Microstructure and rheological behaviour of particulate β-lactoglobulin gels

Food Hydrocolloids YoU no.3 pp.195-212, 1993

Microstructure and rheological behaviour of particulate f3-lactoglobulin gels Mats Stading, Maud Langton and Anne-Marie Hermansson SIK-The Swedish Institute for Food Research, PO Box 5401, S-402 29 Goteborg, Sweden Abstract. The microstructure of the network as well as the strands of particulate 13-lactoglobulin gels formed at pH 5.3 have been characterized by microscopy. The microstructural influence on the rheological properties both at small and large deformations has been measured. It was shown that the microstructure depends on the heating rate used. Gels formed at a fast heating rate (5-100 C / m i n ) consisted of a homogeneous network with pore sizes of 20-30 urn. The strands were formed by evenly sized spherical particles linked like a flexible string of beads. At a slow heating rate (O.l-l°CI min) the network had larger pores, -100-150 urn, The network formed at O.l°C/min was inhomogeneous, with regions of small and large pores. The particle size distribution was broader at a slow heating rate and the strands, formed by several particles fused together, were thicker. Tensile measurements of fracture properties showed that the gels formed at a fast heating rate had higher stress and strain at fracture due to the network structure. The size of the weakest element of the network was deduced from notch sensitivity measurements and correlated well with the pore size, i.e. the fracture starts at the largest pores. Viscoelastic measurements showed that the gels formed at a slow heating rate had a higher storage modulus, G', which was explained by the microstructure of the strands. The thick strands of particles fused together were stiffer, thus causing a higher storage modulus than the flexible strands formed at a fast heating rate. The concentration dependence of G' was measured, and a model assuming clustering of clusters was applied to the results. The model shows that the particulate gels are self-similar within the region of concentration measured, with a fractal dimension of -2.5.

Introduction

Gels consist of a network interspersed by a fluid. In a biopolymer gel the network is built up of strands of some naturally occurring biopolymer and an aqueous phase. In the case of fine-stranded networks the strands are formed by long biopolymer chains, and in the case of particulate gels by particles. A biopolymer network usually forms at a supramolecular level and strands consisting of a single biopolymer chain are rare (1). The fine-stranded gels have pore sizes in the order of nanometers whereas particulate gels may have pore sizes in the order of micrometers (2,3). It is important to be aware of this when choosing experimental methods for characterisation of gel structure. A single method may not cover both types of microstructure (4). With microscopy transmission electron microscopy (TEM) is relevant for a description of a dense fine-stranded structure, whereas scanning electron microscopy (SEM) or light microscopy better describes a coarse particulate structure (5). Gels are usually regarded as homogeneous when viewed on a scale sufficiently larger than the pore-size or persistence length. However some gels have inhomogeneous networks in which some parts are dense and other parts are more dilute. A strict definition of an inhomogeneous network is that it should

