Full Paper

1250

Crystallization Kinetics of BiodegradablePoly(butylene succinate) under Isothermal andNon-Isothermal Conditions

George Z. Papageorgiou, Dimitris S. Achilias,* Dimitris N. Bikiaris

Crystallization kinetics of the biodegradable and fast crystallizing poly(butylene succinate)is studied, under both isothermal and non-isothermal conditions. For the isothermal processat temperatures from 75 to 95 8C it is found that the Avrami model successfully describesthe transformation kinetics. The non-isothermal crystallization data obtained at a wide rangeof cooling rates from 0.1 to 20 8C �min�1 are treated with several models, which include themodified Avrami, the Ozawa, the combined Avra-mi-Ozawa, and the Tobin model. The Lauritzen-Hoffman parameters are estimated from isother-mal and non-isothermal differential scanningcalorimetry data, using different approximationsfor the growth rate and from the effective acti-vation energy equation proposed by Vyazovkinand Sbirrazzuoli. The multiple-melting behaviorhas been interpreted in the context of themelting–recrystallization–remelting phenomena.

9492908886848280787674727068-550

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-300

-250

-200

-150

-100

-50

0E

ffect

ive

Act

ivat

ion

Ene

rgy

(kJ/

mol

)

Temperature (oC)

1-20oC/min 0.1-0.5oC/min 0.5-1.0oC/min 1.0-5.0oC/min 3.5-10oC/min 7.5-20oC/min

Introduction

In recent years, biodegradable polymers have attracted

considerable attention as greenmaterials and biomaterials

in pharmaceutical, medical, and biomedical engineering

applications, including drug delivery systems, artificial

implants, and functional materials in tissue engineering.

Among synthetic polymers, aliphatic polyesters have

attracted considerable attention as they combine the fea-

G. Z. Papageorgiou, D. S. Achilias, D. N. BikiarisLaboratory of Organic Chemical Technology, Department ofChemistry, Aristotle University of Thessaloniki, GR-541 24,Thessaloniki, Macedonia, GreeceFax: þ30 23 1099 7769; E-mail: axilias@chem.auth.gr

Macromol. Chem. Phys. 2007, 208, 1250–1264

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

tures of biodegradability, biocompatibility, and physical or

chemical properties comparable with many traditional

and non-biodegradable polymers such as low-density

polyethylene (LDPE) and poly(propylene) (PP). Biodegrad-

able final products made from these polymers find a

variety of end uses especially as films for packaging,

sheets, bottles, and injection-molded products.[1,2]

To this direction, three polyesters of succinic acid were

prepared in our laboratory using ethylene, propylene, or

butylene glycol by the two-stage melt polycondensation

method, esterification, and polycondensation. The advan-

tage of these polyesters is that despite their low melting

point they have very high thermal stability (a decomposi-

tion temperature higher than 400 8C), which is similar to

aromatic polyesters.[3] Mathematical modeling of the

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

esterification reaction together with comparative biode-

gradability studies of the three polyesters, namely,

poly(ethylene succinate) (PESu), poly(propylene succinate)

(PPSu), and poly(butylene succinate) (PBSu) have already

been presented in previous publications.[4–6] Bikiaris

et al.[5] found that polymer crystallinity plays an

important role in the biodegradability of aliphatic

polyesters and that PBSu exhibited a lower biodegradation

compared to the other two polyesters because of its higher

crystallinity. It is, therefore, very important to study the

parameters that affect polymer crystallization for the

optimization of the processing conditions and the proper-

ties of the final product.

Research on the polymer crystallization process can be

carried out under isothermal or non-isothermal conditions.

Analysis of the overall crystallization rate under isother-

mal conditions is generally accomplished with the use of

the so-called Avrami equation. However, solidification

during polymer processing is always dynamic. Therefore,

several models for the non-isothermal crystallization have

also been reported.

PBSu is a fast crystallizing polymer that allows the

performance of experiments under various conditions. It

also shows large spherulites, and the analysis of its

spherulite growth rates can be effectively described by the

Lauritzen-Hoffman secondary nucleation theory.[6–9] The

crystalline structure of PBSu has been described by several

authors.[10–12] Chatani et al.[10] reported that the crystal

structure of the PBSu a-form is monoclinic with unit cell

dimensions a¼ 0.521 nm, b¼ 0.914 nm, c¼ 1.094 nm:

b¼ 1248, P21/n–C2h. The multiple melting behavior of

PBSu, mainly for samples crystallized under isothermal

conditions, was also studied recently.[7–9,13–15] Non-

isothermal crystallization of PBSu has been reported in a

note by Qiu et al.[16] Finally, the preparation and behavior

of blends of PBSu or related copolymers have also been

described in the literature by several authors.[17–29]

In this work, a detailed study was carried out on the

crystallization kinetics of PBSu under both isothermal and

non-isothermal conditions using differential scanning

calorimetry (DSC) and polarized light microscopy (PLM).

A comprehensive analysis is presented using different

macroscopic models in order to test the validity of the

equations usually elaborated to describe polymer crystal-

lization. The effective activation energy is determined

using isoconversional approaches. This work constitutes a

continuation of our previous studies on the crystallization

kinetics of several polyesters of industrial interest.[30,31]

Experimental Part

Succinic acid (SA, purum 99%), butylene glycol (purum 99%), and

tetrabutoxytitanium (TBT) used as catalyst (analytical grade) were

Macromol. Chem. Phys. 2007, 208, 1250–1264

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

purchased from Aldrich Chemical Co. Polyphosphoric acid (PPA)

used as heat stabilizer was supplied by Fluka. All other materials

and solvents used for the analytical methods were of analytical

grade.

PBSu was prepared by the two-stage melt polycondensation

method (esterification and polycondensation) in a glass batch

reactor.[29] In brief, the proper amount of succinic acid and

butylene glycol in a molar ratio of 1:1.1 and the catalyst (10�3 mol

TBT per mol SA) were charged into the reaction tube of the

polyesterification apparatus. The reactor with the reagents was

evacuated several times and filled with argon in order to

completely remove any oxygen. The reaction mixture was heated

at 190 8C under an argon atmosphere andwas stirred at a constant

speed (500 rpm). This first step (esterification) was considered to

be complete after the collection of the theoretical amount

of H2O, which was removed from the reaction mixture by

distillation and collected in a graduated cylinder.

In the second step of the polycondensation, PPA was added

(5� 10�4 mol PPA per mol SA), in order to prevent side reactions

such as etherification and thermal decomposition. A vacuum

(5.0 Pa) was applied slowly over a period of about 30 min, to avoid

excessive foaming and to minimize oligomer sublimation, which

is a potential problemduring themelt polycondensation. After the

polycondensation reaction was completed, the polyester was

easily removed, milled, and washed with methanol. Detailed

presentation of the synthesis of the samples can be found in a

previous paper.[29]

GPC analysiswas performed using aWaters 150CGPC equipped

with a differential refractometer as detector and three ultrastyra-

gel (103, 104, 105 A) columns in series. CHCl3 was used as the eluent

(1 mL �min�1) and the measurements were performed at 35 8C.Calibration was performed using polystyrene standards with a

narrow molecular weight distribution. The measurement gave a

number-average molecular weight of 6 800 g �mol�1 for the PBSu

sample.

