Colloids and Surfaces B: Biointerfaces 21 (2001) 125– 135 www.elsevier.nl/locate/colsurfb Specific cation adsorption on protein-covered particles and its influence on colloidal stability J.A. Molina-Bolı́var a, F. Galisteo-González b, R. Hidalgo-Alvarez b,* a b Departamento de Fı́sica Aplicada II, Escuela Politécnica, Uni6ersidad de Málaga, Campus de El Ejido, 29013 Málaga, Spain Grupo de Fı́sica de Fluidos y Biocoloides, Departamento de Fı́sica Aplicada, Uni6ersidad de Granada, 18071 Granada, Spain Abstract Protein coated particles present an anomalous colloidal stability at high ionic strength when the classical theory (DLVO) predicts aggregation. This observed deviation from DLVO behaviour appears for electrolyte concentrations above some critical bulk value. As we have suggested in previous publications the existence of an additional short-range repulsive ‘hydration force’ due to specific hydrated cation adsorption could explain this anomalous stability. The overlap of the hydration layers when two particles approach should provoke this repulsive force. New evidence of this mechanism has been observed when electrophoretic mobilities of protein-carrying latex particles were measured at various concentrations of sodium and calcium chloride. In the latter case a sign reversal of zeta-potential was found, probably due to the specific adsorption of Ca2 + ions on protein molecules. The adsorption increases with the medium pH. These results have been analyzed following the treatment proposed by Ohshima and co-workers for large charged colloidal particles coated with a layer of protein. This study shows an increase in the positive fixed-charge density on the protein caused by the adsorption of cations. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Protein colloids; Colloidal stability; Hydration forces; Specific cation adsorption; Electrophoretic mobility 1. Introduction The study of fluids confined between two solid surfaces is of great interest in the areas of adhesion, lubrication, stability of colloids, phase behaviour and critical phenomena in porous media, and the cleaning of semiconductor surfaces. In recent years interest has also been focused in * Corresponding author. fax: + 34-9-58243214. E-mail address: [email protected] (R. Hidalgo-Alvarez). biological systems such as food colloids and cells, bacteria and virus adhesion. When the distance of separation between two solid surfaces immersed in a fluid medium falls within the range of few hundred nanometers, it has long been known that the interaction can be described to a first approximation using the DLVO theory [1,2], which attributes their mutual interaction energy to the Van der Waals attraction and the electrostatic repulsion. The resulting force due to these two long-ranged forces is repulsive at large separations, but become attractive at short distances. As a consequence, the DLVO theory provides a sim- 0927-7765/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 6 5 ( 0 1 ) 0 0 1 6 6 - 7 126 J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 ple treatment for the stability of a colloidal suspension, which decreases with electrolyte concentration due to the screening of the repulsive electrical double layer. In the last decade, several new forces have been invoked to explain a variety of short-ranged phenomena. Direct investigations of the interaction potential between silica surfaces [3,4] and mica surfaces [5] in aqueous electrolyte solutions have revealed agreement with DLVO at separations above a few nanometers but, at smaller separations, a short-range repulsive force appears, often termed as a ‘hydration’ interaction. This interaction was ascribed by Pashley, for the case of mica surfaces in aqueous solutions [5,6], as arising from the removal of hydration water of surface-bound counterions. Hydration-like forces have also been reported in surfactant systems [7] and their origin suggested to be the removal of water of hydration of the surfactant head groups as well. The classical DLVO theory treats the intervening medium as continuous, so it is not surprising that the model breaks down when the liquid medium between two surfaces is only few molecular diameters in width. It