ι-hybrid carrageenan gels in potassium salt using Fourier Transform rheology

Food Hydrocolloids 23 (2009) 2322–2330

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Structural and mechanical characterization of k/i-hybrid carrageenan gels in potassium salt using Fourier Transform rheology Loic Hilliou a, c, *, Manfred Wilhelm b, Mikio Yamanoi a, Maria P. Gonçalves c a

˜es, Portugal I3N-Institute for Nanostructures, Nanomodelling and Nanofabrication, Department of Polymer Engineering, University of Minho, Campus de Azure´m, 4800-458 Guimara ¨ r Technische und Polymerchemie Karlsruhe Institute of Technology, Engesserstraße 18, 76128 Karlsruhe, Germany Institut fu c REQUIMTE, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 March 2009 Accepted 10 June 2009

The mechanical and structural properties of k/i-hybrid carrageenan gels obtained at various concentrations in the presence of 0.1 M KCl were studied with Fourier Transform rheology (FTR) and cryoSEM imaging. FTR data show that gels formed at concentration below 1.25 wt% exhibit a strain hardening behavior. The strain hardening is characterized by a quadratic increase of the scaled third harmonic with the strain and a third harmonic phase angle of zero degree. Both features are weakly depending on the concentration and conform to predictions from a strain hardening model devised for fractal colloidal gels. However, the phase angle of the third harmonic reveals that k/i-hybrid carrageenan gels obtained at higher concentrations show shear thinning behavior. Colloidal gel models used to extract structural information from the concentration scaling of gel equilibrium shear modulus G0 and the strain dependence of FTR parameters suggest that k/i-hybrid carrageenan gels are built from aggregating rod-like strands (with fractal dimension x ¼ 1.13) which essentially stretch under increasing strain. The mechanically relevant structural parameters fairly match the gel fractal dimension (d ¼ 1.66) obtained from the cryoSEM analysis. Ó 2009 Elsevier Ltd. All rights reserved.

Keywords: Fourier transform rheology k/i-hybrid carrageenan Strain hardening Colloidal gel Cellular microstructure

1. Introduction Gelling carrageenans are sulfated galactans extracted from specific species of red seaweeds, such as Eucheuma and Gigartina (Bixler, 1996), and are usually classified into two main groups, namely k-carrageenan and i-carrageenan, as their chemical structures differ resulting in distinctive gel properties in KCl salt solutions (Piculell, 1995; Te Nijenhuis, 1997). Carrageenan gels result from the thermally induced conformational transition from coils to double or single helices, which subsequently aggregate into networking clusters spanning the sample volume to form a gel (Morris, Rees, & Robinson, 1980; Viebke, Piculell, & Nilsson, 1994). Despite decades of structural (Funami et al., 2007; Hermansson, 1989; Ikeda, Morris, & Nishinari, 2001) and rheological studies (Guenet, 2000; Jones & Marques, 1990; Rochas & Landry, 1988; Takemasa, Chiba, & Date, 2001), a clear structural picture of the aggregation in k- or i-carrageenan gels is still missing, and the

* Corresponding author. I3N-Institute for Nanostructures, Nanomodelling and Nanofabrication, Department of Polymer Engineering, University of Minho, Campus de Azure´m, 4800-458 Guimara˜es, Portugal. Tel.: þ351 22 508 1686; fax: þ351 22 508 1449. E-mail address: [email protected] (L. Hilliou). 0268-005X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodhyd.2009.06.008

mechanical efficiency of such aggregates still needs to be assessed (Funami et al., 2007; Piculell, 1995; Te Nijenhuis, 1997). A third group, namely k/i-hybrid carrageenans, has recently received increased interest (van de Velde, 2008), as the demand for gelling additives for food and non food application is steadily increasing and alternative resources for carrageenan production is highly demanded (McHugh, 2003). k/i-hybrid carrageenans are natural copolymers essentially made of statistically distributed blocks of k- or i-carrageenan disaccharide units, and blocks of alternating k- and i-carrageenan disaccharide units (hybrid blocks) (Guibet et al., 2008; van de Velde, Peppelman, Rollema, & Tromp, 2001). The relative amount of k-, i-carrageenan and hybrid blocks depends on a complex interplay between the seaweeds biology (Chopin, Kerin, & Mazerolle, 1999; Guibet et al., 2008; McCandless & Craigie, 1979) and the extraction procedure used to recover the natural polysaccharide (Lahaye, 2001; McHugh, 2003). Indeed, biological precursors such as m- and n-carrageenan naturally occur in the copolymer and are converted into k- and i-carrageenan, respectively, during an alkali treatment performed prior to the extraction. Parameters such as the concentration in alkali or the duration of the treatment affect the extent of precursor conversion (Hilliou, Larotonda, Abreu, et al., 2006), and the extracted k/ihybrid carrageenans may contain residual m- and n-carrageenan disaccharide units (van de Velde et al., 2005). The k- and

