A fractal analysis approach to viscoelasticity of physically cross-linked barley β-glucan gel networks

Colloids and Surfaces B: Biointerfaces 49 (2006) 145–152

A fractal analysis approach to viscoelasticity of physically cross-linked barley ␤-glucan gel networks Vassilis Kontogiorgos 1 , Hariklia Vaikousi, Athina Lazaridou, Costas G. Biliaderis ∗ Laboratory of Food Chemistry and Biochemistry, Department of Food Science and Technology, Faculty of Agriculture, Aristotle University, Thessaloniki 54124, Greece Received 5 December 2005; received in revised form 3 March 2006; accepted 9 March 2006 Available online 18 April 2006

Abstract The structure and gelation kinetics of mixed linkage barley ␤-glucans of varying Mw have been investigated. The fractal concept has been applied to describe the structure development of barley ␤-glucan gels using a scaling model and dynamic rheometry data. The model supports that the gel structure consists of fractal clusters that upon aggregation lead to a three-dimensional network. The analysis showed that with increasing Mw a denser (more packed) network is formed as indicated by the corresponding fractal dimension (df ) values. The microelastic parameter of the model, α, showed that all gel structures were in the transition regime implying structural reordering upon ageing. The description of the microstructure as a fractal network seems to be able to explain syneresis and other observations from large deformation testing of such systems. The molecular treatment of the gelation kinetics suggests that the gelling behavior is governed by the probability of collision of chain fragments with consecutive cellotriosyl units. This is greater for small chains due to their higher diffusion rates, for chains having lower amounts of cellulose like fragments and finally for those showing smaller degree of intrachain interactions. As a result, the faster gelling systems exhibit lower fractal dimensionality (more disordered systems) something that is in accordance with current kinetic theories. © 2006 Elsevier B.V. All rights reserved. Keywords: Fractal; Dynamic rheometry; ␤-Glucans; Gels; Molecular size; Structure; Scaling

1. Introduction Biopolymers, such as proteins and polysaccharides, have the ability under certain conditions to form larger complex structures, often referred to as aggregates, clusters or flocs. When the extent of these aggregates in an aqueous medium is large, the aggregating system may form a gel. Intermolecular associations in macromolecular aggregates are affected via non-covalent (van der Waals attractive forces, electrostatic interactions, hydrogen bonding and hydrophobic interactions) and covalent cross-links (e.g. disulphide bonds in proteins, diferulate bridges in plant cell wall polysaccharides such as arabinoxylans). There is a continuing interest in understanding the structure of biopolymer gels as well as the relations between the structure of aggregates and the macroscopic properties of such network systems in order to con-

∗

Corresponding author. E-mail address: [email protected] (C.G. Biliaderis). 1 Present address: Department of Food Science, University of Guelph, Guelph, Ont., N1G2W1 Canada. 0927-7765/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfb.2006.03.011

trol them for various applications. Information on biopolymer aggregates and gel network structures can be obtained by various experimental techniques such as rheometry, microscopy and other imaging techniques, light scattering, X-ray and neutron diffraction techniques, calorimetry, and permeability measurements. The gel network structures are highly disordered molecular or particle assemblies, although with some types of polysaccharide gels there is indication for conformational ordering and interchain associations, at least at a chain segmental level. Although on a large scale the structure of the gels is highly disordered, it can be described as a connection of clusters regarded as fractal objects [1] and therefore characterized by one parameter, i.e. the fractal dimension. Fractals are defined as disordered systems with a non-integral dimension. The term fractal dimension, df , is often used to quantify the disordered nature of an object. The fractal dimension of an aggregate is related to the packing of the particles forming the aggregate and varies between 1 and 3, with the value of 3 corresponding to a solid spherical structure. A distinct property of fractal aggregates is the power law behavior; i.e. the cluster mass, M, varies with the radius, R, according

