Studies of aggregation behaviours of cereal β-glucans in dilute aqueous solutions by light scattering: Part I. Structure effects

Food Hydrocolloids 25 (2011) 189e195

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Food Hydrocolloids journal homepage: www.elsevier.com/locate/foodhyd

Studies of aggregation behaviours of cereal b-glucans in dilute aqueous solutions by light scattering: Part I. Structure effects Wei Li a, Steve W. Cui b, *, Qi Wang b, Rickey Y. Yada c a

CP Kelco Inc., 8225 Aero Drive, San Diego, CA 92123, USA Guelph Food Research Centre, Agriculture and Agri-Food Canada, Guelph, ON N1G 5C9, Canada c Department of Food Science, University of Guelph, Guelph, ON N1G 2W1, Canada b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 August 2009 Accepted 25 February 2010

Cereal b-glucans form aggregates even in dilute aqueous solution. Their aggregation behaviours were studied by static and dynamic light scattering. It was shown that the aggregation of cereal b-glucans in aqueous solution was a very fast dynamic process and the equilibrium of molecular association and dissociation were reached quickly. The concentration dependence of the average apparent diameters of cereal b-glucans suggested that the clusterecluster aggregation was dominant. The structural features of cereal b-glucans played an important role on their aggregation behaviours. As molecular weight increased, the degree of aggregation decreased due to the lower diffusion rate of large molecules. For the more rigid conformation (lower diffusion rate) of b-glucans with higher tri/tetra ratio, their degrees of aggregation were lower. These results suggested that the aggregation process was diffusion limited. Ó 2010 Published by Elsevier Ltd.

Keywords: Cereal b-glucans Aggregation Light scattering Molecular weight tri/tetra ratio

1. Introduction Mixed 1e3, 1e4 linked cereal b-glucans, the linear neutral polysaccharides occurring in the subaleurone and endosperm cell walls of grains, have been accepted as functional, bioactive ingredients over the last two decades due to their abilities to improve blood glucose regulation, reduce serum cholesterol levels, and relieve constipation. The bioactivities are largely due to their ability to form viscous solutions in the gut, but also possibly due to their ability of forming gels when their molecular weights are low. It has been demonstrated that structural features such as tri/tetra saccharide ratio (varies with the order of 4.2e4.5 for wheat, 2.8e3.3 for barley, and 2.0e2.4 for oat) (Cui & Wood, 2000), and molecular weight are the two important factors affecting their solution properties and gel forming abilities. For example, the smaller the polymer chain, and the higher the tri-/ tetra ratio, the faster of the gel formation and more brittle the gels formed within the molecular weight range from 50,000 to 100,000. The network formation of b-glucans can be mainly considered as the association of consecutive cellotriosyl segments along the polymer chains (reaction sites) via hydrogen bonding. Therefore, the mount of reaction sites and their accessibility play the major roles for the network formation. Higher tri/tetra ratio

* Corresponding author. Tel.: þ1 519 780 8028; fax: þ1 519 829 2600. E-mail address: [email protected] (S.W. Cui). 0268-005X/$ e see front matter Ó 2010 Published by Elsevier Ltd. doi:10.1016/j.foodhyd.2010.02.005

directly leads to more reaction sites in the polymer chain, thus bglucans with higher tri/tetra ratio have faster and more compact network formation (more molecular association). Due to the higher mobility and less spatial hindrance of the shorter chains, the probabilities of low molecular weight samples for both collision (translational diffusion) and sticking (rotational diffusion) increase leading to the faster gelation rate and stronger gels. The increase of brittleness of gels formed by smaller or higher tri/tetra ratio b-glucan molecules was caused by their compact networks, which leads to less spatial allowance for deformation upon stress. However, it is unclear how the polysaccharides are aligning themselves or how the 3-dimensional network has been formed. To elucidate the mechanism of molecular association of cereal bglucans in aqueous solution, it is essential to understand the aggregation phenomena in dilute solutions first. The tendency of cereal b-glucan molecules to associate in dilute solutions has been reported and some models and mechanisms for the formation of aggregates were proposed. By using light scattering and High Performance Size Exclusion Chromatography (HPSEC), Vårum and co-workers (Vårum, Smidsr¢d, & Brant, 1992) reported that approximately 10% of the oat b-glucan in aqueous solution formed labile aggregates and assumed micelle-like aggregation. Grimm et al. (Grimm, Kruger, & Burchard, 1995) proposed a fringed micelle structure model with side to side aggregation of chains based on light scattering and viscometry measurements on b-glucan isolated from beer. This fringed micelle aggregation was visualized by confocal scanning laser microscopy for oat b-glucan (Wu, Zhang,