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i-carrageenan blocks impart gel properties and thereby make k/ihybrid carrageenans good candidates for applications such as dairy food where mixtures of k- and i-carrageenans are conventionally used (Arltoft, Ipsen, Madsen, & de Vries, 2007; Bixler, 1996; Villa˜ o, 2004). However, nueva, Mendoza, Rodrigueza, Romero, & Montan there is a lack in the literature for the structural and mechanical characterization of gels made from k/i-hybrid carrageenans (Arltoft et al., 2007; van de Velde, 2008). We recently extracted gelling k/i-hybrid carrageenans from Mastocarpus stellatus seaweeds, following an optimized process (Hilliou, Larotonda, Abreu, et al., 2006; Hilliou, Larotonda, Sereno, & Gonçalves, 2006). Preliminary studies (Hilliou & Gonçalves, 2007) of gels obtained in the presence of KCl salt indicated that the biopolymer show rheological properties which are intermediate between i-carrageenan gels at low concentrations and k-carrageenan gels at higher concentrations. Here, we use cryoSEM and Fourier Transform rheology (FTR) (Wilhelm, 2002) to address the coupling between the microstructure and the mechanical properties of k/i-hybrid carrageenan gels in KCl salt. Recent improvement in data acquisition systems (van Dusschoten & Wilhelm, 2001; Hilliou, van Dusschoten, Wilhelm, Burhin, & Rodger, 2004; Klein, Venema, et al., 2007) now permit to apply FTR concepts to the viscoelastic characterization of materials submitted to large deformations. When large amplitude oscillatory and sinusoidal (LAOS) shear strains are applied to a material, its stress response is no more a single sinusoidal (the stress–strain curve departs from linearity). Parameters obtained from the Fourier transform of the stress waveforms showed to be very sensitive to material structural properties such as the branching of polymer chains (Neidho¨fer, Sioula, Hadjichristidis, & Wilhelm, 2004), polymer blend morphology (Carotenuto, Grosso, & Maffetone, 2008) or structural assets of colloidal gels (Hyun, Nam, Wilhelm, & Ahn, 2006; Le Grand & Petekidis, 2008). FTR seems therefore to be the adequate toolbox to simultaneously study both structural and mechanical characteristics of k/i-hybrid carrageenan gels. To the best of our knowledge, FTR results obtained with carrageenan gels have not been reported yet. Another motivation for exploring the FTR response of k/i-hybrid carrageenan gels originates from theoretical considerations for colloidal gels (Gisler, Ball, & Weitz, 1999; Shih, Shih, Kim, Liu, & Aksay, 1990; Wu & Morbidelli, 2001). In these systems, the interplay between structure and mechanical properties is not only mirrored in the concentration dependence of the gel elastic shear modulus G0, but also in the gel mechanical behavior in the large strain regime. Namely a strain hardening behavior that scales with the concentration (Gisler et al., 1999) is predicted. This is alike with the non linear behavior of protein globular gels (Pouzot, Nicolai, Benyahia, & Durand, 2006). In addition, power laws for the concentration dependence of the critical strain gC that signals the onset of break-up of weakest elastic links in the fractal network (gel fracture) are also predicted. The exponent can be related to structural parameters such as the fractal dimension of networking clusters in silica gels (Shih et al., 1990) or protein gels (Wu & Morbidelli, 2001). The FTR characterization of k/i-hybrid carrageenan gels is first presented. Next, fractal colloidal gel models are used to extract mechanically relevant structural parameters from FTR data. Finally, the obtained structural parameters are discussed in light of the gels microstructure imaged by cryoSEM. 2. Materials and methods 2.1. Carrageenan A k/i-hybrid carrageenan was isolated from Mastocarpus s. seaweeds hand-collected in November 2004 on intertidal rocks located at Vila Praia de Ancora (4148.93N, 8 51.94W). A single batch

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of k/i-hybrid carrageenan was extracted from the seaweeds by using an optimized extraction process described in length elsewhere (Hilliou, Larotonda, Abreu, et al., 2006; Hilliou, Larotonda, Sereno, et al., 2006). Briefly, right after sampling, seaweeds were washed several times with tap water in order to remove non algal materials, dried at 60  C for 48 h in a ventilated oven, and stored at room temperature in sealed plastic bags until extraction. Dried seaweeds were then submitted to an alkaline treatment (72 h in 0.1 mol/dm3 Na2CO3 and at room temperature) before extraction at 95  C during 2 h and at a pH of 8. Then, seaweeds were separated from the carrageenan solution by filtration. The k/i-hybrid carrageenan was recovered from the solution by precipitation of the filtrate in 2 volumes of ethanol (95%). The precipitate was further washed with ethanol and dried in a ventilated oven before grinding to a powder. The powder was then further purified by dissolving in hot distilled water and performing centrifugation at 50 000g and 38  C during 40 min. The supernatant was then recovered and dried at 60  C under vacuum to give a purified k/i-hybrid carrageenan sample. Size exclusion chromatography (Waters Co. apparatus with a Waters Ultrhydrogel Linear column and a Waters 2410 differential refractive index detector) performed with 0.1 wt% k/i-hybrid carrageenan solutions in 0.1 mol/dm3 NaCl at 40  C indicated a high molecular mass (Mw ¼ 1.6  106 g/mol) and a rather polydisperse (Mw/Mn ¼ 2.3) polysaccharide. Proton NMR spectra recorded at 80  C with a Bruker ARX 400 NMR spectrometer (400 MHz) on polysaccharides dissolved in D2O, using TMSPSA as internal standard, showed that the k/ i-hybrid carrageenan consists of 51.2 mol% of k-carrageeenan disaccharide units, 31.7 mol% i-carrageenan disaccharide units and 17.1 mol% non gelling carrageenan disaccharides such as m- and n-carrageenan. The cation content in the k/i-hybrid carrageenan sample was quantified by Inductively Coupled Plasma-Atomic Emission Spectroscopy. Results showed that the polysaccharide is essentially recovered in the sodium form (roughly 3 wt% Naþ), whereas all other cations remained below the sensitivity of the apparatus. Carrageenan solutions at various concentrations c were produced by dissolving during 1 h under strong stirring and at 80  C the appropriate carrageenan mass in 0.1 mol/dm3 KCl. Such solvent was chosen to virtually eliminate any change in the ionic strength resulting from the addition of the residual sodium salt associated with the k/i-hybrid carrageenan (Meunier, Nicolai, & Durand, 2000). The rheological properties of k- and i-carrageenan gels are known to depend on the ionic strength (Te Nijenhuis, 1997), and one might suspect that this holds true for k/i-hybrid carrageenan (Chanvrier et al., 2004). Since mechanical properties are to be scaled here with a single parameter, namely the concentration c, the ionic strength is to be kept constant. In addition, k/i-hybrid carrageenan gels obtained under such salt conditions show sufficient elasticity and strength on a wide enough concentration range to be studied by FTR (see also below) and to be further handled for cryoSEM imaging. 2.2. Fourier-transform rheology A Rheometric Scientific advanced rheometer expansion system (ARES) equipped with a dual range force rebalance transducer (100FRTN1) and a cross-hatched plate-plate geometry was used. This geometry was chosen to avoid wall slip, although it does not permit to apply a spatially homogeneous strain rate across the sample. However, it has been shown (see Fig. 4 in Wilhelm, Reinheimer, & Ortseifer, 1999) that for strain amplitudes below 1000%, such issue is not important as FTR data obtained with plate-plate geometry collapse onto FTR data obtained with cone and plate geometry. Hot carrageenan solutions were directly loaded in the shearing geometry pre-heated to 70  C. The gap between the plates

