Dark chocolate’s compositional effects revealed by oscillatory rheology

ORIGINAL PAPER

Dark chocolate’s compositional effects revealed by oscillatoryrheology

Kasper van der Vaart • Frederic Depypere •

Veerle De Graef • Peter Schall • Abdoulaye Fall •

Daniel Bonn • Koen Dewettinck

Received: 14 November 2012 / Revised: 11 February 2013 / Accepted: 17 February 2013 / Published online: 21 March 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract In this study, two types of oscillatory shear

rheology are applied on dark chocolate with varying vol-

ume fraction, particle size distribution, and soy lecithin

concentration. The first, a conventional strain sweep,

allows for the separation of the elastic and viscous prop-

erties during the yielding. The second, a constant strain rate

sweep, where the strain rate amplitude is fixed as the fre-

quency is varied, is analyzed to obtain Lissajous curves,

dissipated energy, and higher order nonlinear contributions.

It is shown that chocolate exhibits complex nonlinear

behavior, namely shear thinning, shear thickening, and

strain stiffening. The effects on this behavior related to

volume fraction, particle size distribution, and lecithin

concentration are investigated, and comparison with simple

monodisperse hard-sphere suspensions is made.

Keywords Oscillatory rheology � Chocolate � Yielding �Viscoelastic properties � Flow behavior � LAOS � Stress

decomposition

Introduction

Chocolate is an important commodity foodstuff. The flavor

of chocolate comes from several processing steps, of which

the most important are as follows: The harvest, fermenta-

tion, and drying of cocoa seeds followed by roasting of the

cocoa and conching of the chocolate [1]. The perceived

taste is determined by the flow properties of the chocolate

[2]. This is one reason why understanding studying

chocolate rheology is of major importance for chocolate

makers. The other reasons are as follows: production

efficiency, economics, and final product characteristics and

applicability.

The flow behavior of chocolate is determined by its

composition, structure, and processing [3–6]. Challenges

lie in controlling these factors in such a way as to ‘‘design’’

a chocolate suited for specific applications (e.g., enrobing,

panning, molding). Despite ongoing research since the

earliest studies of Steiner [7] and Chevalley [8] to more

intense research efforts in the past years [9–15], chocolate

flow behavior and the influence of ingredient composition

are still imperfectly understood.

Dark chocolate is a suspension of solid sugar and cocoa

particles, typically 30 lm in size, dispersed in a continuous

cocoa butter phase [1]. The cocoa butter phase, having a

mass percentage varying between 25 and 36 %, typically

melts when heated above approximately 32 �C. The exact

melting temperature can differ depending on the geo-

graphical origin of the cocoa butter. A surfactant, tradi-

tionally soy lecithin, is mostly added. Its role is to restrict

K. van der Vaart � F. Depypere � V. D. Graef � K. Dewettinck (&)

Laboratory of Food Technology and Engineering, University

of Ghent, Coupure Links 653, 9000 Ghent, Belgium

e-mail: [email protected]

K. van der Vaart

e-mail: [email protected]

Present Address:K. van der Vaart

LHE, Ecole Polytechnique Federale de Lausanne,

Lausanne, Switzerland

Present Address:F. Depypere

Barry Callebaut Belgium N.V, Lebbeke-Wieze, Belgium

P. Schall � A. Fall � D. Bonn

Van der Waals-Zeeman Institute, University of Amsterdam,

Science Park 904, 1098 XH Amsterdam, The Netherlands

123

Eur Food Res Technol (2013) 236:931–942

DOI 10.1007/s00217-013-1949-2

the hydrophilic sugar particles from aggregating and to aid

flow by lubrication. One of the most fascinating aspects of

chocolate, from a rheological perspective, is that small

changes in composition can dramatically change the flow

properties [11].

Liquid chocolate, being non-Newtonian and shear thin-

ning, is traditionally characterized by two parameters: a

yield stress and a viscosity. The viscosity is usually

determined by fitting the Casson model [16] or the Wind-

hab model [17] to a steady-state flow curve [18]. The latter

being recommended by the International Confectionery

Association [19]. The Herschel–Bulkley model for non-

Newtonian fluids has also been used to characterize choc-

olate rheology [20].

The Casson model in particular provides a good fit to the

data at strain rates above 5 s-1 [13]. At lower strain rates,

the Casson model is not capable of describing the data

well. Therefore, the yield stress, determined by extrapo-

lating a fit to zero strain rate, is not accurate [15]. In

general, it has been shown that determining a yield stress is

difficult and even erroneous [21–25]. Moreover, it is

arguable that a single yield stress description of chocolate

is a too large simplification and that attaining a deeper

understanding of the yielding behavior itself might prove

more useful.

The objective of this paper is to use oscillatory rheol-

ogy to investigate the yielding behavior of chocolate. In

oscillatory rheology, both the elastic and viscous proper-

ties of a material can be examined simultaneously by

applying an oscillatory strain cðtÞ ¼ c0 sin xt: An oscilla-

tory strain automatically imposes a strain rate _cðtÞ ¼c0x cos xt: Here, x is the applied oscillation frequency, c0

is the strain amplitude, and t is time. The applied strain

results in a stress response, allowing the material’s elastic

and viscous properties to be determined from the com-

ponents of the stress in phase with c(t) and _cðtÞ; respec-

tively. The elastic properties are characterized by the

storage modulus G0 and the viscous properties by the loss

modulus G00. The elastic and viscous properties of choc-

olate are greatly influenced by its composition. Therefore,

volume fraction, particle size distribution, and lecithin

concentration are varied and their influence on the yield-

ing behavior is studied.

Oscillatory rheology has already been applied to choc-

olate [12–15]. Recently, De Graef et al. [15] showed that

oscillatory shear provides a viable way of studying the

microstructural arrangement of chocolate. They measured

the complex modulus G* = G0 ? iG00 as a function of

increasing stress to resolve a yield stress. In the study

presented here, the storage and loss moduli, instead of the

complex modulus, are measured, in order to determine both

the elastic and viscous component in the yielding behavior

of chocolate.