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W. Li et al. / Food Hydrocolloids 25 (2011) 189e195

Xie, Wang, & Deng, 2006). However, comparison of these two results showed some discrepancies. For example, Vårum et al. (1992) found complete dissociation into monomers on dilution approaching zero concentration, which was not achieved with barley b-glucan studied by Grimm et al. (1995). A more open molecular association of oat b-glucan was reported by Vårum et al. (1992). On the other hand, formation of aggregates of barley b-glucan was analyzed through its viscoelastic and flow behaviour (Gómez, Navarro, Manzanares, Horta, & Carbonell, 1997a). It was suggested that the aggregation mechanism of barley b-glucan involved temporary links between short chain fragments and the association was enhanced in elevated temperature and weakened by added salt (Gómez et al., 1997a). The authors did not explain why the aggregation of barley b-glucan would be enhanced at elevated temperatures since these were mainly hydrophilic associations. In fact, most molecular associations via hydrogen bonding of barley b-glucans are weakened upon heating. However, high mobility and extended chain conformation caused by heating may lead to the super-aggregate formation (aggregateeaggregate association) between the molecules which have relatively longer regular segments. The thermal energy at the elevated temperature (70  C) may not be high enough to overcome the hydrogen bonding between such long junction zones. Even small amounts of super-aggregates could increase the light scattering intensity dramatically. However, studies on aggregation of cereal b-glucans in solution are not conclusive: both the mechanism of aggregate formation and the structure of aggregates still remain unclear. For example, the assumption of the micelle-like structure of aggregates (Grimm et al., 1995; Vårum et al., 1992) could not be used to explain the gelation properties of cereal b-glucans in concentrated solution. The aim of present work was thus to elucidate the aggregation mechanism of cereal b-glucans and characterize their aggregate structures. Using static and dynamic light scattering, aggregation behaviours of fractions with different molecular weights from each of wheat, barley, and oat b-glucans were investigated, which allows for the study of the effect of molecular weight and structures (tri/tetra ratio) on aggregation behaviour. 2. Materials and methods 2.1. Materials Fractions differing in molecular weights from wheat (6 fractions), barley (5 fractions) and oat (6 fractions) of b-glucans were used for this study. These fractions were obtained from the purified b-glucan samples using the gradient ammonium sulphate precipitation method as described previously (Wang, Wood, Huang, & Cui, 2003; Li, Cui, & Kakuda, 2006a). 2.2. Preparation of cereal b-glucan solutions Cereal b-glucan aqueous solutions were prepared by heating at 90  C with magnetic stirring for 3 h. After 30 min (the period for cooling solutions down to room temperature naturally), the solutions were filtered through 0.45 mm nylon syringe filter (Chromatographic Specialties Inc., USA) directly into dust-free scattering cell and the measurements were performed immediately. To provide equivalent macromolecular overlap space for each fraction in solutions, the differences of molecular weights of the samples were taken into account, which are directly related to their intrinsic viscosities [h]. Therefore, the reduced polymer concentration c[h], corresponding to the volume filled in solution by polymers, was kept the same (0.4) for each fraction. The concentration of each fraction was then obtained based on their intrinsic viscosities.

2.3. Intrinsic viscosity measurement The intrinsic viscosities were determined by dilute solution viscometry using a Cannon Ubbelohde Dilution B glass viscometer (size 75, Glass Artefact Viscometers, Braintree, Essex, UK) in a constant temperature water bath at 25  C. The measurements were made on a concentration range so that the relative viscosity, hr, was kept from 1.2 to 2.0 and the viscosity was essentially Newtonian. Intrinsic viscosity [h] was calculated using the following relationship:


 ½h ¼ lim hsp =C ¼ lim ðln hr =CÞ C/0

C/0

(1)

where C is concentration of polymer, hr is relative viscosity and hsp is specific viscosity, defined as hr  1. HugginseKramer plots of hsp/C and ln (hr)/C versus C were then used to estimate the intrinsic viscosity [h] by extrapolation to zero concentration. 2.4. Light scattering 2.4.1. Zimm method Static light scattering allows the determination of weight average molecular weight Mw, radius of gyration Rg and the second virial coefficient A2 using the following equation:


 Kc=Rq ¼ 1=Mw þ 1=3 R2g =Mw q2 þ 2A2 c:

(2)

where K is an optical contrast factor, c is the concentration, Rq, Rayleigh ratio (scattering intensity), and q value of the scattering vector defined as:

q ¼ ð4p=lÞsinq=2;

(3)

with l ¼ l0/n0, the wave length of the light in a medium of refractive index n0, l0, the wave length in vacuum. The optical contrast factor K is defined by