Isothermal and non-isothermal crystallizations were per-

formed in a Perkin-Elmer Pyris 1 differential scanning calorimeter.

The instrument was calibrated using high purity indium and zinc

standards. Samples of 5 mg were used. Isothermal crystallization

runs were performed at temperatures (Tcs) between 75 and 95 8C.A fresh sample was initially melted at 150 8C for 5 min and then

cooled to the Tc at 200 8C �min�1. Tests were performed under a

nitrogen atmosphere and it was decided to melt for only 5 min

to prevent thermal degradation of the polyesters. For non-

isothermal crystallizations, after melting at 150 8C for 5 min the

sample was cooled to room temperature. A wide number of

cooling rates were applied, namely 0.1, 0.25, 0.5, 0.75, 1, 1.5, 2.5,

3.5, 5, 7.5, 10, 15, and 20 8C �min�1. An intracooler was connected

to the differential scanning calorimeter apparatus to achieve

reliability at high cooling rates over the whole temperature range

of the experiments.

Measurement of the radius growth rate of PBSu spherulites

under isothermal crystallization was investigated using a

polarizing light microscope (PLM) (Nikon, Optiphot-2) equipped

with a Linkam THMS 600 heating stage, a Linkam TP 91 control

unit, and a Jenoptic camerawith the respective softwarewas used

for HSM observations. For the crystallization experiments the

conditions were very similar as for the DSC ones, i.e., the samples

www.mcp-journal.de 1251

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

1252

were initially melted to 150 8C for 5 min, rapidly cooled to the

crystallization temperature and then held at that temperature to

crystallize. The subsequent growth of a particularly selected PBSu

spherulite was viewed between crossed polarizers and recorded

at appropriate time intervals. By plotting spherulite radius versus

time, the slope of the line, or the spherulitic growth rate G at

different temperatures can be obtained.

Results and Discussion

Isothermal Crystallization Kinetics

Crystallization of polymer melts is usually accompanied

by significant heat release, which can be measured by

differential scanning calorimetry (DSC). Based on the

assumption that the evolution of crystallinity is linearly

proportional to the evolution of heat released during the

crystallization, the relative degree of crystallinity, X(t), can

be obtained according to the following equation:

Rel

ativ

e de

gree

of c

ryst

allin

ity, X

(%

)

Figlizacalrep

Macrom

� 2007

XðtÞ ¼R t0 ðdHc=dtÞdtR10 ðdHc=dtÞdt

(1)

where dHc denotes the measured enthalpy of crystal-

lization during an infinitesimal time interval dt. The limits

t and 1 are used to denote the elapsed time during the

course of crystallization and at the end of the crystal-

lization process, respectively.

Isothermal crystallization of PBSu samples was per-

formed at various temperatures from 75 to 95 8C. In the

DSC traces (not shown here because of space limitations) it

was obvious that as the supercooling, i.e., the difference

between the melting and crystallization temperature,

decreases, the crystallization rate becomes slower and

1001010.10

20

40

60

80

100

Time (min)

75oC 80oC 85oC 90oC 95oC

ure 1. Evolution of relative crystallinity as a function of crystal-tion time for the PBSu at various temperatures. The geometri-points represent experimental data while the continuous lineresents the results of the theoretical Avrami model.

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

the exothermic peak becomes broader. Thus, the time to

reach the peak increases.

Subsequently, the relative crystallinity X(t) at time

t was determined using Equation (1). Figure 1 shows the

evolution of relative crystallinity with crystallization

time for the PBSu sample, at various temperatures. The

experimental data are represented using different geomet-

rical symbols. Notice that the x-axis is used in a log-

arithmic scale in order to easily distinguish the curves at

each temperature. S-Shaped curves were obtained, which

are consistentwith nucleation and growth processes. From

these curves, the half time of crystallization, t1/2, can be

directly determined as the time elapsed from the onset of

crystallization to the point where the crystallization is

half completed. All the t1/2 values are summarized in

Table 1.

From the data displayed in Table 1 it is apparent that the

t1/2 values increase almost exponentially as the crystal-

lization temperature is increased. In order to compare

crystallization rates we made use of the reciprocal

half-time of crystallization, 1/t1/2. A plot of this variable

as a function of Tc for PBSu is shown in Figure 2. Obvi-

ously, the crystallization rates decrease with increasing

temperature.

The total heat released for each crystallization tempera-

ture is also included in Table 1. As it can be seen, the

measured DH values are not much affected by the crystal-

lization temperature and are found to range between 78

and 90.5 J � g�1. Using the value of the equilibrium melting

enthalpy 210 J � g�1,[6] the degree of crystallinity was

deduced to range from 37 to 43%.

The application of different macrokinetic models to the

isothermal crystallization kinetics of various polymers has

been recently investigated by Supaphol et al.[32,33] For

the analysis of the isothermal crystallization, the most

Table 1. Half time of crystallization, total heat release and resultsof Avrami analysis for isothermal crystallization of the PBSusample.

Temp t1/2 DH n k K

-C min J � gS1 minSn minS1

75 0.77 80.1 5.03 2.389 1.189

77.5 0.95 82.1 3.90 0.790 0.941

80 1.51 82.5 3.02 0.193 0.580

82.5 1.93 85.7 3.00 0.094 0.455

85 3.60 78.2 2.72 0.021 0.239

87.5 6.80 83.9 2.97 2.28T 10S3 0.129

90 12.94 88.6 2.28 1.93T 10S3 0.064

92.5 20.84 90.5 2.69 0.19T 10S3 0.041

95 51.12 82.3 2.31 0.08T 10S3 0.017

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

9590858075

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1/t 1/

2, min

-1

T (oC)

Figure 2. Plot of the reciprocal half crystallization time versuscrystallization temperature for PBSu.