195

M.Stading, M.Langton and A.-M.Hermansson

have at least a bimodal pore-size distribution , i.e. the network sho uld contain distinct regions with high density as well as regions with low den sity. According to this definition an inhomogeneous network structure is not to be confused with a network which has a bro ad pore-size distribution . Fine- stranded 13-lactoglobulin gels previously studied had regions of different den sity and were therefore inhomogeneous (6) . In this article, the term inhomogeneous will be used somewhat more loosely, and in some cases it will also cover a broad pore size distribution . I3-Lactoglobulin , which is the major whey protein , was used as a model for particulate networks in this stud y. It forms different network structures depending on pH: a particulate network at intermediate pH (4-6) and a finestr anded network below and above this interval (3,7,8). The network of the particulate gels is composed of almost spherical particles linked together and forming the strands of the network. Partly denatured proteins and mixtures of prot eins such as whey protein mixtures also form particulate gels at intermediate pH , but the pH interval is broader than for pure 13-lactoglobulin gels. In products containing globular proteins, e.g. dairy products, a particulate structure is often more important than a fine-stranded structure due to the pH and ionic strength of the products. Both changes in pore and particle sizes and inhomogeneities influence the properties of a gel. Hermansson has shown that, when particulate blood plasma gels and whey protein gels become inhomogeneous their appearance, texture and water-binding capacit y change drastically (1,9-11) . Hsu et al. measured the self diffusion of water in inhomogeneous polyacrylamide gels and found that the diffusion is higher in the more dilute regions than in the dense regions (12) . Viscoelastic measurements on inhomogeneous fine-stranded 13-lactoglobulin gels showed that the character changed from homogeneous gels with a high storage modulus, G ' , to weaker, more frequency-dependent inhomogeneous gels with low G' when the heating rate was decreased (6) . A fine-stranded inhomogeneous network was also found at the shift from fine-stranded to particulate structure around pH 6 (3,6). Inhomogeneities in gels also cause a broken frequency dependence of the storage modulus, G'(f) . A possible formation mechanism for particulate gels is that particles form in the pre-gel state and then agglomerate into larger aggregates forming the network structure. The aggregates could, for instance , be fractal clusters formed in the sol, and Bremer et al. have developed a model which describes the fractal nature of particulate gels (13,14). It assumes that particle aggregation leads to fractal clusters, which form the network when they occupy the whole volume. The fractal dimension D, of acid casein gels was obtained from measurements of the permeability, turbidity and viscoelasticity and found to be D, = 2.3 (13). This paper will present the microstructure of different particulate 13-lactoglobulin gels and show how the microstructure changes with the heating rate . Two microstructural levels will be discussed: the overall network structure and the strand structure. The microstructural effects on the rheological properties , both at small and large deformations will be demonstrated and explained. 196

Properties of particulate

~.Iactoglobulin gels

Materials and methods

Materials

The 13-lactoglobulin powder used for viscoelastic measurements and microscopy was obtained from the Sigma Chemical Co. , St Louis , LA (L-0130, lot no. 98F8030 and 106F8120). This 13-lactoglobulin powder is denoted 'Sigma'. The 13-lactoglobulin used in the tensile tests was supplied by the Swedish Dairies Association , Lund, Sweden and produced after an industrial- scale fractionation proce ss developed at Institut National de Recherche Agronomique (INRA), Rennes , France (15). This powder is denoted 'INRA' . For details of the 13-lactoglobulin powder, see references (7) and (8). Sample preparation and heat treatment

The 13-lactoglobulin was dissolved in degassed, distilled water. The 'Sigma ' solutions were clear and had a natural pH of 7.5; the 'INRA' solutions had a natural pH of 6.5. The pH was adjusted with ::::;1 mol/drrr' HCI or ::::;1 mol/drrr' KOH, resulting in turbid solutions at pH 5.3. The samples were filtered through a 1.2 urn filter and then heated at a controlled heating rate of between 0.017°C/ min (I °C/h) and 5°C/min from 30 to 90°C. Some samples were also heated directly in a water bath at 90°C, which corresponds to an average heating rate of -12°C/min. The samples were kept at 90°C for 1 h and then cooled at the fastest cooling rate to 20°C, at which they were kept for 30 min. The INRA samples were only used for the tensile measurements and were not filtered. The micrographs presented in this paper all show Sigma gels, but INRA samples have also been analyzed. The 13-lactoglobulin concentrations referred to in this paper are given in weight percent (% w/w). Microscopy

Two different microscopy techniques were used to study particulate network structures: light microscopy (LM) and scanning electron microscopy (SEM) . After the heat treatment small slices of the gel, 1 x 5 x 5 mrn, were cut out and prepared for SEM. Smaller cubes, 1 x 1 x 1 mrn, were cut out and prepared for LM. The following procedure was used (for more details, see references 3 and 6). The samples were immersed in 2% v/v glutaraldehyde with 0.1% w/v ruthenium red for 60 min at 8°C, washed thoroughly at 8°C followed by 2% w/v OS04 for 120 min at 8°C. The samples were then rinsed several times in 0.025 mol/drrr' KCl-solution before being dehydrated in a graded ethanol series. To prevent osmotic effects, 0.025 mol/drrr' KCI was added to the fixative solutions and washing solutions. The LM samples were transferred to propylene oxide after dehydration and were then embedded in Polybed (Polyscience Inc. , Warrington , PA). Semithin section s, 1-2 urn , were cut on a glass knife and were stained with toluidine blue. The sections were examined in a light microscope, Microphot-FX (Nikon Corp., Tokyo, Japan). SEM samples were critical-point dried through CO 2 , in a critical-point drier 197