4 K ¼ 2p2 n20 ðdn=dcÞ2 = N0 l0 ;

(4)

where dn/dc is the refractive index increment of the solution, N0 is Avogadro’s number. The Zimm method is a graphical technique to extrapolate simultaneously Kc/Rq to zero angle and infinite dilution. In a Zimm plot, Kc/Rq is plotted as a function of q2 þ kc, where k is a freely chosen constant. The slope of the angular dependence at c ¼ 0 corresponds to the z-average mean square radius of gyration (Rg)2. A2 can be calculated from the slope of concentration dependence at q ¼ 0.1. Mw is obtained from the intercept of both c ¼ 0 and q ¼ 0 extrapolated lines. 2.4.2. Dynamic light scattering The measured intensity autocorrelation function G(2)(s) is related to the electric field autocorrelation function g(1)(s) by the Siegert relation:

i h 2 Gð2Þ ðsÞ ¼ A 1 þ bjg ð1Þ ðsÞj :

(5)

where A is the baseline constant, b is coherence factor, which is generally considered as an adjustable parameter in the data analysis procedure, s is the correlation time. For continuous distribution of decay rate G,

gð1Þ ðsÞ ¼

ZþN

GðGÞexpðGsÞdG:

(6)

0

where G(G) is a continuous distribution function of decay rates, which is correlated with g(1)(s) by a Laplace transformation. The

W. Li et al. / Food Hydrocolloids 25 (2011) 189e195

Rh ¼ kT=6phD:

(7)

where T is absolute temperature, k is the Boltzmann constant, and h is the solvent viscosity. In the case of a polydispersed solute, the distribution of diffusion constants and, the hydrodynamic diameter distribution function required are obtained from g(1)(s) by inverse Laplace transformation using the non-negatively constrained least square method (NNLS). 2.4.3. Apparatus of light scattering A 35 mW helium neon laser (Melles Criot Laser Group, Carlsbad, CA, USA) with wave length of 632.8 nm was focused on to a precision cylindrical cell (quartz, diameter 25 mm) containing a sample solution. Both static and dynamic measurements were conducted using a Brookhaven light scattering instrument including a precision goniometer, a photomultiplier and a 128-channel BI-9000AT digital autocorrelator (Brookhaven Instruments, Holtsville, NY, USA). Light scattering measurements were carried out in the angular range of 30e140 for static measurement and at 90 for dynamic measurement. Toluene was used as a reference with the Rayleigh ratio of 1.398  105 cm1 in the static light scattering measurements. The refractive index increment, dn/dc, was determined as 0.146 ml/g for b-glucan in aqueous solution. All the light scattering measurements were performed at 25  C. The duration of dynamic measurements was 30 min. The particle size distributions were calculated by the NNLS method, which is suitable for characterization of solutions containing aggregates.

3. Results and discussion 3.1. The presence of aggregates Fig. 1 is an example of the apparent molecular size distribution of cereal b-glucans measured by dynamic light scattering. The presence of aggregates in aqueous solutions was clearly illustrated by the bimodal distribution. The group with smaller size represents the original molecules or non-aggregates, whereas the group with larger size is designated as aggregates. Li et al. (Li, Wang, Cui, Huang, & Kakuda, 2006c) reported that the aggregates were very stable and could not be removed by heat, filtration, sonication, or urea solution. However, the use of 0.5 M NaOH solution can remove aggregates completely, which allowed accurate measurement of molecular parameters by light scattering of cereal b-glucans. Physical method cannot eliminate aggregates completely in aqueous solutions, since the inter-molecular hydrogen bonding leads to the molecular re-associations after the removal of physical treatments. The molecular re-associations of b-glucans are so rapid

Fig. 1. Size distribution of wheat b-glucan fraction 4 measured by dynamic light scattering.

1.2E-06

Kc/ R (mol/g)

decay rate is defined as G ¼ K2D, where D is the diffusion coefficient and K is the optical contrast factor. The hydrodynamic radius (Rh) can be calculated by applying StokeseEinstein relation:

191

9.0E-07 6.0E-07 3.0E-07 0.0E+00 0

1. 5

3

4. 5

2

Sin ( /2) + 8000c Fig. 2. Zimm plot of oat b-glucan fraction 1.