Materials and methods

Sample preparation

Chocolate samples were produced on a 4 kg batch labo-

ratory production line available at UGent Cacaolab

(http://www.cacaolab.be). The raw materials are commer-

cially available cocoa mass, cocoa butter, sugar, and soy

lecithin. Cocoa mass, sugar, and part of the cocoa butter

were mixed for 10 min using a Planetary mixer VEMA

BM30/20 (Vemaconstruct, NV machinery Verhoest, Ize-

gem, Belgium). The mixture was then refined [1] with an

Exakt 80S 3-roll refiner (Exakt Apparatebau GmbH & Co.,

KG, Norderstedt, Germany). The refined product was fed

to a Buhler ELK’olino conche (Richard Frisse GmbH, Bad

Salzuflen, Germany) and dry conched [1] for five hours at

85 �C and 800 rpm. At the start of wet conching [1], soy

lecithin and the remaining cocoa butter were added. Wet

conching lasted 30 min at 60 �C and 1,600 rpm, after

which the chocolate was stored at room temperature.

The particle size distribution of the solid content (sugar

and cocoa solids) was determined by dynamic light scat-

tering (Malvern Mastersizer S), see Fig. 1. Approximately

0.3 g of refined chocolate was dispersed in vegetable oil.

To ensure particles were independently dispersed, ultra-

sonic dispersion was done for 20 min.

To characterize a size distribution with a single value,

the D90 diameter [26] is used, which is the diameter below

which 90 % of the distribution lies. The D90 diameter is

chosen because it gives a useful representation of the

amount of larger particles present, which relates to the

mouthfeel of chocolate [1].

Fig. 1 Volume based particle size distributions of the studied

samples and of the sugar used for production. The curve with

D90 = 21 lm (triangles) belongs to the one single sample that is used

in all three sets (with a volume fraction of 0.62 and lecithin

concentration of 0.6 %). The samples with D90 of 18, 21, and 26 lm

have a bimodal distribution, whereas the samples with D90 of 34 and

42 lm have a trimodal distribution

932 Eur Food Res Technol (2013) 236:931–942

123

http://www.cacaolab.be

Samples

Three sets of chocolate samples were produced and studied

as follows: Set I varied in the solids—sugar and cocoa—

volume fraction, set II in the particle size distribution, and

set III in the lecithin concentration.

Set I consists of six samples with volume fractions: 0.53,

0.60, 0.62, 0.65, 0.68, and 0.71. Each sample has a D90

diameter of 21 lm and a lecithin concentration of 0.6 %.

Set II is produced by modifying the refining conditions

(gap size, number of passes) during production. Set II

consists of five samples, which have a D90 of approxi-

mately 18, 21, 26, 34, and 42 lm. The volume fraction is

0.62, and lecithin concentration is 0.6 %. Set III consists of

five samples with varying lecithin concentration: 0.15,

0.30, 0.45, 0.60, and 0.75 %. The volume fraction is 0.62

and D90 is 21 lm. The production ingredients for all the

samples are given in Table 1, and the exact composition is

given in Table 2.

Traditionally, in chocolate research, the mass percentage

of cocoa butter is taken as a material measure, which

amounts to the free and bound cocoa butter combined. The

free cocoa butter (added during production) is determinant

for the flow behavior. On the other hand, the bound cocoa

butter, residing inside the cocoa particles, is not. One

downside of using the mass percentage is that depending

on the ratio of free to bound cocoa butter the flow prop-

erties change, while the cocoa butter mass percentage

remains constant. We argue that volume fraction (solids

volume divided by total volume) is a material property

better suited to be related to flow behavior, because it takes

into account only the free cocoa butter.

An approximation of the volume fraction of the choc-

olate samples is determined from the total free cocoa butter

mass mfreeCB, the sugar mass mS, and cocoa solids mass

mCS. Here, the total free cocoa butter content corresponds

to the non-bound cocoa butter in the cocoa mass plus the,

during production, added cocoa butter. The cocoa solids

mass corresponds to the solids mass in the added cocoa

mass. These particles contain bound fat that does not

contribute to the flow behavior. The volume fraction/ is

calculated using the masses and material densities:

/ ¼ solids volume

total volume¼ mCS=qCS

mfreeCB=qCB þmCS=qCS þmS=qS

ð1Þ

The densities of the materials are as follows: sugar

1,426 kg m-3, cocoa solids 1,350 kg m-3, cocoa butter

892 kg m-3 (at 40 �C), lecithin 893 kg m-3 [1, 13]. The

free cocoa butter content in the cocoa mass is determined by

dissolving the free cocoa butter with diethyl-ether [27]. An

amount of 50 g cocoa mass was mixed with 200 ml diethyl-

ether for 1 min and left to rest for 10 min. The mixture was

filtrated through a filter paper together with 10 g of Na2SO4,

which is added to capture moisture. The filtrate was put in a

rotary evaporator overnight at 60 �C, to evaporate the

diethyl-ether. The remaining cocoa butter was weighed.

The free cocoa butter content in the cocoa mass (total cocoa

butter content of 54.4 %) was found to be 34.3 %. This is

the minimum amount of free cocoa butter in the final

chocolate. It is quite likely that during production additional

cocoa butter is released from the cocoa solids depending on

the effects of temperature, time, and shear.

In addition to the chocolate samples, measurements are

taken on a monodisperse, dense hard-sphere suspension

Table 1 Ingredients (added during production) of the chocolate

samples given for each volume fraction: cocoa butter (CB), cocoa

mass (CM), sugar, and lecithin

Ingredients Set I Set I Sets I, II

and III

Set I Set I Set I

Volume

fraction

0.53 0.60 0.62 0.65 0.68 0.71

Free CB pure

(w/w %)

25.46 17.80 15.80 12.70 9.40 6.50

CM (w/w %) 29.34 33.40 34.00 35.70 38.10 39.20

Sugar (w/w %) 44.60 48.20 49.60 51.00 51.90 53.70

Lecithin (w/w

%)

