Effect of Surfactant on the Bridging Conformation of Associating Polymer and Suspension Rheology

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1 Article Nihon Reoroji Gakkaishi Vol.35, No.1, 27~34 (Journal of the Society of Rheology, Japan) 2007 The Society of Rheology, Japan Effect of Surfactant on the Bridging Conformation of Associating Polymer and Suspension Rheology Masashi KAMIBAYASHI, Hironao OGURA, and Yasufumi OTSUBO * Department of Urban Environment Systems, Faculty of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba-shi, Japan (Received : October 16, 2006) Associating polymers which consist of hydrophilic long-chain molecules containing a small amount of hydrophobic groups(hydrophobes) behave as flocculants in aqueous suspensions. The effects of surfactant on the rheological behavior are studied for latex, silica, and mixed suspensions flocculated by associating polymer. Because the hydrophobes are adsorbed onto hydrophobic surfaces and water-soluble chains onto hydrophilic surfaces, two single suspensions are highly flocculated by a bridging mechanism. In latex suspensions, the surfactant molecules force to desorb the polymer chains from the particles and at the same time enhance the micellar formation between the adsorbed chains. As a result, the flow becomes shear-thickening due to the elastic forces generated in extended multichain bridges under shear fields. In silica suspensions, the additions of surfactant cause the viscosity increase which may be attributed to enhancement of micellar formation between the adsorbed chains. By mixing the silica and latex suspensions, the viscosity is substantially reduced and the flow becomes nearly Newtonian. The associating polymer in complex suspensions acts as binder between the silica and latex particles. The hetero-flocculation which leads to the formation of composite particles may be responsible for the viscosity reduction of complex suspensions. Key Words: Associating polymer / Complex suspensions / Hetero-flocculation / Polymer bridging / Shear-thickening flow 1. INTRODUCTION Associating polymers are hydrophilic long-chain molecules to which small amounts of hydrophobic substituents, so-called hydrophobes are incorporated. In aqueous solution, the hydrophobes tend to aggregate and create three-dimensional network which gives rise to interesting rheological effects. 1-3) The associating polymers have received increasing interests as rheology control agents for paints and coatings over the last two decades, 4-7) because they can impart appropriate rheological properties to water-borne latex suspensions. The major advantage is the ability to produce high viscosity with Newtonian flow profiles over a wide range of shear rates, in contrast to traditional thickeners such as cellulose polymers. Basically the associating polymers behave as flocculants in latex suspensions. Since the hydrophobes can be adsorbed onto the hydrophobic surfaces, the suspensions are flocculated by bridging at low polymer concentrations. Under limited conditions at relatively high concentrations, the depletion flocculation is induced 8,9) in similar manner that the suspensions containing non-adsorbed polymer are * To whom correspondence should be addressed. yas.otsubo@faculty.chiba-u.jp flocculated. 10,11) In previous papers 12-14), we have studied the effects of associating polymers on the rheological properties of latex suspensions and proposed two bridging models. One is the direct bridging of a single chain, in which two hydrophobes are adsorbed onto different particles to bind them together. The other is the multichain bridging, in which the particles are connected by linkage of interchain associations. When the nonionic surfactant is added above some concentration, the rheological values such as viscosity, elasticity, and relaxation time are decreased due to the ruptures of polymer bridges by surfactant adsorption onto the particle surfaces. In adsorption of associating polymers onto hydrophilic surfaces, the chain may adopt a conformation with the watersoluble backbone attached to the particle surfaces. The adsorption of associating polymers also causes flocculation in silica suspensions by multichain bridging. Since the nonionic surfactants have similar molecular structures to hydrophobes, they can contribute to micelle formation by association with hydrophobes ) The hydrophobes extending from the chains adsorbed onto different particles can form micelles by association with surfactant molecules. Therefore, the viscosity of silica suspensions is increased by surfactant due to the 27