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to the expression: M∼R

df

There are several experimental techniques available to analyze fractal structures in aggregates or gels. These measure physical quantities related to the distribution of mass in space and can be based on scattering (light, X-ray or neutron), settling or imaging [2], microscopy or permeametry [3] and rheometry [4]. Scattering techniques are probably the most reliable, but they are mostly used in dilute systems with particle volume fractions substantially smaller than 1%. For higher volume fractions the techniques based on rheological measurements are better suited to characterize the structure of gels [5–8]. Rheological methods have the advantage that they are easy to conduct, can be nondestructive and applied to highly concentrated systems where the structure cannot be characterized by the common scattering techniques. For structure characterization of colloidal gels using measurements on their rheological properties, a scaling model was developed by Shih et al. [9], which defines two separate regimes: the strong-link regime, at low particle concentrations, and the weak-link regime, at high particle concentrations. In their model it is assumed that the structure of gels consists of fractal clusters, which during gelation aggregate with each other. In the strong-link regime where the interfloc links are stronger than the intrafloc links, the macroscopic elasticity of the gel is provided by the intralinks. In the weak-link regime, where the clusters are more rigid than the interfloc links, the macroscopic elasticity of the gel is given by that of interlinks. It is evident that the strong-link and weak-link regimes represent only two extreme situations; i.e. the transition from one to the other with the change in particle concentration must be continuous, leading to intermediate situations where both inter- and intrafloc links contribute to the overall gel elasticity. Wu and Morbidelli [4] extended the Shih et al. [9] model by introducing an appropriate microscopic elastic constant to account for the mutual elastic contributions of both inter- and intrafloc links. While for protein gels, often described as particle network systems, the fractal analysis for further characterization of the structure has been broadly applied by means of rheological methods [5–8,10,11], for polysaccharide gels, to our knowledge, there are a few reports in the literature, mostly referring to light, neutron and X-ray small angle scattering measurements on polysaccharide chain aggregates in aqueous solutions and gelling systems [12–16]. Linear mixed-linkage (1 → 3)(1 → 4)–␤-dglucan, a major structural cell wall polysaccharide of cereal grains, is known to exhibit health benefits such as reducing blood serum cholesterol and regulating blood glucose levels [17]. These polysaccharides are also known to increase the viscosity of aqueous solutions and to gel under certain conditions. The gelling behavior of cereal (1 → 3)(1 → 4) ␤-glucans has been recently explored by rheological methods [18,19]. The rate and extent of gelation of these polysaccharides were found to depend on their molecular size and fine structure; the process is believed to originate from interchain associations (segments of chains), giving rise to chain aggregation [18–22]. The aim of the present work was to apply the scaling laws of colloidal systems in order to describe the elasticity and