has long been postulated that a modified water structure exists at solid/water interfaces (in fact, hydrophobicity is a manifestation of water structure at surfaces [8]). For colloids and interfaces in aqueous media the predominant effect is attributed to the hydration of adsorbed counterions and ionic functional groups on the surface. As such surfaces approach each other closely during interaction, some dehydration of the ions and the surface would have to occur, leading to an increase in the free energy and hence a repulsion. These effects are usually referred to as hydration or structural forces. This explanation, however, is far from being completely understood (and theoretically modelled) yet. The ‘hydration forces’ name reflects the proposition that the force is caused by the structure of water between surfaces, which depends on the hydrophobic/hydrophilic character of the surface and on the hydration of adsorbed counterions and ionic functional groups in the surface [9,10]. Pashley and Israelachvili [5,11,12] have shown that the hydration repulsion occurring between two mica surfaces across a monovalent electrolyte is intimately related to the hydration number of the cation, i.e. the average number of water molecules in the first shell. The results showed clearly that the strength and the range of the force increased with the series Cs+ B Rb+ B K+ B Na+ B Li+. According to these authors, hydrated cations adsorb to hydrophilic surfaces, and they presumably retain some of their water of hydration. On the other hand, electrophoresis of colloidal particles is a convenient method to obtain information about surface structure, specially about the distribution of ionogenic groups along this surface. For example, specifically adsorbed ions can be recognized by their ability to reverse the sign of the n-potential, whereas indifferent ions can only reduce it asymptotically to zero [13,14]. Ohshima et al. [15–17] proposed a membrane model in which the membrane-fixed charges are distributed at an uniform density through a surface layer of thickness d. The membrane is permeable to electrolyte ions and shows the mentioned fixed-charged groups in electrolyte solution. With this model it is possible to calculate the fixedcharge density on a protein layer from the measured n-potential which depends on a weighted average of the Donnan potential and the potential at the boundary between the surface charge layer and the surrounding solution. Many biocolloids are stabilized by surface protein molecules. The protein may form an integral part of the particle structure or may have been adsorbed from solution. As yet, there is no quantitative theory of colloid stabilization by proteins, but it seems clear that specific cation adsorption effects play an important role [18]. In the important commercial field of dairy products, it is observed that casein micelle stability does not conform to the DLVO theory. This system may tolerate divalent ion concentrations before coagulation [19,20]. In previous publications we have described the anomalous stability of protein-covered colloidal systems [21,22]. They can be considered as another exception to the DLVO theory, because they are stable at high salt concentrations where the theory predicts aggregation. This stability was J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 attributed to a repulsive hydration force which prevents protein-covered particles from aggregating. Experimental data suggests that hydrated cations adsorbed on the protein surface could be responsible for this behaviour. In the present work new evidence is presented in relation to this proposed mechanism of anomalous stabilization, by analyzing electrophoretic measurements of protein-covered particles. 