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Skim Milk Acidification
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
185, 19–25 (1997)
CS964548
Skim Milk Acidification C. G.
DE
KRUIF
Netherlands Institute for Dairy Research (NIZO), Kernhemseweg 2, P.O. Box 20, 6710 BA Ede, The Netherlands Received December 26, 1995; accepted August 12, 1996
there is a small pH range where stability is only diminished. The particles exhibit attractive or adhesive interactions that are smaller or of the order of a few kT. If the attractive interactions are strong the system will aggregate and eventually form a permanent gel network. Here we present a quantitative model that describes the properties of the micellar dispersion up to the gelation point. For this we apply the so-called adhesive hard sphere (AHS) model to describe the macroscopic properties of the system. At this point it should be said that the classical view on the flocculation of casein micelles involves a destabilization followed by Smoluchowski flocculation kinetics. Here we present a new model and provide evidence supporting that model. In the next section we present the basic ideas and equations for this AHS model, also called sticky spheres model. Then we describe the experiments and the results obtained. The model holds for weak attractions; i.e., the attraction energy is smaller than a few kT. At strong attractions, the system forms permanent clusters and the kinetics may then be described by Smoluchowski kinetics.
Skim milk was acidified slowly using glucono-d-lactone and HCl. On lowering the pH the steric stabilization of the casein micelles diminishes and as a result the micelles exhibit attractive interactions. These interactions can be quantitatively described using an adhesive hard sphere (AHS) model. The strength of the attraction is found to be proportional to 1/(pH 0 pC); it is suggested that pC may be related to an effective dissociation constant of the carboxylic acid groups along the k-casein backbone. If pH approaches pC, the polyelectrolyte-like k-casein brush collapses onto the surface of the micelles. The AHS model is quantitatively tested using viscosity and dynamic light scattering measurements. q 1997 Academic Press
Key Words: skim milk; casein micelles; adhesive hard spheres; pH; aggregation; yoghurt; glucono-d-lactone.
1. INTRODUCTION
The casein micelles in milk are association colloids of mainly four casein proteins and calcium phosphate. The radius of the micelles is about 100 nm and they are sterically stabilized by a protein called k-casein that carries a number of carboxylic acid groups (1–4). During the production of yoghurt, or similar products, the pH of milk is lowered from 6.7 to 4–4.5. Usually this is done with the help of lactic acid bacteria, which convert lactose (milk sugar) into lactic acid. The viscosity of the milk changes during this process, because the casein micelles present in the milk lose their colloidal stability. The colloidal stability of particles stabilized by neutral polymeric layers or ‘‘brushes’’ is quite well understood and is described by Napper (5). If solvent quality for the stabilizing layer is lowered, the brush condenses on the surface of the particle and the repulsion between the particles is lost. Casein micelle particles are protected by a k-casein layer that behaves as a polyelectrolyte/polyampholyte brush and provides the stability of the micelles. The behavior of polyelectrolyte brushes (6, 7) under various conditions (e.g., ionic strength and charge density) is far more complex than that of neutral brushes. Nevertheless qualitatively it is clear, as depicted by Horne in his barbershop cartoon (8), that the k-casein brush shrinks and finally collapses on lowering the pH. Although the brush collapse seems to be rather abrupt,
2. THEORY
We present a description of the onset to flocculation and gelation of skim milk. These changes are induced by lowering the pH of the milk. In dairy practice this is the result of the conversion of lactose into lactic acid by lactic acid bacteria. For model experiments it is much easier to mimic this process by the addition of an ester that slowly hydrolyzes and thus produces a weak acid. This procedure is common practice in dairy research and actually also applied in certain products. Since the kinetics of acidification is relevant to the experiment we describe the hydrolysis of the ester in some detail first. Glucono-d-lactone Hydrolysis Glucono-d-lactone (GDL) is an internal ester; on addition to milk, the GDL hydrolyzes to form gluconic acid (GH), which is a weak acid and further dissociates, according to the reaction 19
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0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
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C. G. DE KRUIF k1
k2
GDL / H2O } GH } G 0 / H / . k01
[1]
Although both reaction steps are basically equilibrium reactions, we can treat the first step as a first-order degradation reaction at pH values greater than say 4.6. Above this pH the concentration of GH is so low that the backreaction is negligible. Furthermore, k1 is much greater than k01 . Hence the hydrolysis kinetics of GDL is considered to be first order and written as [GDL] Å [GDL]0e 0 k1t ,
[2]
where the subscript zero refers to the moment at which the GDL was added. If sufficient GDL is added, [GDL]0 § 0.85% (w/w) (see Experimental), a point will eventually be reached where sufficient hydrogen ions (H / ) are produced so as to clot or to flocculate the skim milk. For the moment we defer from a precise definition but we call the time needed tcl . Using an added concentration of GDL [GDL]0 , we have (H / )cl Å [GDL]0 0 [GDL]
[3]
and so, with Eq. [2], Å [GDL]0 (1 0 e 0 k1tcl )
[4]
Assuming that on changing the temperature the required amount of (H / )cl does not change but only the value of the reaction constant k1 we find, since 0k1tcl must then be constant, that DHhydro d ln(tcl ) Å/ , d1/T R
[5]
where DHhydro is the reaction enthalpy involved in the hydrolysis of GDL. The point to be made here is that clotting time strongly depends on the hydrolysis kinetics of GDL. The clotting pH of skim milk is also a (weak) function of temperature.
