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J. Non-Newtonian Fluid Mech. 151 (2008) 145–150

Rheological discrimination and characterization of carrageenans andstarches by Fourier transform-rheology in the non-linear viscous regime

Christopher Klein, Paul Venema ∗, Leonard Sagis, Erik van der LindenFood Physics Group, Bomenweg 2, Wageningen University, 6700 EV Wageningen, The Netherlands

Received 29 June 2007; received in revised form 8 January 2008; accepted 11 January 2008

bstract

Classical rheological methods are often insufficient to characterize and to differentiate the non-linear rheological behavior of polysaccharideystems such as carrageenan or starch. In this article the non-linear rheological method of characteristic functions is used to discriminate between

he different polysaccharides. This method is based on the Fourier transform-rheology (FT-rheology). The response of a sample is decomposedsing simple characteristic functions. We show that there are differences in the response of a number of carrageenan and starch samples, which areot distinguishable with classical rheometry.

2008 Elsevier B.V. All rights reserved.

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eywords: FT-rheology; Polysaccharides; LAOS; Non-linear regime; Characte

. Introduction

Polysaccharides are widely used in food systems as, e.g.hickeners [1]. The use as a thickener has an influence on theheology of those food systems, like e.g. a desired increase ofhe viscosity [1]. The processing, pumping and extrusion of foodystems are processes in which the sample is deformed at highates, thus often in the non-linear regime. However, the rhe-logical analysis performed on such food systems is mostlyone in the linear mechanical regime [1], e.g. dynamic mea-urements like frequency and strain variation to determine G′r G′′. These measurements are used despite the fact that G′nd G′′ are not defined in the non-linear regime. On the otheride non-linear measurements, like e.g. shear rate dependentiscosity measurements, are destructive and give only a limitedmount of information. Therefore a non-invasive rheologicalethod is needed, which gives additional information on the

esponse in the non-linear regime. In this article FT-rheology2–6] is used to describe the non-linear rheological behaviorf polysaccharides. FT-rheology is based on large amplitude

scillatory shear (LAOS). For one measurement 20–40 oscilla-ions are acquired and subsequently analyzed with the help of aourier transform. The information on the non-linear behaviour

∗ Corresponding author. Tel.: +31 317 485023; fax: +31 317 483669.E-mail address: paul.venema@wur.nl (P. Venema).

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377-0257/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.jnnfm.2008.01.001

functions

s available as magnitudes and phases at frequencies that areultiples of the excitation frequency. Afterwards these higher

armonics are analyzed using four different characteristic func-ions [7], which correlate to the rheological properties as linearehavior, shear thickening, shear thinning, and wall slip or shearands. FT-rheology in combination with an analysis based onhe above mentioned characteristic functions makes it possibleo measure and quantify the non-linear behavior, and relate it tohysical phenomena. Additionally, using this method polysac-harides showing similar behavior in the linear regime can beifferentiated from each other in the non-linear regime.

. Theory

A simple physical interpretation of large amplitude oscilla-ory shear (LAOS) data in the non-linear regime is not alwaysossible [8,9]. The non-linear oscillatory mechanical data ofolysaccharides analysed here, is no exception. In a first step theAOS response is analysed by Fourier transform. In a secondtep the non-linear information, represented by the intensitiesnd the phases of the higher harmonics is described by character-stic response functions [7]. This is a newly developed analysis

f the non-linear information originating from FT-rheology. Thisnalysis method considers the whole frequency spectrum as auperposition of different overtone spectra of typical non-linearheological effects. These rheological archetypes are described

146 C. Klein et al. / J. Non-Newtonian Fluid Mech. 151 (2008) 145–150

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heated up to 60 ◦C to allow the polysaccharides to dissolve. Thesample was then pored into the Couette-cell of the rheometer forperforming the measurements. No salt was added in the processof the preparation.

