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The effect of depolymerised guar gum on the stability of skim milk
Food Hydrocolloids 14 (2000) 1–7 www.elsevier.com/locate/foodhyd
The effect of depolymerised guar gum on the stability of skim milk R. Tuinier a,b, E. ten Grotenhuis a,*, C.G. de Kruif a,b a
b
NIZO food research, P.O. Box 20, 6710 BA Ede, Netherlands Van’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, University of Utrecht, Padualaan 8, 3584 CH Utrecht, Netherlands Received 10 May 1999; accepted 25 August 1999
Abstract We studied the interactions between casein micelles and (depolymerised) guar gum, degraded by heating its aqueous solutions at low pH. The guar samples were characterised by a combination of size-exclusion chromatography and light scattering, which yielded the distribution of molar mass and corresponding radius of gyration. The relation between molar mass and radius of gyration showed that guar can be described as a random coil. Mixing guar gum with casein micelles led to a phase separation. This phase separation originates from a depletion interaction leading to an effective attraction between the casein micelles by non-adsorbing guar. The polymer concentration at the phase boundary increases with decreasing guar chain length. Vrij’s theory for depletion interaction was used to calculate the phase boundary from the size of the casein micelles and the size and molar mass of the guar samples. The theory of Vrij predicts the trends for the phase boundary with respect to the molar mass dependence as found experimentally. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Guar; Degradation; Casein micelles; Phase separation; Depletion interaction
1. Introduction Polysaccharides are often added as food thickeners to milk-protein suspensions in order to attain a desired texture and viscosity. However, the addition of polysaccharides to milk can result in a phase separation into a polysaccharideenriched and a casein-enriched phase if the polysaccharide concentration exceeds a certain concentration (Grinberg & Tolstoguzov, 1997; Tolstoguzov, 1991). It is important to achieve a high viscosity while maintaining a stable suspension. Phase separation in mixtures of polysaccharides and proteins is often due to a segregative interaction between these biopolymers. In order to obtain a better understanding of biopolymer interactions it is convenient to use a relatively simple model system containing only two biopolymers. In this paper we focus on the phase behaviour of mixtures of guar gum and casein micelles from cow’s milk; both are well-characterised food biopolymers. A segregative interaction between polysaccharides and proteins results in an effective attraction between the proteins through a depletion mechanism. Asakura and Oosawa (1954) derived a theoretical expression for this so-called depletion interaction and Vrij (1976) developed a model for the depletion in a mixture of colloidal spherical particles and non-adsorbing polymer
* Corresponding author. Tel.: 131-318-659-511; fax: 131-318-50400. E-mail address: [email protected] (E. ten Grotenhuis)
molecules. More recently, Lekkerkerker, Poon, Pusey, Stroobants and Warren (1992) and Poon and Pusey (1995) have developed more sophisticated theoretical models for depletion interaction which also assign the nature of the coexisting phases. By preparing low-heat skim milk it is possible to produce a stable suspension with casein micelles as the main component. Skim milk can be regarded as a suspension of casein micelles with a volume fraction of ,10%. The large amount of other but very small (,5 nm) components (salts, lactose and whey proteins) is considered to belong to the continuous phase since mixtures of guar and skim milk without casein micelles are stable in all proportions. Casein micelles are association colloids and are composed of casein proteins and calcium phosphate. The casein micelles are rather stable since they are not influenced strongly by temperature or salt. The mean size of the micelles is 100 nm radius with a relatively low polydispersity (De Kruif, 1998). Galactomannans are a group of polysaccharides of which tara gum, guar gum and locust bean gum (LGB) are well known as food thickeners. The guar plant Cyamopsis tetragonoloba, which grows in Pakistan, India and Texas, USA, produces guar gum. The backbone of the guar gum polysaccharide consists of b 1 ! 6-linked mannoses with side groups or branches of b 1 ! 4-linked galactose units. The ratio of mannose to galactose is 2:1 (Lapasin & Pricl, 1995). Guar can easily be depolymerised, for instance by chemical hydrolysis. This hydrolysis occurs at low pH and high
0268-005X/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0268-005 X( 99)00 039-9
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R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
temperatures and can be used to prepare a series of guar gums varying in molar mass (Lapasin & Pricl, 1995). Mixtures of guar gum and casein micelles phase separate when a certain concentration is exceeded. In this study a series of guar gum samples was first characterised by light scattering and subsequently the experimental phase boundary of guar gum–casein micelle mixtures was determined and compared with depletion interaction theory. When the chains are made shorter (degradation), polysaccharides are somewhat less effective as a thickener. At the same time the phase boundary shifts to higher guar concentrations when the chains are shorter, so that a higher guar concentration can be used without inducing a phase separation. It will be demonstrated by a calculation that guar preparations of low molar mass are more suitable as food thickeners than native guar.
mass (Mw) equals: X c i Mi i X Mw ci
3
i
The ratio M w =M n is often used to characterise the polydispersity. In each fraction light scattering also yields the radius of gyration, which makes it possible to study the relation between Rg and M. 2.2. Polysaccharides in solution In order to describe guar gum the random walk model, introduced by Kuhn (1934) for long flexible chains, is used. The root-mean-square end-to-end distance of a random walk polymer chain, kR2 l1=2 ; follows from the number NK of Kuhn segments and the length lK of such a segment as (Flory, 1953, 1969):
2. Theoretical background
kR2 l a2 l2K NK
2.1. Static light scattering
where a is the linear expansion coefficient.pFor long chains the radius of gyration Rg equals kR2 l1=2 = 6: Since NK is proportional to the molar mass, Rg is proportional to M 0.5. However, real chains with N segments, each of length l, cannot be directly regarded as purely random walks. The values for l and N can be translated to lK and NK by demanding equal contour lengths for the Kuhn chain and the real chain:
The molecular size and molar mass of the galactomannans were measured by static light scattering. In static light scattering the scattering intensity is measured as a function of the scattering wave vector Q, of which the length is equal to 4pn=l0 sin u=2; where l 0 is the wavelength of the incident beam in vacuo, u the angle under which scattered light is detected and n the refractive index of the continuous phase. A scaled quantity used in light scattering is the Rayleigh ratio R Q; which is the ratio of the scattered intensity over the intensity of the (vertically polarised) primary beam, taking into account the scattering volume and the distance to the detector. At very low concentration R Q can be expressed as a function of Q in a simple way (Kerker, 1969): Q2 R2g Kc 1 < 11 3 R Q M
! 1
where K is a material constant, M the molar mass, Rg the radius of gyration, and c the polymer concentration. Hence, measurement of R Q as a function of Q yields the molar mass Q ! 0 and the radius of gyration (Q dependence). By studying several narrow fractions of a polymer by light scattering, the number averaged molar mass (Mn) can be calculated: X Mn Xi
4
5
L ; 1N 1K NK
When Rg has been measured, the quantity lK can then be calculated from lK kRl2 =L 6R2g =L and NK follows as L/ lK. A prerequisite for the validity of this approach is that NK must not be too small N K . 10: For stiffer polymers the worm-like chain model applies and the radius of gyration depends as follows on lK and NK (Yamakawa, 1971): " !2 !3 1 lK 1 lK 2 2 1 lK 2 1 Rg L 6 L 4 L 4 L 1 2 8
lK L
!4 ( 1 2 exp
ci =Mi
2
i
where Mi is the molar mass in fraction i and ci is the mass concentration in that fraction. The weight-averaged molar
!)# (6)
For a polymer in a good solvent the coefficient a in Eq. (4) depends also (weakly) on N. Flory (1953, 1969) derived an expression which relates the expansion coefficient a to N:
a5 2 a3 , 1 2 2xN 1=2 ci
2L 2 lK
7
where x is the Flory–Huggins segment–solvent interaction parameter; it is equal to 0.5 for a u -solvent and it is zero for a good solvent (Flory, 1953, 1969). According to Eq. (7), for high a (good solvent) the expansion coefficient scales with the number of segments as a , N 0:1 : Then, from Eq. (4) it follows that Rg , N 0:6 for high a . More generally, we can
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
write: Rg , M v
8
where for flexible chains the exponent v is in between 0.5 (u -solvent) and 0.6 (good solvent). In order to describe the polydispersity of the galactomannans the Schulz–Flory distribution for the fraction of polymers f M as a function of M is used (Flory, 1953, 1969): f M
zy11 y 2zM M e y!
