.5281 1.5376 1.64 10.975+6/7 1.24 0.65 1.5376 0.4225 3.64 8.756/7+8/9/10 0.77 0.65 0.5929 0.4225 1.40 9.15

30% 1+2 1.04 1.01 1.0816 1.0201 1.06 5.732+3 1.01 0.55 1.0201 0.3025 3.37 6.033+4 0.65 0.55 0.4225 0.3025 1.40 6.034+5 1.46 0.65 2.1316 0.4225 5.05 6.635+6/7 1.46 0.83 2.1316 0.6889 3.09 7.466/7+8/9/10 0.83 0.74 0.6889 0.5476 1.26 5.20

Table 9.1: Results of the F-test for the cracking values of 7.5% trehalose (w/v), 10% trehalose(w/v), 20% trehalose (w/v), 30% trehalose (w/v). Conc.= trehalose concentration(w/v). F-values that indicate rows with inhomogeneous variances are printed inbold text.

226 9 Appendix

Conc. Row s1 s2 σ1 σ2 F Fc

7.5% 1+2 5.44 1.32 29.5936 1.7424 16.98 7.872+3 2.68 1.32 7.1824 1.7424 4.12 6.723+4 10.14 2.68 102.8196 7.1824 14.32 6.424+5 10.14 1.64 102.8196 2.6896 38.23 7.855+6/7 4.68 1.64 21.9024 2.6896 8.14 6.546/7+8/9/10 4.68 1.43 21.9024 2.0449 10.71 14.45

10% 1+2 5.84 4.01 34.1056 16.0801 2.12 4.462+3 5.40 4.01 29.16 16.0801 1.81 4.633+4 6.28 5.40 39.4384 29.16 1.35 5.354+5 6.28 5.81 39.4384 33.7561 1.17 6.725+6/7 5.81 5.80 33.7561 33.64 1.00 5.616/7+8/9/10 6.62 5.80 43.8244 33.64 1.30 5.80

20% 1+2 0.99 0.48 0.9801 0.2304 4.25 4.632+3 0.99 0.40 0.9801 0.16 6.13 5.913+4 1.15 0.40 1.3225 0.16 8.27 6.634+5 1.15 0.57 1.3225 0.3249 4.07 10.975+6/7 0.64 0.57 0.4096 0.3249 1.26 10.676/7+8/9/10 0.76 0.64 0.5776 0.4096 1.41 9.15

30% 1+2 1.53 1.09 2.3409 1.1881 1.97 4.742+3 1.53 1.47 2.3409 2.1609 1.08 6.033+4 1.47 0.22 2.1609 0.0484 44.65 6.034+5 1.31 0.22 1.7161 0.0484 35.46 6.635+6/7 1.63 1.31 2.6569 1.7161 1.55 10.466/7+8/9/10 1.63 0.46 2.6569 0.2116 12.56 5.20

Table 9.2: Results of the F-test for the shrinkage values of 7.5% trehalose (w/v), 10% tre-halose (w/v), 20% trehalose (w/v), 30% trehalose (w/v). Conc.= trehalose con-centration (w/v). F-values that indicate rows with inhomogeneous variances areprinted in bold text.

227

Conc. Row s1 s2 sm−m µ1 µ2 t df tc

7.5% 1+2 0.78 1.85 0.7460 1.49 3.22 4.60 14 2.982+3 1.85 1.70 0.9496 3.22 3.31 0.18 12 3.053+4 1.70 3.91 2.8385 3.31 4.74 0.63 7 3.504+5 3.91 1.36 2.8122 4.74 2.23 1.11 7 3.505+6/7 1.36 2.08 0.8631 2.23 2.95 1.66 14 2.986/7+8/9/10 2.08 0.77 0.8236 2.95 2.72 0.42 10 3.17

10% 1+2 2.30 1.57 0.8883 6.10 5.01 2.64 17 2.902+3 1.57 2.48 1.2402 5.01 7.05 2.89 11 3.113+4 2.48 0.96 1.1763 7.05 7.05 0.00 9 3.254+5 0.96 1.17 0.7042 7.05 5.51 3.39 8 3.365+6/7 1.17 2.20 1.1447 5.51 6.20 0.90 7 3.506/7+8/9/10 2.20 3.09 2.3962 6.20 7.87 0.83 5 4.03