2.01.91.81.71.61.51.4-5

-4

-3

-2

-1

0

ln(t

max

)

107/(Tc

2 T)

Figure 3. Plot of the time at which the crystallization rate ismaximized versus 1/T2

cDT.

common approach is the so-called Avrami method.[34–36]

Accordingly, the relative degree of crystallinity, X(t), is

related to the crystallization time, t, according to:

Macrom

� 2007

XðtÞ ¼ 1� expð�ktnÞ or

XðtÞ ¼ 1� exp½�ðKtÞn�(2)

where, n is the Avrami exponent, which is a function of the

nucleation process, and k is the growth function, which is

dependent on nucleation and crystal growth. Since the

units of k are a function of n, Equation (2) can be written in

the composite–Avrami form using K instead of k (where

k¼Kn).[31–33] The Avrami equation in the simple form

represents unimpeded spherical crystal growth. However,

the sample does not reach complete crystallization as

required for the model. In order to estimate the Avrami

parameters, KAvrami and n, a non-linear curve-fitting

procedure based on the Levenberg-Marquardt method

was employed in this work. The estimated values of n and

k or K (i.e., k1/n) are summarized in Table 1. Using these

values for k and n, the relative crystallinity as a function of

time can be calculated using Equation (2). The theoretical

lines thus produced are also plotted in Figure 1 and

compared to the experimental data. As it can be seen, the

fit is very good, meaning that the Avrami Equation (2) is

adequate to describe the isothermal crystallization

kinetics of PBSu. Some minor deviations appear only for

data that correspond to very low (<5%) or very high (>95%)

relative degrees of crystallinity.

It is known that the value of n strongly depends on both

the mechanism of nucleation and the morphology of

crystal growth, and that ideally n would be an inte-

ger.[34–36] The n values found in the case of PBSu were in

the vicinity of 3 for the crystallization temperatures from

75 to 95 8C, and they should possibly be related with

three-dimensional growth. The Avrami parameters k andK

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

are indicative of the crystallization rate. Both of the

parameters decrease with increasing temperature.

On the basis of the Avrami and Turnbull-Fisher[37]

equations, Lin obtained the following relationship to

analyze the crystallization kinetics:[38]

ln tmax ¼ A� B

T2cDT

(3)

where A and B are constants, and DT is the degree of

supercooling (DT¼ T0m � Tc). Tc is the crystallization tem-

perature and tmax is the time at which the crystallization

rate ismaximized. The values for tmax can be obtained from

the heat flow curves.

Equation (3) was often used to test the possibility that

the primary stage of the isothermal crystallization of a

polymer could be described by the Avrami equation, by

drawing a plot of ln(tmax) versus 1/(T2cDT ). For PBSu the

respective plots are shown in Figure 3. The good linearity

(correlation coefficient R2¼ 0.995) indicated that the

Avrami equation could describe the primary stage of the

isothermal crystallization of PBSu. The values of A and B

were estimated to be 12.73 and 8.9� 107, respectively.

Spherulitic Growth Rate

It has been suggested that the kinetic data of isothermal

polymer crystallization can be analyzed using the

spherulitic growth rate in the context of the Lauritzen-

Hoffman secondary nucleation theory.[39,40] Accordingly,

the growth rate G is given as a function of the crystal-

lization temperature, Tc by the following bi-exponential

equation:

G ¼ G0 exp � U�

RðTc � T1Þ

� �exp � Kg

Tc DTð Þf

� �(4)

www.mcp-journal.de 1253

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

7.67.26.86.46.05.65.24.8

7

8

9

10

11

12

13

14

15

16

ln(G

) +

420

0/[R

(Tc-T

oo)]

105/(Tc

T f)

PLM iso-DSC/G~1/t

1/2

iso-DSC/G~1/t0.02

iso-DSC/G~kAvrami

noniso-DSC/G~kOzawa

1254

where, G0 is the pre-exponential factor, the first exponen-

tial term contains the contribution of the diffusion process

to the growth rate, while the second exponential term is

the contribution of the nucleation process. U� denotes the

activation energy that characterizes molecular diffusion

across the interfacial boundary between melt and crystals

and T1 is the temperature belowwhich diffusion stops. Kg

is a nucleation constant and DT denotes the degree of

undercooling (DT¼ T0m � Tc). f is a correction factor that is

close to unity at high temperatures and is given as f¼ 2Tc /

(T0m þ Tc). The equilibrium melting temperature, T0m, was

estimated to be equal to 133.5 8C using the Hoffman–

Weeks linear extrapolation.[6] The nucleation parameter,

Kg, is usually calculated from Equation (4) using the double

logarithmic transformation:

Figure 4. Lauritzen-Hoffmann-type plots for the PBSu resinobtained either from PLM measurements or from isothermal(iso-DSC) and non-isothermal DSC (noniso-DSC) using differentapproximations in place of the growth rate, G.

Tabpar

Me

PLM

DSC

DSC

DSC

DSC

DSC

DSC

DSC

DSC

DSC

a)Best

Macrom

� 2007

lnðGÞ þ U�

RðTc � T1Þ ¼ lnðG0Þ �Kg

Tc DTð Þf (5)

Plotting the left-hand side of Equation (5)with respect to

1/(Tc(DT ) f ), a straight line should appear that has a slope

equal to Kg. Critical break points that appear in such a plot,

identified by the change in the slope of the line, have been

attributed to regime transitions accompanied by morpho-

logical changes of the crystals formed (i.e., a change from

axialite-like to banded spherulite and non-banded spher-

ulite morphology).

In a previous study,[6] the spherulite growth rates were

obtained from PLM measurements and analyzed with

le 2. Values of the Lauritzen-Hoffman parameters, Kg and U� obtaenthesis denotes Kg estimated if the temperature range 80–95 8

thod used Approximation used for G

/iso None 1.88T 1

/iso G� 1/t1/2 2.64T 1

/iso G� 1/t0.02 2.40T 1

/iso G�KAvrami 2.67T 1

/non-iso G� 1/t1/2 2.80T 1

/non-iso G� 1/t0.02 2.40T 1

/non-iso G�KOzawa 3.30T 1

/non-iso G� (dX/dt)X¼ 0.02 2.60T 1

/non-iso Isoconversional

(all cooling-rate regions)

3.1T 1

/non-iso Isoconversional (cooling-rate

region 1–5 -C �minS1)

2

fit value.

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Equation (5). It was reported that using theWLF (Williams-

Landel-Ferry) values (i.e., U�¼ 4 200 cal �mol�1 (17 590

J � mol�1) and T1¼ Tg� 51.6 K) for PBSu, a regime II to

regime III transition was observable at approximately

96 8C. The Tg was measured using DSC and found equal to

�43.9 8C. The best fit gave a Kg¼ 1.9� 105 K2.[6] At

temperatures below 96 8C regime III is assumed.

Instead of using PLM measurements, several authors

have treated the isothermal crystallization rate data

obtained by DSC according to the Lauritzen-Hoffmann

analysis (Equation (5)).[33,41–46] The basic assumption used

ined from different approximations of G in Equation (4). The value inC is considered.