9
3
This leads to Bcoll 2 4 for hard spheres and a decreasing value with the increasing polymer concentration as a result of depletion interactions. The phase boundary can now be calculated from Eq. (11). For a certain volume fraction at the spinodal Eq. (11) gives Bcoll 2 ; corresponding to the limiting polymer concentration as calculated from Eqs. (10) and (12).
3. Experimental 3.1. Material
where y is an integer describing the narrowness of the distribution (for smaller y, the polydispersity is higher) and z determines the top of the distribution. The distributions of the guar gum samples were fitted to a0 M × exp 2a1 M; where a0 and a1 are fitting parameters. By hydrolysing or depolymerising the native guar gum we lower the molar mass, and change the polydispersity. Therefore the depolymerisation was also simulated in a simple way by assuming that the linkages between the monosaccharides are cut at random.
3.1.1. Guar Guar was a gift from SKW (Baupte, France). It was extracted in pure form by precipitation of the raw guar with ethanol. Degraded guar was produced by adding 1 M hydrochloric acid to a solution of native guar, to set the pH at 1.5, and heating the sample at 808C, for various heating times. After heating, the pH was set at 7 by adding a sufficient amount of 1 M Na2CO3 solution and the ions present (Na 1, Cl 2, H2CO3/HCO32) were removed from the guar by dialysis. After that the samples were freeze-dried.
2.3. Depletion interaction theory Vrij (1976) considered a system containing hard spheres immersed in a solvent with ideal polymers, which are thus freely permeable towards one another. The polymer molecules are defined by their effective diameter s p (twice the depletion layer thickness D ) and behave as hard spheres towards the colloids. Vrij (1976) derived that the potential between two spherical colloidal particles, with diameter s c, reads in the range sc , r , sc 1 sp equals: 1∞
0 , r , sc
U r 2Pp Voverlap r sc # r # sc 1 sp 0
10
r . sc 1 sp
where r is the Q distance between the centres of two colloidal spheres and p represents the (ideal) osmotic pressure cp RT=M of a polymer solution with concentration cp. The overlap volume Voverlap depends on s p and s c. If the depletion-induced attraction between two particles exceeds a certain value, the system tends to phase separate into a colloid-enriched and a polymer-enriched phase (Vrij, 1976). For low volume fractions the colloid volume fraction at the spinodal f sp can be approximated by (Vrij, 1976): Bcoll 2 2
1 2fsp
11
can be The second virial coefficient of the colloids Bcoll 2 calculated by statistical mechanics from which follows (McQuarrie, 1976): 2p Z∞ 2 U r coll r 1 2 exp 2 dr 12 B2 Vc 0 kB T
3.1.2. Skim milk Reconstituted skim milk was prepared as described by Jeurnink and De Kruif (1993). The volume fraction of casein micelles in the reconstituted skim milk was determined by Jeurnink and De Kruif (1993) and found to be 0.13. 3.1.3. Permeate Skim milk permeate (i.e. the ‘solvent’ of the casein micelles) was prepared from skim milk by a membrane filtration process. An Amicon hollow-cartridge HIMPO 143 membrane with a cut-off of 0.1 mm was used. The pH of permeate was the same as that of the skim milk 6:60 ^ 0:10: 3.1.4. Mixtures The mixtures were prepared by dissolving guar diluted in skim milk permeate and mixing this guar-(skim milk) permeate solution with skim milk. All mixtures were studied at room temperature. 3.1.5. Preservative Since phase separation was sometimes observed after a week we used anti-microbial agents (preservatives) in order to prevent growth of microorganisms during the experiments. We used 0.02% (w/w) sodium ethylmercurithiosalicylate (C2H5HgSC6H4COONa—thiomersal, BDH Chemicals), with which we did not observe any bacterial growth or any pH changes for more than six weeks.
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R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
the column. The gel permeation separation was carried out at room temperature with 0.10 M NaNO3 as the eluent. The eluent from the column was analysed on-line by RI (refractive index) detection (ERC-7510 detector from ERMA optical works), by UV transmission at a wavelength of 280 nm, and by static light scattering (SLS). Integration of the RI signal was used to determine the polysaccharide concentration in the fractions; dextran and pullulan were used as standards. The on-line UV transmission measurements were made with a LKB 2140 rapid spectral detector. Static light scattering was performed with a Wyatt Technology DAWN apparatus with a 5 mW He–Ne laser (l0 632:8 nm: The laser is linearly polarised and has a narrow beam diameter to enhance the intensity. The experiments were done using 12 angles, giving a Q-range from 10.0 to 25.6 mm 21. The refractive index increment was taken as 0.135 ml/g, as reported by Robinson, Ross-Murphy and Morris (1982).
Fig. 1. Molar mass (M) and radius of gyration (Rg) dependence on time of acid heat-treatment. The triangles refer to the radius of gyration and the circles to the molar mass.
3.2. Size-exclusion chromatography and static light scattering Gel permeation or size-exclusion chromatography (SEC) was performed using TSK-gel 6000 PW columns (Phenomenex). The molar exclusion limit as stated by the supplier is 8 × 103 kg=mol: A pre-column (PWH TSK-gel, Phenomenex) was used to give a crude first separation and to protect
Fig. 2. Radius of gyration plotted as a function of the molar mass for the various guar samples. The dotted line refers to the random walk chain prediction.