FIG. 1. Schematic representation of two casein micelles [ free after Holt (29)] and the adhesive hard sphere interaction potential.
charge density and is expected at pH å pC, which is larger than the isoelectric pH Å pI of the k-casein. The casein micelles are mainly sterically stabilized by the k-casein ‘‘hairs’’ on the surface (2, 4, 5). At large distances there is no interaction between the micelles; at very short distances there is a strong repulsion. Inbetween is a short range where the pair potential is attractive. The potential well changes in depth as a result of external influences. For instance it was shown that during renneting, where the ‘‘hairs’’ are cut by an enzyme (chymosin), the potential well depth is directly related to enzyme activity or, rather, to the number of hairs left on the surface (9). Here we suppose that the well depth is a function of pH. On lowering the pH, the k-casein hairs will become ‘‘insoluble’’ on approach of the isoelectric pH of k-casein. As said this collapse of the hairs occurs at pH ú pI but due to the collapse, the steric stabilization is lost (gradually). Since screening of the charges is strong in milk (ionic strength is about 0.1 mol) attractive short-ranged forces become operative. We therefore assumed a very simple expression for the well depth:
Adhesive Hard Sphere Model
e /kT Å
To describe the onset of flocculation we use the AHS model. The interaction potential between two casein micelles is depicted in Fig. 1. This hairy layer can be viewed as a so-called ‘‘salted brush’’ (7) of casein polyelectrolyte molecules anchored to the casein micelle. The essence of such a brush is that the charges along the polyelectrolyte chain are highly screened by salt ions within the brush. The transition from a stretched to a collapsed state is a function of chain density, ionic strength, and charge density along the chain. As a rule the collapse happens already at a low but finite
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1 . (pH 0 pC) m
[6]
The adjustable value of pC appeared to be 4.70, while m turned out to be 1. A higher value of m, e.g., 2, would predict an even sharper transition on approach of pC. We found the expression for the well depth by heuristics; in retrospect, however, it can be said that the difference (pH 0 pC) also appears in the scaling expression for the stretched brush-to-collapsed brush transition of a polyelectrolyte brush; however, pC is then replaced by pKa , the effective
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SKIM MILK ACIDIFICATION
dissociation constant of the carboxylic groups on the k-casein molecule. This subject will be discussed in a separate paper (10). At pH Å pKa the charge density of the hairs is nonzero. The width of the well was taken as the same as for the renneted micelles D Å f /6, where f is the length of the glycomacropeptide part (GMP) of the k-casein, f Å 7 nm. Now it is a simple matter to calculate the second osmotic virial coefficient from B *2 Å 2p
*
`
(1 0 e 0£ ( r ) kT )r 2 dr,
[7]
0
The relative viscosity of an AHS dispersion can be described by hr Å 1 / 2.5f /
6D e / kT (e 0 1). s
F S
s £ r õ s / D V (r) Å kT ln 12t
[8]
V (r) Å ` ; lim D r O; D s/D
DG
D
1.9 f 2. t
[11]
Depending on the scale and time of the particle diffusion one can recognize three different diffusion processes. Here we discuss only the so-called short-time self-diffusion. For adhesive spheres one finds (18) Dself /D0 Å 1 0
S
1.8315 /
D
0.295 f. t
[12]
This equation was tested by De Kruif (19) on (renneted) casein micelles and shown to be consistent with experiment.
; lim D r O;
V (r) Å O; lim D r O.
rús/D
5.9 /
where f is the volume fraction of the particles. This equation was shown to be correct up to f Å 0.2 (15). It was basically derived by Batchelor (16) and Russel (17), and later refined by Cichocki and Felderhof (18).
In theoretical calculations of the properties of AHS dispersions, use is made of a particular interaction potential which was introduced by Baxter (11). It is defined by rõs
S
Diffusion Coefficient
and performing the integration, we find B2 Å 4 0
Viscosity
3. EXPERIMENTAL
Skim Milk
[9]
The parameter t can be viewed as a reduced temperature. At high ‘‘temperature’’ the particles behave as hard spheres, whereas at low values of t there is an adhesive potential. The form of this potential was defined for mathematical convenience. It was shown by Regnault and Ravey (12) that the precise form of the adhesive potential is not of importance for the equilibrium properties of the system provided that the range is short compared with the size s of the particle. Cichocki and Felderhof (13) showed that the width of the square well strongly influences the calculated transport properties if D becomes very small. For practical systems this seems not to be the case, probably also because the shape of the well is not so well defined, i.e., rounded off. The connection between theory and experiment is made on the level of B2 . For the Baxter potential the second osmotic virial coefficient is given by: B2 Å 4 0 1/ t
[10]
Menon et al. (14) showed that perturbation theory leads to similar results, thus avoiding the physically unrealistic infinite well depth.
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Low-heat skim milk powder (Nilac) (NIZO Ede) meant for use in standardizing rennet activity was reconstituted as follows. Ten grams of the powder was dispersed in 100 ml of distilled water under gentle stirring at 40–457C. The stirring was maintained for 30 min and then the milk was equilibrated at 407C for an additional 45 min. This procedure ensures that (renneting) properties of the milk are equal to those of the fresh skim milk before drying. To prevent bacterial growth 0.05% w/w sodium azide was added. The glucono-d-lactone was obtained from Sigma. The pH of the milk was measured using glass electrodes standardized against buffer solutions of known pH. The initial pH of the milk was always 6.7. Viscosity The viscosity was measured using automated Ubbelohde viscometers (Schott Gera¨te, Germany). There was no detectable influence of the diameter of the capillaries used on the results. Dynamic Light Scattering In dynamic light scattering one measures the so-called intensity autocorrelation function. By using a cumulant anal-
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C. G. DE KRUIF
FIG. 2. Acidification of skim milk by various concentrations of GDL. Top to bottom: 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, and 2.0% (w/w).
ysis we derived from that an effective relaxation/diffusion constant, and with the help of the Stokes Einstein equation, kT DÅ , 6pha
[13]
this was translated into an apparent particle radius. Depending on the scattering geometry one can measure either collective diffusion (zero wave vector limit) or short-time self-diffusion (large wave vector limit). Here we made use of the Malvern HI-C, which measures in the back-scattering mode and essentially measures the short-time self-diffusion coefficient (20).