M.Stading, M.Langton and A.-M.Hermansson

(Balzers Union Ltd , Liechtenstein) . Dried samples were fractured and mounted with ' Leit-C', coated with Au/Pd by diode sputter coating in a Sputter Coater E5100 (Polaron Equipment Ltd, Watford , UK) . A Stereoscan200 (Leica Cambridge Ltd, Cambridge , UK ) was used for examination at an acceleration voltage between 5 and 10 kV.

Dynamic measurements A [3-lactoglobulin solution (Sigma) of 2.5 ml was heated in the me asuring cup of a Bohlin VOR Rheometer using a couette type cup and bob measuring system (DIN 53 019). A thin layer of paraffin oil was applied on top of the sample to avoid evaporation. The bob was suspended from an interchangeable torsion bar with a torque at a maximum deflection of between 3 x 10- 5 and 2 x 10- 3 nm . The frequency was 1 Hz when temperature was the independent variable, and during the frequency sweep 0.001-5 Hz. As [3-lactoglobulin is strain-sensitive during the gelation, the strain was kept low, 4-10 X 10- 4 , so as not to disturb the gelation (7). This was well within the linear region. The sample was oscillated only when recording G*. The cup holder of the rheometer was modified to reduce axial deformations caused by thermal elongation of the cup holder.

Tensile measurements Th e [3-lactoglobulin solution (INRA, 12%) was heated in square moulds with inner dimensions 13 x 13 x 60 mm, and the gels were then cut into 20 mm-long test-pieces with a scape!. A notch was cut along one side of the test-piece perpendicular to the direction of elongation. The samples that were fractured without a notch were moulded in a separate mould with a narrow mid-section. The test-piece was attached to the measuring instrument with cyanoacrylate glue (8). The samples were fractured in tension in an Instron 1122. A constant crosshead speed of 10 mm/min was used which corresponds to an initial strain rate of 3 E = 8.3 X 10- S-1 for a 20 mm long sample. It is difficult to measure the stress at fracture for small notches, because the samples tend to break at the glued ends instead of at the notch. The theoretical notch sensitivity was therefore fitted to experimental data using linear regression, which averages the experimental results. The main contribution to the error was probably the measurement of the notch depth. This could lead to both an overestimate and an underestimate of the fracture property measured, which justifies an averaging method. The measurements of the un notched samples, on the other hand, did not involve measurement of the notch depth. The handling of the sample and the possibility of trapped air bubbles were then the main sources of error, which always decreases the strength of the samples. The measurements of the fracture properties therefore gave too small an estimate of the true fracture properties, and a jackknife method was used to estimate a maximum (16). The errors of mixing were assumed to be negligible . 198

Properties of particulate 13-lactoglobulingels

The strain during the tensile deformation was defined as Hencky strain

E

=

In(lllo), where 10 is the original length of the sample and 1 is the present length (17). The stress cr was calculated as c = FIA, where F is the force and A is the

area at fracture. The sample got narrower as the strain increased, since the volume of the sample was approximately constant. The shape of a sample was therefore photographed during the deformation, and the area at fracture was calculated from the photographs of the fracture surfaces.