Fig. 2. Classical rheometry: (a) strain sweep plot at a frequency ω1/2π = 1 Hz

ig. 1. Time domain data of the four characteristic functions: a sine, a rectanguoftening, strain hardening, and shear bands.

y characteristic response functions. The total response can thenimply be characterized by a superposition of these functionsnd their relative contributions quantify the non-linear response.or simplicity only four rheological effects are considered (one

inear and three non-linear): linear response, strain hardening,train softening, and stick-slip as being the most importantnes, under LAOS conditions. Background information on theesponse type versus rheological behaviour can be found in theiterature [7]. The suggested analysis is based on the determi-ation of the magnitude of the higher harmonics (In/I1), relativeo the excitation frequency, and the determination of the cor-esponding phases φn of the generated higher harmonics. Theeasured signal is then fitted in the time domain and the fre-

uency domain with up to four characteristic contributions (seeig. 1). These characteristic contributions are a sinusoidal func-

ion (see Fig. 1a), describing the linear response, a rectangularunction (see Fig. 1b), describing strain softening, a triangularunction (see Fig. 1c), describing strain hardening, and finally aaw tooth function (see Fig. 1d), describing shear bands or walllip. Each one of these functions can be varied with respect to thethers via the amplitude and the relative time-lag (phase-lag).

. Materials

�-carrageenan and �-carrageenan was acquired from Her-ules, Copenhagen Pectin A/S, Denmark. The native starchnd pathogen-inducible oxygenase (PIOX) starch were acquiredrom CP Kelco. The analysed concentrations are 1 wt.%, further-ore 0.5 wt.%, 1.5 wt.%, and 2 wt.% were also analysed, but

he data is not shown here because the results were similar. Theample preparation was performed in the following way. All the

amples were prepared with deionized water. The polysaccha-ide powder was put into a beaker. A drop of ethanol was addedo allow a complete wetting of the powder, so that while addinghe water no clumping occured. Afterwards the samples were

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triangular, and a saw tooth shaped wave, representing linear behaviour, strain

nd a temperature of 293 K for the �-carrageenan, �-carrageenan. The datasetsrom �-carrageenan and �-carrageenan overlay well and (b) viscosity as a func-ion of the shear rate for �-carrageenan, �-carrageenan. The datasets from-carrageenan and �-carrageenan overlay also here. The concentration waswt.%.

C. Klein et al. / J. Non-Newtonian Fluid Mech. 151 (2008) 145–150 147

Fig. 3. Classical rheometry: (a) strain sweep plot at a frequency ω1/2π = 1 Hzand a temperature of 293 K for the native starch and PIOX starch. The datasetsfos

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Fig. 4. Dependence of the amplitude of the characteristic functions on the strainamplitude of the samples �-carrageenan and �-carrageenan. The linear and rect-ai

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rom native starch, and PIOX starch overlay well and (b) viscosity as a functionf the shear rate for native starch and PIOX starch. The datasets from nativetarch, and PIOX starch overlay well. The concentration was 1 wt.%.

. Apparatus

The FT-rheology set-up used here consists of a rheomet-ics scientific advanced rheometer expansion system (ARES)nd two computers. The ARES rheometer is a strain controlledheometer equipped with a dual range force rebalance trans-ucer (2K FRTN1), capable of measuring torques ranging from× 10−6 N m to 2 × 10−1 N m. All experiments were carriedut using a Couette-cell. The static inner bob has a diame-er of 30 mm. The rotating outer cup has an inner diameter of3.8 mm. It has a high resolution (HR) motor, applying frequen-ies from 10−5 rad/s to 500 rad/s and deformation amplitudesanging from 0.005 mrad to 500 mrad. The temperature waset to 24 ◦C. One PC controls the ARES-rheometer via a serialable. The strain, torque, and normal force outputs are con-ected to a second computer via BNC cables, where the data forhe FT-rheology is acquired, digitised, and analysed using a 16-it ADC-card (PCI-MIO-16XE-10 from National Instruments,SA). The maximum sampling rate of this card is 100 kHz,

nd it is capable of multiplexing up to 16 channels. It canimultaneously acquire and transfer the data to the PC memory

y data-buffering techniques. Therefore, the rheological datas intrinsically synchronised. After acquisition the time data isveraged on-the-fly and subsequently Fourier transformed usingome-written Lab VIEW software programs [2,9].

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ngular contribution are shown in figure (a) and the saw tooth function is shownn figure (b). The concentration was 1 wt.%.