that it is almost impossible to obtain an aggregate-free solution for the evaluation. However, the addition of alkali causes ionisation of hydroxyl groups, i.e. conversion from eOH to eO-, resulting electrostatic repulsions which inhibit inter-molecular association. These molecular parameters measured in 0.5 M NaOH solution provide true information of the single molecules, which can be used as references for their aggregates. A Zimm plot of the static light scattering data for a typical sample OF1 is shown in Fig. 2. The small negative slope of the concentration dependence, hence the negative A2 value, is typical for a partially reversible aggregation system in which the aggregates dissociate as the solution is diluted. The negative value of A2 indicates that water is a poor solvent for cereal b-glucans (Elias, 1972; Vårum et al., 1992). Weight average molecular weight (Mw), second virial coefficient (A2), radius of gyration (Rg), and average hydrodynamic radius (Rh) of all the fractions of each cereal b-glucans measured by light scattering in aqueous solution are given in Table 1 along with intrinsic viscosities ([h]) measured by capillary viscometry. 3.2. Aggregation kinetics Dynamic light scattering is a powerful tool for monitoring the aggregate growth. The evolution of the hydrodynamic radius of samples with time can be recorded without any disruption to measured solutions. However, the aggregation process of cereal b-glucans was too fast to be monitored by DLS. The aggregates were Table 1 Molecular characteristics of cereal b-glucan samples in aqueous solution. Mw (g/mol)

A2  104 (mol ml/g2)

Rg (nm)

Rh (nm)

[h] (dL/g)

WF1 WF2 WF3 WF4 WF5 WF6

919,000 575,000 367,100 319,500 171,500 103,500

2.18 4.49 2.01 2.46 2.71 1.44

80.5 62.2 53.2 51.9 47.3 44.6

99.0 79.9 73.4 72.5 69.8 53.9

6.5 6.1 5.2 3.7 2.8 1.5

BF1 BF2 BF3 BF4 BF5

581,100 492,800 290,300 242,000 150,100

2.70 1.69 1.20 0.82 3.30

60.4 55.2 45.4 49.8 39.2

109.5 105.7 96.2 86.3 73.8

5.9 4.4 4.0 3.5 2.3

OF1 OF2 OF3 OF4 OF5 OF6

2,025,000 2,076,000 811,000 438,300 364,300 128,100

4.98 2.09 2.11 2.71 1.71 3.50

75.8 73.9 52.0 48.8 50.7 44.3

191.4 183.6 165.3 128.2 135.9 70.7

4.2 4.2 3.2 1.8 1.4 0.9

Note: Molecular weight (Mw), the second virial coefficient (A2), and radius of gyration (Rg) were measured by SLS; hydrodynamic radius (Rh) was measured by DLS.

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W. Li et al. / Food Hydrocolloids 25 (2011) 189e195

b 200

400 Aggregates

Non-aggregates

300

150

200

100

100

50

0

0

60

40

20 Apparent diameter

0

1

2

3

Percentage

Diameter (nm)

a

percentage of aggregates 0

0

Concentration (mg/ml)

1

2

3

Concentration (mg/ml)

Fig. 3. Example of concentration dependence of the apparent diameter and aggregate percentage of wheat b-glucan fraction 5 (Apparent Mw: 171,500).

detected when freshly prepared samples were cooled down to room temperature (within 30 min). The fast aggregate formation was caused by the poor solvent quality of water for cereal b-glucans. However, when the solutions were monitored for a sufficiently long period (2 weeks), the size of aggregates kept constant with the initial values. This phenomenon indicates that molecular dissociation may be present during the aggregation process and the equilibrium of molecular association and dissociation is quickly reached, which limited the further growth of the aggregates. In the following sections, all measurements were performed in the equilibrium stage. 3.3. Concentration dependence of aggregation Fig. 3 shows the concentration dependence of apparent hydrodynamic radius of cereal b-glucans, wheat b-glucan fraction 5 was chosen as an example. As concentration increased, the average apparent hydrodynamic radius increased gradually. When the concentration reached a critical point, a dramatic increase of the apparent hydrodynamic radius was observed compared with that at lower concentrations. This changing point probably corresponded to the critical concentration of the samples. To confirm this assumption, the concentration at changing points for wheat b-glucan fractions were compared with the predicted critical concentration of the same samples from the intrinsic viscosity results based on the empirical formulas of c*[h] z 0.59 for wheat b-glucan fraction 1e5 and c*[h] z 0.33 for fraction 6 (Li, Cui, & Wang, 2006b). A good agreement was obtained as shown in Table 2. Due to the spatial overlap of polymer molecules, the chances of molecular association were greatly increased in semidilute solution, which led to the dramatic increase of the apparent hydrodynamic radius. However, the percentage of aggregates stays constant with the increase of concentration even above the critical point (Fig. 3, right). The increase of average apparent diameters is caused by the increase of apparent diameters of aggregates (Fig. 3, left). These results imply a possible clusterecluster aggregation model of cereal b-glucans in aqueous solution. The clusterecluster aggregates were featured as its anisotropic structures and low fractal dimensions compared with particle-cluster aggregates. The detailed model of clusterecluster aggregation was discussed by Jullien and Botet (1987).