Kg U� Temp.range R2

K2 cal �molS1 -C

05 4 200 80–95 0.9952

05 (2.60T 105) 4 200 75–95 0.9972

05 (2.37T 105) 4 200 75–95 0.9956

05 (2.63T 105) 4 200 75–95 0.9968

05 (2.58T 105) 4 200 70–92 0.9940

05 (2.30T 105) 4 200 76–95 0.9904

05 (3.23T 105) 4 200 70–92 0.9964

05 (2.53T 105) 4 200 76–95 0.9962

05 (3.0T 105) 4 860a) 70–94 0.9070

.17T 105 1 860a) 78–87 0.9312

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

10090807060-5

-4

-3

-2

-1

0

1

0.1oC/min

0.5oC/min0.25oC/min

1.5oC/min1oC/min

3.5oC/min2.5oC/min

5oC/min

7.5oC/min

10oC/min

15oC/min

Hea

t Flo

w E

ndo

Up

(a.u

)

Temperature (oC)

20oC/min

Figure 5. DSC thermograms of non-isothermal crystallization forPBSu at various cooling rates.

Table 3. Characteristic data of non-isothermal crystallization ofPBSu.

a T0 Tp T1/2 t1/2 DH

for the evaluation of Gwas that the spherulite growth rate

is inversely proportional to the crystallization half-time,

G� 1/t1/2.[41] This approximation, although it is purely

empirical, has been widely used in the literature.[42–46]

Moreover, Dangseeyun et al.[33] proposed that bulk

crystallization rate parameters such as the Avrami

constant, should have a similar temperature dependence

to that of the growth rate. Therefore, G could be approxi-

mated by the Avrami constant, G�KAvrami. Finally, the

assumption that the spherulite growth rate is inversely

proportional to the time to achieve 2% relative crystal-

linity, G� 1/t0.02, was also used.[44] All the above three

approximations for G were employed in this work to

evaluate the nucleation parameter Kg. The respective plots

appear in Figure 4. It should be emphasized again here that

all these assumptions are purely empirical and require

further theoretical justification.

The results of the Lauritzen-Hoffman analysis are

summarized in Table 2. The Kg estimated assuming

G� 1/t1/2 was similar to that for G�KAvrami, but higher

than the value estimated from PLM data. A good

explanation for this result was given by Muller et al.[47]

Accordingly, the values obtained from DSC measurements

that deal with overall crystallization rates correspond to

both nucleation and growth, while those estimated from

PLMmeasurements are growth-only dependent. Therefore,

it seems that the process of nucleation and growth has a

larger energetic barrier than the process of spherulite

growth only. The increase in the estimation of Kg is almost

38%.

Moreover, it was examined if a better estimation of the

Kg values (i.e., that resembled those measured from PLM)

could be obtained if a different characteristic time was

used in place of G. Therefore, the assumption G� 1/t0.02was used. Although the value of Kg calculated was slightly

lower, it was still much higher than that obtained from

PLM measurements.

-C �minS1 -C -C -C min J � gS1

20 82.4 69.7 70.10 0.615 77.3

15 83.6 71.8 72.15 0.76 79.2

10 84.3 73.8 74.08 1.02 80.4

7.5 86.8 75.75 76.08 1.43 81.2

5.0 88.3 77.2 77.54 2.15 83.4

3.5 89.3 79.3 79.60 2.77 84.2

2.5 90.4 81.6 81.49 3.56 86.1

1.5 91.5 83.4 83.68 5.21 87.5

1.0 92.2 85.3 85.55 6.65 89.4

0.75 94.2 86.6 86.94 9.75 90.5

0.50 94.8 88.1 88.41 12.78 91.1

0.25 95.3 89.7 90.08 20.88 92.5

0.10 95.9 91.8 92.06 38.60 94.8

Non-Isothermal Crystallization Kinetics

From dynamic crystallization experiments, data for the

crystallization exotherms as a function of temperature can

be obtained, at each cooling rate, as one can see in Figure 5

for the crystallization on cooling of PBSu. The crystal-

lization exotherm becomes broader and it shifts to lower

temperatures with increasing cooling rate.

As it can be seen, many experiments at several cooling

rates were carried out. Values of some characteristic

parameters, such as, the temperature when crystallization

begins, T0, the peak temperature, Tp, the time and

temperature when the degree of crystallinity reached

50%, and the final value for the heat of crystallization are

shown in Table 3. As it is expected, with increasing cooling

Macromol. Chem. Phys. 2007, 208, 1250–1264

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

rate all the aforementioned characteristic temperatures

and the t1/2 values decrease, which means that the higher

the cooling rate the later the crystallization process starts

and is completed. In a previous study[6] we found that the

enthalpy of fusion of the 100% crystalline PBSu is about

210 J � g�1, which is close to the value of 200 J � g�1 that has

been reported in the literature.[7] Using the value 210 J � g�1

the crystallinity of the samples after crystallization during

cooling was found to range from 37 to 45%, which is close

to the values measured during isothermal crystallization

(37–43%).

From the data for the crystallization exotherms as a

function of temperature dHc/dT the relative crystallinity

as a function of temperature X(T) can be calculated as

www.mcp-journal.de 1255

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

9692888480767268640

20

40

60

80

100

20 15 10 7,5 5 3,5 2,5 1,5 1 0,75 0.5 0.25 0.1

Rel

ativ

e de

gree

of c

ryst

allin

ity (

%)

Temperature (oC)

Figure 6. Evolution of relative crystallinity as a function oftemperature for the PBSu resin during cooling at various coolingrates.

1001010.1

0

20

40

60

80

100

Rel

ativ

e de

gree

of c

ryst

allin

ity (

%)

Time (min)

20 15 10 7,5 5 3,5 2,5 1,5 1 0,75 0.5 0.25 0.1

Figure 7. Evolution of relative crystallinity as a function of time forthe PBSu at various cooling rates. The geometrical pointsrepresent experimental data while the continuous line representsthe results of the theoretical Avrami model.

1256

follows:

Macrom

� 2007

XðTÞ ¼R TcTo

ðdHc=dTÞdTR T1To

ðdHc=dTÞdT(6)

Table 4. Results of the Avrami analysis for non-isothermal crystal-lization of PBSu.

Cooling rate n Zt KAvrami Zc

-C �minS1 minSn minS1

20 5.40 9.723 1.5238 1.1204

15 5.30 2.959 1.2273 1.0750

10 4.85 0.636 0.9110 0.9558

7.5 5.50 0.096 0.6532 0.7318

5.0 5.34 0.0117 0.4345 0.4108

3.5 5.45 0.00268 0.3376 0.1841

where T0 denotes the initial crystallization temperature

and Tc and T1 the crystallization temperature at time t and

after the completion of the crystallization process,

respectively.

The evolution of the relative crystallinity as a function

of temperature at all different cooling rates appears in

Figure 6.

Once the X(T) is obtained, conversion into X(t) can be

carried out by transforming the temperature axis to

time axis using the transformation: t¼ (T0� T)/a.[42] The

relative crystallinity data thus obtained (X(t)), are illu-

strated in Figure 7 using geometrical points for the

different cooling rates used. All data gave S-type curves,

which is consistent for a nucleation and growth process.

Furthermore, for the analysis of the experimental

results, the modified-Avrami,[48] the Ozawa,[49] the com-

bined Avrami-Ozawa method developed by Liu et al.,[50,51]

and the Tobin method[52–54] were tested.