0.6 0.6 0.6 0.6 0.6 0.6

Set I: six samples with varying volume fraction, D90 = 21 lm and

lecithin concentration is 0.6 %. Set II: five samples with varying D90

diameter (18, 21, 26, 34 and 42 lm) and lecithin concentration is

0.6 %. Set III: five samples with varying lecithin concentration (0.15,

0.30, 0.45, 0.60 and 0.75 %) and D90 = 21 lm

Table 2 Composition of the chocolate samples: the volume fraction,

total free cocoa butter (CB) (consisting of the cocoa butter from the

cocoa mass and added pure cocoa butter during production), cocoa

solids (CS) from the cocoa mass (CM) (calculated using the per-

centage (34.3 %) of free cocoa butter in the CM), sugar, and lecithin

Set I: six samples with varying volume fraction, D90 = 21 lm and

lecithin concentration is 0.6 %

Composition Set I Set I Sets I, II

and III

Set I Set I Set I

Volume

fraction

0.53 0.60 0.62 0.65 0.68 0.71

Total free CB

(w/w %)

35.53 29.26 27.46 24.95 22.47 19.95

CS from CM

(w/w %)

19.27 21.94 22.34 23.45 25.03 25.75

Sugar (w/w %) 44.60 48.20 49.60 51.00 51.90 53.70

Lecithin (w/w

%)

0.6 0.6 0.6 0.6 0.6 0.6

Set II: five samples with varying D90 diameter (18, 21, 26, 34 and

42 lm) and lecithin concentration is 0.6 %. Set III: five samples with

varying lecithin concentration (0.15, 0.30, 0.45, 0.60, and 0.75 %)

and D90 = 21 lm

Eur Food Res Technol (2013) 236:931–942 933

123

consisting of polymethylmethacrylate (PMMA) particles

suspended in cis-decahydronaphthalene (cis-decalin). Par-

ticles are sterically stabilized with a layer of grafted poly-

12-hydroxystearic acid (PHSA), 10nm in length, to prevent

aggregation. This also makes the system have only hard-

sphere interactions [28]. The suspension has a volume

fraction of 0.63, very close to the random close packing

limit for spheres /rcp = 0.64. The particle size is approx-

imately 15 lm. For comparison, the smallest D90 diameter

of the chocolate samples is 18 lm.

Rheology

Two types of oscillatory shear rheology have been per-

formed as follows: a strain sweep and a constant strain rate

sweep. In the case of the strain sweep, the frequency x is

held constant and the strain amplitude c0 is varied. During

the constant strain rate sweep, the strain amplitude is

increased while the frequency decreases, keeping fre-

quency inversely proportional to strain amplitude, to

maintain a constant strain rate amplitude _c0 ¼ c0x:The strain sweeps have been performed on a stress-

controlled AR 2000ex rheometer (TA Instruments Rheol-

ogy) with a Starch Cell geometry (cup: diameter 37 mm

and height 65 mm; rotor blade: diameter 32 mm and height

12 mm). The constant strain rate sweeps have been per-

formed on a stress-controlled Physica MCR rheometer

(Anton Paar) with vane-in-cup geometry (cup: diameter

28.80 mm and height 67.83 mm; vane with four blades:

diameter 22 mm and height 16 mm). The vane geometry

was chosen because it prevents the wall slip artifact for

chocolate [10]. The (serrated) plate–plate geometry could

not be used, because the low volume fraction could not be

contained between the plates during measuring.

In both setups, the geometry is kept at a constant tem-

perature of 40 �C during measurements, as prescribed by

ICA [19]. To prepare the samples for measurement, they

are put to melt in an oven at 50 �C for a minimum of two

hours, to ensure complete melting. After loading, a con-

ditioning step is applied where the sample is pre-sheared at

an apparent shear rate of 10 s-1 for one minute and left to

equilibrate for 10 s. At this point, the sample temperature,

as determined by the rheometer, has reached the desired

value. With this temperature and shear conditioning, the

reproducibility of the measurements is good (deviations are

less than 5 %). About three or four subsequent measure-

ments were taken to check the reproducibility.

Strain sweeps

During the strain sweeps, an oscillating strain of logarith-

mically increasing amplitude is applied. A constant fre-

quency x of 10 rad s-1 is used because it allows for fast

measurements. The storage modulus G0 and the loss

modulus G00 are subsequently obtained. For each data point,

the rheometer (controlled by the rheometer software) per-

formed as many oscillations as required to reach a steady-

state, which amounted in most cases to 2 or 3 oscillations.

A yield stress ry is calculated using ry = cyG0, with the

yield strain cy and storage modulus G0 chosen at the point

of deviation from linear behavior where G0 has decreased

by 5 %.

Stress sweeps, wherein the viscoelastic moduli are

measured as a function of increasing applied shear stress,

were not used to determine a yield stress, because the

reproducibility of these measurements was not very good.

A variation in the yield stress of more than 25 % occurred

regularly between subsequent measurements for samples

with low volume fraction.

Constant strain rate sweeps

During a constant strain rate sweep, both frequency and

strain amplitude are varied at the same time. The strain

amplitude is increased while the frequency decreases,

keeping frequency inversely proportional to strain ampli-

tude. The result is a measurement at constant strain rate

amplitude _c0 ¼ xc0: The reasoning behind this approach is

related to the choice of probing timescale. Conventional

strain sweeps are performed at a constant frequency x,

probing the sample at a fixed timescale t = 2p/x. The

second timescale that can be imposed is the strain rate

amplitude. However, in a strain sweep, the strain rate

amplitude increases when the strain amplitude increases,

hence changing this timescale. The same occurs with fre-

quency sweeps, where the frequency is varied and the

strain amplitude is fixed.

A viscoelastic material has an inherent relaxation

times, determining on what timescale the material will

‘‘flow’’. If a viscoelastic material with a yield stress is at

rest, the relaxation time can be considered long. When the

material is forced to flow, the relaxation time is decreased

to a value depending on the strain rate. Therefore, yielding

at a specific strain rate implies yielding at a constant

relaxation time.

Wyss et al. [29] recently performed constant strain rate

(CSR) sweeps1 and argue about the importance of this

approach in view of the relaxation time of the probed

material. CSR sweeps can be used to study the breakdown

of the internal structure of a material, circumventing

complex effects related to increasing strain rates.