Results and discussion

Network characteristics Microstructure. I3-Lactoglobulin forms a coarse, particulate network at pH 5.3. The particles forming the strands are spherical with a diameter in the order of urn. The network is coarse enough to be studied even with light microscopy, as shown in Figure 1. The strands form a three-dimensional network, which is visualized by SEM in Figure 2. The microstructure of the particulate 13-lactoglobulin gels at pH 5.3 was studied at four different heating rates ranging from 0.1 to 12°Cfmin at a concentration of 10% w/w. The gels formed at the fastest heating rate had a homogeneous structure of evenly sized particles and pores, as observed earlier for 13-lactoglobulin gels between pH 5.0 and 5.5 (3). Figure lea) shows a micrograph of the gel formed at the fastest heating rate, 12°Cfmin consisting of a homogeneous network with -20 urn large pores and strands formed of spherical particles. Figure l(b) shows the microstructure of the gel formed at a heating rate of 5°Cfmin, with slightly larger pores and particles but rather similar in structure to the most rapidly heated gel. When the heating rate was decreased further the microstructure became more open. Figure 1(c) shows a less homogeneous network formed of larger particles and pores. Figure l(d) shows the gel formed at the slowest heating rate, O.loC/min; it is inhomogeneous with large pores of size -100 urn. Figure 2 shows SEM micrographs of the gels formed at the same four heating rates as in Figure 1. Figure 2(a) and (b) show the two more homogeneous networks of evenly sized particles formed at fast heating rates. Figure 2(c) shows a more open network formed at lOC/min. The magnification is -7 times higher in Figure 2 than in Figure 1, i.e. 1000x compared to l50x. The largest pores of the gel in Figure l(d) are, for comparison, larger than the whole micrograph in Figure 2(d), and both figures show the same gels. The network structure at lOCI min is formed by both large and small pores, and the strands consist of many particles which have fused together. The microstructure of the strand will be discussed separately. All the micrographs presented in this article have been prepared from Sigma l3-lactoglobulin gels at pH 5.3, but the microstructure has also been examined at other pH (5.2-5.6), at varying heating rates and with different batches and concentrations. All samples showed the same type of behaviour. Gels prepared from INRA 13-lactoglobulin were less clean, and the spherical particles were surrounded by appendages. 199

M.Stading, M.Langton and A.-M.Her mansson

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200

Properties of particulate 13-lactoglobulin gels

Fig. 2. SE M micrographs of 10% 13-1actoglobul in gels at pH 5.3 formed at (a) 12°0min , (b) 5°C/min, (c) IOOmin , (d ) D. l oOmin.

Fractal structure. Information on the gel structure can also be obtained from rheological measurements by, e.g. the concentration dependence of the storag e modulus. A model developed by Bremer et al. was fitted to the experimental dat a to get the fractal dimension Dr as a measure of the self-similarity of the networks (13,14). The model was earlier tested on casein gels, and a fractal dimension of -2.3 was obtained from the concentration dependence and from 20 1

M.Stading, M.Langton and A.-M.Hermansson

measurements of permeability and turbidity (13). The model describes the concentration dependence of the elastic modulus G by 2

(1)

where is the volume fraction of particles and K is a constant. If G is measured by e.g., G' and is known, D, can be calculated. Equation (1) was fitted to the experimental results of G'(e) to calculate the fractal dimension of the ~-lactoglobulin gels, see Figure 3 and Table 1. The volume fraction of particles was not known as they were formed in solution, but the density of the particles was assumed to be constant, and the weight fraction was then used instead of the volume fraction. The microstructure of the gels formed at 5°C/min was very different from that of the gels formed at O.I°C/min, as shown in Figures 1 and 2. The fractal dimension was the same though, i.e. the similarity was not affected by the inhomogeneity of the network. The calculated fractal dimension of -2.5 was