Modified Avrami Method

According to the modified Avrami method, the relative

degree of crystallinity, X, can be calculated from:[48]

2.5 5.27 0.00086 0.2617 0.0594

1.5 4.96 0.00020 0.1794 0.0034S4

X ¼ 1� expð�ZttnÞ ¼ 1� exp½�ðKAvramitÞn� (7)

1.0 4.58 0.00012 0.1392 1.2T 10

0.75 5.09 6.55T 10S6 0.0957 1.2T 10S7

0.50 4.87 2.95T 10S6 0.0733 8.7T 10S12

0.25 4.30 1.52T 10S6 0.0444 5.3T 10S24

0.10 3.67 1.09T 10S6 0.0236 2.3T 10S60

where Zt and n denote the growth rate constant and the

Avrami exponent, respectively. Again the composite–

Avrami method can be used with KAvrami¼ Z1=nt .

In order to estimate the parameters Zt (or KAvrami) and n

instead of using the well-known linear fitting transforma-

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

tion of Equation (7), a non-linear curve fitting procedure

was employed. In this way, theoretical model simulation

results fitted the experimental data over thewhole relative

degree of crystallinity range (i.e., for 0–100%). The

non-linear curve-fitting algorithm used was based on

the Levenberg-Marquardt method and the best fitting

values for the parameters are presented in Table 4. Using

the values thus obtained, the theoretical Equation (7) was

used and simulation results are compared to experimental

data for all cooling rates examined in Figure 7. In all

different samples and cooling rates the correlation

coefficient, R2, was greater than 0.999. It is obvious that

the modified Avrami method can describe the experi-

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

mental data verywell, at every cooling rate used. Although

physical meanings of Zt and n cannot be related to the

non-isothermal case in a simple way, their use provides

further insight into the kinetics of non-isothermal crystal-

lization.

Since the rate of non-isothermal crystallization depends

on the cooling rate, the following correction has been

proposed to obtain the corresponding rate constant at unit

cooling rate, Zc:[48]

Avr

ami r

ate

cons

tant

Figrat

Macrom

� 2007

log Zc ¼log Zta

(8)

Table 4 summarizes values of the Avrami parameters n,

Zt, KAvrami, and Zc calculated using Equation (8) for PBSu at

each cooling rate. The crystallization constant, Zt, increases

with increasing cooling rate, while the exponent n does

not seem to follow any trend. This is reasonable, since Ztmeasures the crystallization rate, which gets faster with

supercooling. The values of Zc become constant only at

high cooling rates (greater than 10 8C �min�1). Moreover, it

was observed that the values of Zc at cooling rates less than

1 8C �min�1 were very low, even as low as 10�60, which

means that this correction (Equation (8)) can not be applied

at low cooling rates. Therefore, we sought another

correlation of the Avrami rate constant KAvrami with

cooling rate. It was noticed that by plotting ln(KAvrami)

versus ln(a) a very good straight line was obtained

(Figure 8). Thus, the following correlation is proposed:

lnðKAvramiÞ ¼ C1 þ C2 lnðaÞ (9)

where C1 and C2 denote the intercept and the slope of the

straight line obtained, respectively.

According to the values estimated for PBSu the follow-

ing correlation could be proposed: KAvrami¼ 0.133� a0.8,

1010.1

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

Cooling rate (oC/min)

Zt

KAvrami

ure 8. Plot of Avrami rate constants as a function of the coolinge for PBSu non-isothermal crystallization.

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

with a correlation coefficient R2¼ 0.9975. This finding

allows prediction of KAvrami for all cooling rates if a few

experiments (let’s say 4) have been carefully carried out for

moderate cooling rates.

If instead of KAvrami the Zt values are used, then a

deviation from linearity at low cooling rates (below

1.5 8C �min�1) was observed.

Ozawa Analysis

According to the Ozawa theory the non-isothermal

crystallization process is the result of an infinite number

of small isothermal crystallization steps and the degree of

conversion at temperature T, X(T), can be calculated as:[49]

log[

-ln(1

-X)]

FiguPBS

ln½1� XðTÞ� ¼ � koðTÞam

(10)

where m is the Ozawa exponent that depends on the

dimension of crystal growth and ko is the cooling or

heating crystallization function. ko is related to the overall

crystallization rate and indicates how fast crystallization

occurs. Taking the double-logarithmic form of Equation (10),

it follows:

logf� ln½1� XðTÞ�g ¼ log kðTÞ �m log a (11)

By plotting log{�ln[1�X(T)]} versus log a, a straight line

should be obtained and the kinetic parameters, m and

ko can be achieved from the slope and the intercept,

respectively. Since the units of ko are a function of m,

Equation (10) can be written in a composite form using

KOzawa instead of ko (where ko¼KmOzawa). Indicative Ozawa

plots for crystallization of PBSu are shown in Figure 9. It is

important to note that using values that correspond to a

degree of crystallinity in the range between 5 and 95%, the

linearity in the plots is very satisfactory in the range from

70 to 95 8C. Because of the number of the available

1.41.21.00.80.60.40.20.0-0.2-0.4

-2.0

-1.5

-1.0

-0.5

0.0

0.5

log[α (oC/min)]

70oC 74oC 78oC 82oC 86oC

re 9. . Ozawa-type plots for non-isothermal crystallization ofu.

www.mcp-journal.de 1257

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

43210-1-3

-2

-1

0

1

2

3

ln (α

[K/m

in])

ln(t [min])

20% 40% 60% 80%

Figure 10. ln(a) versus ln(t) from the combined Avrami and Ozawaequation for non-isothermal crystallization of PBSu.

1258

experimental data very good straight lines were obtained

using this method. It seems that the model works well for

the specific polymer. In other cases of polymers where

extensive secondary crystallization occurs, the Ozawa

model could not describe non-isothermal crystallization,

but in general major problems were found for very low

(less than 5%) or very high (exceeding 95%) crystallinity

values, which induce curvature of the plots.[50] The

calculated values for the Ozawa exponent m seemed to

increase from 2 to 3.5 (see Table 5). Thus, the Ozawa

exponent was less than the Avrami exponent. Also the

Ozawa crystallization function KOzawawas found to increase

rather exponentially with the crystallization temperature.

This means that the crystallization rates increase exponen-

tially with temperature, as would be expected.