Table 2 Comparison of critical concentrations (c*) of wheat b-glucan fractions.

c* (mg/ml) c*0 (mg/ml)

WF1

WF2

WF3

WF4

WF5

WF6

0.9 0.8

1.0 0.9

1.1 1.0

1.6 1.4

2.1 2.0

2.2 2.6

0

Note: c* were calculated from their intrinsic viscosities; c* were obtained from the concentration dependence of apparent hydrodynamic radius.

3.4. The degree of aggregation The degree of aggregation can be indicated from the increase of the apparent hydrodynamic radius measured by DLS. Table 3 shows that the apparent hydrodynamic radius increased with the increase of molecular weight. Due to the original size differences between fractions, it is difficult to compare the degree of aggregation using Rh. Therefore, the ratio (x) of the apparent hydrodynamic radius of the aggregate (Rh) to that of the non-aggregate (Rh0) measured in 0.5 M NaOH solutions was used to indicate the degree of aggregation. As shown in Table 3,  ( ¼ Rh/Rh0) values increased with the decrease of molecular weight indicating the smaller molecules (should be above minimum molecular weight requirement for network formation) are likely to form aggregates. The higher mobility of smaller molecules may provide them more opportunities to associate with each other. In order to investigate the structural effect (tri/tetra ratio) on degree of aggregation, the average “X” values of b-glucans from oat, barley and wheat were calculated as oat (7.5) > barley (4.4) > wheat (3.9), which has the opposite order of their tri/tetra ratios, namely wheat (4.2e4.5) > barley (2.8e3.3) > oat (2.0e2.4). As discussed previously (Li, Cui, & Wang, 2006b), b-glucan molecules with higher tri/tetra ratio possessed more rigid chain conformation in aqueous solution leading to a lower diffusion rate. The lower diffusion rate in solution reduced the chances for molecular interaction, thus the lower degree of molecular association. This result is consistent with the molecular weight effects. Both the molecular

Table 3 Aggregation numbers of cereal b-glucan fractions. Rh (nm)

Rh0 (nm)

x (Rh/Rh0)

WF1 WF2 WF3 WF4 WF5 WF6

99.0 79.9 73.4 72.5 69.8 53.9

36.7 28.5 24.3 19.8 16.8 7.8

2.7 2.8 3.0 3.7 4.2 6.9

BF1 BF2 BF3 BF4 BF5

109.5 105.7 96.2 86.3 73.8

53.0 47.2 37.2 17.7 7.1

2.1 2.2 2.6 4.9 10.4

OF1 OF2 OF3 OF4 OF5 OF6

191.4 183.6 165.3 128.2 135.9 70.7

45.7 30.9 23.8 15.3 17.8 6.0

4.2 5.9 6.9 8.4 7.6 11.8

Note: N ¼ 2. Rh is apparent hydrodynamic radius of b-glucans with aggregates; Rh0 is apparent hydrodynamic radius of b-glucans without aggregates; x is aggregation number. cereal b-glucan fractions are denoted as WF1e6 for wheat, BF1e5 for barley, and OF1e6 for oat b-glucan, respectively.

W. Li et al. / Food Hydrocolloids 25 (2011) 189e195

1

0.6

y = 0.6063x - 2.7487 R2 = 0.9218 Barley

0.4 0.2 0

Wheat

Barley

y = 0.5821x - 3.0294 R2 = 0.9705 Oat

Oat

-0.2 5

5.5

6

6.5

y = 0.288x + 0.3876 R2 = 0.9648 Barley

2.3

Log (Rh)

Log ([ ])

2.5

y = 0.6795x - 3.1589 R2 = 0.9202 Wheat

0.8

193

2.1 1.9 1.7

Wheat

Barley

1.5

7

5

5.5

6

weight and tri/tetra ratio effects on the aggregation behaviours of b-glucans suggest that the degree of aggregation of cereal b-glucans mainly depends on the translational diffusion rate of molecules implying the diffusion limited aggregation process in dilute aqueous solution. Due to the long distance between the molecules in dilute solution, the diffusion rate becomes more important than the structural features of monomers. 3.5. The structure of aggregates Since it is impossible to isolate aggregates from solutions, the determination of aggregate structure becomes very difficult. In present study, several approaches such as by studying the relationship between intrinsic viscosity, hydrodynamic radius and molecular weight were explored to demonstrate the structures of aggregates as clear as possible. First, the scaling law was applied to interpret the structural parameters. The molecular weight dependences of the parameters [h], Rg, and Rh were plotted in Figs. 4e6 respectively. The extracted exponents are listed in Table 4. The relationship between molecular weight and intrinsic viscosity follows Mark-Houwink-Sakurada equation a ½h ¼ KMw