CSR sweeps were performed at a strain rate amplitude of

_c0 ¼ 0:01 s�1: This strain rate was chosen for three practical

reasons. Firstly, at higher strain rates, the signal exhibited

1 Wyss et al. [29] named it constant-rate frequency sweeps.


123

more noise. Secondly, a higher strain rate requires a higher

frequency (because the strain amplitude range is not varied)

which inevitably is limited by the rheometer. Thirdly, lower

strain rates result in longer measurements.

Data analysis

The rheometer control software RheoPlus (Anton Paar) of

the Physica MCR rheometer can be used to collect the ‘‘raw’’

stress-strain data within a steady-state cycle of the rheome-

ter. Steady-state cycle refers to a single oscillation at fixed

strain amplitude and frequency. One cycle recorded for every

strain amplitude data point of the CSR sweeps. The raw data

collected for each data point of the constant strain rate

sweeps were submitted to two different analyses. The first

analysis consists of determining the dissipated energy from

Lissajous curves of the raw stress vs strain. Subsequently, the

second analysis is the stress decomposition of the raw data,

which provided insight into the nonlinear elastic and viscous

behavior. In both studies, the effects (on the yielding

behavior) of volume fraction, particle diameter, and lecithin

concentration have been investigated.

Lissajous curves

Lissajous curves are obtained by plotting the raw strain

data versus the raw stress data in a steady-state oscillation

cycle at fixed strain amplitude and frequency. From the

surface enclosed by a Lissajous curve, the dissipated

energy per volume Ed (J m-3) can be calculated using the

integral

Ed ¼Z

cycle

rdc: ð2Þ

Stress decomposition

The technique of stress decomposition, developed by Cho

et al. [30] and extended by Ewoldt et al. [31], introduced a

number of physically meaningful measures to characterize

nonlinear behavior. Cho et al. [30] decomposed the non-

linear stress response r(t) into an elastic stress r0(x), where

x � c=c0 ¼ sin xt; and a viscous stress r00(y), where y �_c= _c0 ¼ cos xt: The total stress is the superposition of these

two contributions: r(t) = r0(x) ? r00(y). Ewoldt et al. [31]

proposed an odd sum of Chebyshev polynomials of the first

kind as solutions for the elastic and viscous stresses:

r0ðxÞ ¼ c0

Xn:odd

enðx; c0ÞTnðxÞ;

r00ðyÞ ¼ _c0

Xn:odd

vnðx; c0ÞTnðyÞ;ð3Þ

where Tn(x) and Tn(y) are nth-order Chebyshev polynomials

of the first kind and en and vn are the nth-order Chebyshev

coefficients. The first-order Chebyshev coefficients characterize

the linear viscoelasticity and are given by e1 = G0 and

v1 = G00/x. For symmetry reasons, the quadratic and other

even terms vanish.

e3 �[ 0 strain stiffening

¼ 0 linear elastic

\0 strain softening;

8<: ð4Þ

v3 �[ 0 shear thickening

¼ 0 linear viscous

\0 shear thinning;

8<: ð5Þ

where strain stiffening and strain softening correspond to

an intracycle increase and decrease in G0, respectively, and

shear thickening and shear thinning correspond to intra-

cycle increase and decrease in G00, respectively. To com-

pare higher order coefficients between measurements, the

coefficients can be normalized by their first-order coun-

terparts e1 and v1.

As stated above, the even harmonics vanish in the der-

ivation; however, they can occur in the measured signal.

The main reason for this is supposed to be wall slip [32].

For stress decomposition, the raw data were processed

with MATLABTM (R2010b, MathWorks), using a freely

available data analyses package, MITlaos (Beta 2.1),

developed by Ewoldt et al. [33]. The MITlaos software

uses Fourier Transform analyses to filter out the noise and

smoothen the signal. Subsequently, the smoothed data are

decomposed in an elastic and viscous stress and the third-

order viscous (v3) and elastic (e3) Chebyshev coefficients.

Results and discussion

Strain sweeps

Figure 2 shows the storage G0 and loss G00 moduli as a

function of strain amplitude for the samples with varying

volume fraction, D90 diameter, and lecithin concentration

as well as the yield values.

Generally, all measurements show the same trend for G0

and G00 and can be divided into three characteristic

regimes. At small strain amplitude, the linear viscoelastic

regime (LVR) is observed, where the viscoelastic moduli

are independent of strain amplitude and G0 is larger than

G00, corresponding to solid-like behavior. Upon yielding—

and entering the nonlinear regime—the viscoelastic moduli

decrease, signifying shear thinning, and G00 becomes larger

than G0. At large strain amplitude (c0 [ 2� 10�1), a

regime exists where the moduli increase again.

Figure 2a, b shows clearly that for a higher volume

fraction and a smaller D90 diameter, the chocolate is more

difficult to deform, that is, higher values for G0 and G00 are


123

observed in the LVR. In agreement with this behavior, the

yield stress increases as well. This is shown in Fig. 2d, e,

where the yield stress is plotted as a function of volume

fraction and D90 diameter. The yield stress data as a

function of volume fraction are fitted with a power law

(/max - /)-a incorporating a maximum volume fraction

/max. It is found that a = 0.7 and /max = 0.84, the latter

value corresponding to the theoretical limit for a bimodal

particle size distribution [34], which the samples with

varying volume fraction have (see Fig. 1).

The yield stress data as a function of D90 diameter are

fitted with a simple power law (D90)-a, and a power

a = 1.4 is found. It is clear that the volume fraction has a

much stronger effect on the rheology, compared to the D90

diameter. Yield stresses that were determined from the

point where G0 crosses with G00 show a slightly steeper

scaling (data not included), which may be the result of

increased nonlinear effects when probing further into the

nonlinear regime.

In general, decreasing overall particle diameter and/or

increasing volume fraction result in a more viscous choc-

olate [1]. Afoakwa et al. [34] showed that chocolates with

high volume fractions have extensive particle–particle

interaction, with smaller particles filling the spaces

between the larger. At smaller particle diameters, the par-

ticle density increased in parallel with particle–particle

interactions. Decreasing the volume fraction reduced the

structure network density, creating more open and void

spaces filled with fat [35].

The specific surface area (m2 g-1) is usually given as an

explanation for the influence of particle diameter: Smaller

particles have a larger specific surface area resulting in

more particle interactions and a higher yield stress [9–11].