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c [%W/W] Fig. 3. The storage modulus of the particulate gels as a function of 13-lactoglobulin concentration for different heating rates. Table I. The concentration dependence and calculated fractal dimension of 13-lactoglobulin gels Gel structure Particulate

pH 5.3

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Heating rate DC/min

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Properties of particulate [3-lactoglobulin gels

higher than D, = 2.3 reported for casein gels (13) , i.e. the storage modulus of the casein gels was more concentration dependent than that of the particulate J3-lactoglobulin gels . Clark has used a kinetic model based on Flory-Stockmeyer kinetics to describe the concentration dependence of the modulus (18 ,19). The model predicts a limiting power-law behaviour at high concentrations with A = 1.6 (G' oc c A ) . However, the slope increases when concentration is decreased towards the critical gel concentration. The concentration dependence of the fine-stranded gels of 13-lactoglobulin is given for comparison in Table 1. The rather high slope thus indicates that the concentrations measured (12-15 %) are too close to the critical gel concentration to give a true linear relationship of log G' versus log c. The particulate gels had a linear relationship over a larger concentration interval (4-15 %) and Figure 3 shows no increase of the slope at low concentrations. It is possible that it is not a linear relationship at even lower concentrations but these gels were too weak to give a measurable result, and gels of higher concentrations were difficult to prepare. Fracture properties. Structural information on the network can be obtained by measuring the stress at fracture for varying depth of an applied notch . A gel is not sensitive to notches smaller than the largest naturally occurring notch. This natural notch can be , for instance, an air bubble or a crack induced during the sample preparation but, most important , it can also be a natural element of the structure. The natural element may correspond to a weak element such as a large pore , or it may be a dense area or even a particle causing stress concentration. A particulate gel may contain both types, as shown in Figures 1 and 9. The stress

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M.Stading, M.Langton and A.·M.Hermansson

eq.2

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In a material naturally containing notches or inhomogeneities , e.g. a biopolymer network, the fracture stress is not sensitive to notches smaller than the size of the natural notches , i.e. equation (2) applies. For notches deeper than those , the fracture stress becomes notch-sensitive and equation (3) applies . The notch-sensitivity curve ,
204

Properties of particulate

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The particulate gels formed at pH 4.0-5.2 had an inhomogeneous microstructure and lower stress at fracture than gels formed at pH 5.5-6.0, which had a homogeneous microstructure. The notch dependence of fine-stranded ~-lactoglobulin gels did not show the same clear distinction between homogeneous and inhomogeneous gels (20). The size of the natural notches, x, increased with decreasing heating rate but was much larger than any measure of the network microstructure revealed by electron microscopy. A fine-stranded network cannot be characterized as well with large deformation measurements as a particulate network can, because the scale of the fine-stranded network is too small. The notch dependence shown in Figure 5 can be compared to earlier measurements of notch dependence for ~-lactoglobulin gels at pH 4.5,5.5,6.5 and 7.5 (8). The fracture stress of the gels formed at pH 5.3 is lower than that of the gels at pH 5.5, in accordance with the earlier measurements of the pH dependence. It is notable that the difference between the gels at pH 5.3 heated at 12°C/min and at 1°C/min (Figure 5a) is almost as big as the greatest difference between ~-lactoglobulin caused by pH in the interval 4.5-7.5. The fracture stress of the notched samples is equal to earlier measurements, but the higher fracture stress of the samples without a notch in this study may be attributed to improved measuring technique. Strand characteristics Strand microstructure. Figure 6 shows SEM micrographs at a high magnification

205

M.Stadin2. M.Lan2ton and A.-M.Hermansson

Fig. 6. SEM micrographs of 10% (c) IOC/min, (d) D.loC/min.

~-l actoglobulin

gels at pH 5.3 formed at (a) l2°C/min, (b) 5°C/min,

of gels formed at four different heating rates. In Figure 6 the strands are shown and only parts of the smallest pores are imaged. The SEM micrographs shown in Figure 6 reveal that the strands consisted of almost spherical particles. Figure 6(a) and (b) show the evenly sized particles forming the strands at the two fastest heating rates.

206

Properties of particulate 13-lactoglobulingels

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Fig. 7. A schematic repre sentation of the strand microstructure of particul ate 13-lactoglobulin gels at pH 5.3 at (a) fast heating rates (5-12°C/min) and at (b) slow heating rates (O.I-loC/min).