Mo’s Analysis

Non-isothermal crystallization is difficult to describe with

a single equation since there are a lot of parameters that

have to be taken into account simultaneously. Liu et al.[51]

proposed a different kinetic model by combining the

Ozawa and Avrami equations. The importance of this

method is that it correlates the cooling rate to temperature,

time, and morphology. As the degree of crystallinity was

related to the cooling rate, a, and the crystallization time t

or temperature T, the relation between a and t could be

defined for a given degree of crystallinity. Consequently,

combining Equation (7) and (10) derived a new kinetic

model for non-isothermal crystallization:

Tabliza

Tem

-C

70

72

74

76

78

80

82

84

86

88

90

92

Macrom

� 2007

lnðZtÞ þ n lnðtÞ ¼ ln½koðTÞ� �m lnðaÞ (12)

le 5. Results of the Ozawa analysis for non-isothermal crystal-tion of PBSu.

p. m ko KOzawa

(-C �minS1)m -C �minS1

2.27 691.83 17.942

2.56 660.69 12.635

2.60 273.53 8.6558

2.77 134.90 5.8893

2.84 54.702 4.0923

3.07 25.293 2.8642

3.07 6.8865 1.8729

3.09 1.7906 1.2072

3.15 0.4699 0.7866

3.55 0.0955 0.5160

2.35 0.0302 0.2255

2.03 0.0069 0.0867

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

By rearrangement at a given crystallinity and solving for

the cooling rate, Equation (12) becomes:

Tabon

Par

b

ln(F

lnðaÞ ¼ ln½FðTÞ� � b lnðtÞ (13)

where F(T )¼ [ko(T )/Zt]1/m refers to the value of the cooling

rate chosen at unit crystallization time, when the system

has a certain degree of crystallinity, b is the ratio of the

Avrami exponent to Ozawa exponents, i.e., b¼n/m.

According to Equation (13) at a given degree of crystallinity

the plot of ln(a) against ln(t) will give a straight line with

an intercept of ln[F(T )] and a slope of �b. As it is shown in

Figure 10, plotting ln(a) versus ln(t), at a given degree of

crystallinity, a linear relationship was observed (correla-

tion coefficient R> 0.998). The values of F(T) and the slope b

are listed in Table 6. The F(T) values increased with the

relative degree of crystallinity. These equations success-

fully described the non-isothermal crystallization process

of PP/silica nanocomposites.[43]

Tobin Analysis

The Avrami model is suitable for describing the early

stages of crystallization. Complications arise from the

effects of growth site impingement and secondary crystal-

lization process, which were disregarded for the sake of

simplicity in the original derivation of the model. Tobin

proposed a theory for crystallization with growth site

le 6. Values of b and F(T) versus degree of crystallinity basedMo’s treatment for PBSu.

ameter Relative degree of crystallinity

2% 20% 40% 60% 80%

1.38 1.28 1.26 1.25 1.24

) 1.434 2.18 2.37 2.51 2.63

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

80

100

ity (

%)

20 15 10 7,5

impingement.[52–54] According to this approach, the

relative crystallinity function of time X(t) can be expressed

in the following form:

Tabliza

Coo

-C �

20

15

10

7.

5.

3.

2.

1.

1.

0.

0.

0.

0.

40

60

e of

cry

stal

lin 5 3,5 2,5 1,5 1 0,75 0.5

Macrom

� 2007

XðtÞ ¼ ðKTtÞnT

1þ ðKTtÞnT(14)

1001010.1

0

20

Rel

ativ

e de

gre

Time (min)

0.25 0.1

Figure 11. Evolution of relative crystallinity as a function of timefor the PBSu at various cooling rates. The geometrical pointsrepresent experimental data while the continuous line the resultsof the theoretical Tobin model.

where KT and nT are the Tobin crystallization rate constant

and the Tobin exponent, respectively. The exponent nT

need not be an integer and is governed by different types

of nucleation and growth mechanisms.

In order to estimate the parameters KT and nT a non-

linear curve fitting procedure based on the Levenberg-

Marquardt method was employed. In this way, the

theoretical model Equation (14) was used to fit the

experimental data over the whole relative degree of

crystallinity range (i.e., for 0–100%). The best fitting values

for the parameters KT and nT are presented in Table 7.

Using these values the theoretical Equation (14) was used

and simulation results are compared to experimental data

for all cooling rates examined in Figure 11. The Tobin

exponent was found to increase with cooling rate from 5.7

to 8.1 and it was always higher compared to the Avrami

exponent. In the plots of Figure 11 it is obvious that there

exists a negative deviation from the experimental data for

very low or very high degrees of crystallinity, since it

predicts lower crystallinity values than the experimental

ones. This proves that there is an overestimation of the

spherulite impingement in the case of PBSu. Maybe it is

because of the small nucleation density of PBSu, which

was observed during the course of the PLM experiments, in

le 7. Results of the Tobin’s analysis for non-isothermal crystal-tion of PBSu.

ling rate nT KTobin

minS1 minS1

8.12 1.6573

7.95 1.337

7.30 1.000

5 8.20 0.7093

0 7.98 0.4732

5 8.20 0.3668

5 7.94 0.2855

5 7.52 0.1957

0 6.95 0.1537

75 7.71 0.1046

50 7.52 0.0803

25 6.73 0.0492

10 5.74 0.0267

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

comparison to other polyesters, which have also been

studied in our lab, such as poly(ethylene terephthalate)

(PET), poly(ethylene naphthalate) (PEN), poly(butylene

terephthalate) (PBT), and poly(butylene naphthalate)

(PBN), which posses semi-rigid macromolecular chains

because of the presence of aromatics.

Effective Activation Energy of Non-IsothermalCrystallization

Apart from the aforementioned macroscopic kinetic

models it is interesting to also evaluate the effective

activation energy, DE, for a non-isothermal crystallization

process. Several mathematical procedures have been

proposed in the literature for the calculation of DE,

considering the variation of the peak temperature with

the cooling rate, a,[50] such as the Kissinger’s method

which has been widely applied to evaluate the overall

effective activation energy. However, these methods have

been formulated for heating experiments (i.e., positive

values of a). Vyazovkin et al.[55,56] have demonstrated that

dropping the negative sign for a is a mathematically

invalid procedure that generally makes the Kissinger

equation inapplicable to the processes that occur on

cooling. Moreover, the use of this invalid procedure may

result in erroneous values of the effective energy barrier,

DE. The use of multiple heating rate methods such as

isoconversional methods is recommended.[56,57] An iso-

conversional method can, in principle, be applied to

non-isothermal crystallizations to evaluate the depen-

dence of the effective activation energy on conversion and

temperature. Such dependencies have been quite helpful

in detecting and elucidating complex kinetics in poly-

meric systems. The differential isoconversional method of

www.mcp-journal.de 1259

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

-300

-250

-200

-150

-100

on e

nerg

y (k

J/m

ol)

1-20oC/min 1-5oC/min 3.5-10oC/min

1260

Friedman[58] and the advanced integral isoconversional

method of Vyazovkin[59] are the most appropriate. In this

investigation themethod of Friedmanwas used. According

to the differential isoconversional method of Friedman,

different effective activation energies are calculated for

every degree of crystallinity from:

ln(d

X/d

t)

Figcrycry

-450

-400

-350

ectiv

e ac

tivat

i

7.5-20oC/min 0.5-1oC/min 0.1-0.5oC/min

Macrom

� 2007

lndX

dt

� �X;i

¼ Const� DEXRTX;i

(15)

1.00.80.60.40.20.0

-500Eff

Relative degree of crystallinity

Figure 13. Dependence of the effective activation energy on therelative degree of crystallinity (isoconversional analysis) at differ-ent cooling-rate regions.