4. Results and discussion 4.1. Molar mass (distribution) and radius of gyration of (degraded) guar gum The SEC fractions of the guar material in each sample were analysed by SLS. Eq. (1) was used to determine the radius of gyration and molar mass of the polysaccharide in each fraction. The number-averaged radius of gyration and molar mass of each sample are plotted as a function of heating time in Fig. 1. It follows that both the molar mass and the radius of gyration decrease strongly during heating at pH 1.5 at 808C; after 10 min the molar mass had already decreased to 45% of its native value. The measured radii of gyration are plotted as a function of the molar mass on a double logarithmic scale in Fig. 2. Best fits of the fractions with the highest polymer concentrations yield an exponent v < 0:54 ^ 0:01 for native guar which decreases to v < 0:50 for the low molar mass samples. The value of v 0:54 is in between the theoretical value for flexible polymer molecules in a good solvent v 3=5; and that in a u -solvent v 1=2; allowing a description of guar as random-walk chains. In Table 1 the Kuhn lengths and the number of Kuhn elements of the chains are given for the various samples, as well as the number-averaged molar mass (Mn), the number-averaged radius of gyration (Rg) and the polydispersity index M w =M n ; where Mw equals the weight-averaged molar mass. For native guar the Kuhn parameters were calculated from the random walk model (RW) as follows. The obtained value of Mn is 1:26 ^ 0:07103 kg=mol and Rg is 109 ^ 3 nm: We defined N as the number of repeating units. The molar mass M0 of the repeating unit is 486 g/mol, since each repeating unit contains three backbone monosaccharides (Lapasin & Pricl, 1995), which gives N Mn =M0 2:6 × 103 repeating units. The mannoses have a
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
5
Table 1 Overview of the number-averaged molar mass (Mn), the polydispersity index M w =M n ; where Mw equals the weight-averaged molar mass), the numberaveraged radius of gyration (Rg), and the calculated Kuhn lengths (lK) and number of Kuhn segments (NK) for both the random walk model (RW) and the wormlike chain model (WC) Heating time
Mn (kg/mol) Mw/Mn Rg (nm) lk (nm) (RW) NK (RW) lK (nm) (WC) NK (WC)
Native
10 min
20 min
30 min
1h
2h
1260 ^ 10 1.81 109 ^ 3 27 ^ 3 96 ^ 11 28 ^ 3 93 ^ 11
564 ^ 20 1.36 73 ^ 2 27 ^ 3 43 ^ 6 29 ^ 3 41 ^ 6
274 ^ 9 1.27 47 ^ 3 24 ^ 4 24 ^ 5 25 ^ 4 22 ^ 5
184 ^ 7 1.23 35 ^ 4 19 ^ 5 20 ^ 6 21 ^ 6 18 ^ 5
108 ^ 5 1.22 33 ^ 5 29 ^ 10 8^3 37 ^ 13 6^2
61 ^ 3 1.29 29 ^ 6 40 ^ 18 3.0 ^ 1.5 96 ^ 43 1.3 ^ 0.7
length of approximately 0.505 nm, as for glucose (Granath, 1958), giving a length of 1.0 nm for the repeating unit. Then, and according to Eq. (5), we find for the contour length, L, 2.6 mm. In a first simple approach we set a 1 (u -solvent). With Rg 109 ^3 nm; lK 6R2g =L (see Eq. (4)) follows as lK 27 ^3 nm; and for NK we find 96 ^ 16: This means that about 54 ^ 6 monosaccharide backbone units (about 27 ^ 3 repeating units) are required to mimic a freely rotational Kuhn segment, which indicates that guar is a rather stiff polysaccharide. In the same way the Kuhn lengths of the degraded samples were computed. Going from native to 30 min of pH/heat treatment the Kuhn length decreases somewhat (see Table 1). This is probably due to a decrease in excluded volume effect of the chains (the value of v decreases from 0.54 to 0.50) which decreases with the chain length (see Eq. (7)). The samples degraded for 60 and 120 min have large Kuhn lengths, as follows from the RW
Fig. 3. Molar mass distributions of the guar samples. Drawn curves are best fits to the Schulz–Flory distribution f M a0 M × exp 2a1 M; where a0 and a1 are fitting parameters.
model. However, the error bars are large because the accuracy of the radius of gyration in the scattering experiments is low for small (short) polymers. Moreover, the RW model no longer applies, since the number of Kuhn segments is smaller than 10. The worm-like chain (WC) model would apply for these smaller, relatively stiff chains. However, the accuracy of the measurements for these smaller chains is insufficient for a proper analysis. The molar mass distributions of the samples are given in Fig. 3 as well as a best fit of the Schulz–Flory distribution (Flory, 1953, 1969). The data follow a general trend with the peak of the distribution shifting with heating time to lower molar mass values. The fit of the Schulz–Flory distribution becomes worse with increasing degradation. This is due to the high molar mass tail containing a small fraction of native guar. Of course Schulz and Flory did not take into account such effects in the original derivation of the molar mass distributions. We have also simulated the degradation process in a simple manner by assuming that all bonds can be cut with equal probability. All polymers consist of m monomers, having m 2 1 bonds between the monomers. After every cut we calculated the average molar masses. In Fig. 4 we plotted some results from the simulation of the degradation process. The molar mass decrease was plotted as the molar mass after time t, M t; divided by the molar mass at t 0 M t 0; as a function of time divided by the time at the end of the process, tend, where all bonds are cut. The polydispersity, plotted as M w =M n ; is given in the same plot as a function of t=tend : At the beginning of the process the polydispersity increases, since the process of random cutting obviously broadens the size distribution. However, after t < 0:25tend the polydispersity reaches a maximum and decreases subsequently. At t tend the mixture only contains monomers and the polydispersity is unity. The simulation results agree with the molar mass decrease given in Fig. 1 and the data given for the polydispersity in Table 1. Probably, the polydispersity reaches a maximum between 0 and 10 min of heating. Between 10 min and 1 h of heating the polydispersity decreases as a function of heating time, which agrees with the simulation results.
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R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
Fig. 4. Simulation results of the degradation process. The molar mass, divided by its value at t 0; is given as a function of time, normalised by the process time (tend), as the dashed curve. The solid curve is the polydispersity, M w =M n ; as a function of t=tend :
4.2. Experimental and theoretical phase diagram Firstly, we dissolved guar in low-heat skim milk permeate (skim milk without casein micelles). In permeate solutions no phase separation could be observed for months when guar was added. Apparently, a stable mixture can be prepared by mixing whey proteins and guar. Therefore we used the permeate to dissolve guar after which this guarpermeate solution was mixed with skim milk. In this way the required final concentration cp of guar and the volume fraction f of casein micelles could be adjusted
Fig. 5. Experimental phase boundaries as derived from visual observation for three heating times of the guar samples as indicated in the plot.