The argument of the specific surface area does neglect the

possible influence of particle aggregates (with larger

effective volume) or colloidal (electrostatic, van der

Waals) interactions. However, it was suggested by Taylor

et al. [13] that the elasticity of chocolate in the LVR is not

due to protein bonding or colloidal interactions or any

unique properties of the liquid phase, but is the result

entirely of the interactions of the densely packed particles

in suspension. We therefore compare the results on choc-

olate with measurements on simple monodisperse hard-

sphere suspensions.

The strain-dependent viscoelastic moduli of a mono-

disperse hard-sphere suspension are shown in Fig. 3. The

characteristic LVR can be observed, where G0 is larger than

G00, followed by the nonlinear regime, where both moduli

decrease. Eventually G00 should become larger than G0,however not within the range of the shown measurement.

The hard-sphere suspension has a volume fraction /= 0.63 and particle diameter of 15 lm; therefore, the data

can best be compared with those of the chocolates with

varying D90 diameter—which have / = 0.62—in Fig. 3b.

Fig. 2 a–c Storage modulus G0

(closed symbols) and loss

modulus G00 (open symbols) as a

function of strain amplitude at a

constant frequency of

10 rad s-1, for chocolate

samples with varying volume

fraction (a), D90 diameter

(b) and lecithin concentration

(c). d–f Yield stress ry

determined from the curves in

(a–c) at a 5 % decrease of G0.The dashed line in (d) is a fit of

ry � (/max - /)-a, where / is

the volume fraction, the

maximum volume fraction is

/max = 0.84 and a power

a = 0.7. The dashed line in

(e) is a fit ofry � ( D90)-a, with

a power a = 1.4


123

Surprisingly, the observed behavior for the simple hard-

sphere suspension is quite similar to that of chocolate. The

length of the LVR is comparable and also the magnitude of

the moduli. The values of G0 and G00 in the LVR for the

suspension are quite similar to those of the chocolate

sample with D90 = 18 lm. The strain amplitude at which

the storage modulus starts to decrease, signifying the

nonlinear regime, is close to 10-3 for both materials. The

yielding behavior of hard-sphere suspensions can be

ascribed completely to the frictional behavior of the

granular matrix under normal stresses due to gravity [25].

The similarity of the response of chocolate and hard-sphere

suspensions in the LVR suggests that the yield behavior of

chocolate has a similar origin.

Although the similarity in behavior between the two

materials is large, the specific differences are interesting as

well. The crossover of G0 and G00 occurs at a much larger

strain amplitude, approximately 10-1 compared to 10-2 for

chocolate. The loss modulus starts to decrease at a smaller

strain amplitude and has a stronger decrease. This suggests

that the increase in dissipated energy, as a function of strain

amplitude, in the hard-sphere suspension is less steep than

in chocolate. In the LVR, the phase angle tan d ¼ G00=G0 of

the hard-sphere suspension is larger by a factor 3, indi-

cating that the hard-sphere system is more elastic. This

difference could be attributed to the smaller particle

diameter (3 lm) and slightly higher volume fraction of the

hard-sphere suspension. Interestingly, the hard-sphere

suspension has a larger G00 in the LVR, while in the non-

linear regime, it is chocolate that has a larger G00. This

could be interpreted as follows: Outside the LVR chocolate

is more viscous, because of the irregularity and roughness

of the solid particles, in contrast to the smooth spherical

particles of the hard-sphere suspension. In the LVR, the

hard-sphere suspension is more elastic and more viscous

because of the closer packing and smaller particles.

Another complexity arises from the added lecithin.

Addition of lecithin to chocolate is known to lower

viscosity and yield stress [1, 11]. The amphiphilic nature of

lecithin causes it to migrate to sugar–fat interfaces [1, 36,

37]. There it disperses sugar in the fat phase, deagglom-

erates particle clumps, and decreases particle–particle

interaction, consequently weakening the chocolate. An

increase in viscosity is expected at high lecithin concen-

tration and is thought to be related to micelle formation in

the fat phase [37]. Alternatively, excess lecithin may form

multilayers around the sugar, negating viscosity lowering

effect of a monolayer lecithin and hindering flow [1, 11].

The optimal concentration of lecithin, for lowering the

viscosity, typically lies between 0.3 and 0.5 %, depending

on the particle size distribution, volume fraction, and

ingredient composition. The nonlinear part of the data

shown in Fig. 2c corresponds with this expected behavior:

The viscoelastic moduli are lowest for the intermediate

lecithin concentration 0.45 %, while the concentrations

0.15 and 0.75 % show higher moduli. Interestingly, in the

LVR, the smallest moduli are found for the concentration

of 0.15 % instead of 0.45 %, although the difference is

minimal. The highest moduli are found for a concentration

of 0.75 %, which should be caused by the formation of

micelles or multilayers of excess lecithin. Accordingly,

also the highest yield stress was noticed for the concen-

tration of 0.75 % lecithin, as shown in Fig. 2f. For the

lower concentrations, the effect on yield stress is not

apparent considering the standard deviations on the data.

The next section shows that the local maximum of the

viscoelastic moduli in the far nonlinear regime originates

from inertia related to the high strain rates at the end of the

strain sweeps and is not inherent to the yielding of the

sample.

Constant strain rate sweeps

The constant strain rate (CSR) sweep is not dominated by

strain rate-related effects, as is the case for the strain

sweep. For this reason, the CSR sweep might provide a

more viable means to study the fundamental yielding

behavior of chocolate. Results of a CSR sweep and a tra-

ditional strain sweep measurement are compared in Fig. 4.

An important feature that CSR sweeps and strain sweeps

have in common is that they both exhibit the LVR and

nonlinear regime. However, at small strains, the strain

sweep produces lower viscoelastic moduli compared to the

CSR sweep because the strain rate of the strain sweep is an

order of magnitude lower than that of the CSR sweep at the

same strain amplitude.

At the onset of yielding, both measurements overlap

because the strain rate is similar. When the viscoelastic

moduli decrease and G00 becomes larger than G0, the strain

rate curve deviates again from the CSR sweep curve and

shows a lower G0 and a higher G00.