-200

-150

-100

-50

0

rgy

(kJ/

mol

)

PLM

G~1/t0.02

G~1/t0.5

Best fit to

where dX/dt is the instantaneous crystallization rate as a

function of time at a given conversion X, DEX is the

effective activation energy at a given conversion X, TX,i is

the set of temperatures related to a given conversion X at

different cooling rates, ai and the subscript i refers to every

individual cooling rate used.

According to this method, the X(t) function obtained

from the integration of the experimentally measured

crystallization rates is initially differentiated with respect

to time to obtain the instantaneous crystallization

rate, dX/dt. Furthermore, by selecting appropriate degrees

of crystallinity (i.e., from 2 to 98%) the values of dX/dt at a

specific X are correlated to the corresponding crystal-

lization temperature at this X, i.e., TX. By then plotting the

left-hand side of Equation (15) with respect to 1/TX a

straight line must be obtained with a slope equal to DEX/R.

Indicative plots appear in Figure 12. For every X for cooling

rates greater than 1 8C �min�1 almost linear curves were

obtained, whereas at lower cooling rates a departure from

linearity appeared. It was, therefore, decided to examine

different ranges of cooling rates and compare the results.

The effective activation energy thus obtained was subse-

quently plotted as a function of the relative degree of

crystallinity, as one can see in Figure 13. It is obvious that

for low cooling rates very small negative values (large

0.002920.002880.002840.002800.002760.00272

-4

-3

-2

-1

0

1

2

1/T (K-1)

10% 20% 40%

ure 12. Plot of ln(dX/dt) versus 1/T for the PBSu non-isothermalstallization at different cooling rates and relative degrees ofstallinities 10, 20, and 40%.

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

absolute values) were obtained. It should be mentioned

here that results presented at cooling rates less than

1 8C �min�1 are indicative since the sensitivity of the DSC

at these cooling rates is rather low. However, they were

included in Figure 13 in order to expand the temperature

range covered and because they worked well in the calcu-

lation of the Avrami rate constant (Figure 8). From the

other side, when using high cooling rates the problem of

thermal lag should be considered, which is important

for fast crystallizing polymers.[31] Therefore, from the

results of Figure 13, it seems that the cooling-rate region

9492908886848280787674727068-550

-500

-450

-400

-350

-300

-250

Effe

ctiv

e A

ctiv

atio

n E

ne

Temperature (oC)

1-20oC/min 0.1-0.5oC/min 0.5-1.0oC/min 1.0-5.0oC/min 3.5-10oC/min 7.5-20oC/min

G~KOzawa

G~KAvrami

Best fit withall cooling rates

1-5oC/min

Figure 14. Effective activation energy as a function of tempera-ture calculated using the method of Friedman and differentcooling-rate regions (geometrical points), as well as Equation (17)with Kg values estimated from: PLM isothermal measure-ments (- - -), DSC isothermal measurements with the approxi-mation G� 1/t1/2 (-. -), G� 1/t0.02 (. . .), G� KAvrami (- - - -), and DSCnon-isothermal measurements with the approximationG�KOzawa (-..). The continuous line and the (-.-) line representthe best fit to the geometrical points using all cooling-rateregions and that of 1–5 8C �min�1, respectively.

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

from 1 to 5 8C could be used as the best choice. In addition,

results in the cooling-rate region from 1 to 10 8C �min�1 did

not differ significantly.

If an average temperature for the corresponding X is

evaluated, DEX can then be plotted versus temperature.

Such plots, for different cooling-rate sets, appear in

Figure 14. Negative values for DE are always observed.

The results in the region usually used in the literature (i.e.,

from 1 to 15 8C �min�1) are not influenced greatly by the

cooling rate. However, expanding the temperature region

using slower cooling rates, very different values of DEXwere estimated. It should be mentioned again that these

results are rather indicative and need further investigation

for other polymers.

According to Vyazovkin[60,61] themost attractive feature

in applying the isoconversional methods to DSC data is

that the resulting DEX dependencies can be utilized for

estimating the parameters of the Lauritzen-Hoffman

theory. Extensive experimental measurements by Toda

et al.[62] demonstrate that the logarithmic derivative of the

microscopic growth rate is equivalent to the logarithmic

derivative of the overall crystallization rate, F, according

to:

Macrom

� 2007

d lnðGÞdT�1

¼ d lnðFÞdT�1

(16)

where F¼DhSG with Dh the volumetric heat of crystal-

lization and S the total area of the growth surface.

Equation (16) and (4) have been used by Vyazovkin and

Sbirrazzuoli[60] to derive the temperature dependence of

the effective activation energy of the growth rate as

follows:

DE ¼ �RdðlnGÞdð1=TÞ

¼ U� T2

ðT � T1Þ2þ KgR

ðT0mÞ

2 � T2 � T0mT

ðT0m � TÞ2T

(17)

The validity of Equation (17) has been recently tested by

Achilias et al.[63] using different polymers. The tempera-

ture dependence of the effective activation energy derived

from DSC data (e.g., from the method of Friedman) can be

fit to Equation (17) to evaluate the Lauritzen-Hoffman

parameters Kg and U�. It is obvious that the inverse also

holds, meaning that if Kg and U� are known, the

temperature dependence of DE can then be calculated

from Equation (17). Thus, using the Kg values reported

previously for isothermal crystallization data (Table 2) in

Equation (17), the effective activation energy can be

calculated for each case. The plots are illustrated in

Figure 14 as continuous lines. It seems that the curves

obtained when using the assumptions: G� 1/t1/2 or

ol. Chem. Phys. 2007, 208, 1250–1264

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

G�KAvrami are somehow close to the data points

estimated from the Friedman method in the cooling-rate

region 1–5 8C �min�1. Therefore, results from the Friedman

method at this specific cooling-rate region were used

together with Equation (17) to estimate the Lauritzen-

Hoffman parameters, Kg andU�. The Levenberg-Marquardt

method was used again as a non-linear fitting algorithm.

The best fit values for Kg andU�were estimated to be equal

to 2.17� 105 K2 and 1 860 cal �mol�1, respectively (Table 2).

This Kg value is close to the one estimated from PLM

measurements although the U� is much lower.

Furthermore, results from the Friedman method at all

different cooling-rate regions were used together with

Equation (17) to estimate the Lauritzen-Hoffman para-

meters. The Levenberg-Marquardt method was used

again as a non-linear fitting algorithm. The best fit values

forKg andU�were estimated to be equal to 3.1� 105 K2 and

4 860 cal �mol�1, respectively (Table 2). In this test, the

U� value estimated is close to the constant value of

4 200 cal �mol�1 used in the isothermal crystallization

experiments, while the Kg is much higher. For a U� value

fixed at 4 200 cal �mol�1 the resultant Kg was estimated

equal toKg¼ 3� 105 K2, which is larger than that from PLM

measurements, and in general than all others from

isothermal data.