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was adjusted to 1 mm and both sample and geometry were immediately covered with paraffin oil to avoid water evaporation. The solution was slowly cooled down (1  C/min) to 20  C, and 3 h were left to the gelled sample to equilibrate, while both storage (G0 ) and loss (G00 ) moduli were recorded with a 0.1% oscillatory strain amplitude applied at 1 Hz. Samples showing more than 5% evolution in G0 and G00 values during the last 20 min of the equilibration step were not further studied as a typical FTR characterization took roughly 30 min. Such experimental requirement limits the range of polysaccharide concentration studied here, as solutions with lower concentrations exhibit slower kinetics for gel structural build up. FTR experiments consist in performing a strain sweep at a frequency of 1 Hz. This excitation frequency was chosen based on the good linearity displayed by the strain rheometer (Wilhelm, 2002) (for both motor and force transducer) for all strain amplitudes used and torque levels measured. Furthermore, as all equilibrated gels showed no relaxation process within the frequency range accessed by the rheometer, the characteristic time of the flow is not a pertinent parameter here (Neidho¨fer et al., 2004). An excitation frequency u1/2p ¼ 1 Hz was therefore chosen which enables fast enough FTR characterization to be performed while no measurable structural evolution takes place in the gels. For each strain value, typically 30 cycles are applied to the sample and both applied strain and sample stress response were recorded and Fourier transformed as described in detail elsewhere (Wilhelm, 2002), using home-written Lab VIEW programs. After a first transient, the oscillatory stress response reaches a steady state, and the 20 last cycles were used to compute the Fourier transforms for both strain and torque signals. 2.3. Cryogenic scanning electron microscopy (CryoSEM) and image analysis Carrageen gels were produced within the parallel plates (diameter 40 mm) of a stress-controlled rheometer (ARG2, TA instruments), using the same thermal and mechanical histories as for the FTR characterization. Then gels were gently removed from the shearing tools by first unscrewing the upper plate from the rheometer to avoid fracturing the sample when lifting up the shearing geometry. Then, sliding the upper plate on the gel disk and cutting roughly 1 cm2 portions within the sample using a scalpel, allowed for the smooth ungluing of the entire sections from the bottom plate. Gel portions were then stored overnight at 20  C in sealed plastic cups prior to cryoSEM analysis. 1 mm thick cubes were cut from the gel parts, rapidly immersed in liquid nitrogen slush at 210  C for 2 min and vacuum transferred to an Alto 2500 (Gatan Inc., CA) cryo preparation chamber attached to a JEOL JSM 6301F scanning electron microscope. Frozen samples were fractured at 185  C, etched during 2 min at 90  C to partially sublimate water from the fractured gel surface which was finally gold-coated for 2 min. Samples were viewed at 130  C using a primary accelerating voltage of 10 kV and resulting SEM images were analyzed using ImageJ software (National Institutes of Health, USA). For each sample, the averaged fractal dimension d of the imaged structure was computed from 10 pictures captured at different locations with magnification of 2000, and analyzed using the Fractal Dimension and Lacunarity plug-in. For each picture, the software computes a mean fractal dimension obtained from 8 randomly chosen sub areas in the picture which are individually submitted to the box counting method. Therefore for each gel sample, 80 images are used to compute a mean fractal dimension d with associated statistical standard error. Software parameters were calibrated using model fractal objects, namely the Koch box and the Sierpinski carpet, with known theoretical fractal dimensions d.

3. Results and discussion 3.1. FTR response of k/i-hybrid carrageenan gels Examples for the torque time transient and respective Fourier transform at 2 different strains are presented in Fig. 1. These data were recorded during a strain sweep performed on a k/i-hybrid carrageenan gel with a concentration c ¼ 0.5 wt%. For large enough oscillatory and sinusoidal strain amplitudes, the gel torque response is no more sinusoidal and the amplitude spectrum of the torque Fourier transform shows harmonics Inu1 (see Fig. 1b and c). The quantitative and qualitative analysis of the strain dependence of the harmonics relative amplitudes Inu1 =Iu1 (with respect to the fundamental amplitude Iu1 ) and phases fnu1  nfu1 (with respect to the fundamental phase fu1 ) of the torque Fourier transform allows for the accurate characterization of the non linear rheological behavior of materials (see Fig. 1d), in contrast to both G0 and G00 which loose their mathematical definition as they are no more constant (Cho, Hyun, Ahn, & Lee, 2005). Instead, both moduli depend on the strain whenever the stress response shows departure from sinusoidal waveform. Here, we restrict the FTR data analysis to second and third harmonics relative amplitude, namely I2u1 =Iu1 and I3u1 =Iu1 , respectively, as well as to the third harmonic phase angle f3u1  3fu1 . Such data analysis is illustrated in Fig. 2 for two k/i-hybrid carrageenan gels. Data over sampling techniques (van Duschotten & Wilhelm, 2001) significantly improve the signal to noise ratio (Hilliou et al., 2004) and therefore turn parameter I3u1 =Iu1 into a very sensitive indicator of the cross over between linear and non linear mechanical behavior (Wilhelm, Reinheimer, Ortseifer, Neidhofer, & Spiess, 2000). As a result, a criterion for the onset of non linear behavior (namely a zero strain non-linearity coefficient) has been recently introduced (Hyun & Wilhelm, 2009). The occurrence of even harmonics in the Fourier transform of the stress response relates to a loss of symmetry in the stress waveform. In simple words, even harmonics show up whenever rotating to the left is different from rotating to the right (Wilhelm, 2002). Therefore, I2u1 =Iu1 is very sensitive to flow behaviors such as wall slip (Graham, 1995), shear banding or yield phenomena (Klein, Spiess, Calin, Balan, & Wilhelm, 2007) which both relate to spatially non homogeneous shear fields, and shear-induced orientation of anisotropic structures (Sagis, Ramaekers, & van der Linden, 2001; Sim, Ahn, & Lee, 2003). Neidho¨fer et al. (2004) recently showed that the third harmonic phase angle f3u1  3fu1 is particularly sensitive to macromolecular chain topologies such as star branched of linear chains. These authors suggested to use this FTR parameter to characterize the strain softening (for values ranging from 0 to 180 ) or strain hardening behaviors (for values approaching asymptotically 0 ) of the stressed sample. Fig. 2 shows the strain dependence of FTR parameters for two representative k/i-hybrid carrageenan gels obtained at different concentrations. After a first local minimum displayed at lower strains and assigned to the interplay between the inherent rheometer non-linearity and the increase in torque transducer sensitivity, the third scaled harmonic I3u1 =Iu1 shows a power law increase with the strain, characterized by an exponent approaching the value of 2. At strains higher than 50%, I3u1 =Iu1 shows a maximum and eventually levels off to values between 10% and 20%. For the same range of strains, the second harmonic continuously increases above 1%, suggesting that the maximum in I3u1 =Iu1 relates to a non symmetric stress response. Second harmonics were also measured with a xanthan solution (Sagis et al., 2001), and attributed to the shear-induced alignment of anisotropic colloidal particles. Three-dimensional dynamics simulations of electrorheological fluids recently correlated the emergence of significant I2u1 =Iu1 to the shear-induced structural rearrangement of oriented