Fig. 3 Storage modulus G0 and loss modulus G00 as a function of

strain amplitude for a dense PMMA suspension with volume fraction

/ = 0.63 and particle diameter of 15 lm


123

At the largest strain amplitude, the strain sweep shows

an increase in the viscoelastic moduli, which is not

observed for the CSR sweep. As the strain sweep probes

the chocolate with an increasing strain rate for each data

point, whereas the CSR sweep does not, the increase in

viscoelastic moduli can be assumed to be strain rate rela-

ted. Moreover, an increase in viscosity is not observed

during steady-state flow curves at strain rates up to 103 s-1

(data not shown). The strain rate during strain sweeps only

reaches 102 s-1, which supports the idea that the observed

increase in viscoelastic moduli is related to inertia resulting

from oscillation at high strain rate, and not in fact inherent

to the yielding mechanism. This finding might very well

hold for other types of concentrated suspensions [38–40],

which also show the local maximum of the viscoelastic

moduli.

Previous research on chocolate by means of oscillatory

rheology has either totally neglected the nonlinear regime

or lacked an in-depth study of nonlinear effects [12–15].

The objective of the present research is to study the

behavior of chocolate with a focus on the nonlinear regime.

A useful way to graphically represent the relationship

between the stress r(t) and strain c(t) is via Lissajous

curves of a steady-state cycle. Figure 5 shows Lissajous

curves, at different strain amplitudes, for a chocolate

sample with volume fraction 0.65. In this representation, a

linear viscoelastic response is characterized by an ellipse,

symmetric about the line c = r. The two limiting cases of

purely elastic and purely viscous response are character-

ized by a line and a circle, respectively. Therefore, in the

linear regime, the Lissajous curve is an ellipse with aspect

ratio given by the ratio of the storage and loss modulus.

In the nonlinear regime, the stress–strain relation is not

a single-harmonic sinusoid: The structure of the visco-

elastic material is destroyed, and the material response

becomes nonlinear. However, the structure that is

destroyed during flow might be restored again at rest in

the reversal point of the oscillation cycle. This structure

buildup and breakdown is related to the nonlinearity in

the stress and shows up as deviations from ellipticity in

the Lissajous curve (Fig. 5). These deviations, which are

not present if one considers only the linear viscoelastic

moduli G0 and G00, can be characterized by strain stiff-

ening/softening or shear thickening/thinning, correspond-

ing to an increase/decreasein the effective G0 and G00,respectively [31].

Dissipated energy

The area enclosed within the trajectory of a Lissajous curve

has units of energy density Pa = N m-3 = Nm m-2 =

J m-3 and is directly related to the dissipated energy in a

steady-state cycle. The dissipated energy gives a physical

interpretation to the Lissajous curve and presents an

alternative way to review the yielding behavior of a

material.

The dissipated energy Ed has been calculated for each

CSR sweep experiment. The dissipated energy results are

shown in Fig. 6 as a function of strain amplitude. For all

samples, Ed shows two power law regimes; a power of 2 in

the LVR and a power of 1 in the nonlinear regime. The

power of 2 is in agreement with the expected dissipated

energy Ed = p c02G00 [41] that can be directly derived from

Eq. (2). In the nonlinear regime, G00 is shown in Fig. 4 to

decrease roughly inversely proportional to the strain

amplitude; this accounts for the linear dependence of Ed on

the strain amplitude

Figure 6 shows that an increase in volume fraction shifts

the whole curve of Ed upwards, indicating that the overall

yielding mechanism does not change with volume fraction,

only the energy dissipation related to the internal structure

and its breakdown changes. Very similar behavior is

observed in colloidal hard-sphere suspensions [42], where

for increasing volume fraction, the entire dissipated energy

curve shifts upwards.

The effect of lecithin concentration appears to be similar

as that of volume fraction, leading to a shift of the whole

curve, with the two power law regimes remaining unaf-

fected. Possibly the added lecithin increases the viscosity

of the interstitial cocoa butter, thereby slightly increasing

energy dissipation in both the LVR and nonlinear regime.

For changes in the D90 diameter, the observed behavior

is different. The two power law regimes are present;

Fig. 4 Storage modulus G0 (closed symbols) and loss modulus G00

(open symbols) as a function of strain amplitude during a constant

strain rate sweep (circles) ( _c ¼ 0:01 s�1) and a strain sweep (trian-gles) (x = 10 rad s-1). Inset zoomed in portion, with a linear verticalscale, of the large strain amplitude region


123

however, the dissipated energy is almost independent of the

D90 diameter in the LVR. The strain sweeps in Fig. 2b

agree with this; G00 appears not to change in the LVR when

changing the D90 diameter. Furthermore, Fig. 6 shows that

the length of the LVR for the dissipated energy is longer

for smaller D90 diameter. This is additional information on

the yielding behavior related to particle diameter, which is

not clearly observed in the strain sweep measurements in

Fig. 2b.

Stress decomposition

Figure 7a–c shows the normalized third-order elastic

Chebyshev coefficient e3/e1 as a function of strain ampli-

tude. For all samples, the overall behavior is similar. The

curves show a transition from e3/e1 & 0 indicating the

LVR, to positive values, indicating strain stiffening. There

occurs only strain stiffening, since e3/e1 is positive, over

the whole nonlinear regime.

Fig. 5 Lissajous curves. Stress

versus strain data for steady-

state cycles with different strain

amplitudes c0 a 0.001; b 0.0025;

c 0.01; and d 0.04, during a

constant strain rate sweep. The

sweep is performed on a

chocolate sample with volume

fraction 0.65. The curves are

approached within two

oscillations. In the LVR (a), the

Lissajous curve resembles an

ellipse, signifying that the stress

and strain are single sinusoidal.