Finally, in order to estimate the Kg using non-isothermal

crystallization data obtained from DSC, a modified

Lauritzen-Hoffman model was used by substituting Tcwith Toþ at:

lnGþ U�

RðTo þ at � T1Þ

¼ lnGo �Kg

ðTo þ atÞ½Tom � ðTo þ atÞ�f (18)

As in the case of isothermal DSC measurements, the

approximation that G is inversely proportional to the time

to achieve 50 and 2% relative degree of crystallinity, i.e.,

G� 1/t1/2 and G� 1/t0.02, respectively, were tested. The

results for Kg were in good agreement with the corre-

sponding results from isothermal DSC data.

Moreover, the approximation G�KOzawa was tested

with the parameters taken from the Ozawa analysis for

non-isothermal crystallization. This was done, since the

Ozawa constant,KOzawa, is a function of temperature and is

related to the overall crystallization rate. The obtained

Lauritzen-Hoffman-type plot appears in Figure 4. The best

fit gave Kg¼ 3.3� 105 K2 for a fixed U� ¼ 4 200 cal �mol�1.

These values were very close to those estimated when the

isoconversional analysis of Friedman was used with all

cooling-rate regions.

Since, as it was reported previously, in the isothermal

crystallization the above approximations are empirical, a

www.mcp-journal.de 1261

G. Z. Papageorgiou, D. S. Achilias, D. N. Bikiaris

13012011010090

T

a) b)

c=95oC

Tc=92.5oC

Tc=90oC

T=87.5c

oC

Tc=85oC

Tc=82.5oC

Tc=80oC

Tc=77.5oC

Tc=75oC

Tc=72.5oC

Nor

mal

ized

Hea

t Flo

w (

W/g

) E

ndo

Up

Temperature (oC)

130125120115110105100959085

20o

C/min

10o

C/min

5o

C/min

3.5o

C/min

2.5o

C/min

1.5o

C/min

0.75o

C/min

0.5o

C/min

0.25o

C/min

0.1o

C/min

Nor

mal

ized

Hea

t Flo

w (

J/g)

End

o U

p

Temperature (oC)

Figure 15. DSC traces on heating for PBSu samples crystallized a) isothermally at the indicatedtemperatures, and b) on cooling at different cooling rates.

1262

more theoretically sound

approximation for G was used

next. This is to assume G

directly proportional to the

overall crystallization rate dX/

dt at a specific relative degree of

crystallinity. As such the 2%

was selected, i.e., G� (dX/

dt)X¼ 0.02, since at the early

stages of non-isothermal crys-

tallization it is supposed that

the linear spherulite growth

rates could be effectively approx-

imated and spherulite impinge-

ments have not occurred yet.

The Kg value thus estimated

(2.6� 105 K2) is similar to corre-

sponding values calculated from

other approximations using

non-isothermal data and are

certainly again larger than that

from PLM measurements.

Melting

Finally, the melting behavior after non-isothermal crystal-

lization was studied. The heating scans recorded at a rate

of 20 8C �min�1, showed a multiple melting behavior. This

was similar to what was observed for isothermally

crystallized PBSu.[29] Figure 15 shows the DSC traces for

both cases. Though the non-isothermal crystallization

occurred over a range of temperatures, which is rather

wide for fast cooling rates and quite narrow for slow ones,

most of the crystallization in every case happened at about

the peak temperature Tp. Thus, it would be reasonable to

suppose that the resulting morphology is similar to that

generated during an isothermal crystallization at a Tcequal to the respective Tp observed in the cooling scan. For

example, the peak temperature observed on cooling at

0.25 8C �min�1 was 89.7 8C. The subsequent heating

showed a melting behavior that was very similar to that

of the isothermally crystallized sample at 90 8C, which

means that in both cases a triple melting was observed

with the peak temperatures being essentially the same. A

difference, however, is that in general in themelting traces

after isothermal crystallization, the low temperature peak

before the recrystallization exotherm was always larger

than in the corresponding melting traces after non-

isothermal crystallization. Also, in the case of the

non-isothermally crystallized samples, the recrystalliza-

tion exothermic peak was broader. These, observations

prove that after non-isothermal crystallization the result-

ing morphology is always more defective, and extended

Macromol. Chem. Phys. 2007, 208, 1250–1264

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

crystal perfection processes take place during the sub-

sequent heating scan. In our previous paperwe interpreted

the multiple melting behavior of isothermally crystallized

PBSu as a continuous melting–recrystallization–remelting

process.[6] It seems that this should most probably be

adopted for both isothermally and non-isothermally

crystallized samples. The same was supposed by Yasuniva

and Satou who studied the multiple melting behavior of

non-isothermally crystallized PBSu samples with higher

molecular weight.[14] In this study it seems that the use of

a sample with lower molecular weight resulted in three

instead of two melting peaks because of more pronounced

recrystallization.

Conclusion

In this investigation, the isothermal and non-isothermal

crystallization kinetics of biodegradable poly(butylene

succinate) was examined in detail. A comprehensive

analysis was presented using different macroscopic

models in order to test the validity of the equations

usually elaborated to describe polymer crystallization.

From the results it can be concluded that the isothermal

process can be successfully described by the Avrami

equation, while the modified-Avrami, the Ozawa and the

combined Avrami-Ozawa methods were adequate in fit-

ting the experimental data obtained during non-isothermal

crystallization over a wide range of cooling rates from

0.1 to 20 8C �min�1. Furthermore, the Lauritzen-Hoffman

DOI: 10.1002/macp.200700084

Crystallization Kinetics of Biodegradable . . .

parameters were estimated from isothermal and non-

isothermal DSC data, using different approximations for the

growth rate, as well as from the effective activation energy

equation proposed by Vyazovkin and Sbirrazzuoli. It was

found that Kg obtained from PLM measurements is always

lower than that estimated from overall crystallization rates

since in the latter technique bothnucleation and growth are

included instead of only growth considered in the former.

From the effective activation energy calculations it was

found that the best set of cooling rates is from 1 to

5 8C �min�1, which combines satisfactory sensitivity of the

instrument and avoidance of the thermal lag. Finally, the

melting behaviors of isothermally and non-isothermally

crystallized samples were studied. In both cases, similar

multiple meltings were observed and attributed to

sequential melting–recrystallization–remelting phenom-

ena taking place during heating scans.

Received: February 12, 2007; Revised: May 2, 2007; Accepted:May 2, 2007; DOI: 10.1002/macp.200700084

Keywords: biodegradable; crystallization; isoconversional analy-sis; poly(butylene succinate); spherulite growth

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DOI: 10.1002/macp.200700084