Fig. 6. Calculated phase boundaries from the theory of Vrij (1976). The curves were calculated from the radii of gyration and molar masses given in Table 1 and a radius of the casein micelles of 100 nm.
independently. Phase separation was indicated by the observation of the upper phase becoming clearer with time while the lower phase became highly turbid (white). The guar concentration in the upper phase was analysed and was always higher than expected for a homogeneous distribution, indicating that guar is always concentrated in the upper phase due to a segregative interaction. In Fig. 5 a phase diagram is presented describing the experimentally observed phase boundaries of casein micelles in skim milk as mixed with three guar samples; native guar, guar degraded for 10 min and guar degraded for 30 min. The results are comparable with those of Bourriot, Garnier and Doublier (1997) for native guar gum. In Fig. 6 the predictions for the spinodal as calculated from Vrij’s theory (Vrij, 1976) are given. For the casein micelles a radius of 100 nm (the number-average, De Kruif, 1998) was used in the calculations, and for the molar mass and radius of gyration of the guar samples the data given in Table 1 were used. It must be noted that no adjustable parameters were used. Comparison with Fig. 5 shows that the trends are well described by the theory of Vrij; with the increasing chain length of the guar samples the phase boundary moves to smaller polymer concentrations. This is due to an increasing depletion layer thickness with increasing radius of gyration, which leads to a smaller value of the second osmotic virial coefficient (see Eqs. (10) and (12)) at the same polymer concentration. Hence, fewer polymers are required in order to attain a certain value of to reach the spinodal. The order of magnitude of the Bcoll 2 experimental phase boundary also agrees with the predictions of Vrij’s theory. The experimental phase boundary lies systematically higher than the calculated spinodal, which is
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
ascribed to polydispersity of both the casein micelles and the guar samples (see Chu, Nikolov & Wasan, 1996, for the effect of polydispersity). Further, the radius of gyration of especially the native guar gum is so large that it is questionable whether the Vrij theory still applies. Large chains (compared to the radius of the casein micelles) can also assume conformations around the sphere, so that the depletion interaction is less effective (Odijk, 1996). In order to speculate on the efficiency of the guar samples as thickener in milk products we approximated the viscosity of the guar solution at the guar concentration corresponding to the experimentally observed phase boundary, at 10% (v/ v) casein micelles (as in milk). The viscosity was calculated as the dimensionless number clim [h ], where [h ] is the intrinsic viscosity calculated as 10=3pR3g NAV =Mn ; calculated from Table 1, and clim is the limiting guar concentration at the phase boundary. This finally gave clim h 0:32; 1.7 and 3.7 for native guar, 10 and 30 min degraded, respectively. Since a plot of the viscosity as a function of ch is a master curve for all flexible polysaccharides (Robinson et al., 1982) these results indicate that a low molar mass of guar gum is more suitable as a thickener than native guar gum. Although native guar has the highest intrinsic viscosity, the limiting polymer concentration is low to such a degree that the guar gum–casein micelle mixture phase separates below the overlap concentration for native guar. For smaller guar molecules phase separation takes place above the overlap concentration where the viscosity increases strongly with polymer concentration. This analysis is based on a simple, approximate, calculation and measurement of the viscosity of the mixtures of guar gum and casein micelles could test these speculations. Further the depletion induced attractions increase the viscosity at low shear rates (see for instance Woutersen & De Kruif, 1991) so that a rheological study would be an interesting follow-up of this work. 5. Conclusions Native guar gum could be degraded to lower molar mass guar samples by heating at low pH. A simple simulation of randomly cutting the bonds between the monomers could describe the degradation process. The various guar samples could be described as random-walk chains. Mixing guar gum with casein micelles gave a phase separation due to a depletion interaction leading to an effective attraction between the casein micelles by non-adsorbing guar. The polymer concentration at the phase boundary increases with decreasing guar chain length. The theory of Vrij
7
predicts the same trends as the experimental phase boundary with respect to the molar mass dependence. The location of the phase boundary is predicted reasonably well. It is speculated that the maximum attainable viscosity of the guar solution in the one-phase region increases with decreasing guar chain length. Therefore it can be useful to degrade native guar in milky systems. Acknowledgements We would like to thank Annie Layani for performing many experiments and Jan van Riel for performing the SEC-MALLS analysis. A. Parker, SKW-France, is acknowledged for providing us with the purified native guar gum. Dr G.A. van Aken (NIZO food research) is thanked for a critical reading of the manuscript. References Asakura, S., & Oosawa, F. (1954). Journal of Chemical Physics, 22, 1255. Bourriot, S., Garnier, C., & Doublier, J-L. (1997). Les Cahiers de Rhe´ologie, 15, 284. Chu, X. L., Nikolov, A. D., & Wasan, D. T. (1996). Langmuir, 12, 5004. De Kruif, C. G. (1998). Journal of Dairy Science, 81, 3019. Flory, P. J. (1953). Principles of polymer chemistry, New York: Cornell University Press. Flory, P. J. (1969). Statistical mechanics of chain molecules, New York: Interscience. Granath, K. A. (1958). Journal of Colloid Science, 13, 308. Grinberg, V. Ya., & Tolstoguzov, V. B. (1997). Food Hydrocolloids, 11, 145. Jeurnink, Th. J. M., & De Kruif, C. G. (1993). Journal of Dairy Research, 60, 139. Kerker, M. (1969). Scattering of light and other electromagnetic radiation, New York: Academic Press. Kuhn, W. (1934). Kolloid Z., 68, 2. Lapasin, R., & Pricl, S. (1995). Rheology of industrial polysaccharides: theory and applications, London: Blackie Academic. Lekkerkerker, H. N. W., Poon, W. C. K., Pusey, P. N., Stroobants, A., & Warren, P. B. (1992). Europhysics Letters, 20, 559. McQuarrie, D. A. (1969)–(1976). Statistical mechanics, New York: Harper & Row. Odijk, T. (1996). Macromolecules, 29, 1842. Poon, W. C. K., & Pusey, P. N. (1995). In M. Baus, L. F. Rull & J. -P. Ryckaert (Eds.), Observation and simulation of phase transitions in complex fluids, Dordrecht (Netherlands): Kluwer (pp. 3). Robinson, G., Ross-Murphy, S. B., & Morris, E. R. (1982). Carbohydrate Research, 107, 17. Tolstoguzov, V. B. (1991). Food Hydrocolloids, 4, 429. Vrij, A. (1976). Pure and Applied Chemistry, 48, 471. Woutersen, A. T. J. M., & De Kruif, C. G. (1991). Journal of Chemical Physics, 94, 5739. Yamakawa, H. (1971). Modern theory of polymer solutions, New York: Harper & Row.