(8)

As shown in Table 4, the values of the exponent a are 0.68, 0.61, and 0.58 for wheat, barley, and oat b-glucans, respectively. These values are lower than those of their non-aggregate counterparts (above 0.71) (Böhm & Kulicke, 1999a; Gómez, Navarro, Manzanares, Horta, & Carbonell, 1997b; Grimm et al., 1995; Li, Cui, & Wang, 2006b; Roubroeks, Andersson, Mastromauro, Christensen, & Åman, 2001; Wang, Wood, Cui, & Ross-Murphy, 2001) but still in the range of random coil regime (0.5e0.8) indicating that the percentage of aggregates in such dilute aqueous solution is so low that the bulk solution behaviours are still dominated by the single y = 0.3148x - 0.0014 R2 = 0.9117 Wheat

1.9

Log (Rg)

6.5

Log (Mw)

Fig. 4. Double logarithmic plot of [h] against Mw of cereal b-glucans in aqueous solutions.

y = 0.2904x + 0.098 R2 = 0.8944 Barley

y = 0.2375x + 0.5589 R2 = 0.9089 Wheat

Oat

Log (Mw)

2

y = 0.3211x + 0.2775 R2 = 0.8902 Oat

Fig. 6. Double logarithmic plot of Rh against Mw of cereal b-glucans in aqueous solutions.

molecules especially in viscometry measurements. The lower values of a may be caused by the growth of aggregates, which leads to branched chain structure. However, since the growing branches screen the interior from the incoming molecules, the more opened structure of aggregates is formed. There is a slight increase of a values with the tri/tetra ratio indicating that the aggregate structure of oat b-glucan is more branched than those of barley and wheat b-glucans. The n and n0 values were obtained (Table 4) from the following relations n or R ¼ KM n Rg ¼ KMw h w 0

(9)

Such power laws indicates fractal objects with fractal dimension of Df ¼ 1/n. The n values of 0.25e0.31 for cereal b-glucans lead to an apparent fractal dimension of Df > 3, which has no physical meaning. Therefore, this parameter cannot explain any geometrical architecture. The failures of fitting the power law relationship indicate that the aggregates may not be big enough to form fractals which have self-similarity. Therefore, a different method to study the relationship between radius of gyration and molecular weight other than power law relationship was adapted from Benoit and Doty (1953). The radius of gyration could be expressed by



h
 R2g ¼ qM=3ML  q2 þ 2q3 ML =M 1  qML =M i
 1  eM=qML ;

ð10Þ

with the molecular weight M, the persistence length q, and the linear mass density ML. Equation (10) can be approximated by




M=Rg 2

1=2

¼ ð3ML =qÞ1=2 ð1 þ 3qML =2MÞ;

(11)

the maximum deviation from the exact value being 0.5% for M/2qML > 4 and 1% for M/2qML > 2. Thus, if M/2qML > 2, the values of (M/R2g)1/2/2 plotted against 1/M should give a straight line whose intercept and slope are equal to (3 ML/q)1/2 and 3 ML(3qML)1/2/2 respectively, which allows the determination of q and ML (Murakami, Norisuye, & Fujita, 1980). ML can be used to calculate the number of laterally aggregated strands n, which is defined as

1.8 1.7 y = 0.2511x + 0.2781 R2 = 0.904 Oat

1.6 Wheat

Barley

Oat

1.5 5

5.2

5.4

5.6

5.8

6

6.2

6.4

Log (Mw) Fig. 5. Double logarithmic plot of Rg against Mw of cereal b-glucans in aqueous solutions.

Table 4 Worm-like chain parameter of cereal b-glucans.

a Wheat b-glucan Barley b-glucan Oat b-glucan

0.68 0.61 0.58

n 0.24 0.29 0.32

n0 0.31 0.29 0.25

q (nm)

ML (g/mol nm)

n

q0 (nm)

31.42 29.27 28.36

1726.0 1821.0 3271.4

5.6 5.9 10.5

4.42 3.47 2.3

Note: a,n,n0 are exponents from plot log [h], Rg, Rh versus Log Mw respectively. q and q0 are the persistent length with and without aggregates respectively. ML is linear mass density, and n ¼ ML/ML0, multiplicity of aggregate structure.