2 Nihon Reoroji Gakkaishi Vol enhancement of particle-particle bonds. 19) The adsorption conformation of associating polymer and flocculation mechanisms vary depending on the surface chemistry of the particles. It is essential to understand the relationships among the adsorption interactions, bridging conformation and suspensions rheology. In a previous paper 20), we also reported the rheology of suspensions consisting of two kinds of particles with hydrophilic and hydrophobic surfaces. The important finding is that when the silica and latex suspensions are mixed, the viscosity is drastically reduced. The associating polymer in complex suspensions acts as binder between the silica and latex particles, because the hydrophobes are adsorbed onto the hydrophobic surfaces and water-soluble chains onto the hydrophilic surfaces. The hetero-flocculation leads to the formation of composite particles in which the silica particles are covered with a layer of latex particles. The present study is designed to provide more insight into the hetero-flocculation induced by associating polymers. The rheology of complex suspensions will be discussed in relation to bridging conformation. 2. EXPERIMENTAL 2.1 Materials The suspensions were composed of fine particles, associating polymer, surfactant, and water. The particles were silica and styrene-methyl acrylate copolymer latex. The silica particles with a diameter of 1.3 μm and density of kgm 3 were manufactured by Catalysts and Chemicals Industries Co., Ltd. and used as received. The latex particles were formed by emulsion copolymerization with a styrene/methyl acrylate monomer ratio of 40/60, the diameter and density of which were 240 nm and kgm 3, respectively. The associating polymer was hydrophobically modified ethoxylated urethane (HEUR)(RM-825 from Rohm and Haas), the molecular weight of which was about The hydrophobes are incorporated on the ends of molecule as terminal groups. The surfactant was an ethoxylated octylphenol(triton X-100 from Union Carbide Co.). The suspensions were prepared at a particle concentration of 30 % by volume. The polymer and surfactant concentrations were in the range of % by weight based on the water. The complex suspensions were prepared by mixing the silica and latex suspensions that contain the additives at the same concentration. The composition of complex suspensions is expressed as the mixing ratio of latex(w L ) and silica(w S ) suspensions. The rheological measurements were carried out after the suspensions were stored at room temperature under gentle shear on a rolling device for one week. 2.2 Measurements Steady-shear viscosity and dynamic viscoelastic properties were measured using a parallel plate geometry on a stresscontrolled rheometer(haake Rheo-Stress RS100). The diameter of plates was 35 mm and the gap between two plates was 0.5 mm. The measuring part was surrounded with a glass cover for preventing the evaporation of solvent. The shear rates varied from 2.0 to s 1 in steady-flow measurements. The dynamic viscoelasticity was measured as a function of frequency at small strains in the linear regions and as a function of strain at a constant frequency. The frequencies were from to s 1 and strain amplitudes were from to Since the suspensions were sheared at s 1 for 300 s to give the initial conditioning prior to measurements, the results were highly reproducible. The temperature was 25 C for all runs. Adsorption of polymer on the particle surface was determined by the sedimentation experiments. To calculate the concentration of non-adsorbed polymer, the particles or flocs were separated by centrifugation at 3000 g for more than 5 h. The final sedimentation volume gives the concentration of the dispersed phase, from which the surface separation between particles in the flocs can be determined. 21) The amounts of polymer adsorbed on the particles were calculated from the residual polymer concentrations which were determined through the viscosity reduction. 3. RESULTS AND DISCUSSION 3.1 Effect of Associating Polymer on the Rheology of Single Suspensions Figure 1 shows the shear rate dependence of viscosity for latex and silica suspensions prepared with HEUR solutions at different concentrations. Both suspensions without additives are Newtonian with low viscosity. The addition of associating polymer results in an increase in viscosity and the overall flow profile becomes shear-thinning. The suspensions may be highly flocculated in the presence of associating polymer. It is accepted for the flow curves of ordinary flocculated suspensions that with increasing degree of flocculation the viscosity increases and the shear-thinning tendency becomes striking. When the flocculated structures are fully developed over the system, the viscosity curves are correlated by a straight line, the slope of which is -1 on the log-log plot. The 28