20% 1+2 0.97 1.07 0.4392 11.47 12.32 4.52 20 2.852+3 1.07 1.14 0.5088 12.32 11.34 4.19 17 2.903+4 1.14 1.59 0.7522 11.34 11.76 1.06 13 3.014+5 1.59 1.24 0.8232 11.76 11.43 0.69 10 3.505+6/7 1.24 0.65 0.5627 11.43 11.87 1.41 11 3.116/7+8/9/10 0.65 0.77 0.4230 11.87 11.02 3.43 10 3.50

30% 1+2 1.04 1.01 0.4511 12.79 12.02 3.87 19 2.862+3 1.01 0.55 0.3833 12.02 12.07 0.28 16 2.923+4 0.55 0.65 0.2838 12.07 11.40 5.01 16 2.924+5 0.65 1.46 0.6342 11.40 12.40 2.99 13 3.015+6/7 1.46 0.83 0.6644 12.40 12.48 0.22 12 3.056/7+8/9/10 0.83 0.74 0.3686 12.48 12.11 2.16 17 2.90

Table 9.3: Results of the t-test for the cracking values of 7.5% trehalose (w/v), 10% trehalose(w/v), 20% trehalose (w/v), 30% trehalose (w/v) with homogeneous variances.Conc.= trehalose concentration (w/v). Rows with differences in the mean valuesare printed in bold text.

228 9 Appendix

Conc. Row s1 s2 sm−m µ1 µ2 t df tc

7.5% 2+3 1.32 2.68 0.9834 11.26 12.35 2.25 15 2.956/7+8/9/10 4.68 1.43 1.4947 12.98 11.51 1.85 15 2.95

10% 1+2 5.84 4.01 2.0450 16.48 18.24 2.11 22 2.822+3 4.01 5.40 2.0630 18.24 17.36 1.00 20 2.853+4 5.40 6.28 2.6191 17.36 15.65 1.46 18 2.884+5 6.28 5.81 2.8571 15.65 17.49 1.36 16 2.925+6/7 5.81 5.80 2.7538 17.49 15.81 1.29 16 2.926/7+8/9/10 5.80 6.62 3.1024 15.81 18.84 1.98 15 2.95

20% 1+2 0.48 0.99 0.3424 7.29 7.91 4.23 20 2.854+5 1.15 0.57 0.5240 7.27 7.14 0.43 10 3.175+6/7 0.57 0.64 0.3357 7.14 6.78 1.93 11 3.116/7+8/9/10 0.64 0.76 0.4172 6.78 7.04 1.06 10 3.17

30% 1+2 1.09 1.53 0.5992 7.51 8.34 3.14 19 2.862+3 1.53 1.47 0.7072 8.34 7.63 2.13 16 2.925+6/7 1.31 1.63 0.7862 7.62 8.07 1.06 12 3.05

Table 9.4: Results of the t-test for the shrinkage values of 7.5% trehalose (w/v), 10% tre-halose (w/v), 20% trehalose (w/v), 30% trehalose (w/v) with homogeneous vari-ances. Conc.= trehalose concentration (w/v). Rows with differences in the meanvalues are printed in bold text.

Conc. Row s1 s2 sm−m c µ1 µ2 t df tc

7.5% 1+2 5,44 1,32 1,7144 0,92 14,82 11,26 2,08 12 3,653+4 2,68 10,14 4,6133 0,03 12,35 18,60 1,35 4 4,604+5 10,14 1,64 4,5717 0,98 18,60 12,86 1,26 4 4,605+6/7 1,64 4,68 1,4701 0,16 12,86 12,98 0,08 15 2,95

20% 2+3 0,99 0,40 0,3403 0,85 7,91 7,09 2,41 12 3,053+4 0,40 1,15 0,4881 0,07 7,09 7,27 0,37 6 3,71

30% 3+4 1,47 0,22 0,4955 0,98 7,63 6,87 1,54 8 3,364+5 0,22 1,31 0,5398 0,02 6,87 7,62 1,39 5 4,036/7+8/9/10 1,31 0,46 0,5525 0,94 7,62 7,01 1,10 6 3,71

Table 9.5: Results of the t-test for the shrinkage values of 7.5% trehalose (w/v), 10% tre-halose (w/v), 20% trehalose (w/v), 30% trehalose (w/v) with inhomogeneous vari-ances. Conc.= trehalose concentration (w/v). Rows with differences in the meanvalues are printed in bold text.