2. Experimental 2.1. Materials The latex sample used in this study was kindly provided by Joxe Sarobe (Chemical Engineering Group, University of Basque Country), and prepared by means of a core-shell emulsion polymerization in a batch reactor [23]. The core was a seed of polystyrene and the shell was a styrene/ chloromethylstyrene copolymer, rendering particles with a chloroactivated functionality at the surface which can covalently link proteins [24]. The mean diameter of these particles was, as determined by TEM, 20195 nm. Latex was cleaned by three cycles of centrifugation and redispersion of the pellet in acidic water, and then thoroughly washed with deionized water in a serum replacement cell until constant conductivity was achieved. Surface charged groups were determined by conductimetric titration (− 3.79 0.2 mC cm − 2, strong acid), and chloride surface groups by hydrolysis with glycine/NaOH, acidification with HNO3, and subsequent titration of free Cl− with AgNO3 (59 94 mequiv g − 1, 2.119 0.14 mequiv m − 2). F(ab%)2 fragments, which were obtained from polyclonal rabbit IgG, and purified by affinity chromatography, were kindly supplied by Biokit, S.A. (Barcelona). The isoelectric points (i.e.p.) range, determined by isoelectric focussing, was rather wide (4.7– 5.9) as a consequence of the polyclonal nature of the IgG. All chemicals were analytical grade quality. Water was purified by reverse osmosis, followed by percolation through charcoal and a mixed bed of ion-exchange resins. 127 Protein was attached to the latex particles by incubating the latex (0.4 m2) and protein solution in phosphate buffer (pH 7.2) at 35°C for 5 h. The amount of protein adsorbed was determined by measuring the difference in concentration before and after adsorption with an spectrophotometer at 280 nm (Spectronic 601, Milton Roy). After incubation, the sample was separated from the supernatant by high-speed centrifugation and the supernatant filtered using a polyvinyldene difluoride filter (Millipore, pore diameter 0.1 mm) before measuring the remaining protein concentration. Such a filter has an extremely low affinity for protein adsorption, so the filtration step does not interfere with the calculation of the amount of adsorbed protein. Protein-covered particles were separated from the supernatant by high-speed centrifugation, and redispersed in corresponding buffer (phosphate for pH 7.2, acetate for pH 5.8). The protein coverage of the latex-F(ab%)2 complex used in this work is 3.2 mg/m2. 2.2. Stability The stability ratio (W) has been used as a criterion for the stability of the colloidal system: W= kr ks (1) in which the rate constant kr describes rapid coagulation, and ks is the rate constant for the slow coagulation regime. Thus, the inverse of the stability ratio provides a measure of the effectiveness of collisions leading to coagulation. In this work, the stability ratio was obtained experimentally from the rate constant of coagulation of the colloidal particles measured using the low angle light scattering technique developed by Lips and Willis [25], where the total scattering intensity for a dispersion of identical primary particles with a time varying distribution sizes is [26]: I(t,q) =1+ 2knst Iq (0) (2) where Iu (0) is the initial intensity of light scattered at angle q, ns the number of primary particles and k the rate constant. The scattered light J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 128 intensity at low angles increases linearly with time, and then an absolute coagulation rate can be obtained from the slope if the number of primary particles is known.The scattering cell shape is rectangular, with a 2-mm path length. The cell was thoroughly cleaned with chromic acid, rinsed with distilled water and then dried using an infrared lamp. Equal quantities (1 ml) of salt and protein-carrying particle solutions were mixed and introduced into the cell using an automatic mixing device. Dead time is quite short. The latex dispersions used for such coagulation experiments have to be sufficiently dilute to minimize multiple scattering effects, whilst still having an experimentally convenient coagulation time. For the protein-carrying particle system used here, a concentration of 2×1010 particles per ml was determined to be satisfactory. 2.3. Electrokinetic The electrophoretic mobility of the coated particles was determined with a Zeta-Sizer IV (Malvern), by taking the average of five measurements at the stationary level in a cylindrical cell, and changing the sample three times. Experimental conditions were previously worked out to ensure minimal influence of particle aggregation in the electrophoretic measurements. Standard deviations always fell in the range 2– 4%. The n-potential was calculated according to the Smoluchowski equation: n= p v mrm0 e (3) where p is the viscosity of the medium, ve is the electrophoretic mobility and or and m0 are the relative permittivity of the medium and the permittivity of the vacuum, respectively. 