Figure 6(c) and (d) show the strands formed at slower heating rates, 1 and O.loC/min. These strands were formed of particles from a broader particle size distribution, which seemed to be bimodal, with one typical size -1 urn and another -0.1 urn (see also Figure 7). The largest particles were found at -loCI min. Figure 7 illustrates the difference in strand structure between a fast heating rate , 5-12°C/min , and a slow heating rate O.l-loC/min. Figure 7(a) shows strands formed at fast heating rate. The particles are linked like 'beads on a string ' in a chain of single particles and are therefore assumed to be more flexible than the strands formed at slower heating rates. The particles are not associated in a perfectly linear arrangement, but in one more like a zig-zag band. The strands are therefore 'curled' rather than stiff, and junctions between one particle and its neighbour are not on opposite sides. When 'curled' chains are extended, they first straighten out and can therefore be extended further than straight chains. The mechanical properties of the strands is one factor influencing the rheological behaviour of the whole gel. This was reflected by the strain at fracture , Ef, which was higher for a heating rate of 12°C/min than at I°C/ min . It was Ef = 0.15 for the gels heated at 12°C/min compared to Ef = 0.12 for 1°C/min, both values being taken for a notch depth of 1 mm. Figure 7(b) demonstrates the construction of a strand formed at slow heating rates, 0.1 and 1°C/min. Slow heating rates resulted in a broad particle-size distribution. The particles appeared to 'fuse' together into thick strands with 207

M.Stading, M.Langton and A.-M.Hermansson

several particles in a cross-section. Especially at the slowest heating rate, 0.1 DC! min, many particles fused together, with the result that one particle had more junctions to other particles than at a faster heating rate, compare Figure 6(a) and (b) with Figure 6(c) and (d). The thickness of the strands increased with decreasing heating rate, both due to increasing particle size and to the number of particles forming the strand. The formation of many tightly packed particles in each strand led to stiffer strands, which was reflected by the viscoelastic properties, as discussed below. Strand structures similar to the ones illustrated in Figure 7(a) and (b) have previously been shown for yoghurt formed of heated and unheated milk prior to incubation (22,23). It has been proposed earlier that not only the pore size but also the strand structure has an impact on the rheolgoical and functional properties. Viscoelastic properties. Figure 8 shows that the storage modulus increased at slow heating rates. The modulus depends on both network properties such as the number of stress carrying strands, and on strand properties. The strand microstructure varied significantly and can probably to a great extent explain the rheological behaviour. The strands formed at slow heating rates consisted of many 'fused' particles and were therefore stiffer than the 'curled' strands formed at fast heating rates (see Figure 7). In a recent article we showed that fine-stranded gels of 13-lactoglobulin at pH 7.5 were inhomogeneous when heated slowly (6,24). The gels heated slowly had lower G' than the gels heated quickly, the opposite to the particulate gels. For

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208

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Properties of particulate I)-lactoglobulin gels

the fine-stranded gels, the network microstructure changed relatively more than the strand microstructure did when the heating rate was changed. For the particulate gels the change in strand microstructure was more pronounced. This indicates that the change in strand microstructure of the particulate gels contributed significantly to the overall network properties . Fine-stranded f3-lactoglobulin gels also form flexible or stiff strands depending on pH. The stiff strands formed at low pH had a higher G', whereas flexible strands formed at high pH had a lower G'. The fine-stranded gels formed at low pH also had lower strain and stress at fracture, whereas at high pH they had higher strain and relatively high stress at fracture (3,7 ,8). A material containing region s of different densities with different relaxation times was shown to give a broken frequency curve , G'(f), with one slope at low frequency and another at high (6). Fine-stranded f3-lactoglobulin gels were studied, and the inhomogeneous gels had broken frequency curves, whereas the homogeneous did not. The frequency curves of the particulate gels shown in Figure 8 give a flat impression, but the gel heated most slowly, O.loC/min, gives an indication of two slopes . The difference in slope between low and high frequency is far less obvious for the particulate gels. It may depend on the much larger typical scale of the particulate gels, which corresponds to relaxation times less suited for the frequency region studied. The particle size distribution varied significantly with heating rate but a specific, significant rheological effect could not be distinguished. The strand microstructure, pore size and number of stress-carrying strands influenced the rheological properties much more than the particle size . Effect of clusters