The effect of depolymerised guar gum on the stability of skim milk R. Tuinier a,b, E. ten Grotenhuis a,*, C.G. de Kruif a,b a
b
NIZO food research, P.O. Box 20, 6710 BA Ede, Netherlands Van’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, University of Utrecht, Padualaan 8, 3584 CH Utrecht, Netherlands Received 10 May 1999; accepted 25 August 1999
Abstract We studied the interactions between casein micelles and (depolymerised) guar gum, degraded by heating its aqueous solutions at low pH. The guar samples were characterised by a combination of size-exclusion chromatography and light scattering, which yielded the distribution of molar mass and corresponding radius of gyration. The relation between molar mass and radius of gyration showed that guar can be described as a random coil. Mixing guar gum with casein micelles led to a phase separation. This phase separation originates from a depletion interaction leading to an effective attraction between the casein micelles by non-adsorbing guar. The polymer concentration at the phase boundary increases with decreasing guar chain length. Vrij’s theory for depletion interaction was used to calculate the phase boundary from the size of the casein micelles and the size and molar mass of the guar samples. The theory of Vrij predicts the trends for the phase boundary with respect to the molar mass dependence as found experimentally. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Guar; Degradation; Casein micelles; Phase separation; Depletion interaction
1. Introduction Polysaccharides are often added as food thickeners to milk-protein suspensions in order to attain a desired texture and viscosity. However, the addition of polysaccharides to milk can result in a phase separation into a polysaccharideenriched and a casein-enriched phase if the polysaccharide concentration exceeds a certain concentration (Grinberg & Tolstoguzov, 1997; Tolstoguzov, 1991). It is important to achieve a high viscosity while maintaining a stable suspension. Phase separation in mixtures of polysaccharides and proteins is often due to a segregative interaction between these biopolymers. In order to obtain a better understanding of biopolymer interactions it is convenient to use a relatively simple model system containing only two biopolymers. In this paper we focus on the phase behaviour of mixtures of guar gum and casein micelles from cow’s milk; both are well-characterised food biopolymers. A segregative interaction between polysaccharides and proteins results in an effective attraction between the proteins through a depletion mechanism. Asakura and Oosawa (1954) derived a theoretical expression for this so-called depletion interaction and Vrij (1976) developed a model for the depletion in a mixture of colloidal spherical particles and non-adsorbing polymer
* Corresponding author. Tel.: 131-318-659-511; fax: 131-318-50400. E-mail address: [email protected] (E. ten Grotenhuis)
molecules. More recently, Lekkerkerker, Poon, Pusey, Stroobants and Warren (1992) and Poon and Pusey (1995) have developed more sophisticated theoretical models for depletion interaction which also assign the nature of the coexisting phases. By preparing low-heat skim milk it is possible to produce a stable suspension with casein micelles as the main component. Skim milk can be regarded as a suspension of casein micelles with a volume fraction of ,10%. The large amount of other but very small (,5 nm) components (salts, lactose and whey proteins) is considered to belong to the continuous phase since mixtures of guar and skim milk without casein micelles are stable in all proportions. Casein micelles are association colloids and are composed of casein proteins and calcium phosphate. The casein micelles are rather stable since they are not influenced strongly by temperature or salt. The mean size of the micelles is 100 nm radius with a relatively low polydispersity (De Kruif, 1998). Galactomannans are a group of polysaccharides of which tara gum, guar gum and locust bean gum (LGB) are well known as food thickeners. The guar plant Cyamopsis tetragonoloba, which grows in Pakistan, India and Texas, USA, produces guar gum. The backbone of the guar gum polysaccharide consists of b 1 ! 6-linked mannoses with side groups or branches of b 1 ! 4-linked galactose units. The ratio of mannose to galactose is 2:1 (Lapasin & Pricl, 1995). Guar can easily be depolymerised, for instance by chemical hydrolysis. This hydrolysis occurs at low pH and high
0268-005X/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0268-005 X( 99)00 039-9
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temperatures and can be used to prepare a series of guar gums varying in molar mass (Lapasin & Pricl, 1995). Mixtures of guar gum and casein micelles phase separate when a certain concentration is exceeded. In this study a series of guar gum samples was first characterised by light scattering and subsequently the experimental phase boundary of guar gum–casein micelle mixtures was determined and compared with depletion interaction theory. When the chains are made shorter (degradation), polysaccharides are somewhat less effective as a thickener. At the same time the phase boundary shifts to higher guar concentrations when the chains are shorter, so that a higher guar concentration can be used without inducing a phase separation. It will be demonstrated by a calculation that guar preparations of low molar mass are more suitable as food thickeners than native guar.
mass (Mw) equals: X c i Mi i X Mw ci
3
i
The ratio M w =M n is often used to characterise the polydispersity. In each fraction light scattering also yields the radius of gyration, which makes it possible to study the relation between Rg and M. 2.2. Polysaccharides in solution In order to describe guar gum the random walk model, introduced by Kuhn (1934) for long flexible chains, is used. The root-mean-square end-to-end distance of a random walk polymer chain, kR2 l1=2 ; follows from the number NK of Kuhn segments and the length lK of such a segment as (Flory, 1953, 1969):
2. Theoretical background
kR2 l a2 l2K NK
2.1. Static light scattering
where a is the linear expansion coefficient.pFor long chains the radius of gyration Rg equals kR2 l1=2 = 6: Since NK is proportional to the molar mass, Rg is proportional to M 0.5. However, real chains with N segments, each of length l, cannot be directly regarded as purely random walks. The values for l and N can be translated to lK and NK by demanding equal contour lengths for the Kuhn chain and the real chain:
The molecular size and molar mass of the galactomannans were measured by static light scattering. In static light scattering the scattering intensity is measured as a function of the scattering wave vector Q, of which the length is equal to 4pn=l0 sin u=2; where l 0 is the wavelength of the incident beam in vacuo, u the angle under which scattered light is detected and n the refractive index of the continuous phase. A scaled quantity used in light scattering is the Rayleigh ratio R Q; which is the ratio of the scattered intensity over the intensity of the (vertically polarised) primary beam, taking into account the scattering volume and the distance to the detector. At very low concentration R Q can be expressed as a function of Q in a simple way (Kerker, 1969): Q2 R2g Kc 1 < 11 3 R Q M
! 1
where K is a material constant, M the molar mass, Rg the radius of gyration, and c the polymer concentration. Hence, measurement of R Q as a function of Q yields the molar mass Q ! 0 and the radius of gyration (Q dependence). By studying several narrow fractions of a polymer by light scattering, the number averaged molar mass (Mn) can be calculated: X Mn Xi
4
5
L ; 1N 1K NK
When Rg has been measured, the quantity lK can then be calculated from lK kRl2 =L 6R2g =L and NK follows as L/ lK. A prerequisite for the validity of this approach is that NK must not be too small N K . 10: For stiffer polymers the worm-like chain model applies and the radius of gyration depends as follows on lK and NK (Yamakawa, 1971): " !2 !3 1 lK 1 lK 2 2 1 lK 2 1 Rg L 6 L 4 L 4 L 1 2 8
lK L
!4 ( 1 2 exp
ci =Mi
2
i
where Mi is the molar mass in fraction i and ci is the mass concentration in that fraction. The weight-averaged molar
!)# (6)
For a polymer in a good solvent the coefficient a in Eq. (4) depends also (weakly) on N. Flory (1953, 1969) derived an expression which relates the expansion coefficient a to N:
a5 2 a3 , 1 2 2xN 1=2 ci
2L 2 lK
7
where x is the Flory–Huggins segment–solvent interaction parameter; it is equal to 0.5 for a u -solvent and it is zero for a good solvent (Flory, 1953, 1969). According to Eq. (7), for high a (good solvent) the expansion coefficient scales with the number of segments as a , N 0:1 : Then, from Eq. (4) it follows that Rg , N 0:6 for high a . More generally, we can
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
write: Rg , M v
8
where for flexible chains the exponent v is in between 0.5 (u -solvent) and 0.6 (good solvent). In order to describe the polydispersity of the galactomannans the Schulz–Flory distribution for the fraction of polymers f M as a function of M is used (Flory, 1953, 1969): f M
zy11 y 2zM M e y!