microstructure of physically cross-linked ␤-glucans gel network structures, to relate the structure with the molecular size of the polysaccharide, and finally to explore the relationship between gel structure and gelation kinetics. 2. Materials and methods 2.1. β-Glucan extraction Four barley ␤-glucan samples were used in this work. Sample BG40 was an isolate from a barley concentrate provided by CEBA (Lund, Sweden), whereas the samples BG70, BG140 and BG180 were acid-hydrolysates from a ␤-glucan isolate obtained from whole barley flour. The isolation–purification procedures of the ␤-glucans from these sources were described elsewhere in detail [18–20]. The protein content of all ␤-glucan preparations was determined by the method of Lowry et al. [23]. The ␤-glucan content was determined by the enzymic method of McCleary and Glennie-Holmes [24] using the Megazyme® mixed linkage ␤glucan assay kit. Analytical grade reagents and distilled water were used in all experiments. 2.2. Molecular and structural characterization of β-glucan The molecular size distributions and the average molecular weight of ␤-glucans were determined with a high performance size exclusion chromatography (HPSEC) system. Estimates of average Mw of the ␤-glucans were based on the elution volumes of the peak fractions; calibration of the SEC column was carried out using ␤-glucan standards of known molecular weight obtained from Megazyme® and characterized by light scattering techniques. The distributions of cellulosic oligomers in the chain of ␤-glucans were determined by high performance anion exchange chromatography (HPAEC) following hydrolysis of the polysaccharides with lichenase. The purity and some structural features of the ␤-glucan samples were also assessed with 13 C NMR spectroscopy. The experimental conditions as well as the instrumentation used in this context are described elsewhere in detail [18]. 2.3. Gel preparation, dynamic rheological measurements and syneresis measurements The time that storage modulus needs to reach the plateau value for the aqueous dispersions of all ␤-glucan preparations was determined experimentally. Solutions for all samples were made in hermetically sealed glass vials by gentle stirring of the ␤-glucan samples in 25 mM Tris–HCl buffer (pH 7.0) at 85 ◦ C until complete solubilization of the material. Subsequently, the samples were loaded on a rotational Physica MCR 300 rheometer (Physica Messtechnic GmbH, Stuttgard, Germany) using a double-gap cylindrical geometry with internal and external gap 0.42 and 0.47 mm, respectively. The solutions were subjected to oscillatory measurements at 0.1% strain and 1 Hz frequency at 25 ◦ C and the gelation kinetics were monitored; the temperature was regulated at 25 ◦ C by a Paar Physica circulating bath and a controlled peltier system (TEZ 150P/MCR) with an accuracy

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of ±0.1 ◦ C. The data were analyzed with a software supporting the rheometer (US200 V 2.21). Immediately after the end of the gelation process and in order to avoid disruption of the already formed microstructure, a second step was programmed to perform the strain sweep measurement at fixed frequency of 1 Hz and 25 ◦ C. In another set of experiments for the estimation of syneresis, ␤-glucan solutions at 6% (w/w) were casted on small cylindrical plates (4 cm diameter × 1 cm height) and stored for 15 days at 25 ◦ C in a chamber with 100% RH; this was done in order to avoid evaporation during the storage period. After the end of the storage period, a dry pre-weighted filter paper was used to remove the exuded water by each gel (surface free water). The weight of the water released was expressed as a percentage of the total weight of the gel. All measurements were performed at least in triplicate. 2.4. Determination of the fractal dimension The volume fraction of particles (φ) in the gels was assumed to be proportional to the polysaccharide concentration (c). Fractal dimension, df , α and β values were evaluated using the values of slopes of log G versus log c and of log γ 0 versus log c, according to the Wu and Morbidelli [4] model. The scaling dependence of G and γ 0 is as follows: G ∼ φβ/(d−df )

(1)

γ0 ∼ φ(d−β−1)/(d−df )

(2)

β = (d − 2) + (2 + x)(1 − α)

(3)

where, d is the Euclidean dimension of the system (equals to 3 in three-dimensional systems), αε[0, 1], is the microelastic parameter, β is an auxiliary parameter, df is the fractal dimension of the system and x represents the fractal dimension of the aggregate backbone or tortuosity of the network whose value for colloidal gels is within the range of 1–1.3. Thus, in equations (1) and (2) the exponents are equal to the slopes of the respective lines. From these equations calculation of β and df is feasible and with subsequent substitution of the results to the equation (3) the value of the microelastic parameter α was obtained using x = 1 and x = 1.3. The later model was chosen because it was considered as a more thorough model compared to that of Shih et al. [9] which does not take into account the contributions of inter- and intra-aggregate links on the overall elasticity of the network structure.