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W. Li et al. / Food Hydrocolloids 25 (2011) 189e195

n ¼ ML =ML0 ;

(12)

where ML0 is the linear mass density of the single chain (Grimm et al., 1995), ML0 was calculated from the average molar mass and length of a residue. For cereal b-glucans, the averaged length was obtained by the equation (Buliga, Brant, & Fincher, 1986) defined as

l2 ¼ P3 l3 2 þ P4 l4 2 ;

(13)

where P3 and P4 are the mole fraction of b- (1e3) linkages and b- (1e4) linkages, and l3 ¼ 0.48 nm and l4 ¼ 0.54 nm are the corresponding residue length, respectively (Morris & Ross-Murphy, 1981). Using the average molecular mass of residue m ¼ 162, the ML0 of cereal b-glucans were calculated to be 310.2  0.2 g/mol nm. Applying this method to cereal b-glucan samples, straight lines were obtained as shown in Fig. 7 indicating the validity of this method for b-glucan solutions with the presence of aggregates. The values of q, ML, and n determined from the plot are given in Table 4. The persistence lengths of the single molecules q0 obtained from references (Gómez et al., 1997b; Roubroeks, Mastromauro, Andersson, Christensen, & Åman, 2000; Li, Cui, & Wang, 2006b) are also listed for comparison. The persistence lengths of aggregates are around 7e12 times higher than the values of non-aggregates indicting the aggregates have a more rigid conformation than non-aggregates. The number of laterally aggregated strands n slightly follows the order of wheat (5.7) < barley (5.9) < oat (10.5) which agree with the average  values (Rh/Rh0) of wheat (3.9), barley (4.4) and oat (7.5). The similarity of n numbers and average “X” values indicates that the times of the hydrodynamic radius increase of aggregates is almost the same number of single molecular chains involved in aggregates. This finding implies that the growth of aggregates of b-glucans is more likely in axial direction of the molecular chains via the interactions between the consecutive trisaccharide segments. These ordered segments were believed to be the main reaction site to form junction zones (Böhm & Kulicke, 1999b; Cui, 2001; Lazaridou, Biliaderis, Micha-Screttas, & Steele, 2004; Li, Cui, & Wang, 2006b). Due to spatial hindrance and limited reacting sites of cereal b-glucans, the association between monomers is quite random. When the aggregation occurs, the growing branches of aggregates prevent the monomers from penetrating into the centers, which leads to an open structure of aggregates. The concentration dependence study also showed the possible clusterecluster aggregation model. All these results strongly suggested that molecular association of cereal b-glucans in dilute solution lead to an irregular fractal aggregate with more opened structure. This conclusion disagrees with the compact micelle-like structure suggested by Grimm et al. (1995) and Vårum et al. (1992). Vårum et al. (1992) studied aggregation behaviour of oat b-glucans and suggested a spherical micelle model of aggregates with an aggregation number of 4e5. The aggregates are labile and

Mw1/2 /Rg (nm-1)

25

y = -0.6306x + 13.662 R2 = 0.7738 Barley

y = -1.4946x + 18.603 R2 = 0.8546 Oat

y = -0.6069x + 12.837 R2 = 0.9675 Wheat

20

15

10

5

Oat

Barley

Wheat

2

3

0 0

1

4

5

1/Mw x 10

6

7

8

9

6

Fig. 7. Plot of Mw1/2/Rg vs 1/Mw for cereal b-glucans in aqueous solutions.