9
3
This leads to Bcoll 2 4 for hard spheres and a decreasing value with the increasing polymer concentration as a result of depletion interactions. The phase boundary can now be calculated from Eq. (11). For a certain volume fraction at the spinodal Eq. (11) gives Bcoll 2 ; corresponding to the limiting polymer concentration as calculated from Eqs. (10) and (12).
3. Experimental 3.1. Material
where y is an integer describing the narrowness of the distribution (for smaller y, the polydispersity is higher) and z determines the top of the distribution. The distributions of the guar gum samples were fitted to a0 M × exp 2a1 M; where a0 and a1 are fitting parameters. By hydrolysing or depolymerising the native guar gum we lower the molar mass, and change the polydispersity. Therefore the depolymerisation was also simulated in a simple way by assuming that the linkages between the monosaccharides are cut at random.
3.1.1. Guar Guar was a gift from SKW (Baupte, France). It was extracted in pure form by precipitation of the raw guar with ethanol. Degraded guar was produced by adding 1 M hydrochloric acid to a solution of native guar, to set the pH at 1.5, and heating the sample at 808C, for various heating times. After heating, the pH was set at 7 by adding a sufficient amount of 1 M Na2CO3 solution and the ions present (Na 1, Cl 2, H2CO3/HCO32) were removed from the guar by dialysis. After that the samples were freeze-dried.
2.3. Depletion interaction theory Vrij (1976) considered a system containing hard spheres immersed in a solvent with ideal polymers, which are thus freely permeable towards one another. The polymer molecules are defined by their effective diameter s p (twice the depletion layer thickness D ) and behave as hard spheres towards the colloids. Vrij (1976) derived that the potential between two spherical colloidal particles, with diameter s c, reads in the range sc , r , sc 1 sp equals: 1∞
0 , r , sc
U r 2Pp Voverlap r sc # r # sc 1 sp 0
10
r . sc 1 sp
where r is the Q distance between the centres of two colloidal spheres and p represents the (ideal) osmotic pressure cp RT=M of a polymer solution with concentration cp. The overlap volume Voverlap depends on s p and s c. If the depletion-induced attraction between two particles exceeds a certain value, the system tends to phase separate into a colloid-enriched and a polymer-enriched phase (Vrij, 1976). For low volume fractions the colloid volume fraction at the spinodal f sp can be approximated by (Vrij, 1976): Bcoll 2 2
1 2fsp
11
can be The second virial coefficient of the colloids Bcoll 2 calculated by statistical mechanics from which follows (McQuarrie, 1976): 2p Z∞ 2 U r coll r 1 2 exp 2 dr 12 B2 Vc 0 kB T
3.1.2. Skim milk Reconstituted skim milk was prepared as described by Jeurnink and De Kruif (1993). The volume fraction of casein micelles in the reconstituted skim milk was determined by Jeurnink and De Kruif (1993) and found to be 0.13. 3.1.3. Permeate Skim milk permeate (i.e. the ‘solvent’ of the casein micelles) was prepared from skim milk by a membrane filtration process. An Amicon hollow-cartridge HIMPO 143 membrane with a cut-off of 0.1 mm was used. The pH of permeate was the same as that of the skim milk 6:60 ^ 0:10: 3.1.4. Mixtures The mixtures were prepared by dissolving guar diluted in skim milk permeate and mixing this guar-(skim milk) permeate solution with skim milk. All mixtures were studied at room temperature. 3.1.5. Preservative Since phase separation was sometimes observed after a week we used anti-microbial agents (preservatives) in order to prevent growth of microorganisms during the experiments. We used 0.02% (w/w) sodium ethylmercurithiosalicylate (C2H5HgSC6H4COONa—thiomersal, BDH Chemicals), with which we did not observe any bacterial growth or any pH changes for more than six weeks.
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the column. The gel permeation separation was carried out at room temperature with 0.10 M NaNO3 as the eluent. The eluent from the column was analysed on-line by RI (refractive index) detection (ERC-7510 detector from ERMA optical works), by UV transmission at a wavelength of 280 nm, and by static light scattering (SLS). Integration of the RI signal was used to determine the polysaccharide concentration in the fractions; dextran and pullulan were used as standards. The on-line UV transmission measurements were made with a LKB 2140 rapid spectral detector. Static light scattering was performed with a Wyatt Technology DAWN apparatus with a 5 mW He–Ne laser (l0 632:8 nm: The laser is linearly polarised and has a narrow beam diameter to enhance the intensity. The experiments were done using 12 angles, giving a Q-range from 10.0 to 25.6 mm 21. The refractive index increment was taken as 0.135 ml/g, as reported by Robinson, Ross-Murphy and Morris (1982).
Fig. 1. Molar mass (M) and radius of gyration (Rg) dependence on time of acid heat-treatment. The triangles refer to the radius of gyration and the circles to the molar mass.
3.2. Size-exclusion chromatography and static light scattering Gel permeation or size-exclusion chromatography (SEC) was performed using TSK-gel 6000 PW columns (Phenomenex). The molar exclusion limit as stated by the supplier is 8 × 103 kg=mol: A pre-column (PWH TSK-gel, Phenomenex) was used to give a crude first separation and to protect
Fig. 2. Radius of gyration plotted as a function of the molar mass for the various guar samples. The dotted line refers to the random walk chain prediction.