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Table 1 Compositional, molecular and structural features of ␤-glucan samples Samples

BG40

BG70

BG140

BG180

␤-Glucans (%) Protein (%) Mw (×103 ) Molar ratio DP3/DP4a DP5-DP14 (%) (1 → 4)/(1 → 3)

92.3 3.1 41 2.78 7.8 2.0

92.7 1.5 74 2.82 8.4 2.4

91.8 0.6 143 2.81 8.9 2.5

93.7 1.0 176 2.80 8.8 2.8

a

DP, degree of polymerization.

of ␤-glucans is their cellotriosyl/cellotetraosyl (DP3/DP4) ratio, which constitutes a structural fingerprint of cereal ␤-glucans [21]. As this ratio is increased, the ability of ␤-glucans to gel increases [18–20]. The purity of the isolated ␤-glucan samples was further confirmed by 13 C NMR spectroscopy (data not shown). The spectral features were all typical of mixed linkage cereal ␤-glucans, as assigned by Cui and Wood [21] and there were no resonance peaks at 108.4 and 100.4 ppm, which correspond to the C-1 of anhydro-arabinofuranosyl (arabinoxylans) and anhydro-glucopyranosyl (starch) residues, respectively. The calculation of linkage ratio, (1 → 4)/(1 → 3), was based on the ratios of peak areas of the C6 resonances of differently linked glucosyl residues along the polysaccharide chain [20,25]. The time at which gel network formation is established is the time that corresponds to the cross-over point of G and G versus time, and the end of this process when a relatively constant value of the storage modulus (pseudo-plateau value) is attained. The rate of gel formation of barley ␤-glucans is concentration and Mw dependent [19]. Typical gelation kinetic profiles (G versus time) are shown in Fig. 1. B¨ohm and Kulicke [22] introduced a growth rate parameter, named increment of elasticity (IE), as a measure of the gelation rate and equals to IE = [d(log G )/dt]max . Its dimension is reciprocal time and high values imply rapid gelation. The growth of the log G with time for ␤-glucans could be also described by several empirical non-linear equations. After application of such models, it was found that a single exponential (log G (t) = a[b − exp(−ct)]) and exponential relationship, the
a double  Gompertz model, log G (t) = log G∞ [exp(− exp(b − ct))] , could better describe the gelation kinetics of this particular system. In these

3. Results and discussion 3.1. Sample characterization and gelation kinetics The compositional and some important molecular characteristics of the four ␤-glucan samples used in the present work are given in Table 1. The extraction methods adopted provided ␤-glucan samples of relatively high purity; all preparations had high levels of ␤-glucans and low protein contents with the exception of BG40. The Mw of the ␤-glucan isolates varied between 41 and 176 × 103 . Another important structural feature

Fig. 1. Typical kinetic plots of ␤-glucan gelation (BG 140) at three polysaccharide concentrations (pH 7.0, frequency 1 Hz, strain 0.1%).

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Fig. 3. Typical strain sweep measurements of ␤-glucan gels (BG 70) for different polysaccharide concentrations (T = 25 ◦ C, frequency = 1 Hz); the inset shows how the critical strain was calculated. G0 is the G at the linear region.

Fig. 2. Plot of the growth rate parameter (derived from the elasticity increment kinetic model) vs. concentration for the ␤-glucan gels; the inset shows a diagram of the slopes of the growth rate parameter vs. Mw of the samples.

empirical models, t is the time. In the single exponential, c is an empirical parameter, which measures the rate of increase of log G , while for the Gompertz model the rate of increase is given by the ratio (c log G∞ )/e. The log G∞ is the value of log G at the plateau region. Thus, the rate of gelation could be alternatively measured by the value of the growth rate parameters with high growth rate values indicating fast gelation processes. The growth rate values were estimated for all ␤-glucan isolates using the three models, and plotted versus concentration as is indicatively shown in Fig. 2 for the IE model. These values were found to increase with increasing concentration and decreasing Mw of the polysaccharide in agreement with previous findings [18,19,22]. Additionally, there seemed to be linear relationships between the increment of growth rate values and concentration (log IE versus log C),