2.4. Dynamic light scattering measurements Photon correlation spectroscopy measurements were made at a scattering angle of 90° with a 256-channel photon correlator (Malvern 4700c system). Experiments were performed at a particle concentration of about 109 part/ml and a wavelength of 488 nm (Argon laser). This technique employs the laser beam to probe a small volume of the particle suspension. As they undergo Brownian motion, interference with scattered light produces a fluctuation in the intensity with time at the detector. This temporal fluctuation contains information on the motion of particles and may be analyzed by means of a correlator that yields, in real time, the autocorrelation function. The nonexponential behaviour of this function must be analyzed by the method of cumulants. The first cumulant is used to obtain the effective translational diffusion coefficient, and the apparent hydrodynamic radius of the particle obtained from the Stokes–Einstein relation. 3. Theoretical background Several theoretical studies [16,26–29] have been made on the electrophoresis of a colloidal particle covered by an ion-penetrable surface-charged layer consisting of polymer, in relation to the electrophoresis of biocolloids such as cells or vesicles. It has been shown [16,30] that when the surfacecharged layer is thicker than 1/s, being s the Debye –Hückel parameter, the potential within the surface-charged layer is in practice equal to the Donnan potential except in the region very near the boundary between the surface-charged layer and the surrounding solution. On the basis of these observations, Ohshima et al. [15–17] have derived an approximate formula that directly relates the electrophoretic mobility to the charge density in the surface region. They assume an uniform distribution of the fixed charges through the surface region with a finite thickness, d, and penetration of the region by electrolyte ions. This formula has the form: ve = mrm0 DON/u+(0)/sm zeN + 2 pu p 1/u + 1/sm + 8mrm0kT 6en0 e − ud/u−e − smd/sm tan h pu6e kT (1/u)2 − (1/sm)2 (4) where DON and (0) are the Donnan potential and the potential at the boundary of the surface region and the medium, respectively, sm is the Debye– Hückel parameter of the surface region, u is a parameter whose reciprocal has the dimension J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 of length, and the meaning of the depth of the flow penetration in the surface region, 6 is the valence of the electrolyte, z and N are the valence and the density of charged groups in the region, respectively, n0 is the zeta potential of bare latex particle and d is the depth of the protein layer from the latex surface. The Donnan potential, the boundary potential, and the Debye – Hückel parameter of the surface region are given as: ! " n ! " n ! " n n DON = (0) = kT zN ln + 6e 26n kT zN ln + 6e 26n + 26n 1− zN sm =s 1+ zN 26n 2 zN 26n zN 26n zN 26n 1/2 +1 2 (5) 1/2 +1 2 1/2 +1 (6) 2 1/4 (7) 129 where s is the Debye–Hückel parameter of the medium and n is the electrolyte concentration. 4. Results and discussion 4.1. Colloidal stability at high ionic strength The phenomenon of the anomalous stabilization can be observed in Fig. 1 for a protein-covered colloidal system, where the stability ratio is plotted versus the salt concentration in log scales for NaCl at two pH values (5.8 and 7.2), and for CaCl2 at pH 7.2. In the case of NaCl, for example, the stability diagram initially presents the classical DLVO behaviour, decreasing colloidal stability with salt concentration until the rapid aggregation domain where stability is minimal and independent of salt concentration. However, when salt is further increased the stability of this Fig. 1. log W versus log [salt] (M) for a F(ab%)2 –latex particle: , Ca2 + at pH 7.2; , Na+ at pH 5.8; , Na+ at pH 7.2. Open symbol, DLVO zone; closed symbol, non-DLVO zone. 130 