4. Results and discussion 4.1. Molar mass (distribution) and radius of gyration of (degraded) guar gum The SEC fractions of the guar material in each sample were analysed by SLS. Eq. (1) was used to determine the radius of gyration and molar mass of the polysaccharide in each fraction. The number-averaged radius of gyration and molar mass of each sample are plotted as a function of heating time in Fig. 1. It follows that both the molar mass and the radius of gyration decrease strongly during heating at pH 1.5 at 808C; after 10 min the molar mass had already decreased to 45% of its native value. The measured radii of gyration are plotted as a function of the molar mass on a double logarithmic scale in Fig. 2. Best fits of the fractions with the highest polymer concentrations yield an exponent v < 0:54 ^ 0:01 for native guar which decreases to v < 0:50 for the low molar mass samples. The value of v 0:54 is in between the theoretical value for flexible polymer molecules in a good solvent v 3=5; and that in a u -solvent v 1=2; allowing a description of guar as random-walk chains. In Table 1 the Kuhn lengths and the number of Kuhn elements of the chains are given for the various samples, as well as the number-averaged molar mass (Mn), the number-averaged radius of gyration (Rg) and the polydispersity index M w =M n ; where Mw equals the weight-averaged molar mass. For native guar the Kuhn parameters were calculated from the random walk model (RW) as follows. The obtained value of Mn is 1:26 ^ 0:07103 kg=mol and Rg is 109 ^ 3 nm: We defined N as the number of repeating units. The molar mass M0 of the repeating unit is 486 g/mol, since each repeating unit contains three backbone monosaccharides (Lapasin & Pricl, 1995), which gives N Mn =M0 2:6 × 103 repeating units. The mannoses have a
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
5
Table 1 Overview of the number-averaged molar mass (Mn), the polydispersity index M w =M n ; where Mw equals the weight-averaged molar mass), the numberaveraged radius of gyration (Rg), and the calculated Kuhn lengths (lK) and number of Kuhn segments (NK) for both the random walk model (RW) and the wormlike chain model (WC) Heating time
Mn (kg/mol) Mw/Mn Rg (nm) lk (nm) (RW) NK (RW) lK (nm) (WC) NK (WC)
Native
10 min
20 min
30 min
1h
2h
1260 ^ 10 1.81 109 ^ 3 27 ^ 3 96 ^ 11 28 ^ 3 93 ^ 11
564 ^ 20 1.36 73 ^ 2 27 ^ 3 43 ^ 6 29 ^ 3 41 ^ 6
274 ^ 9 1.27 47 ^ 3 24 ^ 4 24 ^ 5 25 ^ 4 22 ^ 5
184 ^ 7 1.23 35 ^ 4 19 ^ 5 20 ^ 6 21 ^ 6 18 ^ 5
108 ^ 5 1.22 33 ^ 5 29 ^ 10 8^3 37 ^ 13 6^2
61 ^ 3 1.29 29 ^ 6 40 ^ 18 3.0 ^ 1.5 96 ^ 43 1.3 ^ 0.7
length of approximately 0.505 nm, as for glucose (Granath, 1958), giving a length of 1.0 nm for the repeating unit. Then, and according to Eq. (5), we find for the contour length, L, 2.6 mm. In a first simple approach we set a 1 (u -solvent). With Rg 109 ^3 nm; lK 6R2g =L (see Eq. (4)) follows as lK 27 ^3 nm; and for NK we find 96 ^ 16: This means that about 54 ^ 6 monosaccharide backbone units (about 27 ^ 3 repeating units) are required to mimic a freely rotational Kuhn segment, which indicates that guar is a rather stiff polysaccharide. In the same way the Kuhn lengths of the degraded samples were computed. Going from native to 30 min of pH/heat treatment the Kuhn length decreases somewhat (see Table 1). This is probably due to a decrease in excluded volume effect of the chains (the value of v decreases from 0.54 to 0.50) which decreases with the chain length (see Eq. (7)). The samples degraded for 60 and 120 min have large Kuhn lengths, as follows from the RW
Fig. 3. Molar mass distributions of the guar samples. Drawn curves are best fits to the Schulz–Flory distribution f M a0 M × exp 2a1 M; where a0 and a1 are fitting parameters.
model. However, the error bars are large because the accuracy of the radius of gyration in the scattering experiments is low for small (short) polymers. Moreover, the RW model no longer applies, since the number of Kuhn segments is smaller than 10. The worm-like chain (WC) model would apply for these smaller, relatively stiff chains. However, the accuracy of the measurements for these smaller chains is insufficient for a proper analysis. The molar mass distributions of the samples are given in Fig. 3 as well as a best fit of the Schulz–Flory distribution (Flory, 1953, 1969). The data follow a general trend with the peak of the distribution shifting with heating time to lower molar mass values. The fit of the Schulz–Flory distribution becomes worse with increasing degradation. This is due to the high molar mass tail containing a small fraction of native guar. Of course Schulz and Flory did not take into account such effects in the original derivation of the molar mass distributions. We have also simulated the degradation process in a simple manner by assuming that all bonds can be cut with equal probability. All polymers consist of m monomers, having m 2 1 bonds between the monomers. After every cut we calculated the average molar masses. In Fig. 4 we plotted some results from the simulation of the degradation process. The molar mass decrease was plotted as the molar mass after time t, M t; divided by the molar mass at t 0 M t 0; as a function of time divided by the time at the end of the process, tend, where all bonds are cut. The polydispersity, plotted as M w =M n ; is given in the same plot as a function of t=tend : At the beginning of the process the polydispersity increases, since the process of random cutting obviously broadens the size distribution. However, after t < 0:25tend the polydispersity reaches a maximum and decreases subsequently. At t tend the mixture only contains monomers and the polydispersity is unity. The simulation results agree with the molar mass decrease given in Fig. 1 and the data given for the polydispersity in Table 1. Probably, the polydispersity reaches a maximum between 0 and 10 min of heating. Between 10 min and 1 h of heating the polydispersity decreases as a function of heating time, which agrees with the simulation results.
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R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
Fig. 4. Simulation results of the degradation process. The molar mass, divided by its value at t 0; is given as a function of time, normalised by the process time (tend), as the dashed curve. The solid curve is the polydispersity, M w =M n ; as a function of t=tend :
4.2. Experimental and theoretical phase diagram Firstly, we dissolved guar in low-heat skim milk permeate (skim milk without casein micelles). In permeate solutions no phase separation could be observed for months when guar was added. Apparently, a stable mixture can be prepared by mixing whey proteins and guar. Therefore we used the permeate to dissolve guar after which this guarpermeate solution was mixed with skim milk. In this way the required final concentration cp of guar and the volume fraction f of casein micelles could be adjusted
Fig. 5. Experimental phase boundaries as derived from visual observation for three heating times of the guar samples as indicated in the plot.