When entering the nonlinear

regime (b, c and d), the

structure of the sample is

destroyed. The structure might

be restored again once at rest, at

the maximum amplitude (leftbottom and top right corners of

the curve). This structure

buildup causes the deviations

from ellipticity in the curves

Fig. 6 Dissipated energy Ed as

a function of strain amplitude

during constant strain rate

sweeps for chocolate samples

with varying volume fraction

(a) D90 diameter (b) and

lecithin concentration (c)


123

At the onset of yielding, the magnitude of strain stiff-

ening shows a fast increase. After reaching a maximum, the

amount of strain stiffening decreases, but does not entirely

disappear. For larger D90 diameter, the overall magnitude

of strain stiffening is higher and the first increase starts at

smaller strain amplitude. No trend can be observed with

changing volume fraction or lecithin concentration. The

variation in the curves for different volume fraction and

lecithin concentration is possibly the result of methodical

variations. However, it is noteworthy that at 0.45 % leci-

thin strain stiffening is strongest, which is around the

optimal concentration for reducing viscosity. For higher

lecithin concentrations, upon formation of micelles and

double layers, strain stiffening is less. This is also the case

for lower lecithin concentration.

Strain stiffening is related to an increase in G0 and a

buildup of the internal structure of the chocolate. The strain

stiffening occurs near the maximum strain amplitude of the

oscillation cycle (Fig. 5d), indicating a jamming of the

solid particles, that is also observed in simple hard-sphere

suspensions [25] and cornstarch suspensions [43]. The

latter which is a material similar to chocolate in that it is a

suspensions of solid non-spherical particles in the same

size range.

Figure 7d–f shows the normalized third-order viscous

Chebyshev coefficient v3/v1. For all samples, the curves

show a transition from v3/v1 & 0, to strongly negative

values, indicating shear thinning. However, a slight shear

thickening occurs at the beginning of the nonlinear regime.

Shear thinning dominates the remainder of the yielding

process. It increases and levels off at multiple times the

maximum value of shear thickening.

While it is known that chocolate shear thins [1], intra-

cycle shear thickening upon yielding has not been previ-

ously observed. Shear thickening is related to an increase

in the effective G00. This may be due to the fact that at the

onset of yielding, the viscous dissipation of energy

increases due to friction of particles that are forced to move

past each other. Hard-sphere suspensions are known to

shear thin after yielding but can also shear thicken at high

strain rates [43, 44].

Upon closer inspection, the results for varying volume

fraction, D90 diameter, and lecithin concentration show

slight differences. The amount of shear thinning appears

not to change as a function of volume fraction. In contrast,

for larger a larger D90 diameter, shear thinning is clearly

stronger. Furthermore, at the lowest lecithin concentration,

shear thinning appears to be somewhat smaller in magni-

tude, which could be related to the lubricating effect of

lecithin.

Concerning the shear thickening; no trend is observed

depending on volume fraction or lecithin concentration.

However, for the chocolates with larger particle diameter,

shear thickening starts at smaller strain amplitude. This is

in agreement with the data for the dissipated energy, which

also shows a shorter LVR for larger particles.

Conclusions

This paper confirms that dark chocolate exhibits complex

rheological behavior, of which some features are similar to

those of simple hard-sphere suspensions. Namely, in the

linear viscoelastic regime, the viscoelastic moduli are

Fig. 7 Normalized third-order

elastic Chebyshev coefficient

e3/e1 (a–c) and viscous

Chebyshev coefficient v3/v1

(d–f) as a function of strain

amplitude, during constant

strain rate sweeps for chocolate

samples with varying volume

fraction (a and d) D90 diameter

(b and e) and lecithin

concentration (c and f)


123

comparable in magnitude, suggesting that the origin of the

yield behavior of chocolate is similar to that of hard-sphere

suspension, that is, the frictional behavior of the structural

packing of particles compacted under gravity. This idea is

supported by the fact that upon yielding chocolate exhibits

some intracycle shear thickening, which might be caused

by increased friction when the particles start to move.

Furthermore, chocolate exhibits both shear thinning and

strain stiffening in the nonlinear regime. The former which

is also a robust feature of hard-sphere suspensions.

However, chocolate shows an additional degree of

complexity regarding the effects of the particle size and the

addition of lecithin on its rheology. Although the general

influence of particle size and lecithin addition on chocolate

rheology is known, the new features reported here

encourage continued research to resolve the exact workings

of these compositional factors. This encouragement

extends to studying the influence of particle size on the

nonlinear (intracycle) rheology of hard-sphere suspensions.

Given the new insights presented here and previous

reported studies, it can be argued that using a simple model fit

to determine a yield stress for dark chocolate is a simplifi-

cation that neglects the underlying origin and mechanism of

its yielding and how this is influenced by compositional

factors. Attempting to gain deeper insight into yielding of

chocolate might prove, in the long run, to be a more worth-

while approach. Both chocolate production and handling

will benefit from a more in-depth understanding of the

compositional influence on the mechanism of yielding.

Acknowledgments The chocolate raw ingredients were provided by

Barry Callebaut (Wieze, Belgium) and Belcolade, a Division of Pu-

ratos (Erembodegem, Belgium).

Conflict of interest None.

Compliance with Ethics Requirements This article does not

contain any studies with human or animal subjects.

References

1. Beckett ST (2009) Industrial chocolate manufacturing and use,

4th edn. Blackwell Science, Oxford

2. Beckett ST (2000) The science of chocolate. RSC Paperbacks,

Royal Society of Chemistry, Cambridge

3. Tscheuschner HD, Wunsche D (1979) Rheological properties of

chocolate masses and the influence of some factors. In: Sherman

P (ed) Food texture and rheology, Academic Press, New York,

pp 355–368

4. Schantz B, Rohm H (2005) Influence of lecithin-pgpr blends on

the rheological properties of chocolate. Lebensmittel-Wis-

senschaft und-Technologie 38(1):41–45

5. Vavreck AN (2004) Flow of molten milk chocolate from an

efflux viscometer under vibration at various frequencies and

displacements. Int J Food Sci Technol 39(4):465–468

6. Afoakwa EO, Paterson A, Fowler M (2007) Factors influencing

rheological and textural qualities in chocolate: a review. Trends

Food Sci Technol 18(6):290–298

7. Steiner EH (1958) A new rheological relationship to express the

flow properties of melted chocolate. Int Choc Rev 13:290–295

8. Chevalley J (1975) Rheology of chocolate. J Texture Stud 6(2):

177–196

9. Mongia G, Ziegler GR (2000) The role of particle size distribu-

tion of suspended solids in defining the flow properties of milk

chocolate. Int J Food Prop 3(1):137–147

10. Servais C, Ranc H, Roberts ID (2003) Determination of chocolate

viscosity. J Texture Stud 34(5–6):467–497

11. Afoakwa EO, Paterson A, Fowler M (2008) Effects of particle

size distribution and composition on rheological properties of

dark chocolate. Eur Food Res Technol 226(6):1259–1268

12. Gabriele D, Migliori M, Baldino N, de Cindio B (2008) Influence

of fat content on chocolate rheology. AIP Conf Proc 1027(1):