The f3-lactoglobuJin particles already start aggregating into compact clusters in solution , and when the solution is filtered the biggest clusters are removed (7). The formation of clusters may be stimulated by shear. When a minimum of shear was applied during preparation of the gels, few clusters were formed , whereas gels formed from vigorously stirred solutions contained more clusters. f3-Lactoglobulin is surface-active, and mechanical treatment of the solution affects the microstructure. Vigorous stirring of the f3-lactoglobuJin solution at pH close to the isoelectrical point results in foaming. When a solution at pH 3.5 was stirred, or if a solution was sheared during heating, aggregation was induced and clusters were formed, which became embedded in the fine-stranded network. However, the effect of shearing before and during heating needs to be further studied and results will be published separately . Investigations of the effect of shearing on whey protein isolate suspensions before and during heating showed that sheared suspensions gelled more rapidly than unsheared ones and produced stronger gels (25). Figure 9 shows the microstructure of a gel containing clusters, heated at 5°C! min (cf . Figure lb). These clusters influence the storage modulus (cf. Figures 8 and 10). The filtered gels in Figure 8 have a lower G', even though they have a higher concentration , the effective concentration after filtration being -9%.

209

M.Stading, M.Langton and A.-M.Hermansson

Fig. 9. LM mcirograph of a 10% j3-lactoglobulin gel at pH 5.3 tor which the solution was not filtered before heating.

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f [Hz] Fig. 10. The frequency dependence G'(f) of 6% j3-lactoglobulin gels at pH 5.3 for different heating rates. The heating rate is given in "Czmin. The solutions were not filtered before heating.

The clusters' influence on the modulus could be explained as a filler effect, i.e. the clusters act as fillers in the network thus making the gel stiffer (26). But most important is that G' increased with decreasing heating rate both for the filtered and the unfiltered samples, showing that this was not an effect of the clusters. Removing the clusters by filtering the solution before heating influenced the fractal dimension which decreased from D, = 2.5 to D, = 2.3. From this it can

210

Properties of particulate fl-lactoglobulin gels

be concluded that the larger clusters formed in solution had a strong influence on rheostructural properties (d. Figure 9). Reducing the length scale over which the network is similar by increasing the lower cut-off length can produce a higher fractal dimension (13). The removal of the compact, large clusters from the network structure could cause this increase in the lower cut-off length and explain the higher fractal dimension of the filtered gels. The heating rate did not, however, influence the fractal dimension of the unfiltered gels either: D, =: 2.27 ± 0.17 for 5°C/min and D, = 2.25 ± 0.10 for O.loC/min. The fractal dimension of gels of a commercial whey protein isolate have been measured for pH 5.4 in the concentration range 4-9% (27). A 10% stock solution at pH 6.7 was heated and then diluted and adjusted to pH 5.4. The Bremer model was applied and the fractal dimension was found to be D, = 2.3 which, despite the different sample preparation, coincides with our results for unfiltered gels containing clusters. Conclusions This study of particulate gels of 13-lactoglobulin can be summarized in three major points: • The fracture properties correlate well with the microstructure of the network. The weakest part of the network is the largest pores as shown by measurements of the fracture stress as a function of notch depth. A depth of an applied notch smaller than the largest pores did not influence the fracture stress. • The viscoelastic properties depend mainly on the composition of the strands. Flexible strands, formed of particles linked together like a string of beads, have a low storage modulus, G', whereas thicker strands, consisting of particles fused together, are stiffer and have a higher G'. The flexible chains can be extended to larger deformations before fracture. • Large deformation tests and small deformation, non-destructive tests are suitable for gels on different scales. Large deformations are suitable for coarse microstructures, such as particulate gels, whereas the dimensions of finestranded 13-lactoglobulin gels are too small. Viscoelastic measurements correlated well with the microstructure of fine-stranded gels and with components of the particulate network, i.e. the strands. Acknowledgements The authors thank Ina Storm and Siw Kidman for their skilled technical assistance. The financial support from the Swedish Council for Forestry and Agricultural Research, SJFR, is also gratefully acknowledged. References 1. Hermansson,A.-M. (1986) In Mitchell,J.R. and Ledward,D.A. (eds), Functional Properties of Food Macromolecules. Elsevier, London, p. 273.