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Fig. 1. Response of a k/i-hybrid carrageenan gel (c ¼ 0.5 wt%) to a strain sweep. Each solid and open squares in a) represent the storage modulus G0 and loss modulus G00 , respectively, measured during the last cycle of the 30 cycles applied for each strain. The torque time dependence recorded for a 10% shear strain is displayed in b), along with the frequency spectrum of the normalized amplitude Inu =Iu of the torque Fourier transform; Note that harmonics are observed in the amplitude spectrum indicating a non linear torque response, whereas the storage modulus G0 in a) does not show any evident strain dependence at 10%. Chart c) displays the torque response and its corresponding Fourier transform spectrum (normalized amplitude spectrumInu =Iu ) recorded at a 160% strain. Note that harmonics are more intense than in b). Chart d) shows the strain dependence of second (solid squares) and third (empty squares) scaled harmonics, I2u1 =Iu1 and I3u1 =Iu1 , respectively, obtained from the Fourier transforms computed for each strain.

Fig. 2. FTR response of k/i-hybrid carrageenan gels with c ¼ 0.9 wt% (squares) and c ¼ 1.5 wt% (triangles), showing the strain dependence of the normalized third harmonic I3u1 =Iu1 (solid symbols), the normalized second harmonic (empty symbols) and the third harmonic angle f3u1  3fu1 (inset). The vertical dashed line indicates the critical strain gC for which I2u1 =Iu1 reaches 1%.

columnar clusters (Sim et al., 2003). However, we do not expect any intrinsic structural anisotropy such as liquid crystalline domains in the k/i-hybrid carrageenan gels studied here. This is actually confirmed by the cryoSEM characterization (see below). We therefore suggest that non reversible mechanical behaviors such as wall slip (Graham, 1995), yielding and shear banding phenomena (Klein, Spiess, et al., 2007), or gel fracture are responsible for the emergence of significant scaled second harmonics and the maximum in I3u1 =Iu1 . Note that for strain levels where significant I2u1 =Iu1 are measured, the stress response shows a dynamic steady state where the scaled higher harmonics remain constant with time, in contrast to the periodic torque which varies slowly with time. The strain dependence of both I3u1 =Iu1 and I2u1 =Iu1 is virtually the same for the two gels. In contrast to this, the third harmonic phase angle underlines differences. For the 0.9 wt% gel, the low strain regime of f3u1  3fu1 shows a strain hardening behavior characterized by a value approaching 0 (Neidho¨fer et al., 2004; Wilhelm, 2002), whereas a shear thinning behavior is assigned to the gel at 1.5 wt% as f3u1  3fu1 increases from 0 to roughly 180 . At strains higher than 100%, both gels show a shear thinning behavior which coincides with the emergence of a significant second harmonic and the plateau in the third harmonic. The weak concentration dependence of the scaled third harmonic I3u1 =Iu1 , together with the strain hardening behavior are in qualitative

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agreement with the non linear rheological behavior of fractal gels formed by diffusion-limited aggregation of colloidal latex particles (Gisler et al., 1999). Heat set-gels obtained from globular proteins also showed strain hardening (Pouzot et al., 2006) in contrast to protein gels obtained by a change in ionic strength or upon acidification. Evidently, the gel mechanism in colloidal and protein gels differs from the aggregation of helical conformers which drives the formation of a carrageenan gel. However, in both latex and protein systems, strain hardening is due to the extension of elastic structural backbones (see below), and the aim of the present exercise is to correlate such gel structural properties (fractal dimensions of gel structure and elastic backbone) with the strain hardening of k/ihybrid carrageenan gels. For gels formed with more than 1.25 wt% of k/i-hybrid carrageenan, the FTR response is reminiscent from the non linear rheological response of hard gels made of closely packed triblock copolymer micelles (Hyun et al., 2006), as these systems show a saturation in I3u1 =Iu1 values between 20% and 30% at higher strains and a shear thinning behavior. A maximum in the strain dependence of I3u1 =Iu1 has also been reported for shear thickening colloidal suspensions of polymer particles (Kallus et al., 2001), and also for colloidal suspensions of fibril clusters close to the percolation point (Veerman, Sagis, Venema, & van der Linden, 2005). For the latter suspension, additional in-situ rheo-optical techniques revealed that the first increase and maximum are related to orientation and further aggregation of fibril clusters, whereas cluster break-up is responsible for the decrease of I3u1 =Iu1 at higher strains. However, neither third harmonic phase angles nor scaled second harmonics are reported in the study of Veerman et al. (2005), thus impeding any direct comparison between cluster break-up mechanisms and data plotted in Fig. 2. 3.2. Concentration scaling of rheological parameters According to theories describing the mechanical properties of fractal colloidal gels, the fractal dimension df of the strongly interconnected clusters forming the gels, and the fractal dimension x of weakly stress bearing backbones in the clusters are related to exponents A and B of the power laws describing the concentration dependence of the elastic shear modulus G0, and of the critical strain for onset of gel fracture gC, respectively, through the following equations (Shih et al., 1990) 3þx

G0 zcA zc3df

Fig. 3. Concentration scaling of the elastic shear modulus G0. The dotted line represents a power law fit to the data for G0, with exponent A ¼ 3.11  0.1.

of gel fracture. gC does not depend on the biopolymer concentration in the gels, for the range of concentrations and shear strains explored. At highest concentrations, I2u1 =Iu1 remains below 1% even for strains as high as g ¼ 1000%, and therefore only a limited number of data for gC are reported in Fig. 4. Thus no structural information can be extracted from this non linear parameter, using equations (1) and (2), or using the recent extension (Wu & Morbidelli, 2001) of the original colloidal gel model (Shih et al., 1990). A constant strain of roughly 200% was reported for the onset of fracture of globular protein gels formed at low protein concentration and showing strain hardening behavior (Pouzot et al., 2006). Although the unbending of rather rigid (x ¼ 1.27) stress bearing links within fractal clusters was shown to be responsible for the concentration scaling of the strain hardening behavior, the fracture mechanism remained unclear. Mellema, van Opheusden, and van Vliet (2002) also measured a constant maximum linear strain with fractal casein gels. These authors developed a model to assign this mechanical behavior to overstretching of stress bearing bonds with fractal dimension x close to unity (straight bonds) and made of flexible links. The stress at which such gels yield was predicted to

(1)

ð1þxÞ

gC zcB zc 3df

(2)