FIG. 3. Final pH of skim milk after adding various amounts of GDL at two different temperatures: /, 207C; s, 307C.
Particle Size In the back-scattering setup the apparent particle size was measured as a function of time after adding GDL, as is plotted in Fig. 4 together with the measured pH. As can be seen the pH decreases very slowly, and only when pH drops below 5 does the apparent particle radius increase. In Fig. 5 the apparent particle radius is plotted as a function of the pH. Now the increase in particle size is much more abrupt. The two different symbols in Fig. 5 correspond
4. RESULTS
Acidification Velocity At 207C we measured the change in pH of the milk as a function of time using different amounts of GDL. By plotting this on a semilogarithmic scale one finds (see Fig. 2) virtually linear plots. Then fitting the data to a linear equation provides an easy way for interpolating values. Note that the plots cannot be extrapolated to lower pH because of the gluconic acid equilibrium and/or the limited amount of GDL used. Actually, adding different amounts of GDL to the milk leads to different final pH values; this is plotted in Fig. 3 for two different temperatures. Although there is some scatter the final pH seems not to depend on temperature. In the following experiments only 1 or 1.5% GDL was used, since it allowed in all cases a slow and gradual acidification.
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FIG. 4. Apparent micelle radius during acidification with 1% (w/w) GDL at 207C. Upper trace, measured pH; lower trace, aapp /a0 .
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FIG. 5. Apparent micelle radius as a function of pH; /, stepwise acidification by 0.1 M HCl; j, continuous acidification by 1% (w/w) GDL. The drawn line represents the AHS model with pC adjusted to 4.7.
to GDL acidification and stepwise acidification with 0.1 M HCl. The two experiments gave virtually the same results. This observation is relevant since adding 1% GDL means a 0.05 mol concentration, which might be of influence. The solid line was obtained by using equations in the theoretical section. The relation between well depth and pH as given in the theoretical section was found by heuristic methods. The physical origin of this relation is tentatively related to the brush transition of the polyelectrolyte hairs. Furthermore, it seems logical that measurable quantities show a divergence at the brush transition at pC Å 4.70. In fact we choose pC as the adjustable parameter. The value of pC strongly determines the position of the asymptote, whereas the value of D influences the more or less gradual upswing of the apparent particle radius. A value of 1.1 nm as used before appeared to be quite satisfactory. The value of pC is temperature dependent and, in addition, depends on the pasteurization treatment of the milk since that may lead to deposition of whey proteins in the brush. Also, pC will depend on salt and calcium ion concentration. Clotting time was operationally defined as the point where viscosity was two times the starting value. This virtually coincides with visible observation of specks on the glassware. In the next experiment, we measured the apparent viscosity of the skim milk for three different GDL concentrations (Fig. 6). With decreasing GDL concentration the acidification rate decreases also and, therefore, the moment in time where the viscosity starts to increase. For the 1.5 and 1% GDL concentrations we can now predict the viscosity using the equations and the parameters derived from the dynamic light scattering experiment. So now we do not have an ad-
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justable parameter anymore. The acidification rate and therefore the pH are determined by the GDL concentration. The solid lines are the theoretical prediction. The lowest GDL concentration used in this experiment (see Fig. 6) was 0.83% and was chosen to reach a final pH that corresponds to the lower part of the viscosity upswing. As can be seen from Fig. 6 it takes a long time before viscosity starts to level off. The reason for that is twofold: first it takes a very long time before all the GDL is transformed; second, the casein micelles change their ionic and casein composition in this pH range and obviously this is a slow process. We refer to this later. The important observation, however, is that viscosity levels off, rather than rising to increasingly larger values, which would be the prediction of the models based on classical Smoluchowski kinetics. In other words, the micelles experience a real reversible particle–particle interaction instead of a probability of being trapped into the primary minimum of a DLVO-type potential. To illustrate this point further we refer also to Fig. 7. In an experiment where 1% GDL was added, the viscosity was followed into the region of increase. At that moment an amount of sodium hydroxide was carefully added so as to increase the pH from pH 5.0 to 5.3. The data in Fig. 7 show that although the pH change is virtually instantaneous it takes a considerable time before the viscosity ‘‘relaxes’’ back to the corresponding level. Meanwhile the GDL acidification continues and the curve resumes the original path. This experiment thus convincingly shows that the changes in the micellar configuration are slow but more importantly are of an equilibrium nature up to pH 5 at 207C. In the existing literature it is assumed that the particles
FIG. 6. Relative viscosity of skim milk at 207C after adding (left to right) 1.5% (w/w), 1% (w/w), and 0.83% (w/w) GDL. Note the leveling off of the viscosity at long times for the 0.83% GDL.
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FIG. 7. Relative viscosity of skim milk after adding 1% (w/w) GDL. When pH 5 was reached, the pH was raised to 5.3 by adding NaOH as indicated by the arrow.