which also showed a downward relation with the Mw of the samples (Fig. 2, inset). Such plots, with kinetic data derived from all empirical models, revealed the importance of the Mw on the gelation kinetics. The influence of the structural features of these polysaccharides such as size and distribution of sequences of consecutive cellotriosyl units to the gelation potential is further discussed below. 3.2. Scaling behavior of the viscoelastic properties A fractal aggregate structure implies that many aggregate properties show a power law scaling [2]. This means that when a scaling parameter is plotted in double logarithmic plot versus concentration a straight-line relationship is revealed. The maximum values of the G in the linear region of the strain sweep measurements (Fig. 3) were collected and plotted as a function of the polysaccharide concentration as shown in Fig. 4 (left). This figure shows that for all ␤-glucan samples, G (at 25 ◦ C) exhibits a power law behavior or a scaling relationship with the polysaccharide concentration that can be fitted to the form G ∝ cn , where n is the power law exponent.

Fig. 4. Double logarithmic plots of the storage modulus, G (left) and the critical strain, γ 0 (right), of ␤-glucan gels varying in Mw as a function of polysaccharide concentration.

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Its values were found to range between 3.3 and 4.7. Clark and Ross-Murphy [26,27] have discussed the dependence of storage modulus on concentration for protein and polysaccharide gels. In this context, linear relationships in double logarithmic plots of storage modulus versus concentration have been reported for amylose [28], curdlan [14] and gellan gels [29] as well as for soy protein [30] and casein gels [31]. In some of these studies the calculated slope values of log G versus concentration varied between 2.5 and 5.9. Even for the same biopolymer, a broad range in the observed exponent values has been reported among different studies, and it may reflect differences in the polymer concentration range, molecular size and polydispersity as well as conditions employed during gelation. Clark and Ross-Murphy [27] have provided a theoretical analysis for the power law dependence of G on polymer concentration according to which a limiting c2.0 relationship is predicted at high c/c0 ratios; c and c0 denote the polymer concentration and the critical concentration below which no macroscopic gel is formed, respectively. The strain amplitude at which G begins to decrease by 5% from its maximum value was determined and taken as a measure of the critical strain (γ 0 ) of the gels (inset of Fig. 3) [9,32]. Fig. 4 (right) presents the changes of critical strain γ 0 (at 25 ◦ C) as a function of polysaccharide concentration. The critical strain showed, likewise G , a power-law relationship with polymer concentration, i.e. γ 0 ∝ cm , with m being the power-law exponent. As is clearly shown in Fig. 4 (right), negative m values were obtained for all gels. The n and m values derived from this analysis are given in Table 2. The limit of linearity (γ 0 ) has been also found to decrease with increasing concentration for egg white protein gels [8], whereas the opposite trend has been reported for BSA gels [6]. 3.3. Fractal analysis Scaling theory applies to polymer properties, which are proportional to some power of the molecular weight and hence to the same power of the chain length [33]. Here, the fractal dimension of the gels was estimated from the power law exponents n and m using the scaling model of Wu and Morbidelli [4], which describes the scaling behavior of two polymer properties, i.e. G and γ 0 . The estimated df values are given in Table 2. Values of df close to 2 correspond to an open structure, while as df increases it means that the structure is becoming more dense (packed). It is clear that with increasing the Mw from 40 to 70 × 103 there is