Fig. 3 displays the concentration dependence of the elastic shear modulus G0 measured on equilibrated gels during the first cycles of the FTR experiments (e.g. in the linear regime). The double logarithmic plot suggests a power law dependence of G0 with the polysaccharide concentration. A linear fitting to the double logarithmic plot of the data is also presented in Fig. 3 and the resulting exponent A is 3.11  0.1. This exponent is identical to the exponent found in a previous study where a lower ionic strength and a faster cooling rate were used (Hilliou & Gonçalves, 2007). This result suggests that k/i-hybrid carraggenan gels in KCl are weakly sensitive to these gelling parameters and as such they differ from kcarrageenan gels (Hermansson, Eriksson, & Jordansson, 1991). Fig. 4 shows the concentration dependence of the critical strain gC for which the second harmonic reaches 1%, along with the concentration dependence of the corresponding stress sY measured at gC. In light of theories for fractal colloidal gels and based on the discussion about the physical meaning of second scaled harmonic, we identify gC with the critical strain for the onset

Fig. 4. Concentration scaling of the critical strain for onset of irreversible gel fracture gC (solid triangles) and of the yield stress sY (open squares) measured at gC. The dotted line is a linear fit to the logarithmically plotted data.

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be an increasing power law function of the concentration. In Fig. 4, sY actually shows a power law dependence with the concentration. The exponent of the power law is 1.9  0.3. The concentration scaling of sY, along with the constant strain for irreversible structural break-up suggest that k/i-hybrid carrageenan gels belong to a category of fractal colloidal gels made of straight strands with flexible links, which unbend and stretch under strain and eventually overstretch thus leading to the gel fracture at higher strains.

3.3. Modeling of the strain hardening An alternative route to the determination of the fractal dimension x is to relate this structural parameter to the strain hardening of the gels (Gisler et al., 1999), rather than to the gel fracture (see equations (1) and (2)). Assuming that the shear-induced affine deformation of stress bearing fractal strands in the clusters is mainly associated with extension rather than compression or rotation, and assuming that the internal structure of the clusters is not affected (both df and x remain the same), the stress response of the gel can be expanded in a series development of the strain as (Do¨tsch, Pollard, & Wilhelm, 2003; Pouzot et al., 2006):

2

sxy ¼ G0 g41 þ

N X b2j j¼1

b0

3

g

2j 5

(3)

with b0 ¼ 4pðx þ 1Þ=15ðx  1Þ. Coefficients b2j are polynomial functions of x as described in detail elsewhere (Pouzot et al., 2006). Equation (3) indicates that the stress response is a function of odd powers of the strain and shows concentration scaling through the concentration scaling of the elastic shear modulus G0. A periodic time dependent stress was computed by inserting an oscillatory sinusoidal strain g ¼ g0sin (u1t) in equation (3) and using 10 series. The time dependent stress was subsequently Fourier transformed with the Lab VIEW routine used for the FTR experiments. Scaled third harmonics I3u1 =Iu1 computed for various strains g using different values of x are presented in Fig. 5. Calculated I3u1 =Iu1 solely

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depend on parameter x and the input strain, whereas all computed third phase angles f3u1  3fu1 remain constant to a value of 0 (results not shown). Note that the corresponding scaled third harmonics at lower strain show a plateau, as a result of the simulation noise originating from the discretization of the input strain. Equation (3) therefore demonstrates that a zeroing third harmonic phase angle definitely qualifies a strain hardening behavior, as previously suggested by Neidho¨fer et al. (2004). The strain hardening model for fractal colloidal gels predicts that all I3u1 =Iu1 curves measured for different concentrations should collapse onto a single curve, which corresponds to a single fractal dimension x. Increasing parameter x has one major effect on the strain dependence of calculated I3u1 =Iu1 : all curves are shifted to higher strains as the fractal dimension of backbones in the clusters is larger. This is expected, based on the fact that more flexible strands with correspondingly increasing x above 1 require more strain to be stretched. Experimental I3u1 =Iu1 curves measured with k/i-hybrid carrageenan gels formed at different concentrations are also displayed in Fig. 5. As mentioned earlier (see also Fig. 2), the I3u1 =Iu1 curves for k/i-hybrid carrageenan gels only weakly depend on the polysaccharide concentration, and experimental curves in Fig. 5 are well described by equation (3) when x values ranging from 1.1 to 1.15 are used. We therefore conclude from this analysis that the fractal dimension of stress bearing backbones in strain hardening k/i-hybrid carrageenan gels is x ¼ 1.13  0.02. Inserting the new x value into equation (1) leads to a new fractal dimension for the interconnected clusters, df ¼ 1.67  0.04. For comparison, a direct analysis of the strain dependence of the scaled shear storage modulus G0 /G0 with the following equation (Pouzot et al., 2006),

2 3 N X b2j 2j G0 g 5 ¼ 41 þ G0 b j¼1 0

(4)

is proposed in the inset of Fig. 5. Experimental curves are bracketed between two curves computed using x ¼ 1.25 and x ¼ 1.4. The error on parameter x is clearly larger than the error obtained using the FTR approach. The better performance of the FTR analysis can be explained as follows. First, the scaled third harmonic shows a larger dependence on the strain than the scaled storage modulus (see equation (3) with higher order in strain than equation (4)). As such, strain hardening results in an increase in I3u1 =Iu1 over 2 decades, whereas G0 /G0 only increases by a factor 2. Second, the range of strains where reversible strain hardening is measured is larger for FTR. This stems from the fact that the onset for non linear behavior is readily obtained with I3u1 =Iu1 (Hyun & Wilhelm, 2009), while G0 / G0 has an asymptotic departure from 1 (see equation (4)) which is inherently hard to quantify and depends on the accuracy of the rheometer. Moreover, I2u1 =Iu1 gives a direct estimate of non reversible phenomena sowing up at higher strains, whereas time consuming reproducibility (Pouzot et al., 2006) tests are needed to establish the limit of validity of equation (4). The question arising now is how the fractal dimension obtained with the FTR analysis of strain hardening relates to the actual gel microstructure. 3.4. Carrageenan gels microstructure obtained from cryoSEM imaging

Fig. 5. Strain dependence of the normalized third harmonic I3u1 =Iu1 calculated with equation (3) using x ¼ 1.1 (dashed line) and x ¼ 1.15 (solid line). Solid symbols represent normalized third harmonics I3u1 =Iu1 measured with k/i-hybrid carrageenan gels formed at various concentration (1.25 wt% (:), 1.1 wt% (C) and 0.75 wt% (-)). Inset: strain dependence of the normalized storage modulus G0 /G0 obtained for k/ihybrid carrageenan gels formed at 1.25 wt% (O), 1.1 wt% (B) and 0.75 wt% (,). Dashed and solid lines correspond to equation (4) computed with x ¼ 1.25 and x ¼ 1.4, respectively.