. Experiments

The rheological experiments cover the range from the linearo the non-linear regime. The conducted measurements are vari-tions of the shear rate (steady shear), the frequency at constanttrain amplitude γ0 and variations of the strain at a constantrequency (both dynamic shear). Especially in the non-linearegime, measurements where frequency and strain amplitudesere varied, are applied. The steady shear rate dependent vis-

osity was measured at shear rates from 1 s−1 to 200 s−1. Strainweeps were applied at a frequency of 1 Hz and strain ampli-udes �0 from 0.001 to 2. The FT-rheology experiments wereerformed at a frequency of 1 Hz and strain amplitudes γ0 from.001 to 2.5. The reproducibility for the FT-rheological measure-ents has errors of below 1%. Shear rate dependent viscosityeasurements and the strain sweep measurements have errorshich are larger than the difference that is seen in the corre-

ponding plots, therefore it is assumed that we do not see anyifference in these plots.

For the rheological measurements an approximate amount

f 12 ml of the sample is filled into the Couette-cell. Followingn initiation of about 10 oscillations to avoid transient effects,ypically 40 oscillations have been acquired, while an ADC scan-

148 C. Klein et al. / J. Non-Newtonian Fluid Mech. 151 (2008) 145–150

Table 1Fit-parameters k and n (including their errors and the quality of the regression R2)from fitting the shear rate dependent viscosity of the samples PIOX starch, nativestarch, �-carrageenan, and �-carrageenan with an Ostwald-de-Waele equation

k �k n �n R2

PIOX starch 0.157 0.001 0.716 0.006 0.99native starch 0.103 0.001 0.665 0.008 0.99�

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-Carrageenan 40.01 0.57 0.178 0.010 0.99-Carrageenan 39.89 0.24 0.085 0.004 0.99

ing rate of 50,000 1/s for each channel and an oversampling of000 [2] raw data points are typically selected. This results in0 pre-averaged data points per second, which is sufficientlyccurate for the purposes of the experiments conducted here.he acquired non-linear oscillatory mechanical data is analysedia Fourier transformation and a subsequently following separa-ion into the characteristic functions. The total response is thenimply described by a superposition of these functions.

. Results and discussion

The polysaccharide samples of 1 wt.%, examined here, werexposed to dynamic and steady shear flow experiments to detectifferences between the samples in the mechanical non-linearegime. The focus was especially on the difference between sam-les of such pairs as �-carrageenan, and �-carrageenan [1,10],nd PIOX starch and native starch. These systems have onlyinor differences in their molecular structure, but are known to

ave a different mouth feel in products [1]. The concentrationsere chosen to be 1%, so that a similar viscosity was reached

s would be used in products [1]. As can be seen in Fig. 2 �-arrageenan and �-carrageenan show a very similar behaviourn classical rheometry, e.g. in a strain sweep. Additionally whileooking at the shear rate dependent viscosity the shear thinningverlays well. For the samples PIOX starch and native starchhe behaviour was also very similar, see Fig. 3. The shear rateependent viscosity data in Figs. 2b and 3b has been fitted withn Ostwald-de-Waele equation:

= kγn (1)

o show how well the measurements of the samples overlay. Thearameters k and n can be found in Table 1 including their errorsnd the quality parameter of the regression R2.

The further non-linear analysis was done via FT-rheology andhe decomposition by the characteristic functions method. Theesults for �-carrageenan and �-carrageenan are shown in Fig. 4amplitude of the characteristic functions), and Fig. 5 (phasef the characteristic functions). The results of native starch andIOX starch are shown in Fig. 6 (amplitude of the characteristicunctions), and Fig. 7 (phase of the characteristic functions). Inhese figures the upper plot (a) shows the dependence of the lin-ar and rectangular contribution on the strain amplitude, and the

ower plot (b) shows the dependence of the saw tooth contribu-ion of the characteristic functions on the strain amplitude. Asan be seen from Figs. 4a, 4b, 6a, and 6b all samples contain notnly a linear contribution but also significant non-linear contri-

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mplitude of the samples �-carrageenan and �-carrageenan. The linear and rect-ngular contributions are shown in figure (a) and the saw tooth function is shownn figure (b). The concentration was 1 wt.%.

utions (rectangular and saw tooth). For questions concerninghe reproducibility of the FT-rheological measurements we refero the literature [3,7,9].