a substantial increase of the df value, while from 70 to 180 × 103 the increase ceases. Syneresis is a well-known undesirable phenomenon of hydrogels, which becomes evident by the expulsion of the water from the structure. The traditional approach of explaining the phenomenon in ␤-glucan gel network structures is that of increasing density of junction-zones during aging [22]. An alternative explanation can be also given; the open structure of the low Mw ␤-glucan gels (as evidenced by the lower df value) denotes that the gel is more prone to rearrangements than their high Mw counterparts, which leads to faster collapse of the structure. This collapse would have as a consequence syneresis. A denser (more packed) structure indicates that syneresis is delayed and this corresponds to the higher Mw samples. In the last column of Table 2 the syneresis results are shown. It is evident that as the Mw is increased, the water released from the structure decreases, something that reconfirms the above reasoning. Furthermore, the large deformation data (stress versus strain) of Vaikousi et al. [19] revealed that with increasing Mw the hardness of the gels also increases. Visualization of the structure as open (low Mw samples) or more packed (high Mw) fractal clusters seems to be appropriate for the interpretation of these results. A more packed structure would withstand more compression until fracture than an open one. From the above discussion it appears that ␤-glucan gels form an open network where the whole structure is prone to rearrangements due to intra- and inter-cluster interactions. Overall, the description of the gel’s microstructure after the application of the fractal concept seems to be able to explain macroscopic properties such as syneresis and fracture behavior. The microelastic parameter, α, of the model is plotted as a function of Mw in Fig. 5. This parameter indicates the relative importance of elastic contributions of both inter- and intracluster links. As is shown in Fig. 5, the gels studied were in the transition regime. For a gel being in this regime, it means that the strength of interactions between the structural elements (chain aggregates) is not sufficiently large to cause kinetic arrest and the network becomes more transient and is prone to gradual structural rearrangements [34]. The transient network will also become more compact as the system separates into distinct aggregate-depleted and aggregate-rich micro phases with a consequent increase of its fractal dimension. The behavior of the parameter α is in agreement with the calculated fractal

Table 2 Structural parameters of barley ␤-glucan gels Samples

n

m

IE slope

df

Exudation of water (%, w/w gel)

BG40 BG70 BG140 BG180

3.3 4.1 4.6 4.7

−0.4 −0.7 −1.1 −1.2

2.60 0.75 0.10 0.01

2.32 a 2.41 b 2.42 b 2.44 b

4.7 a 4.1 a 2.2 b 0.7 c

Values with same letter do not differ significantly at p > 0.05.

149

Fig. 5. Evolution of the microelastic parameter, a, with the Mw.

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Fig. 6. Schematic representation of different levels of structure in a ␤-glucan gel network. The ‘particles’ of the fractal cluster are comprised of aggregated polysaccharide chains. The ‘particles’ aggregate to form the fractal cluster. Subsequently, the fractal clusters aggregate to form a 3D-structure. This pictorial model is adopted with modifications from similar structural models published elsewhere [10,32].

dimensions and the syneresis experiments of these systems. Fig. 6 shows a schematic representation of the different levels of the gel network structure. This scheme is a combination of already proposed depictions of gel fractal microstructure [10] and polymer interactions in the concentrated regime [32,33]; however, several new features were added. Still, in the above discussion there are two important issues that must be addressed. The fractal dimension of the gels depends on the volume fraction of the gelling system and the obtained df value is an average value in the given range of volume fractions [35,36]. Moreover, when comparing the df values of different systems one should determine the df at more or less the same range of volume fractions. In this context, we assumed that the volume fraction of aggregated particles is proportional to the polysaccharide concentration something that is part of the standard procedures in the investigation of biopolymers. In the present system, the concentrations were slightly varied (e.g. within 2–7% for BG40, and 6–10% for BG140 and BG180). This was done because of the inability of each sample to gel below a certain concentration and therefore a narrow concentration range was employed above the critical gelling concentration [19]. On the other hand, working at high concentrations for the BG40, similar to those used for the BG140 and BG180, was not feasible due to very rapid gelation of the former sample. However, despite the variation in the concentration range used for these samples, it is reasonable to assume that such small differences in the respective volume fractions would not have a significant impact on the scaling parameters derived from the analysis and