3 KAMIBAYASHI OGURA OTSUBO : Effect of Surfactant on the Bridging Conformation of Associating Polymer and Suspension Rheology flow behavior of silica suspensions can be characterized nearly plastic at HEUR concentrations above 1.0 wt%. However, for latex suspensions the viscosity level appears to reach the saturation at HEUR concentrations around 1.5 wt%. When the flocculation level approaches the saturation, the viscosity increase at low shear rates is depressed and the slope of the curve is decreased. The Newtonian flow profiles and unique effects of polymer concentration are already reported in our previous papers. 12,13) Figure 2 shows the frequency dependence of storage modulus for two single suspensions prepared with HEUR solutions at different concentrations. The storage modulus of silica suspensions is independent of frequency and the elastic component is predominant over the entire range. In general, the suspensions at low degree of flocculation consist of a collection of discrete flocs. In more flocculated suspensions, the flocs cease to be discrete, and above some critical level a network structure is constructed. When the network of unbounded flocs is built up, the flocculated suspensions respond elastically at low frequencies. The plateau in the frequency-dependent curve of dynamic viscoelastic functions for silica suspensions indicates the existence of threedimensional structures of unbounded network. 22) On the other hand, the modulus of latex suspensions rapidly decreases with decreasing frequency. The elastic energy stored in the flocculated structure is very rapidly dissipated even at high degree of flocculation. The same rheology can be seen from the nearly Newtonian flow profiles at low shear rates in Fig. 1. It must be stressed that the latex suspensions behave as liquids in long time scales. To understand the flocculation mechanism, the adsorption of HEUR on the particle surfaces was measured from the residual polymer concentrations in supernatant solutions. The adsorbance on the silica particles is determined to be 20 mg/(gparticles). Because this corresponds to about 1.8 wt% polymer, all polymer chains are considered to be adsorbed onto the particle surfaces in the silica suspensions. The adsorbance of associating polymer onto the latex particles is estimated to be 0.8 mgm 2. This value corresponds to about 0.8 wt% polymer. Therefore, the flocculated structures can be fully developed over the system, when the polymer concentration is increased up to 1.0 wt%. We can see a good relation between the adsorption behavior and viscosity behavior. Since the flocculation of suspensions is induced by adsorption of HEUR polymer, the mechanism of flocculation may be polymer bridging ) In silica suspensions, the flocculation is induced by adsorption of the water-soluble backbone onto the hydrophilic surfaces whereas in latex suspensions the adsorption of the hydrophobes to the hydrophobic surfaces leads to flocculation. Fig. 1. Shear rate dependence of viscosity for latex (open symbols) and silica (filled symbols) suspensions prepared with HEUR solutions at different concentrations: 0.5 (, ); 1.0 (, ); 1.5 wt% (, ). Fig. 2. Frequency dependence of storage modulus for latex (open symbols) and silica (filled symbols) suspensions prepared with HEUR solutions at different concentrations: 0.5 (, ); 1.0 (, ); 1.5 wt% (, ). 29

4 Nihon Reoroji Gakkaishi Vol Effect of Surfactant on the Polymer Bridging and Rheology of Single Suspensions Figure 3 shows the shear rate dependence of viscosity for latex suspensions in 1.0 wt% HEUR solutions containing surfactant at different concentrations. According to the adsorption experiments, the flocculation level may be very high. The addition of very small amounts of surfactant causes the reduction of viscosity in the whole range of shear rates. From this result, the monotonous decrease of viscosity with increasing surfactant concentration can be expected, but the effect of surfactant on the viscosity behavior is very complicated. The most interesting feature is that the suspensions containing surfactant at concentrations wt% show shear-thickening flow. In shear-thickening region, with increasing surfactant concentration, the viscosity decreases at high shear rates and increases at low shear rates. The surfactant influences the viscosity in two opposing ways depending on the shear rate. Figure 4 shows the shear rate dependence of viscosity for latex suspensions in 0.5 wt% HEUR solutions containing surfactant at different concentrations. Because of low concentration of polymer, the flocculation still does not reach the saturation. The suspensions also show the shear-thickening flow in the presence of surfactant. Compared with suspensions containing 1.0 wt% HEUR polymer, the viscosity enhancement in shear-thickening region is much more striking. The shear rate at the onset of viscosity increase decreases with increasing surfactant concentration. It is of interest to note that the viscosity at shear rates around 5 s 1 and 10 2 s 1 seems independent of surfactant concentration, while the shear thickening patterns are strongly influenced. Figure 5 shows the shear rate dependence of viscosity for silica suspensions in 0.5 wt% HEUR solutions containing surfactant at different concentrations. From the concentration dependence of viscosity behavior shown in Fig.1, the flocculation level is low at HEUR concentration of 0.5 wt%. The viscosity increases over the entire range of shear rates with increasing surfactant concentration. In the absence of associating polymer, the viscosity behavior of suspension was not influenced by surfactant. Therefore, the surfactant does not directly contribute to the bond formation between silica particles, but enhances the flocculating power of associating polymer. Fig. 4. Shear rate dependence of viscosity for latex suspensions in 0.5 wt% HEUR solutions containing surfactant at different concentrations: 0( ), 0.2( ), 0.3( ), 0.5( ), 0.7( ), 1.0 wt%( ). Fig. 3. Shear rate dependence of viscosity for latex suspensions in 1.0 wt% HEUR solutions containing surfactant at different concentrations: 0( ), 0.2( ), 0.7( ), 1.0 wt%( ). Fig. 5. Shear rate dependence of viscosity for silica suspensions in 0.5 wt% HEUR solutions containing surfactant at different concentrations: 0( ), 0.3( ), 0.5( ), 0.7( ), 1.0 wt%( ). 30