The samples �-carrageenan and �-carrageenan show no sig-ificant differences in the conventional mechanical analysis (seeig. 2a and b). In the characteristic functions analysis the dom-

nant non-linear contribution of �-carrageenan is the saw toothontribution, see Fig. 4a and b, which is slowly decreasingith increasing strain amplitude. The rectangular contribution

s mostly a factor of 2 smaller than the saw tooth contribu-ion. At strain amplitudes larger than γ0 = 1 a strong increasean be observed in the rectangular contribution, and it becomeshe dominant non-linear contribution, at the highest measuredalue of the strain amplitude of γ0 = 2.5. In comparison to �-arrageenan the rectangular and the saw tooth contribution of-carrageenan show both a decrease until reaching a strainmplitude value of γ0 = 1. While a further decrease is detected inhe saw tooth contribution, the rectangular contribution shows alight increase, but not as strong as the rectangular contributionn �-carrageenan, see Fig. 4a and b. This results in a larger saw

ooth contribution at very small values of γ0, and a larger rectan-ular contribution at values of γ0 > 1. These differences are evenore significant, when looking at the phase of the characteristic

unctions. In Fig. 5a the values of the phase of the rectangu-

C. Klein et al. / J. Non-Newtonian Fluid Mech. 151 (2008) 145–150 149

Fig. 6. Dependence of the amplitude of the characteristic functions on the strainagi

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mplitude of the samples native starch and PIOX starch. The linear and rectan-ular contributions are shown in figure (a) and the saw tooth function is shownn figure (b). The concentration was 1 wt.%.

ar contribution of �-carrageenan are around 0◦, whereas thealues for �-carrageenan are between 90◦ and 120◦. At γ0 val-es between 0.8 and 1.5 the phases change significantly about80–330◦ for �-carrageenan. The saw tooth contributions showignificant differences too. Over the whole range of the measured0 values they deviate by 180◦. The saw tooth contributions ofoth samples show a slight increase at small values of γ0 andre then levelling off at values of γ0 > 0.6. These results from-carrageenan and �-carrageenan show significant differences

hat cannot be seen in classical rheological experiments.Significant differences can also be seen in the analysis of

he samples PIOX and native starch. The dominant non-linearontribution of both the samples is the rectangular contribution,ee Fig. 6a and b. The rectangular contributions reach a maxi-um around γ0 values of 0.4 and are then decreasing in intensityith increasing γ0. The rectangular contribution for PIOX is sig-ificantly larger than the one from native starch. Only at largetrain amplitudes of about γ0 > 1.5 PIOX starch shows a strongerecrease and therefore the values of both samples overlay. Themplitude of both the saw tooth contributions are decreasing

fter an initial plateau value of As = 0.1. The decrease starts atmaller γ0 values for native starch and the As values decreasey a factor of 10. The decrease of the saw tooth contribution ofIOX starch begins at γ0 = 1. Furthermore the values of the saw

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ular contributions are shown in figure (a) and the saw tooth function is shownn figure (b). The concentration was 1 wt.%.

ooth contribution decrease from a plateau form 0.15 to 0.07. Theifferences are not as significant in the strain dependence of themplitude, as they are in the phase. The value of the phase of theectangular contribution of native starch is around 150◦, exceptor γ0 = 0.25 and 0.4, see Fig. 7a. The rectangular contribution ofhe PIOX starch stays constant at a value of approximately 30◦.lso the phases of the saw tooth contributions show a signifi-

ant difference of 180◦ for γ0 > 0.6. The samples native starchnd PIOX starch can clearly be distinguished with the methodf characteristic functions.

. Conclusion

Classical rheological methods are insufficient to characterizehe non-linear rheological behavior of polysaccharide systemsuch as carrageenan or starch. Different carrageenans or differ-nt starches show a similar or identical behaviour in differentheological experiments, like e.g. strain sweeps, or shear rateependent viscosity. FT-rheology can detect differences between

hese samples. Additionally a further interpretation is possi-le by decomposing the behavior into four different physicallynterpretable contributions. These types of behavior are recog-ized as characteristic functions, namely linear behavior, shear

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[9] T. Neidhofer, M. Wilhelm, B. Debbaut, Fourier-transform rheology exper-

50 C. Klein et al. / J. Non-Newtoni

hinning, shear thickening, and avalanche effects, like e.g. walllip or shear bands. Even small differences like between �-arrageenan and �-carrageenan can result in a significantlyifferent non-linear rheological behavior and can therefore beifferentiated.

cknowledgements

We thank Prof. Manfred Wilhelm for useful discussions, ande thank the carbohydrate research centre (CRC) and the Grad-ate School VLAG for their financial support.

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