Fig. 6 shows selected samples of cryoSEM images of gels obtained with a biopolymer concentration of 2 wt%. Darker areas in the images correspond to the amorphous water which was not sublimated during the sample preparation process, whereas lighter objects correspond to carrageenan structures. Note also that ice crystals with polyhedral shapes (see the zoomed image in Fig. 6B) and carrageenan debris resulting from the fracture of frozen gels,

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Fig. 6. CryoSEM pictures of gels of k/i-hybrid carrageenan. Biopolymer concentration is 2 wt% for all gels. Scale bar in picture (A) indicate 30 microns. Scale bar in picture (B) indicate 6 microns.

appear as white spots in the images. The overall picture emerging from the cryoSEM characterization is that all gels appear as porous and cellular structures made of connected walls. Within walls, carrageenan strands are evidenced (see the lower left corner of the picture in Fig. 6B). Such images conform to earlier cryoSEM characterization of k-carrageenan gels formed in CaCl2 salt (MacArtain, Jacquier, & Dawson, 2003). The analysis of pictures with 256 grey levels transformed into binary images indicates that the cell wall thickness is within 100 and 300 nm k-carrageenan helices with thickness of the order of 1 nm were imaged by atomic force microscopy (Ikeda et al., 2001) performed on diluted solutions of k-carrageenan in 0.1 M KCl. This study also reported helix aggregation in bundles as thick as 6 nm, but obtained at much lower polysaccharide concentration than the one corresponding to the gel imaged in Fig. 6. Based on these structural characteristics and assuming that helices with similar morphology are formed in k/ i-hybrid carrageenan gels, we speculate that the cell walls depicted in Fig. 6 are made of hundreds of stacked helices. Gels obtained at lower concentrations show the same structural features as the pictures displayed in Fig. 6. This is illustrated in Fig. 7 where two k/ i-hybrid carrageenan gels obtained at concentrations corresponding to shear thinning (Fig. 7A) and strain hardening (Fig. 7B) are pictured. Interconnected walls are observed for both gels. Walls are evidently less branched to each other when less carrageenan material is available to build the structure. Therefore the existence of larger pores (the pore size in Fig. 6 is of the order of 6 microns, against roughly 25 microns in Fig. 7B) with free dandling and thinner walls, comes as no surprise. Note that structures imaged in

Fig. 7 appear uniform on length scale as large as 100 microns. The morphological similarity between the two gels pictured in Fig. 7 is also mirrored in the fractal dimension d computed for each gel structure from a set of 10 pictures captured at 10 different locations in each sample. We found d ¼ 1.69  0.04 for the gel pictured in Fig. 7A and d ¼ 1.63  0.05 for the gel imaged in Fig. 7B, thus indicating that the error inherent to the image analysis utilized here does not allow a structural distinction between the two gels. The corresponding averaged fractal dimension d is 1.66  0.05. This is well below the maximal dimension that can be inferred from the present image analysis, and thus geometric opacity can be ruled out (Bushell, Yan, Woodfield, Raper, & Amal, 2002). Note here that d is obtained from a box counting analysis covering a typical length scale of 100 microns (see Fig. 7). In this analysis, the power law dependence of the box number on the box size typically spanned length scales from 0.3 microns to 30 microns. Therefore, d describes the fractal dimension of a structure made by the arrangement of interconnected walls, and is not related to the internal wall structure which cannot be accessed on such length scale. The fractal dimension extracted from the cryoSEM analysis of k/i-hybrid carrageenan gels is in fairly close agreement with the fractal dimension df obtained from the theoretical analysis of FTR experiments performed with less concentrated gels (below roughly 1.5 wt% k/i-hybrid carrageenan). This result suggests that the fractal structures imaged by cryoSEM can be identified with the mechanically effective fractal clusters obtained from the FTR analysis. However, the range of length scale over which a fractal structure is obtained with the present image analysis is rather

Fig. 7. CryoSEM pictures of k/i-hybrid carrageenan gels obtained with a concentration of 2 wt% (A) and 0.7 wt% (B). Scale bars in the pictures indicate 100 microns.

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large: for instance, light scattering experiments performed on k-carrageenan gels report fractal dimension on length scales of the order of hundreds of nanometres (Mangione, Giacomazza, Bulone, Martorana, & San Biagio, 2003). Therefore, alternative techniques such as small angle light scattering or even X-ray scattering (due to the turbidity of gels at higher concentrations) should definitely be tested in the future in an attempt to directly access the fractal dimension d through the power law regime of the angle dependence of the scattered intensity, because image analysis with the box counting method is not the best experimental tool to obtain fractal dimensions (Bushell et al., 2002). The stress bearing links with fractal dimension x ¼ 1.13 still need to be compared to the structures pictured in Figs. 6 and 7. x is close to the fractal dimension of a rod (which is 1) and therefore indicates that these links are rather straight. This result conforms to the string-like arrangement of cell walls as pictured in Fig. 7. We therefore propose that the string-like arrangement of walls corresponds to the straight links (with fractal dimension x) responsible for the elasticity G0 of the fractal network with dimension d. The reversible strain hardening behaviour evidenced in FTR experiments is also due to these links which are stretching under strain. At higher strains, the stretched links eventually break-up in a way similar to the fracture mechanism depicted for fractal colloidal gels (Mellema et al., 2002). The microstructure imaged in Fig. 7a does not provide a direct interpretation to the strain softening observed for gels formed with more that 1.5 wt% k/i-hybrid carrageenan. Nevertheless, the strain softening is related to a change in the microstructure of the stress bearing links rather than in the fractal dimension of the network, because the cryoSEM images suggest that clusters formed at higher concentration remain structurally unchanged with a constant fractal dimension of 1.66. 4. Conclusion FTR experiments performed on k/i-hybrid carrageenan gels formed in 0.1 M KCl with polysaccharide concentrations ranging from 0.5 wt% to 2 wt% show that the non linear mechanical behavior of gels formed at concentration below 1.5 wt% is of the strain hardening type. This behavior is the result of the straininduced unbending and subsequent stretching of fractal and flexible stranded backbones pervading the fractal clusters which are strongly interconnected to build up the gel structure. The strain hardening shows three specific characteristics: i) a third harmonic phase angle which shows no strain dependence with a value of 0 , ii) a scaled second harmonic which remains below 1% and iii) a quadratic increase of the scaled third harmonic with the strain which shows no concentration dependence. These three specifics are rationalized by a fractal colloidal gel model which allows the extraction of the fractal dimension of the stranded backbones (1.13  0.02) and of the fractal dimension of the networked clusters (1.67  0.04) from the strain dependence of the scaled third harmonic, and from the concentration dependence of the equilibrium shear modulus of the gels, respectively. The gels fractal dimension obtained from cryoSEM imaging is in fair agreement with the fractal dimension measured by FTR. However, given the limitations in the general validity of the box counting method, this matching is to be taken with caution. Even though a fractal dimension is only of limited information, we can relate the values from direct imaging techniques to the values obtained from a new mechanical characterization (FTR). As such, the study presented here is, to the best of our knowledge, the first attempt to relate morphological properties to linear and non linear mechanical properties for this type of carrageenan gels. At strains larger than 100%, significant scaled second harmonics show up and suggest the irreversible break-up of the overstretched stranded backbones.