FIG. 8. Relative viscosity of skim milk after adding 1% GDL at 207C and 1.5% (w/w) GDL at 07C. At 07C there is a slight increase in viscosity around pH 5.6.
start to flocculate in the (primary) potential minimum as a result of lowering the potential barrier on lowering the pH. This implies that if the process is started it is irreversible and continues even if the pH is kept stationary. Of course when a certain pH threshold is surpassed, the micelles will flocculate in a strong minimum and then the distinction between ‘‘primary’’ and secondary minima disappears. We estimate that at 257C this threshold is at pH 5, as may be derived from the results of Kim and Kinsella (21) or even higher for heated milk (22). The results in Figs. 6 and 7 indicate that the micelles interact through an attractive potential of a finite depth. The changes in the micelles are more pronounced at lower temperatures, as was shown by Roefs (23) and Creamer et al. (24). Furthermore there is a notion in the literature that acidification at temperatures below 57C does not lead to a gelling. Figure 8 shows viscosity measurements at 0 and 207C. Clearly visible is a slight increase in viscosity at pH 5.6 and this corresponds directly with the maximum release of casein as reported by Creamer et al. (24). After this maximum there is a shallow minimum in the viscosity before the upswing. The paper of Desorby-Banon et al. (22) reports mainly on this local minimum which was plotted on a highly exploded scale. Their data do not, or only partly, incorporate the data on either side of this local minimum. It was suggested in the literature (25) that the casein micelles lose their integrity at or around pH 5, which would, if correct, not allow the treatment given here. Our viscosity and dynamic light scattering measurements and also those of Lin et al. (26) do not support that picture. This matter is
more extensively reviewed by Kala´b et al. (27) and by Mulvihill and Grufferty (28), supporting our view. In addition, dynamic light scattering measurements at 20, 25, and 357C (Fig. 9) show that the reduced particle size does not change until the attraction sets in. Electron micrographs of acidified skim milk (using a starter culture) clearly show a particulate gel. So we conclude that although there are changes in the casein and calcium composition of the
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FIG. 9. Apparent reduced particle radius as measured in dynamic light scattering as a function of scaled acidification time. Measurements were made at 20, 25, and 357C.
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micelles during acidification, they retain their integrity to a large extent on the time scale of our experiments which is similar to that in dairy technology. Our measurements thus indicate that the macroscopic transport properties of a casein micelle dispersion are consistent with a view that the framework or envelope of the particles remains intact. 5. CONCLUSIONS
We have shown that the slow acidification of skim milk can be described using GDL kinetics and an AHS model to account for the particle interactions at a given constant temperature. As long as the interactions are still weak, they are reversible in nature. If the attraction becomes stronger, flocculation becomes permanent. The micelles maintain their integrity to a large extent and the more so at high temperatures. At low temperatures the viscosity curve shows a weak maximum around pH 5.6. This maximum corresponds to the maximum release of b-casein. In dynamic light scattering this maximum is not present, showing that the hydrodynamic radius does not change. Further research will be aimed at the influence of salt concentrations and in particular calcium concentration. Furthermore, we aim at correlating results in that way to the properties and stability of the yoghurt gels formed. REFERENCES 1. Walstra, P., and Jenness, R., ‘‘Dairy Chemistry and Physics.’’ Wiley, New York, 1984. 2. Holt, C., Adv. Protein Chem. 43, 63 (1992). 3. Kumosinski, T. F., Brown, E. M., and Farrell, H. M. Jr., Trends Food Sci. Technol. 2, 190 (1991). 4. Horne, D., J. Colloid Interface Sci. 11, 250 (1986).
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5. Napper, D. H., ‘‘Polymeric Stabilisation of Colloidal Dispersions.’’ Academic Press, New York, 1983. 6. Borisov, O. V., Birshtein, F. M., and Zhulina, E. B., J. Phys. II, 521 (1991). 7. Israels, R., Leermakers, F. A. M., Fleer, G. J., and Zhulina, E. B., Macromolecules 27, 3249 (1994). 8. Horne, D. S., and Leaver, J., Food Hydrocolloids 9, 91 (1995). 9. Kruif, C. G. De, Jeurnink, Th. J. M., and Zoon, P., Neth. Milk Dairy J. 46, 123 (1992). 10. Kruif, C. G. De, and Zhulina, E. B., Colloids and Surfaces A 117, 151 (1996). 11. Baxter, R. J., J. Chem. Phys. 49, 2770 (1968). 12. Regnault, C., and Ravey, J. C., J. Chem. Phys. 91, 1211 (1989). 13. Cichocki, B., and Felderhof, B. U., J. Chem. Phys. 93, 442 (1990). 14. Menon, S. V. G., Manokai, C., and Srinivasa Rao, K., J. Chem. Phys. 95, 9186 (1991). 15. Woutersen, A. T. J. M., and Kruif, C. G. De, J. Chem. Phys. 94, 5739 (1991). 16. Batchelor, G. K., J. Fluid Mech. 83 (Pt. 1), 97 (1977). 17. Russel, W. B., J. Chem. Soc. Faraday Trans. 2 80, 31 (1984). 18. Cichocki, B., and Felderhof, B. U., J. Chem. Phys. 89, 3705 (1988). 19. De Kruif, C. G., Langmuir 8, 2932 (1992). 20. Bremer, L. G. B., Deriemaeker, L., Finsy, R., Gelade´, E., and Joosten, J. G. H., Langmuir 9, 2008 (1993). 21. Kim, B. Y., and Kinsella, J. E., Milchwissenschaft 44, 622 (1989). 22. Desorby-Banon, S., Richard, F., and Hardy, J., J. Dairy Sci. 77, 3267 (1994). 23. Roefs, S. P. F. M., ‘‘Structure of Acid Casein Gels: A Study of Gels Formed after Acidification in the Cold.’’ Thesis, Wageningen University, 1986. 24. Creamer, L. H., Berry, G. P., and Mills, O. E., N.Z. J. Dairy Sci. Technol. 12, 58 (1977). 25. Visser, J., and Smits, P., Food Microstruct. 4, 267 (1985). 26. Lin, S. H. C., Leong, S. L., Dewan, R. K., Bloomfield, V. A., and Morr, C. V., Biochemistry 11, No. 10 (1972). 27. Kala´b, M., Allan-Wojtas, P., and Philipps-Todd, B. E., Food Microstruct. 2, 51 (1983). 28. Mulvihill, D. M., and Grufferty, M. B., in ‘‘Heat Induced Changes in Milk’’ (P. F. Fox, Ed.). International Dairy Federation, Brussels, 1995. 29. Holt, C., in ‘‘Yearbook Hannah Research Institute.’’ Hannah, Ayr, 1994.