thereby on the final interpretation of the results. The other point that must be addressed is the term “particle” that should not be confused with the “rigid spherical particles”, a term that is frequently used in most of the works involving colloidal network systems. The term here is used to denote an increased population of junction zones that are responsible for a higher level of structure (see also Fig. 6, zoom-in). The vague use of the term has been successfully applied on protein gels [3,5–8,10,11], fat crystal networks [37] and powders [38]. We do recognize, however, the importance of the two aforementioned assumptions in our interpretations and that more work needs to be done with this and other polysaccharide gelling systems. This would be necessary in order to explore the general applicability of such an alternative analysis in an effort to describe the microstructure of polysaccharide gelling systems and its relevance to the macroscopic properties of such materials. 3.4. Molecular treatment of the gelation kinetics The gelation of ␤-glucans can be considered as an aggregation process where the association of chain segments with consecutive cellotriosyl units linked by ␤-(1 → 3) glycosidic bonds leads to network formation [22]. The gel point is reached when the effective volume of the macromolecular aggregates equals the sample volume [39]. When this point is reached there is a sudden increase of the storage modulus. At the gelling point, only a part of the total cluster aggregates constitutes the network. Gradually, more aggregates are stuck on the primary network

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structure, which is noticed by a further increase of G . The distance that a cluster must travel before collides with another decreases when c increases (for c > c0 ) so that both gel time (cross-over value) and the time at the end of the aggregation process (plateau value) should decrease as c increases [35]. While this was generally the case for each ␤-glucan sample examined, a molecular weight effect on the kinetics of the system shifting the critical concentration for gelation to higher levels was also observed. The influence of Mw on gelation kinetics is often attributed to the higher mobility of the shorter chains (“diffusion of the chains model”) [22,40]. However, the probability of collision between segments of consecutively linked cellotriose units must also be deemed important and that the diffusion of the chains is not the only responsible factor for aggregation. This seems to be reasonable because ␤-glucan chains have ‘inactive’ patches of chain segments, with respect to chain aggregation. These fragments increase with increasing Mw, as shown in the last two lines of Table 1 (increasing ratio of (1 → 4)/(1 → 3) linkages and increasing proportion of DP5-DP14 oligosaccharides) and thus the probability of collision between the ‘reactive’ segments of the chains is decreased. Moreover, in the “diffusion of the chains” model for ␤-glucan aggregation the intramolecular interactions of the chains are neglected. Such intrachain interactions are probably more significant for the large chains (i.e. high Mw) because they have greater conformational ability as this is expressed by their radius of gyration [41]. When such large loop interactions are included, the probability of collision of the large chains is further decreased. Thus, taking everything into account, the probability for collision of the ‘reactive’ segments of the chains is larger for small chains due to their higher diffusion rates, a lower amount of cellulose like fragments and a smaller degree of intrachain interactions. Since it is generally accepted from the current kinetic theories that faster gelation kinetics lead to more disordered systems with lower fractal dimension, the above analysis explains why low Mw samples can gel at lower concentrations, exhibit faster gelation rates and give lower fractal dimension values than their high Mw counterparts. Furthermore, if one considers the several conformational restrictions of the “real” polysaccharide chain, such a treatment stresses the importance of chain conformation and intrachain interactions on the probability of collision of the “reactive” patches along the polysaccharide chains during gelation.

4. Conclusions In this study a polysaccharide gelling system was examined in the context of fractal scaling, an approach not often taken for such physically aggregating polymeric network. The microstructure of the gel network appeared to be more open for the low Mw ␤-glucan samples (low fractal dimension) than their high Mw counterparts. All gels studied were in a transition regime denoting that a further restructuring takes place upon ageing and since the structure is more open for the low Mw ␤-glucans, the restructuring is more evident for these samples. Moreover, it is suggested that chain diffusion is not the only