229

Conc. Row Shrinkage Cracking

7.5% 1+2 homogeneous inhomogeneous2+3 homogeneous homogeneous3+4 homogeneous homogeneous4+5 homogeneous homogeneous5+6/7 homogeneous homogeneous6/7+8/9/10 homogeneous homogeneous

10% 1+2 homogeneous homogeneous2+3 homogeneous homogeneous3+4 homogeneous homogeneous4+5 homogeneous inhomogeneous5+6/7 homogeneous homogeneous6/7+8/9/10 homogeneous homogeneous

20% 1+2 inhomogeneous inhomogeneous2+3 homogeneous inhomogeneous3+4 homogeneous homogeneous4+5 homogeneous homogeneous5+6/7 homogeneous homogeneous6/7+8/9/10 homogeneous homogeneous

30% 1+2 inhomogeneous inhomogeneous2+3 homogeneous homogeneous3+4 homogeneous inhomogeneous4+5 homogeneous homogeneous5+6/7 homogeneous homogeneous6/7+8/9/10 homogeneous homogeneous

Table 9.6: Overview of the uniformity of shrinkage and cracking with regard to the position ofthe vials.

230 9 Appendix

Values obtained for

2R 2.5 mm, regular vial 5%: n=4, 7.5%: n=32, 10%: n=3315%: n=19, 20%: n=30, 30%: n=26

10R 2.5 mm, regular vial 5%: n=4, 7.5%: n=12, 10%: n=1415%: n=7, 20%: n=14, 30%: n=12

2R 5 mm, regular vial 5%: n=11, 7.5%: n=24, 10%: n=3015%: n=25, 20%: n=25, 30%: n=21

10R 5 mm, regular vial 5%: n=4, 7.5%: n=12, 10%: n=1415%: n=6, 20%: n=14, 30%: n=11

2R 2.5 mm, Toplyo vial 5%: n=5, 7.5%: n=30, 10%: n=2015%: n=5, 20%: n=21, 30%: n=22

10R 2.5 mm, Toplyo vial 5%: n=2, 7.5%: n=13, 10%: n=1315%: n=2, 20%: n=14, 30%: n=10

2R 5 mm, Toplyo vial 5%: n=5, 7.5%: n=13, 10%: n=1415%: n=5, 20%: n=10, 30%: n=11

10R 5 mm, Toplyo vial 5%: n=2, 7.5%: n=27, 10%: n=2315%: n=2, 20%: n=21, 30%: n=20

2R 2.5 mm slow FR 5%: n=8, 7.5%: n=8, 10%: n=915%: n=10, 20%: n=9, 30%: n=10

10R 2.5 mm slow FR 5%: n=4, 7.5%: n=4, 10%: n=415%: n=4, 20%: n=2, 30%: n=2

2R 5 mm slow FR 5%: n=10, 7.5%: n=10, 10%: n=1015%: n=8, 20%: n=8, 30%: n=8

10R 5 mm slow FR 5%: n=5, 7.5%: n=4, 10%: n=415%: n=4, 20%: n=3, 30%: n=4

2R 2.5 mm shock freezing FR 5%: n=6, 7.5%: n=8, 10%: n=815%: n=8, 20%: n=9, 30%: n=8

10R 2.5 mm shock freezing FR 5%: n=5, 7.5%: n=5, 10%: n=515%: n=5, 20%: n=5, 30%: n=5

2R 5 mm shock freezing FR 5%: n=5, 7.5%: n=9, 10%: n=715%: n=10, 20%: n=10, 30%: n=9

10R 5 mm shock freezing FR 5%: n=4, 7.5%: n=4, 10%: n=415%: n=5, 20%: n=5, 30%: n=5

2R 2.5 mm 2stepA 5%: n=9, 7.5%: n=12, 10%: n=915%: n=10, 20%: n=10, 30%: n=10

10R 2.5 mm 2stepA 5%: n=9, 7.5%: n=10, 10%: n=1015%: n=10, 20%: n=10, 30%: n=10

2R 5 mm 2stepA 5%: n=15, 7.5%: n=15, 10%: n=1515%: n=12, 20%: n=14, 30%: n=9

10R 5 mm 2stepA 5%: n=, 7.5%: n=, 10%: n=1015%: n=10, 20%: n=10, 30%: n=10

2R 2.5 mm Toplyo 2stepA 5%: n=8, 7.5%: n=9, 10%: n=815%: n=8, 20%: n=8, 30%: n=8

10R 2.5 mm Toplyo 2stepA 5%: n=4, 7.5%: n=4, 10%: n=415%: n=4, 20%: n=4, 30%: n=3

2R 5 mm Toplyo 2stepA 5%: n=10, 7.5%: n=10, 10%: n=915%: n=10, 20%: n=9, 30%: n=9

10R 5 mm Toplyo 2stepA 5%: n=4, 7.5%: n=4, 10%: n=415%: n=4, 20%: n=4, 30%: n=3

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