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CS964548
Skim Milk Acidification C. G.
DE
KRUIF
Netherlands Institute for Dairy Research (NIZO), Kernhemseweg 2, P.O. Box 20, 6710 BA Ede, The Netherlands Received December 26, 1995; accepted August 12, 1996
there is a small pH range where stability is only diminished. The particles exhibit attractive or adhesive interactions that are smaller or of the order of a few kT. If the attractive interactions are strong the system will aggregate and eventually form a permanent gel network. Here we present a quantitative model that describes the properties of the micellar dispersion up to the gelation point. For this we apply the so-called adhesive hard sphere (AHS) model to describe the macroscopic properties of the system. At this point it should be said that the classical view on the flocculation of casein micelles involves a destabilization followed by Smoluchowski flocculation kinetics. Here we present a new model and provide evidence supporting that model. In the next section we present the basic ideas and equations for this AHS model, also called sticky spheres model. Then we describe the experiments and the results obtained. The model holds for weak attractions; i.e., the attraction energy is smaller than a few kT. At strong attractions, the system forms permanent clusters and the kinetics may then be described by Smoluchowski kinetics.
Skim milk was acidified slowly using glucono-d-lactone and HCl. On lowering the pH the steric stabilization of the casein micelles diminishes and as a result the micelles exhibit attractive interactions. These interactions can be quantitatively described using an adhesive hard sphere (AHS) model. The strength of the attraction is found to be proportional to 1/(pH 0 pC); it is suggested that pC may be related to an effective dissociation constant of the carboxylic acid groups along the k-casein backbone. If pH approaches pC, the polyelectrolyte-like k-casein brush collapses onto the surface of the micelles. The AHS model is quantitatively tested using viscosity and dynamic light scattering measurements. q 1997 Academic Press
Key Words: skim milk; casein micelles; adhesive hard spheres; pH; aggregation; yoghurt; glucono-d-lactone.
1. INTRODUCTION
The casein micelles in milk are association colloids of mainly four casein proteins and calcium phosphate. The radius of the micelles is about 100 nm and they are sterically stabilized by a protein called k-casein that carries a number of carboxylic acid groups (1–4). During the production of yoghurt, or similar products, the pH of milk is lowered from 6.7 to 4–4.5. Usually this is done with the help of lactic acid bacteria, which convert lactose (milk sugar) into lactic acid. The viscosity of the milk changes during this process, because the casein micelles present in the milk lose their colloidal stability. The colloidal stability of particles stabilized by neutral polymeric layers or ‘‘brushes’’ is quite well understood and is described by Napper (5). If solvent quality for the stabilizing layer is lowered, the brush condenses on the surface of the particle and the repulsion between the particles is lost. Casein micelle particles are protected by a k-casein layer that behaves as a polyelectrolyte/polyampholyte brush and provides the stability of the micelles. The behavior of polyelectrolyte brushes (6, 7) under various conditions (e.g., ionic strength and charge density) is far more complex than that of neutral brushes. Nevertheless qualitatively it is clear, as depicted by Horne in his barbershop cartoon (8), that the k-casein brush shrinks and finally collapses on lowering the pH. Although the brush collapse seems to be rather abrupt,
2. THEORY
We present a description of the onset to flocculation and gelation of skim milk. These changes are induced by lowering the pH of the milk. In dairy practice this is the result of the conversion of lactose into lactic acid by lactic acid bacteria. For model experiments it is much easier to mimic this process by the addition of an ester that slowly hydrolyzes and thus produces a weak acid. This procedure is common practice in dairy research and actually also applied in certain products. Since the kinetics of acidification is relevant to the experiment we describe the hydrolysis of the ester in some detail first. Glucono-d-lactone Hydrolysis Glucono-d-lactone (GDL) is an internal ester; on addition to milk, the GDL hydrolyzes to form gluconic acid (GH), which is a weak acid and further dissociates, according to the reaction 19
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C. G. DE KRUIF k1
k2
GDL / H2O } GH } G 0 / H / . k01
[1]
Although both reaction steps are basically equilibrium reactions, we can treat the first step as a first-order degradation reaction at pH values greater than say 4.6. Above this pH the concentration of GH is so low that the backreaction is negligible. Furthermore, k1 is much greater than k01 . Hence the hydrolysis kinetics of GDL is considered to be first order and written as [GDL] Å [GDL]0e 0 k1t ,
[2]
where the subscript zero refers to the moment at which the GDL was added. If sufficient GDL is added, [GDL]0 § 0.85% (w/w) (see Experimental), a point will eventually be reached where sufficient hydrogen ions (H / ) are produced so as to clot or to flocculate the skim milk. For the moment we defer from a precise definition but we call the time needed tcl . Using an added concentration of GDL [GDL]0 , we have (H / )cl Å [GDL]0 0 [GDL]
[3]
and so, with Eq. [2], Å [GDL]0 (1 0 e 0 k1tcl )
[4]
Assuming that on changing the temperature the required amount of (H / )cl does not change but only the value of the reaction constant k1 we find, since 0k1tcl must then be constant, that DHhydro d ln(tcl ) Å/ , d1/T R
[5]
where DHhydro is the reaction enthalpy involved in the hydrolysis of GDL. The point to be made here is that clotting time strongly depends on the hydrolysis kinetics of GDL. The clotting pH of skim milk is also a (weak) function of temperature.