5 KAMIBAYASHI OGURA OTSUBO : Effect of Surfactant on the Bridging Conformation of Associating Polymer and Suspension Rheology As an overall effect, the additions of surfactant lead to the viscosity decrease in latex suspensions and increase in silica suspensions. The contradictory effects of surfactant on the suspension rheology arise from the different surface properties of particles. In latex suspensions, the interparticle bonds are constructed by hydrophobe adsorption onto particles and micellar formation between adsorbed chains. The surfactant molecules have strong affinity for latex particles. When the latex particles are partially covered with surfactant, the sites available for polymer adsorption decrease and the polymer segments are forced to desorb from the particle surfaces. The surfactant molecule serves as a displacer. Therefore, the chains may adopt a stretched conformation with only one hydrophobe attached to the surface. The hydrophobes of associating polymers consist of long alkyl chains, the molecular structures of which are very similar to nonionic surfactants. Since the surfactant molecules can create micelles, the association processes of associating polymers may be strongly affected by surfactant. Many authors have reported that the viscosity of associating polymer solutions is increased by the additions of small amounts of surfactant. 3,15,17,18) Hence, the bridging density can be increased by the additions of small amount of surfactant. The complex effects of surfactant on the latex suspensions flocculated by associating polymer are attributed to a delicate balance of desorption of polymer chains and enhancement of micellar formation between particles. The effect of surfactant on the bridging conformation of associating polymer between latex particles is schematically expressed in Fig. 6(A). Figure 7 shows the strain dependence of storage modulus for latex suspensions in 1.0 wt% HEUR solutions containing surfactant at different concentrations. The storage and loss moduli of ordinary flocculated suspensions are constant at very low strains and drastically decrease with increasing strain. The sharp decrease of moduli can be related to the breakdown of internal structures. However, the storage modulus of the sample suspensions shows an increase, as the strain amplitude exceeds some critical levels. The suspensions are highly elastic under large strains. Presumably the increase of storage modulus in oscillatory shear reflects the same rheology as the shear thickening in steady shear. Based on the statistical mechanical model 26), the shear-thickening flow can be explained by the decrease in entropy of polymer chains in the network during extension under shear field. In previous papers, 27,28) the shear-thickening flow of suspensions flocculated by reversible bridging of non-associating polymers is discussed in connection with the elastic properties under large strains. To quantitatively describe the shear-thickening behavior, a nonlinear elastic model is derived. In a similar manner, the shear-thickening flow of latex suspensions can be primarily attributed to the elastic effect of extended bridges, because the highly elastic micelles and deformable flocs are built up in the presence of surfactant. When the multichain bridges are subjected to rapid extension at shear rates where the time scale of extension is much shorter than that of desorption of polymer chains, the extended bridges can generate the high resistance to flow. The restoring forces produced by rapid extension of flexible bridges are responsible for the shear thickening. Also, the intrinsic mechanism of viscosity increase for silica suspensions may be the interchain associations enhanced by the micellar formation of hydrophobes in the presence of surfactant. The adsorbance data clearly indicate that most polymer chains are considered to be adsorbed onto the silica Fig. 6. Bridging models of associating polymer in the presence of surfactant: (A) Conformation between latex particles; (B) Conformation between silica particles. Fig. 7. Strain dependence of storage modulus for latex suspensions in 0.5 wt% HEUR solutions containing surfactant at different concentrations: 0( ), 1.0 wt%( ). 31