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2. Clark,A .H. and Lee-Tuffnell,C. D. (1986) In Mitchell,l .R . and Led ward ,D .A. (eds), Function al Properties of Food Macromolecules, Elsevier, Barking, UK, pp. 203. 3. Langton ,M. and Herm ansson .A i-M. (1992) Food Hydrocoll., 5, 523. 4. Clark ,A .H. and Ross-Murphy,S.B . (1987) A d~' . Polym. Sci., 88, 57. 5. Hermansson ,A.-M. and Langton.M, ( 1993) In Ross-Murph y,S.B . (ed .) , Physical Techniqu es fo r Food Biop olym ers , Elsevier. London , in press. 6. Stading,M ., Langton .M, and Hermansson ,A .-M. (1992) Food Hydroco/l. , 6, 455. 7. Stading,M . and Hermansson ,A. -M. ( 1990) Food Hydrocoll. , 4, 121. 8. Stading,M. and H erm ansson. A i-M. (1991) Food Hydrocol/., 5, 339. 9. Herm ansson ,A .-M. and Luciano ,M. (1982) J. Food sa., 47, 1955. 10. Herm ansson, A.-M. (1982) J. Food Sci. , 47, 1960 & 1965. I I. Herm ansson ,A .-M. (1983) Qual. Plant Fds. Hum . Nutr. , 32, 369. 12. Hsu ,T . , Dong,S.M . and Cohen.C , (1983) Polym er, 24, 1273. 13. Bremer,L.G .B . , van Vliet,T. and Walstra ,P. (1989) J. Chem. Soc . , Faraday Trans. 1,85 , 3359. 14. Bremer ,L.G .B ., Bijsterbosch,B.H ., Schrijvers.R ,, van Vlient ,T. and Walstra, P. (1990) Col/. Surj., 51, 159. 15. Maubois,l .L. , Pier re ,A ., Fauquant ,l. and Piot ,M . (1987) Bull. IDF , 212, 154. 16. Wonn acott ,RJ . and Wonnacott ,T .H . ( 1985) Introdu ctory Statistics 4th edn. John Wiley and Sons, New York. 17. Peleg,M . (1984) J. Text. Stud . , 15, 317. 18. Clark, A .H. (1992) In Schwartzberg ,H .G. and Hartel,R.W. (eds), Physical Chemistry of Foods , Marcel Dekker, New York , p. 263. 19. Flory,P.l. (1953) Principles of Polym er Chem istry , Cornell Un iversity Press, Ith aca, NY. 20. Kelly,A . (1966) Strong Solids, Clare ndon Press , Oxford. 21. Purslow,P. (1991) J. Mater. sa., 26, 4468. 22. Langton ,M. (1991) SIK-report No 580 , SIK, PO Box 5401, S-402 29 Goteborg, Sweden . 23. Kafab.M., Allan-Wojtas, P. and Phipps-Tod d,B .E . (1983) Food Microstruct. , 12, 51. 24. Sta ding,M., Lan gton ,M. and Hermansson ,A .-M. , Proceedings from Netwo rks '92 co be published in Makro mo l. Chem . , Macromol. Sym p , 25. Ker ,Y.C. and Toledo ,R .T . (1992) J. Food Sci. , 57, 82. 26. Brownsey.G i.l. and Mor ris,V.l. (1988) In Blanshard .Lst.V. and Mitche ll,l .R. (eds) . Food Structure-Its Creation and Evaluation , Butte rworths, Londo n, p. 7. 27. Vree ker,R ., Hoekstr a,L. L. , den Boer,D .C. and Agterof ,W .G .M . (1992) Food Hydrocoll. , 6, 423. Received on April 4, 1993; accepted on May 10, 1993

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