FIG. 1. Schematic representation of two casein micelles [ free after Holt (29)] and the adhesive hard sphere interaction potential.
charge density and is expected at pH å pC, which is larger than the isoelectric pH Å pI of the k-casein. The casein micelles are mainly sterically stabilized by the k-casein ‘‘hairs’’ on the surface (2, 4, 5). At large distances there is no interaction between the micelles; at very short distances there is a strong repulsion. Inbetween is a short range where the pair potential is attractive. The potential well changes in depth as a result of external influences. For instance it was shown that during renneting, where the ‘‘hairs’’ are cut by an enzyme (chymosin), the potential well depth is directly related to enzyme activity or, rather, to the number of hairs left on the surface (9). Here we suppose that the well depth is a function of pH. On lowering the pH, the k-casein hairs will become ‘‘insoluble’’ on approach of the isoelectric pH of k-casein. As said this collapse of the hairs occurs at pH ú pI but due to the collapse, the steric stabilization is lost (gradually). Since screening of the charges is strong in milk (ionic strength is about 0.1 mol) attractive short-ranged forces become operative. We therefore assumed a very simple expression for the well depth:
Adhesive Hard Sphere Model
e /kT Å
To describe the onset of flocculation we use the AHS model. The interaction potential between two casein micelles is depicted in Fig. 1. This hairy layer can be viewed as a so-called ‘‘salted brush’’ (7) of casein polyelectrolyte molecules anchored to the casein micelle. The essence of such a brush is that the charges along the polyelectrolyte chain are highly screened by salt ions within the brush. The transition from a stretched to a collapsed state is a function of chain density, ionic strength, and charge density along the chain. As a rule the collapse happens already at a low but finite
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1 . (pH 0 pC) m
[6]
The adjustable value of pC appeared to be 4.70, while m turned out to be 1. A higher value of m, e.g., 2, would predict an even sharper transition on approach of pC. We found the expression for the well depth by heuristics; in retrospect, however, it can be said that the difference (pH 0 pC) also appears in the scaling expression for the stretched brush-to-collapsed brush transition of a polyelectrolyte brush; however, pC is then replaced by pKa , the effective
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dissociation constant of the carboxylic groups on the k-casein molecule. This subject will be discussed in a separate paper (10). At pH Å pKa the charge density of the hairs is nonzero. The width of the well was taken as the same as for the renneted micelles D Å f /6, where f is the length of the glycomacropeptide part (GMP) of the k-casein, f Å 7 nm. Now it is a simple matter to calculate the second osmotic virial coefficient from B *2 Å 2p
*
`
(1 0 e 0£ ( r ) kT )r 2 dr,
[7]
0
The relative viscosity of an AHS dispersion can be described by hr Å 1 / 2.5f /
6D e / kT (e 0 1). s
F S
s £ r õ s / D V (r) Å kT ln 12t
[8]
V (r) Å ` ; lim D r O; D s/D
DG
D
1.9 f 2. t
[11]
Depending on the scale and time of the particle diffusion one can recognize three different diffusion processes. Here we discuss only the so-called short-time self-diffusion. For adhesive spheres one finds (18) Dself /D0 Å 1 0
S
1.8315 /
D
0.295 f. t
[12]
This equation was tested by De Kruif (19) on (renneted) casein micelles and shown to be consistent with experiment.
; lim D r O;
V (r) Å O; lim D r O.
rús/D
5.9 /
where f is the volume fraction of the particles. This equation was shown to be correct up to f Å 0.2 (15). It was basically derived by Batchelor (16) and Russel (17), and later refined by Cichocki and Felderhof (18).
In theoretical calculations of the properties of AHS dispersions, use is made of a particular interaction potential which was introduced by Baxter (11). It is defined by rõs
S
Diffusion Coefficient
and performing the integration, we find B2 Å 4 0
Viscosity
3. EXPERIMENTAL
Skim Milk
[9]
The parameter t can be viewed as a reduced temperature. At high ‘‘temperature’’ the particles behave as hard spheres, whereas at low values of t there is an adhesive potential. The form of this potential was defined for mathematical convenience. It was shown by Regnault and Ravey (12) that the precise form of the adhesive potential is not of importance for the equilibrium properties of the system provided that the range is short compared with the size s of the particle. Cichocki and Felderhof (13) showed that the width of the square well strongly influences the calculated transport properties if D becomes very small. For practical systems this seems not to be the case, probably also because the shape of the well is not so well defined, i.e., rounded off. The connection between theory and experiment is made on the level of B2 . For the Baxter potential the second osmotic virial coefficient is given by: B2 Å 4 0 1/ t
[10]
Menon et al. (14) showed that perturbation theory leads to similar results, thus avoiding the physically unrealistic infinite well depth.
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Low-heat skim milk powder (Nilac) (NIZO Ede) meant for use in standardizing rennet activity was reconstituted as follows. Ten grams of the powder was dispersed in 100 ml of distilled water under gentle stirring at 40–457C. The stirring was maintained for 30 min and then the milk was equilibrated at 407C for an additional 45 min. This procedure ensures that (renneting) properties of the milk are equal to those of the fresh skim milk before drying. To prevent bacterial growth 0.05% w/w sodium azide was added. The glucono-d-lactone was obtained from Sigma. The pH of the milk was measured using glass electrodes standardized against buffer solutions of known pH. The initial pH of the milk was always 6.7. Viscosity The viscosity was measured using automated Ubbelohde viscometers (Schott Gera¨te, Germany). There was no detectable influence of the diameter of the capillaries used on the results. Dynamic Light Scattering In dynamic light scattering one measures the so-called intensity autocorrelation function. By using a cumulant anal-
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FIG. 2. Acidification of skim milk by various concentrations of GDL. Top to bottom: 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, and 2.0% (w/w).
ysis we derived from that an effective relaxation/diffusion constant, and with the help of the Stokes Einstein equation, kT DÅ , 6pha
[13]
this was translated into an apparent particle radius. Depending on the scattering geometry one can measure either collective diffusion (zero wave vector limit) or short-time self-diffusion (large wave vector limit). Here we made use of the Malvern HI-C, which measures in the back-scattering mode and essentially measures the short-time self-diffusion coefficient (20).