Fig. 6. Calculated phase boundaries from the theory of Vrij (1976). The curves were calculated from the radii of gyration and molar masses given in Table 1 and a radius of the casein micelles of 100 nm.
independently. Phase separation was indicated by the observation of the upper phase becoming clearer with time while the lower phase became highly turbid (white). The guar concentration in the upper phase was analysed and was always higher than expected for a homogeneous distribution, indicating that guar is always concentrated in the upper phase due to a segregative interaction. In Fig. 5 a phase diagram is presented describing the experimentally observed phase boundaries of casein micelles in skim milk as mixed with three guar samples; native guar, guar degraded for 10 min and guar degraded for 30 min. The results are comparable with those of Bourriot, Garnier and Doublier (1997) for native guar gum. In Fig. 6 the predictions for the spinodal as calculated from Vrij’s theory (Vrij, 1976) are given. For the casein micelles a radius of 100 nm (the number-average, De Kruif, 1998) was used in the calculations, and for the molar mass and radius of gyration of the guar samples the data given in Table 1 were used. It must be noted that no adjustable parameters were used. Comparison with Fig. 5 shows that the trends are well described by the theory of Vrij; with the increasing chain length of the guar samples the phase boundary moves to smaller polymer concentrations. This is due to an increasing depletion layer thickness with increasing radius of gyration, which leads to a smaller value of the second osmotic virial coefficient (see Eqs. (10) and (12)) at the same polymer concentration. Hence, fewer polymers are required in order to attain a certain value of to reach the spinodal. The order of magnitude of the Bcoll 2 experimental phase boundary also agrees with the predictions of Vrij’s theory. The experimental phase boundary lies systematically higher than the calculated spinodal, which is
R. Tuinier et al. / Food Hydrocolloids 14 (2000) 1–7
ascribed to polydispersity of both the casein micelles and the guar samples (see Chu, Nikolov & Wasan, 1996, for the effect of polydispersity). Further, the radius of gyration of especially the native guar gum is so large that it is questionable whether the Vrij theory still applies. Large chains (compared to the radius of the casein micelles) can also assume conformations around the sphere, so that the depletion interaction is less effective (Odijk, 1996). In order to speculate on the efficiency of the guar samples as thickener in milk products we approximated the viscosity of the guar solution at the guar concentration corresponding to the experimentally observed phase boundary, at 10% (v/ v) casein micelles (as in milk). The viscosity was calculated as the dimensionless number clim [h ], where [h ] is the intrinsic viscosity calculated as 10=3pR3g NAV =Mn ; calculated from Table 1, and clim is the limiting guar concentration at the phase boundary. This finally gave clim h 0:32; 1.7 and 3.7 for native guar, 10 and 30 min degraded, respectively. Since a plot of the viscosity as a function of ch is a master curve for all flexible polysaccharides (Robinson et al., 1982) these results indicate that a low molar mass of guar gum is more suitable as a thickener than native guar gum. Although native guar has the highest intrinsic viscosity, the limiting polymer concentration is low to such a degree that the guar gum–casein micelle mixture phase separates below the overlap concentration for native guar. For smaller guar molecules phase separation takes place above the overlap concentration where the viscosity increases strongly with polymer concentration. This analysis is based on a simple, approximate, calculation and measurement of the viscosity of the mixtures of guar gum and casein micelles could test these speculations. Further the depletion induced attractions increase the viscosity at low shear rates (see for instance Woutersen & De Kruif, 1991) so that a rheological study would be an interesting follow-up of this work. 5. Conclusions Native guar gum could be degraded to lower molar mass guar samples by heating at low pH. A simple simulation of randomly cutting the bonds between the monomers could describe the degradation process. The various guar samples could be described as random-walk chains. Mixing guar gum with casein micelles gave a phase separation due to a depletion interaction leading to an effective attraction between the casein micelles by non-adsorbing guar. The polymer concentration at the phase boundary increases with decreasing guar chain length. The theory of Vrij
7
predicts the same trends as the experimental phase boundary with respect to the molar mass dependence. The location of the phase boundary is predicted reasonably well. It is speculated that the maximum attainable viscosity of the guar solution in the one-phase region increases with decreasing guar chain length. Therefore it can be useful to degrade native guar in milky systems. Acknowledgements We would like to thank Annie Layani for performing many experiments and Jan van Riel for performing the SEC-MALLS analysis. A. Parker, SKW-France, is acknowledged for providing us with the purified native guar gum. Dr G.A. van Aken (NIZO food research) is thanked for a critical reading of the manuscript. References Asakura, S., & Oosawa, F. (1954). Journal of Chemical Physics, 22, 1255. Bourriot, S., Garnier, C., & Doublier, J-L. (1997). Les Cahiers de Rhe´ologie, 15, 284. Chu, X. L., Nikolov, A. D., & Wasan, D. T. (1996). Langmuir, 12, 5004. De Kruif, C. G. (1998). Journal of Dairy Science, 81, 3019. Flory, P. J. (1953). Principles of polymer chemistry, New York: Cornell University Press. Flory, P. J. (1969). Statistical mechanics of chain molecules, New York: Interscience. Granath, K. A. (1958). Journal of Colloid Science, 13, 308. Grinberg, V. Ya., & Tolstoguzov, V. B. (1997). Food Hydrocolloids, 11, 145. Jeurnink, Th. J. M., & De Kruif, C. G. (1993). Journal of Dairy Research, 60, 139. Kerker, M. (1969). Scattering of light and other electromagnetic radiation, New York: Academic Press. Kuhn, W. (1934). Kolloid Z., 68, 2. Lapasin, R., & Pricl, S. (1995). Rheology of industrial polysaccharides: theory and applications, London: Blackie Academic. Lekkerkerker, H. N. W., Poon, W. C. K., Pusey, P. N., Stroobants, A., & Warren, P. B. (1992). Europhysics Letters, 20, 559. McQuarrie, D. A. (1969)–(1976). Statistical mechanics, New York: Harper & Row. Odijk, T. (1996). Macromolecules, 29, 1842. Poon, W. C. K., & Pusey, P. N. (1995). In M. Baus, L. F. Rull & J. -P. Ryckaert (Eds.), Observation and simulation of phase transitions in complex fluids, Dordrecht (Netherlands): Kluwer (pp. 3). Robinson, G., Ross-Murphy, S. B., & Morris, E. R. (1982). Carbohydrate Research, 107, 17. Tolstoguzov, V. B. (1991). Food Hydrocolloids, 4, 429. Vrij, A. (1976). Pure and Applied Chemistry, 48, 471. Woutersen, A. T. J. M., & De Kruif, C. G. (1991). Journal of Chemical Physics, 94, 5739. Yamakawa, H. (1971). Modern theory of polymer solutions, New York: Harper & Row.