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Eventually, k/i-hybrid carrageenan gels fracture when a yield stress is reached. The latter shows a quadratic dependence with the polysaccharide concentration and such result is in agreement with a straight stranded morphology showing finite flexibility.

Acknowledgments The authors thank the Project Based Personal Exchange Program - DAAD/GRICES (Proc. 4. 1.1/DAAD 00674) for funding. L.H. thanks Dr. Daniela Silva at the Materials Centre of the University of Porto (CEMUP) for her help during the cryoSEM experiments.

References Arltoft, D., Ipsen, R., Madsen, F., & de Vries, J. (2007). Interactions between carrageenans and milk proteins: a microstructural and rheological study. Biomacromolecules, 8, 729–736. Bixler, H. J. (1996). Recent developments in manufacturing and marketing carrageenan. Hydrobiologia, 326/327, 35–57. Bushell, G. C., Yan, Y. D., Woodfield, D., Raper, J., & Amal, R. (2002). On techniques for the measurement of the mass fractal dimension of aggregates. Advances in Colloid and Interface Science, 95, 1–50. Carotenuto, C., Grosso, M., & Maffetone, P. L. (2008). Fourier transform rheology of dilute immiscible polymer blends: a novel procedure to probe blend morphology. Macromolecules, 41, 4492–4500. Chanvrier, H., Durand, S., Garnier, C., Sworn, G., Bouriot, S., & Doublier, J. L. (2004). Gelation behavior and rheological properties of k/i-hybrid carrageenans. In P. A. Williams, & G. O. Phillips (Eds.), Gums and stabilisers for the food industry, vol. 12 (pp. 139–144). Cambridge: The Royal Society of Chemistry. Cho, K. S., Hyun, K., Ahn, K. H., & Lee, S. J. (2005). A geometrical interpretation of large amplitude oscillatory shear response. Journal of Rheology, 49, 747–758. Chopin, T., Kerin, B. F., & Mazerolle, R. (1999). Phycocolloid chemistry as a taxonomic indicator of phylogeny in the Gigartinales, Rhodophyceae: a review and current developments using Fourier transform infrared diffuse reflectance spectroscopy. Phycological Research, 47, 167–188. Do¨tsch, T., Pollard, M., & Wilhelm, M. (2003). Kinetics of isothermal crystallization in isotactic polypropylene monitored with rheology and Fourier-transform rheology. Journal of Physics: Condensed Matter, 15, S923–S931. van Dusschoten, D., & Wilhelm, M. (2001). Increased torque transducer sensitivity via oversampling. Rheologica Acta, 40, 395–399. Funami, T., Hiroe, M., Noda, S., Asai, I., Ikeda, S., & Nishinari, K. (2007). Influence of molecular structure imaged with atomic force microscopy on the rheological behavior of carrageenan aqueous systems in the presence or absence of cations. Food Hydrocolloids, 21, 617–629. Gisler, T., Ball, R. C., & Weitz, D. A. (1999). Strain hardening of fractal colloidal gels. Physical Review Letters, 82, 1064–1067. Graham, M. D. (1995). Wall slip and the non linear dynamics of large amplitude oscillatory shear flows. Journal of Rheology, 39, 697–712. Guenet, J. M. (2000). Structure versus rheological properties in fibrillar thermoreversible gels from polymers and biopolymers. Journal of Rheology, 44, 947–960. Guibet, M., Boulenguer, P., Mazoyer, J., Kervarec, N., Antonopoulos, A., Lafosse, M., et al. (2008). Composition and distribution of carrabiose moieties in hybrid kappa-/ iota-carrageenans using carrageenases. Biomacromolecules, 9, 408–415. Hermansson, A.-M. (1989). Rheological and microstructural evidence for transient states during gelation of kappa-carrageenan in the presence of potassium. Carbohydrate Polymers, 10, 163–181. Hermansson, A.-M., Eriksson, E., & Jordansson, E. (1991). Effect of potassium, sodium and calcium on the microstructure and rheological behaviour of kappacarrageenan gels. Carbohydrate Polymers, 16, 297–320. Hilliou, L., & Gonçalves, M. P. (2007). Gelling properties of a kappa/iota hybrid carrageenan: effect of concentration and steady shear. International Journal of Food Science and Technology, 42, 678–685. Hilliou, L., Larotonda, F. D. S., Abreu, P., Ramos, A. M., Sereno, A. M., & Gonçalves, M. P. (2006). Effect of extraction parameters on the chemical structure and gel properties of kappa/iota-hybrid carrageenans obtained from Mastocarpus stellatus. Biomolecular Engineering, 23, 201–208. Hilliou, L., Larotonda, F. D. S., Sereno, A. M., & Gonçalves, M. P. (2006). Thermal and viscoelastic properties of kappa/iota-hybrid carrageenan gels obtained from the Portuguese seaweed Mastocarpus stellatus. Journal of Agricultural and Food Chemistry, 54, 7870–7878. Hilliou, L., van Dusschoten, D., Wilhelm, M., Burhin, H., & Rodger, E. R. (2004). Increasing the force torque transducer sensitivity of an RPA 2000 by a factor 510 via advanced data acquisition. Rubber Chemistry and Technology, 76, 192–200. Hyun, K., Nam, J. G., Wilhelm, M., & Ahn, K. H. (2006). Large amplitude oscillatory shear behavior of PEO-PPO-PEO triblock copolymer solutions. Rheologica Acta, 45, 239–249. Hyun, K., & Wilhelm, M. (2009). Establishing a new mechanical nonlinear coefficient Q from FT-rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules, 42, 411–422.