1265–1267

13. Taylor JE, Van Damme I, Johns ML, Routh AF, Wilson DI

(2009) Shear rheology of molten crumb chocolate. J Food Sci

74(2):E55–E61

14. Baldino N, Gabriele D, Migliori M (2010) The influence of for-

mulation and cooling rate on the rheological properties of choc-

olate. Eur Food Res Technol 231:821–828

15. De Graef V, Depypere F, Minnaert M, Dewettinck K (2011)

Chocolate yield stress as measured by oscillatory rheology. Food

Res Int 44(9):2660–2665

16. Casson N (1959) A flow equation for pigment oil suspensions of

the printing ink type. In: Mill C.C. (eds) Rheology of disperse

systems. Pergamon Press, London

17. Windhab E (1995) Physico-chemical aspects of food processing.

Chapman & Hall, London

18. Chevalley J (1994) Industrial chocolate manufacture and use, 3rd

edn. Blackwell Science, London

19. ICA (2000) International confectionery association. Viscosity of

chocolate and chocolate products. Analaytical method 46,

Available from CAOBISCO, Belgium

20. Chevalley J (1999) Chocolate flow properties. Chapman and Hall,

New York, pp 182–199

21. Nguyen QD, Boger D (1992) Measuring the flow properties of

yield stress fluids. Annu Rev Fluid Mech 24:47–88

22. Barnes HA (1999) The yield stress–a review or ‘pamsaqei’—everything flows? J Non-Newtonian Fluid Mech 81(1–2):

133–178

23. Møller PCF, Mewis J, Bonn D (2006) Yield stress and thixotropy:

on the difficulty of measuring yield stresses in practice. Soft

Matter 2(4):274–283

24. Bonn D, Denn MM (2009) Yield stress fluids slowly yield to

analysis. Science 324(5933):1401–1402

25. Fall A, Bertrand F, Ovarlez G, Bonn D (2009) Yield stress and

shear banding in granular suspensions. Phys Rev Lett 103(17):

178301

26. ASTM E 799-03 (2007) Standard practice for determining data

criteria and processing for liquid drop size analysis

27. Akoh CC, Min DB (2002) Food lipids: chemistry, nutrition, and

biochemistry, 2nd edn. Marcel Dekker Inc, New York

28. Bryant G, Williams SR, Qian L, Snook IK, Perez E, Pincet F

(2002) How hard is a colloidal ‘‘hard-sphere’’ interaction?. Phys

Rev E 66(6):060501

29. Wyss HM, Miyazaki K, Mattsson J, Hu Z, Reichman DR, Weitz

DA (2007) Strain-rate frequency superposition: a rheological

probe of structural relaxation in soft materials. Phys Rev Lett

98(23):238,303

30. Cho KS, Hyun K, Ahn KH, Lee SJ (2005) A geometrical inter-

pretation of large amplitude oscillatory shear response. J Rheol

49(3):747–758


123

31. Ewoldt RH, Hosoi AE, McKinley GH (2008) New measures for

characterizing nonlinear viscoelasticity in large amplitude oscil-

latory shear. J Rheol 52(6):1427–1458

32. Reimers MJ, Dealy JM (1996) Sliding plate rheometer studies of

concentrated polystyrene solutions: large amplitude oscillatory

shear of a very high molecular weight polymer in diethyl

phthalate. J Rheol 40(1):167–186

33. Ewoldt RH, Winter P, McKinley GH (2007) ‘‘MITlaos‘‘ version

2.1 Beta for MATLAB, MATLAB-based data analysis software

for characterizing nonlinear viscoelastic responses to oscillatory

shear strain. Self-published, Cambridge

34. Farris RJ (1968) Prediction of the viscosity of multimodal sus-

pensions from unimodal viscosity data. Trans Soc Rheol 12(2):

281–301

35. Afoakwa EO, Paterson A, Fowler M, Vieira J (2009) Micro-

structure and mechanical properties related to particle size dis-

tribution and composition in dark chocolate. Int J Food Sci

Technol 44(1):111–119

36. Rousset P, Sellappan P, Daoud P (2002) Effect of emulsifiers on

surface properties of sucrose by inverse gas chromatography.

J Chromatogr A 969(1-2):97–101

37. Vernier F (1997) Influence of emulsifiers on the rheology of

chocolate and suspensions of cocoa or sugar particles in oil. PhD

thesis, University of Reading

38. Citerne GP, Carreau PJ, Moan M (2001) Rheological properties

of peanut butter. Rheol Acta 40(1):86–96

39. Heymann L, Peukert S, Aksel N (2002) Investigation of the

solid–liquid transition of highly concentrated suspensions in

oscillatory amplitude sweeps. J Rheol 46(1):93–112

40. Sumita I, Manga M (2008) Suspension rheology under oscillatory

shear and its geophysical implications. Earth Planet Sci Lett

269(3-4):468–477

41. Tschoegl NW (1989) The phenomenological theory of linear

viscoelastic behavior: an introduction. Springer, Berlin

42. van der Vaart K, Rahmani Y, Hu Z, Bonn D, Schall P (2012)

Rheology of concentrated soft and hard-sphere suspensions

(submitted)

43. Fall A, Huang N, Bertrand F, Ovarlez G, Bonn D (2008) Shear

thickening of cornstarch suspensions as a reentrant jamming

transition. Phys Rev Lett 100(1):018301

44. Fall A, Lemaıtre A, Bertrand F, Bonn D, Ovarlez G (2010) Shear

thickening and migration in granular suspensions. Phys Rev Lett

105(26):26303


123

Dark chocolate’s compositional effects revealed by oscillatory rheology

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