J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 Fig. 2. Electrophoretic mobility of F(ab%)2 –latex particles as a function of pH in the presence of two NaCl concentrations: , 2.1 × 10 − 3 M; , 10 − 2 M. system increases again, appearing as the so-called non-classical DLVO region. This anomalous behaviour clearly depends on the pH and counterion nature. With divalent cations such as Ca2 + the effect is much more pronounced, whilst the dependence on pH can be attributed to the increase in net protein negative charge. Both results suggest that the specific adsorption of hydrated cations on protein molecules may be responsible for this anomalous stability, creating an energy barrier opposing aggregation referred to as hydration forces [31]. 4.2. Effects of pH and ionic strength on electrokinetic beha6iour In order to corroborate this assumption with new experimental evidences, electrophoretic measurements of protein-covered particles as a function of pH and ionic strength have been carried out. As can be seen in Fig. 2, for the case of NaCl, the mobilities depend on pH remarkably, as expected from the amphoteric nature of proteins, showing positive values below the i.e.p. of the protein-covered particle and negative values above this point. If the salt concentration is increased, the absolute values of the electrophoretic mobility decrease due to the screening effect of electrolyte ions on the electrical charge in the protein-carrying surface region. Nevertheless, Fig. 3 shows that this usual influence of electrolyte concentration on mobility is not observed when Ca2 + is employed. For the highest concentration presented, electrophoretic mobility is positive all over the pH range, whereas net charge is negative over the i.e.p. of the protein-covered particle. This sign reversal in the mobility may be attributable to the specific adsorption of Ca2 + ions onto the surrounding protein surface [13,14,32,33]. In the case of Na+ (see Fig. 2) there exists no sign J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 reversal, but some specific adsorption may also be suspected from the shift in the point of zero charge (p.z.c.) that happens when the NaCl concentration is increased [14,32]. Although Ca2 + ions are clearly much more effective than Na+ ions in reducing the electrokinetic potential of the colloidal particle, this major effect of Ca2 + is a general divalent counterion phenomenon, and is not related only to direct ion-binding on the protein. The specific adsorption of cations should depend, in principle, on the electrolyte concentration in solution [34]. This fact can be observed from the experimental data shown in Figs. 4 and 5, where the n-potential of the protein-covered particles is plotted against NaCl and CaCl2, respectively, for two pH values, namely 5.8 and 7.2. With regard to the NaCl electrolyte, the n-potential at pH 7.2 is higher, in absolute values, than at pH 5.8. This feature can be readily explained 131 by considering that at pH 5.8, closer to the i.e.p. range of this protein, the average charge density must be lower than at pH 7.2. This clearly indicates an important contribution of the charge of the bound protein molecule to the n-potential, correlating with the highest colloidal stability in the DLVO region at pH 7.2 (see Fig. 1). As shown also in Fig. 4, the ionic strength of the medium affects the n-potential of the proteincovered particle, but this influence depends on the pH. At pH 5.8, the behaviour is the expected from theory [14], with the n-potential decreasing first in absolute value, and then levelling off, converging to a non-zero value, with increasing ionic strength. This trend arises from the screening effect of electrolyte ions on the protein charge groups. Nevertheless, in the case of pH 7.2, after an initial screening effect similar to that occurring at pH 5.8, instead of reaching a plateau in the n-potential, it continues decreasing probably due Fig. 3. Electrophoretic mobility of F(ab%)2 –latex particles as a function of pH in the presence of two CaCl2 concentrations: , 2 × 10 − 3 M; , 3.8× 10 − 2 M. 132 J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 Fig. 4. n potential of F(ab%)2 –latex particles as a