2330

L. Hilliou et al. / Food Hydrocolloids 23 (2009) 2322–2330

Ikeda, S., Morris, V. J., & Nishinari, K. (2001). Microstructure of aggregated and nonaggregated kappa-carrageenan helices visualized by atomic force microscopy. Biomacromolecules, 2, 1331–1337. Jones, J. L., & Marques, C. M. (1990). Rigid polymer network models. Journal de Physique (Paris), 51, 1113–1127. Kallus, S., Willenbacher, N., Kirsch, S., Distler, D., Neidho¨fer, T., Wilhelm, M., et al. (2001). Characterization of polymer dispersions by Fourier transform rheology. Rheologica Acta, 40, 552–559. Klein, C. O., Spiess, H. W., Calin, A., Balan, C., & Wilhelm, M. (2007). Separation of the nonlinear oscillatory response into a superposition of linear, strain hardening, strain softening, and wall slip response. Macromolecules, 40, 4250–4259. Klein, C., Venema, P., Sagis, L., van Dusschoten, D., Wilhelm, M., Spiess, H. W., et al. (2007). Optimized rheo-optical measurements using fast fourier transform and oversampling. Applied Rheology, 17, 45210. Lahaye, M. (2001). Developments on gelling algal galactans, their structure and physico-chemistry. Journal of Applied Phycology, 13, 173–184. Le Grand, A., & Petekidis, G. (2008). Effects of particle softness on the rheology and yielding of colloidal glasses. Rheologica Acta, 47, 579–590. MacArtain, P., Jacquier, J. C., & Dawson, K. A. (2003). Physical characteristics of calcium induced kappa-carrageenan networks. Carbohydrate Polymers, 53, 395–400. McCandless, E. L., & Craigie, J. S. (1979). Sulfated polysaccharides in red and brown algae. Annual Review of Plant Physiology, 30, 41–53. McHugh, D. J. (2003). A guide to the seaweed industry. Rome: FAO Fisheries Technical Paper No. 441. Mangione, M. R., Giacomazza, D., Bulone, D., Martorana, V., & San Biagio, P. L. (2003). Thermoreversible gelation of kappa-carrageenan: relation between conformational transition and aggregation. Biophysical Chemistry, 104, 95–105. Mellema, M., van Opheusden, J. H. J., & van Vliet, T. (2002). Categorization of rheological scaling models for particle gels applied to casein gels. Journal of Rheology, 46, 11–29. Meunier, V., Nicolai, T., & Durand, D. (2000). Structure and kinetics of aggregating kappa-carrageenan studied by light scattering. Macromolecules, 33, 2497–2504. Morris, E. R., Rees, D. A., & Robinson, G. (1980). Cation-specific aggregation of carrageenan helices – domain model of polymer gel structure. Journal of Molecular Biology, 138, 349–362. Neidho¨fer, T., Sioula, S., Hadjichristidis, N., & Wilhelm, M. (2004). Distinguishing linear from star-branched polystyrene solutions with Fourier-transform rheology. Macromolecular Rapid Communications, 25, 1921–1926. Piculell, L. (1995). Gelling carrageenans. In A. M. Stephen (Ed.), Food polysaccharides and their applications (pp. 205–244). New York: Marcel Dekker Inc. Pouzot, M., Nicolai, T., Benyahia, L., & Durand, D. (2006). Strain hardening and fracture of heat-set fractal globular protein gels. Journal of Colloid and Interface Science, 293, 376–383.

Rochas, C., & Landry, S. (1988). Rheological characterization of kappa carrageenan gels. In G. O. Phillips, P. A. Williams, & D. J. Wedlock (Eds.), Gums and stabilisers for the food industry, Vol. 4 (pp. 445). Oxford: IRL Press. Sagis, L. M. C., Ramaekers, M., & van der Linden, E. (2001). Constitutive equations for an elastic material with anisotropic rigid particles. Physical Review E, 63, 051504. Shih, W., –HShih, W. Y., Kim, S., –ILiu, J., & Aksay, I. A. (1990). Scaling behavior of the elastic properties of colloidal gels. Physical Review A, 42, 4772–4780. Sim, H. G., Ahn, K. H., & Lee, S. J. (2003). Three-dimensional dynamics simulation of electrorheological fluids under large amplitude oscillatory shear flow. Journal of Rheology, 47, 879–895. Takemasa, M., Chiba, A., & Date, M. (2001). Gelation mechanism of kappa- and iotacarrageenan investigated by correlation between the strain-optical coefficient and the dynamic shear modulus. Macromolecules, 34, 7427–7434. Te Nijenhuis, K. (1997). Thermoreversible networks. Advances in Polymer Science, 130, 203–218. Veerman, C., Sagis, L. M. C., Venema, P., & van der Linden, E. (2005). Shear-induced aggregation and break up of fibril clusters close to the percolation concentration. Rheologica Acta, 44, 244–249. van de Velde, F. (2008). Structure and function of hybrid carrageenans. Food Hydrocolloids, 22, 727–734. van de Velde, F., Antipova, A. S., Rollema, H. S., Burova, T. V., Grinberg, N. V., Pereira, L., et al. (2005). The structure of kappa/iota-hybrid carrageenans II. Coilhelix transition as a function of chain composition. Carbohydrate Research, 340, 1113–1129. van de Velde, F., Peppelman, H. A., Rollema, H. S., & Tromp, R. H. (2001). On the structure of kappa/iota-hybrid carrageenans. Carbohydrate Research, 331, 271–283. Viebke, C., Piculell, L., & Nilsson, S. (1994). On the mechanism of gelation of helixforming biopolymers. Macromolecules, 27, 4160–4166. Villanueva, R. D., Mendoza, W. G., Rodrigueza, M. R. C., Romero, J. B., & ˜ o, M. N. E. (2004). Structure and functional performance of gigaMontan rtinacean kappa-iota hybrid carrageenan and solieriacean kappa-iota carrageenan blends. Food Hydrocolloids, 18, 283–292. Wilhelm, M. (2002). Fourier-transform rheology. Macromolecular Materials and Engineering, 287, 83–105. Wilhelm, M., Reinheimer, P., & Ortseifer, M. (1999). High sensitivity Fourier-transform rheology. Rheologica Acta, 38, 349–356. Wilhelm, M., Reinheimer, P., Ortseifer, M., Neidhofer, T., & Spiess, H. W. (2000). The crossover between linear and non-linear mechanical behaviour in polymer solutions as detected by Fourier-transform rheology. Rheologica Acta, 39, 241–246. Wu, H., & Morbidelli, M. (2001). A model relating structure of colloidal gels to their elastic properties. Langmuir, 17, 1030–1036.