FIG. 3. Final pH of skim milk after adding various amounts of GDL at two different temperatures: /, 207C; s, 307C.
Particle Size In the back-scattering setup the apparent particle size was measured as a function of time after adding GDL, as is plotted in Fig. 4 together with the measured pH. As can be seen the pH decreases very slowly, and only when pH drops below 5 does the apparent particle radius increase. In Fig. 5 the apparent particle radius is plotted as a function of the pH. Now the increase in particle size is much more abrupt. The two different symbols in Fig. 5 correspond
4. RESULTS
Acidification Velocity At 207C we measured the change in pH of the milk as a function of time using different amounts of GDL. By plotting this on a semilogarithmic scale one finds (see Fig. 2) virtually linear plots. Then fitting the data to a linear equation provides an easy way for interpolating values. Note that the plots cannot be extrapolated to lower pH because of the gluconic acid equilibrium and/or the limited amount of GDL used. Actually, adding different amounts of GDL to the milk leads to different final pH values; this is plotted in Fig. 3 for two different temperatures. Although there is some scatter the final pH seems not to depend on temperature. In the following experiments only 1 or 1.5% GDL was used, since it allowed in all cases a slow and gradual acidification.
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FIG. 4. Apparent micelle radius during acidification with 1% (w/w) GDL at 207C. Upper trace, measured pH; lower trace, aapp /a0 .
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FIG. 5. Apparent micelle radius as a function of pH; /, stepwise acidification by 0.1 M HCl; j, continuous acidification by 1% (w/w) GDL. The drawn line represents the AHS model with pC adjusted to 4.7.
to GDL acidification and stepwise acidification with 0.1 M HCl. The two experiments gave virtually the same results. This observation is relevant since adding 1% GDL means a 0.05 mol concentration, which might be of influence. The solid line was obtained by using equations in the theoretical section. The relation between well depth and pH as given in the theoretical section was found by heuristic methods. The physical origin of this relation is tentatively related to the brush transition of the polyelectrolyte hairs. Furthermore, it seems logical that measurable quantities show a divergence at the brush transition at pC Å 4.70. In fact we choose pC as the adjustable parameter. The value of pC strongly determines the position of the asymptote, whereas the value of D influences the more or less gradual upswing of the apparent particle radius. A value of 1.1 nm as used before appeared to be quite satisfactory. The value of pC is temperature dependent and, in addition, depends on the pasteurization treatment of the milk since that may lead to deposition of whey proteins in the brush. Also, pC will depend on salt and calcium ion concentration. Clotting time was operationally defined as the point where viscosity was two times the starting value. This virtually coincides with visible observation of specks on the glassware. In the next experiment, we measured the apparent viscosity of the skim milk for three different GDL concentrations (Fig. 6). With decreasing GDL concentration the acidification rate decreases also and, therefore, the moment in time where the viscosity starts to increase. For the 1.5 and 1% GDL concentrations we can now predict the viscosity using the equations and the parameters derived from the dynamic light scattering experiment. So now we do not have an ad-
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justable parameter anymore. The acidification rate and therefore the pH are determined by the GDL concentration. The solid lines are the theoretical prediction. The lowest GDL concentration used in this experiment (see Fig. 6) was 0.83% and was chosen to reach a final pH that corresponds to the lower part of the viscosity upswing. As can be seen from Fig. 6 it takes a long time before viscosity starts to level off. The reason for that is twofold: first it takes a very long time before all the GDL is transformed; second, the casein micelles change their ionic and casein composition in this pH range and obviously this is a slow process. We refer to this later. The important observation, however, is that viscosity levels off, rather than rising to increasingly larger values, which would be the prediction of the models based on classical Smoluchowski kinetics. In other words, the micelles experience a real reversible particle–particle interaction instead of a probability of being trapped into the primary minimum of a DLVO-type potential. To illustrate this point further we refer also to Fig. 7. In an experiment where 1% GDL was added, the viscosity was followed into the region of increase. At that moment an amount of sodium hydroxide was carefully added so as to increase the pH from pH 5.0 to 5.3. The data in Fig. 7 show that although the pH change is virtually instantaneous it takes a considerable time before the viscosity ‘‘relaxes’’ back to the corresponding level. Meanwhile the GDL acidification continues and the curve resumes the original path. This experiment thus convincingly shows that the changes in the micellar configuration are slow but more importantly are of an equilibrium nature up to pH 5 at 207C. In the existing literature it is assumed that the particles
FIG. 6. Relative viscosity of skim milk at 207C after adding (left to right) 1.5% (w/w), 1% (w/w), and 0.83% (w/w) GDL. Note the leveling off of the viscosity at long times for the 0.83% GDL.
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FIG. 7. Relative viscosity of skim milk after adding 1% (w/w) GDL. When pH 5 was reached, the pH was raised to 5.3 by adding NaOH as indicated by the arrow.
FIG. 8. Relative viscosity of skim milk after adding 1% GDL at 207C and 1.5% (w/w) GDL at 07C. At 07C there is a slight increase in viscosity around pH 5.6.