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factor that influences ␤-glucans gelation kinetics. The probability of collision of chain fragments with consecutive cellotriosyl units and the degree of intrachain interactions also seem to play a key role in gel network formation leading to systems with different fractal dimensionality and gelation behavior. Acknowledgments This work has been carried out in part with the financial support from the Greek Ministry of Education (PYTHAGORAS program, 97436 8, 2005-06). The authors wish to thank Dr. M. Izydorczyk from the Canadian Grain Research Commission, Winnipeg, Manitoba, Canada, for conducting the lichenase experiments and Prof. A. Marangoni, University of Guelph, Canada for his valuable comments concerning the interpretation of some of the research findings. References [1] W.C.K. Poon, M.D. Haw, Adv. Colloid Interf. Sci. 73 (1997) 71. [2] G.C. Bushell, Y.D. Yan, D. Woodfield, J. Raper, R. Amal, Adv. Colloid Interf. Sci. 95 (2002) 1. [3] M. Mellema, J.W.M. Heesakkers, J.H.J. van Opheusden, T. van Vliet, Langmuir 16 (2000) 6847. [4] H. Wu, M. Morbidelli, Langmuir 17 (2001) 1030. [5] T. Hagiwara, H. Kumagai, T. Matsunaga, J. Agric. Food Chem. 45 (1997) 3807. [6] T. Hagiwara, H. Kumagai, K. Nakamura, Food Hydrocolloids 12 (1990) 29. [7] S. Ikeda, E.A. Foegeding, T. Hagiwara, Langmuir 15 (1999) 8584. [8] M.M.O. Eleya, S. Ko, S. Gunasekaran, Food Hydrocolloids 18 (2004) 315. [9] W.H. Shih, W.Y. Shih, S.I. Kim, J. Lin, I.A. Aksay, Phys. Rev. A 42 (1990) 4772. [10] A.G. Marangoni, S. Barbut, S.E. McGauley, M. Marcone, S.S. Narine, Food Hydrocolloids 14 (2000) 61. [11] A.C. Alting, R.J. Hamer, C.G. de Kruif, R.W. Visschers, J. Agric. Food Chem. 48 (2003) 5001. [12] M.R. Gittings, L. Cipelletti, V. Trappe, D.A. Weitz, M. In, C. Marques, J. Phys. Chem. B 104 (2000) 4381. [13] M.R. Gittings, L. Cipelletti, V. Trappe, D.A. Weitz, M. In, J. Lal, J. Phys. Chem. A 105 (2001) 9310. [14] T. Tada, T. Matsumoto, T. Masuda, Carbohydr. Polym. 39 (1999) 53. [15] A.M. Vallera, M.M. Cruz, S. Ring, F. Boue, J. Phys.: Condens. Matter 6 (1994) 311. [16] T. Suzuki, A. Chiba, T. Yano, Carbohydr. Polym. 34 (1997) 357. [17] P.J. Wood, Carbohydr. Polym. 25 (1994) 331. [18] A. Lazaridou, C.G. Biliaderis, M.S. Izydorczyk, Food Hydrocolloids 17 (2003) 693. [19] H. Vaikousi, C.G. Biliaderis, M.S. Izydorzcyk, J. Cereal Sci. 39 (2004) 119. [20] M. Irakli, C.G. Biliaderis, M.S. Izydorczyk, I.N. Papadoyannis, J. Sci. Food Agric. 84 (2004) 1170. [21] W. Cui, P.J. Wood, Relationships between structural features, molecular weight and rheological properties of cereal ␤-d-glucans, in: K. Nishimari (Ed.), Hydrocolloids—Part I, vol. 159, Elsevier, Amsterdam, 2000. [22] N. B¨ohm, W.M. Kulicke, Carbohydr. Res. 315 (1999) 302. [23] O.H. Lowry, N.J. Rosenbrough, A.L. Farr, R.J. Randall, J. Biol. Chem. 193 (1951) 265. [24] B.V. McCleary, M. Glennie-Holmes, J. Inst. Brewing 91 (1985) 285. [25] W. Cui, P.J. Wood, B. Blackwell, J. Nikiforuk, Carbohydr. Polym. 41 (2000) 249. [26] A.H. Clark, S.B. Ross-Murphy, Adv. Polym. Sci. 83 (1987) 57. [27] A.H. Clark, S.B. Ross-Murphy, Br. Polym. J. 17 (1985) 164.

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