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dissociated into monomers on dilution to zero concentration. Due to small amount of negative charges on the oat beta-glucan chains, the aggregation tendency is strongly reduced by repulsive interaction and allows complete dissociation on dilution. In Grimm et al.’s study (1995) on barley beta-glucans, a modified fringed micelle model was suggested for aggregates with an aggregation number (the number of laterally aggregated strands) of 14.7 and 17e70 times of apparent molecular weight difference. Compared with oat b-glucans aggregates studied by Vårum et al. the more compacted structure of barley b-glucan aggregates is formed and these aggregates do not dissociate completely on dilution. No charged group is found on barley b-glucan chains as well. These two micelle models cannot explain the gelation behaviour of cereal b-glucans at concentrated solution, since the micelle like structure of aggregates would prevent further growth of aggregates and network formation. In present study on aggregation behaviours of oat, barley and wheat b-glucans, the aggregation is irreversible on dilution which agrees with Grimm et al. However, a more opened irregular fractal like structure is proposed. The aggregation numbers of 5.7 (wheat), 5.9 (barley), and 10.5 (oat) agree with the ratios of hydrodynamic radius, which are 3.9, 4.4, and 7.5 for wheat, barley and oat b-glucans respectively. This opened irregular structure allows network formation in concentrated solutions. 3.6. Discussions of the aggregation mechanism In order to better understand the aggregation mechanism of cereal b-glucans, two common used models to describe colloidal aggregation process of polymers were introduced here, namely, diffusion limited cluster aggregation (DLCA) and reaction limited cluster aggregation (RLCA) (Lin et al., 1989, 1990; Meakin, 1983; Weitz, Huang, Lin, & Sung, 1985; Witten & Sander, 1981). In DLCA model, the aggregation process is only based on the Brownian motion of the monomers, therefore the aggregation rate is limited by diffusion. Since the growing branches during aggregation prevent approaching molecules to penetrate and enter the center of formed aggregates, more opened aggregation structures are formed. In RLCA model, the aggregation rate is limited by the possibility that two clusters will stick upon impact. If this sticking probability is small the clusters will have to come into contact many times before they stick, and this will allow the diffusing molecules to penetrate further into a cluster before sticking. This reduces the screening effect and alters both the aggregation rate and structure. In a real aggregation system, which model is dominant depends on the solution conditions. It is believed that the molecular association of cereal b-glucans occurs in the junction zones via the inter-molecular hydrogen bonding. There are two typical junction zones formed between cereal b-glucan molecules, the cellulose-like junction zone formed between the longer cellulose-like sequences of more than three continuous b-(1 / 4) linked monomers and the cellotriosyl sequence junction zone associated through consecutive trisaccharide units. Due to the small amount of cellulose-like segments (<10%) among cereal b-glucan chains, the interactions between the consecutive cellotriosyl units are mainly responsible for the aggregation and gel formations of cereal b-glucans. Higher tri/tetra ratio leads to the higher probability of the presence of consecutive cellotriosyl units, thus the higher ability for molecular association. Another important factor for aggregation, from the hydrodynamic point of view, is the diffusion rate, which controls the aggregation process. Smaller molecular weight b-glucan fractions have smaller hydrodynamic radius, thus higher mobility, while the higher tri/tetra ratio molecules have more rigid conformation, thus lower diffusion rate. This high mobility increases the opportunities for forming aggregates.

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In cereal b-glucan dilute solutions, the degree of aggregation increased with molecular weight and decreased with tri/tetra ratio implying the diffusion limited cluster aggregation mechanism. Due to the long distance between the molecules in dilute aqueous solution, the diffusion rate becomes more important than the structural features of monomers. On the other hand, in concentrated solution, the molecular overlap makes the importance of diffusion reduced, and the rigidity effect caused by the tri/tetra ratio could be omitted. The availability of the reacting sites (consecutive cellotriosyl units) along the molecular chains becomes more important. Therefore, molecules with higher tri/tetra ratio have a higher ability to form aggregates or gels in concentrated solutions. 4. Conclusions Cereal b-glucans form aggregates in aqueous solution. Aggregation kinetic study showed that the aggregation process was too fast to be monitored by DLS and the equilibrium of molecular association and dissociation were quickly reached. The presence of aggregate dissociation limited the further growth of aggregates. The average apparent diameters of cereal b-glucans showed concentration dependence, but the percentage of aggregates did not show such dependence; and the increase of average apparent diameters was caused by the increase of apparent diameters of aggregates, which implied that the clusterecluster aggregation is dominant. As molecular weight increased, the degree of aggregation decreased due to the lower diffusion rate of large molecules. For the more rigid conformation (lower diffusion rate) of b-glucans with higher tri/tetra ratio, their degrees of aggregation were lower. These results suggested the aggregation process was diffusion limited. References Benoit, H., & Doty, P. (1953). Light scattering from non-gaussian chains. Journal of Physical Chemistry, 57, 958. Böhm, N., & Kulicke, W.-M. (1999a). Rheological studies of barley (1 / 3)(1 / 4)-bD-glucan in concentrated solution: investigation of the viscoelastic flow behaviour in the sol state. Carbohydrate Research, 315, 293e301. Böhm, N., & Kulicke, W.-M. (1999b). Rheological studies of barley (1 / 3)(1 / 4)-bglucan in concentrated solution: mechanistic and kinetic investigation of the gel formation. Carbohydrate Research, 315, 302e311. Buliga, G. S., Brant, D. A., & Fincher, G. B. (1986). The sequence statistics and solution configuration of a barley (1 / 3), (1 / 4)-b-D-glucan. Carbohydrate Research, 157, 139e156. Cui, W. (2001). Polysaccharides gums from agricultural products: processing, structure and functionality. Lancaster, USA: Technomic Publishing Company. Cui, W., & Wood, P. J. (2000). Relationships between structural features, molecular weight and rheological properties of cereal b-D-glucan. In K. Nishinari (Ed.), Hydrocolloids, part 1 (pp. 159e168). Amsterdam: Elsevier. Elias, H.-G. (1972). In M. B. Huglin (Ed.), Light scattering from polymer solution (pp. 165e331). New York: Academic Press.

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