start to flocculate in the (primary) potential minimum as a result of lowering the potential barrier on lowering the pH. This implies that if the process is started it is irreversible and continues even if the pH is kept stationary. Of course when a certain pH threshold is surpassed, the micelles will flocculate in a strong minimum and then the distinction between ‘‘primary’’ and secondary minima disappears. We estimate that at 257C this threshold is at pH 5, as may be derived from the results of Kim and Kinsella (21) or even higher for heated milk (22). The results in Figs. 6 and 7 indicate that the micelles interact through an attractive potential of a finite depth. The changes in the micelles are more pronounced at lower temperatures, as was shown by Roefs (23) and Creamer et al. (24). Furthermore there is a notion in the literature that acidification at temperatures below 57C does not lead to a gelling. Figure 8 shows viscosity measurements at 0 and 207C. Clearly visible is a slight increase in viscosity at pH 5.6 and this corresponds directly with the maximum release of casein as reported by Creamer et al. (24). After this maximum there is a shallow minimum in the viscosity before the upswing. The paper of Desorby-Banon et al. (22) reports mainly on this local minimum which was plotted on a highly exploded scale. Their data do not, or only partly, incorporate the data on either side of this local minimum. It was suggested in the literature (25) that the casein micelles lose their integrity at or around pH 5, which would, if correct, not allow the treatment given here. Our viscosity and dynamic light scattering measurements and also those of Lin et al. (26) do not support that picture. This matter is
more extensively reviewed by Kala´b et al. (27) and by Mulvihill and Grufferty (28), supporting our view. In addition, dynamic light scattering measurements at 20, 25, and 357C (Fig. 9) show that the reduced particle size does not change until the attraction sets in. Electron micrographs of acidified skim milk (using a starter culture) clearly show a particulate gel. So we conclude that although there are changes in the casein and calcium composition of the
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FIG. 9. Apparent reduced particle radius as measured in dynamic light scattering as a function of scaled acidification time. Measurements were made at 20, 25, and 357C.
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micelles during acidification, they retain their integrity to a large extent on the time scale of our experiments which is similar to that in dairy technology. Our measurements thus indicate that the macroscopic transport properties of a casein micelle dispersion are consistent with a view that the framework or envelope of the particles remains intact. 5. CONCLUSIONS
We have shown that the slow acidification of skim milk can be described using GDL kinetics and an AHS model to account for the particle interactions at a given constant temperature. As long as the interactions are still weak, they are reversible in nature. If the attraction becomes stronger, flocculation becomes permanent. The micelles maintain their integrity to a large extent and the more so at high temperatures. At low temperatures the viscosity curve shows a weak maximum around pH 5.6. This maximum corresponds to the maximum release of b-casein. In dynamic light scattering this maximum is not present, showing that the hydrodynamic radius does not change. Further research will be aimed at the influence of salt concentrations and in particular calcium concentration. Furthermore, we aim at correlating results in that way to the properties and stability of the yoghurt gels formed. REFERENCES 1. Walstra, P., and Jenness, R., ‘‘Dairy Chemistry and Physics.’’ Wiley, New York, 1984. 2. Holt, C., Adv. Protein Chem. 43, 63 (1992). 3. Kumosinski, T. F., Brown, E. M., and Farrell, H. M. Jr., Trends Food Sci. Technol. 2, 190 (1991). 4. Horne, D., J. Colloid Interface Sci. 11, 250 (1986).
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5. Napper, D. H., ‘‘Polymeric Stabilisation of Colloidal Dispersions.’’ Academic Press, New York, 1983. 6. Borisov, O. V., Birshtein, F. M., and Zhulina, E. B., J. Phys. II, 521 (1991). 7. Israels, R., Leermakers, F. A. M., Fleer, G. J., and Zhulina, E. B., Macromolecules 27, 3249 (1994). 8. Horne, D. S., and Leaver, J., Food Hydrocolloids 9, 91 (1995). 9. Kruif, C. G. De, Jeurnink, Th. J. M., and Zoon, P., Neth. Milk Dairy J. 46, 123 (1992). 10. Kruif, C. G. De, and Zhulina, E. B., Colloids and Surfaces A 117, 151 (1996). 11. Baxter, R. J., J. Chem. Phys. 49, 2770 (1968). 12. Regnault, C., and Ravey, J. C., J. Chem. Phys. 91, 1211 (1989). 13. Cichocki, B., and Felderhof, B. U., J. Chem. Phys. 93, 442 (1990). 14. Menon, S. V. G., Manokai, C., and Srinivasa Rao, K., J. Chem. Phys. 95, 9186 (1991). 15. Woutersen, A. T. J. M., and Kruif, C. G. De, J. Chem. Phys. 94, 5739 (1991). 16. Batchelor, G. K., J. Fluid Mech. 83 (Pt. 1), 97 (1977). 17. Russel, W. B., J. Chem. Soc. Faraday Trans. 2 80, 31 (1984). 18. Cichocki, B., and Felderhof, B. U., J. Chem. Phys. 89, 3705 (1988). 19. De Kruif, C. G., Langmuir 8, 2932 (1992). 20. Bremer, L. G. B., Deriemaeker, L., Finsy, R., Gelade´, E., and Joosten, J. G. H., Langmuir 9, 2008 (1993). 21. Kim, B. Y., and Kinsella, J. E., Milchwissenschaft 44, 622 (1989). 22. Desorby-Banon, S., Richard, F., and Hardy, J., J. Dairy Sci. 77, 3267 (1994). 23. Roefs, S. P. F. M., ‘‘Structure of Acid Casein Gels: A Study of Gels Formed after Acidification in the Cold.’’ Thesis, Wageningen University, 1986. 24. Creamer, L. H., Berry, G. P., and Mills, O. E., N.Z. J. Dairy Sci. Technol. 12, 58 (1977). 25. Visser, J., and Smits, P., Food Microstruct. 4, 267 (1985). 26. Lin, S. H. C., Leong, S. L., Dewan, R. K., Bloomfield, V. A., and Morr, C. V., Biochemistry 11, No. 10 (1972). 27. Kala´b, M., Allan-Wojtas, P., and Philipps-Todd, B. E., Food Microstruct. 2, 51 (1983). 28. Mulvihill, D. M., and Grufferty, M. B., in ‘‘Heat Induced Changes in Milk’’ (P. F. Fox, Ed.). International Dairy Federation, Brussels, 1995. 29. Holt, C., in ‘‘Yearbook Hannah Research Institute.’’ Hannah, Ayr, 1994.
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