function of NaCl concentration at two pHs: , 7.2; , 5.8. to adsorption of Na+ ions on protein surface. The effect is so pronounced that the curves at both pHs tend to converge. This greater tendency for cation adsorption at pH 7.2 may justify the highest colloidal stability of the system in the non-DLVO region shown in Fig. 1. In the case of Ca2 + ions, it can be observed in Fig. 5 that at both pH values the plateau in the n-potential is not reached, but it presents a continuous derive that even passes from negative to positive values. The only possible explanation for these positive values of n-potential, when the net charge of the protein is negative, is the assumption of specific binding of cations to the surface. As in the case of Na+, this phenomenon is more extended the higher the pH. By comparison of these two cations, it can be inferred that Ca2 + ions, due to their improved specific adsorption, are more likely to stabilize the protein-covered particle in the non-DLVO region, as shown in Fig. 1. The influence of ionic strength on the electrophoretic mobility of casein-coated polystyrene particles was investigated by Douglas et al. [35] who also showed the Ca2 + -binding properties of casein molecules. 4.3. Analysis of electrokinetic data In order to calculate the charge distribution in the protein-carrying particle from the experimentally obtained n-potential values, the membrane model proposed by Ohshima et al. [15– 17] was employed. This model revealed that the n-potential loses its meaning for colloidal particles with a structured surface, since the electrophoretic mobility is insensitive to the precise position of the slipping plane. Sakuma et al. [36,37] have indicated that the n-potential in protein-covered particles is approximately equal to the surface potential relative to the external bulk solution (Eq. (5)). It is possible J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 to calculate the charge density in the protein layer per area unit from the measured n-potential (|p = zeNd). For this purpose, the layer thickness of protein adsorbed on the particle (d) can be determined by Photon Correlation Spectroscopy (PCS) from the difference between the mean diameter of bare latex and protein–latex particles. In this case, the value of d may be estimated as 591 nm. In Fig. 6 the charge density (|p) calculated from the n-potential as a function of the CaCl2 concentration of the medium at two different pH values, 5.8 and 7.2, is shown. Here, the charge density is a net value, which is given by the sum of positive and negative charges per area unit of the protein layer. These charges should proceed only from the ionic groups on the protein, which depend exclusively on pH. This fact is observed at low electrolyte concentration, but with increasing concentration the value of |p increases, reaching positive values due to the adsorption of cations to the surface. 133 From the data shown in Fig. 6, the molecular size of F(ab%)2 [38] and the adsorbed amount of protein per unit area, the average number of charges per protein molecule may be estimated (Table 1). The values obtained are within expectations, with a net charge slightly more negative at pH 7.2 than at pH 5.8 at low electrolyte concentrations, but changing to positive values as the salt concentration increases, due to the specific adsorption of cations. Moreover, this effect is more pronounced at pH 7.2. This method seems to provide a good way for calculating molecular effective charges in adsorbed systems. 5. Conclusions Colloidal particles covered with protein are stable at high ionic strength, when the classical DLVO theory predicts aggregation. In previous Fig. 5. n potential of F(ab%)2 –latex particles as a function of CaCl2 concentration at two pHs: , 7.2; , 5.8. 134 J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 Fig. 6. Charge density on protein layer (|p) for F(ab%)2 – latex particles as a function of CaCl2 concentration at two pHs: , 7.2; , 5.8. publications we have suggested the existence of a repulsive hydration force originated from the specific adsorption of cations in the protein surface. This assumption has been further corroborated by studying the electrokinetic behaviour of proteincovered particles at different pH and ionic strength conditions, and using two chloride salts, namely NaCl and CaCl2. Experimental data suggest that both cations are adsorbed specifically at the protein– aqueous interface, although in the case of Ca2 + the adsorption may even provoke a sign reversal in the electrokinetic charge density. This effect is more pronounced the higher the pH. The analysis of the electrokinetic data by the Ohshima et al. model has allowed us to obtain the average number of charges per protein molecule. It can be observed that this parameter changes from a negative to a positive value as the Ca2 + concentration increases and is then probably adsorbed onto the protein surface. Acknowledgements Financial support from ‘Comisión Interministerial de Ciencia y Tecnologı́a’, project no MAT1999-0662-03-C02 y FEDER project no. 1FD97-1366 are gratefully acknowledged. The authors are very grateful to Joxe Sarobe and Jacqueline Forcada for providing the latex sample. Table 1 Dependence of net charge per protein molecule (zp) on pH and CaCl2 concentration CaCl2 (M) zp at pH 7.2 zp at pH 5.8 1.16×10−3 5.1×10−3 1×10−2 5×10−2 7.5×10−2 −3.0 −2.7 −2.5 +5.1 +10.5 −1.9 −1.8 −1.7 −1.3 +8.2 J.A. Molina-Bolı́6ar et al. / Colloids and Surfaces B: Biointerfaces 21 (2001) 125–135 References [1] B.V. Derjaguin, L. Landau, D. Acta Phys. Chim. U.R.S.S. 14, (1941) 633; JETP1. (USSR) 15 (1945) 633. [2] E.J.W. Verwey, J.Th.G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948. [3] J.P. Chapel, J. Colloid Interface Sci. 162 (1994) 517. [4] G. Vigil, Z. Xu, S. Steinberg, J. Israelachvili, J. Colloid Interface Sci. 165 (1994) 367. [5] R.M. Pashley, J. Israelachvili, J. Colloid Interface Sci. 97 (1984) 446. [6] R.M. Pashley, J. Colloid Interfac Sci. 80 (1981) 153. [7] D.M. LeNeveu, R.P. Rand, V.A. Parsegian, Nature 259 (1976) 601. [8] E.A. Vogler, Adv. Colloid Interface Sci. 74 (1998) 69. [9] J.N. Israelachvili, Chem. Scr. 25 (1985) 7. [10] H.K. Christenson, J. Dispersion Sci. Technol. 9 (1988) 171. [11] R.M. Pashley, J. Colloid Interface Sci. 83 (1981) 531. [12] R.M. Pashley, Adv. Colloid Interface Sci. 16 (1982) 57. [13] H.J. Modi, D.W. Fuerstenau, J. Phys. Chem. 61 (1957) 640. [14] R.J. Hunter, Zeta Potential in Colloid Science. Principles and Applications, Academic Press, London, 1981. [15] H. Ohshima, S. Ohki, Biophys. J. 47 (1985) 673. [16] H. Ohshima, T. Kondo, Colloid Polym. Sci. 264 (1986) 1080. [17] H. Ohshima, M. Nakamura, T. Kondo, Colloid Polym. Sci. 270 (1992) 873. [18] H. Tamai, A. Fujii, T. Suzawa, J. Colloid Interface Sci. 118 (1987) 176. [19] T.A.J. Payens, J. Dairy Res. 46 (1979) 291. [20] Z. Saito, Neth. Milk Dairy J. 27 (1973) 143. . 135 [21] J.A. Molina-Bolı́var, F. Galisteo-González, R. HidalgoÁlvarez, Phys. Rev. E 55 (1997) 4522. [22] J.A. Molina-Bolı́var, F. Galisteo-González, R. HidalgoÁlvarez, J. Chem. Phys. 110 (1999) 5410. [23] J. Sarobe, J. Forcada, Colloid Polym. Sci. 274 (1996) 8. [24] J. Sarobe, J.A. Molina-Bolı́var, J. Forcada, F. Galisteo, R. Hidalgo-Álvarez, Macromolecules 31 (13) (1998) 4282. [25] A. Lips, E.J. Willis, J. Chem. Soc. Faraday I 67 (1971) 2979. [26] A. Lips, E.J. Willis, J. Chem. Soc. Faraday I 69 (1973) 1226. [27] R.W. Wunderlich, J. Colloid Interface Sci. 88 (1982) 385. [28] S. Levine, M. Levine, K.A. Sharp, D.E. Brooks, Biophys. J. 42 (1983) 127. [29] K.A. Sharp, D.E. Brooks, Biophys. J. 47 (1985) 563. [30] H. Ohshima, T. Kondo, J. Colloid Interface Sci. 116 (1987) 305. [31] J.A. Molina-Bolı́var, F. Galisteo-González, R. HidalgoÁlvarez, Colloids Surf. B: Biointerfaces 14 (1999) 3. [32] T.H.F. Tadros, Solid/Liquid Dispersions, Academic Press, New York, 1987. [33] R.K. Mishra, S. Shander, D.W. Fuerstenau, Colloids Surfaces 1 (1980) 105. [34] K.E. van Holde, Physical Biochemistry, 2nd edn, Prentice-Hall, Englewood Cliffs, New Jersey, 1985. [35] G.D. Douglas, D. Eric, H.W. Richard, J. Colloid Interface Sci. 108 (1985) 174. [36] H Sukuma, T. Ohshima, J. Kondo, J. Colloid Interface Sci. 133 (1989) 252. [37] H. Sukuma, T. Ohshima, J. Kondo, J. Colloid Interface Sci. 135 (1990) 455. [38] J. Buijs, J.W.T. Lichtenbelt, W. Norde, J. Lyklema, Colloids Surf. B: Biointerfaces 5 (1995) 11.
© Copyright 2026 Paperzz