6 Nihon Reoroji Gakkaishi Vol surfaces. Although the small amounts of non-adsorbed chains can remain in solution phase, the viscosity increase induced by surfactant may directly reflect the change in the flocculation structures of silica particles. In adsorption of associating polymers onto hydrophilic surfaces, the chain may adopt a conformation with water-soluble backbone attached to the silica particles. The dangling ends of the adsorbed chain can aggregate to make micelles. The micellar formation causes the multilayer adsorption of chains on isolated particles and the hydrophobic association between chains adsorbed on two close particles. The hydrophobes extending from the chains adsorbed onto different particles can be incorporated in one micelle to make the bridge. In concentrated suspensions, the particles can be connected by the multichain bridging. The bridging conformation of associating polymer between silica particles is schematically shown in Fig. 6(B). Because of increase in the strength of each bridge and bridging density over the system, the viscosity of suspensions is markedly increased. The association between the adsorbed chains and surfactant may be responsible for the reinforced flocculation. 3.3 Rheology of Complex Suspensions Figure 8 shows the shear rate dependence of viscosity for two single suspensions and complex suspensions with different mixing ratios in 0.5 wt% HEUR solution containing surfactant at 0.5 wt%. When two kinds of particles with different surface properties are dispersed in a liquid in ordinary Fig. 8. Effect of mixing ratio on the viscosity for complex suspensions in 0.5 wt% HEUR solution containing surfactant at 0.5 wt%: W S / W L = 0/1 ( ); 1/3( ); 1/2( ); 1/1( ); 1/0( ). conditions, the hetero-flocculation is easily induced, which results in the viscosity increase. However, the viscosity of sample suspensions is substantially reduced and the flow becomes nearly Newtonian by mixing. Before mixing, each single suspension is regarded as a highly flocculated system. It looks likely that the particles are completely dispersed in complex suspensions, as if the interparticle interactions are no longer present. The sedimentation experiments can be used as a tool for understanding of the floc structures in complex suspensions. The suspension with a mixing ratio of W S =1/2 yielded the sediment and clear supernatant solution at volume fractions of 0.52 and 0.48, respectively. The particle concentration in the sediment is 58 vol%. This value nearly corresponds to the maximum random packing of monodisperse spheres (63.5 vol). However, the latex suspensions without additives were not separated by centrifugation at 3000 g. Unless flocculation occurs, the latex suspensions exhibit very high stability against sedimentation. The sedimentation behavior implies that the complex suspensions are characterized as flocculated systems. The surface separation can be calculated from the mean distance between particle surfaces in the sediment. On the assumption that the silica particles are arranged in random sphere packing in the sediment, the obtained value is about 0.64 μm. The surface separation between silica particles is comparable to twice the diameter of latex particles. In adsorption of associating polymer, the watersoluble backbones have strong affinity for the hydrophilic surfaces and the hydrophobes for the hydrophobic surfaces. The hydrophobes extending from the chains adsorbed onto silica particles can be adsorbed onto latex particles. Since the associating polymer chain behaves like a binder, the heteroflocculation between silica and latex can be induced by a bridging mechanism. Due to the difference in the particle diameters, the silica particles can be covered with fine latex particles. As a result the hetero-flocculation leads to the formation of composite particles. 20) The associating polymer chains are adsorbed between silica and latex particles and hardly contribute to the colloidal interaction between complex particles. Therefore, the drastic reduction of viscosity is induced by formation of composite particles which are completely dispersed in the systems. Figure 9 shows the effect of surfactant concentration on the viscosity behavior for complex suspensions with a mixing ratio of W S =1/1 in 0.5 wt% HEUR solution. The viscosity with nearly Newtonian profiles increases with increasing surfactant concentration. The volume fraction of sediment 32

7 KAMIBAYASHI OGURA OTSUBO : Effect of Surfactant on the Bridging Conformation of Associating Polymer and Suspension Rheology formed by centrifugation was The suspension with W S / W L =1/1 is regarded as more flocculated systems than that with W S =1/2. Because of relatively high concentration of silica, the flocculation between silica particles can be generated in the former suspension. Referring back to Fig. 5, the viscosity of silica suspensions flocculated by associating polymer is increased by the additions of surfactant. Therefore, the surfactant effects on the viscosity increase in complex suspension with W S =1/1 can be attributed to the enhancement of micellar formation of hydrophobes extending from the chains adsorbed onto silica particles. 4. CONCLUSIONS (1) The addition of associating polymer causes the flocculation for both silica and latex suspensions. Because the flocculation is induced by the polymer adsorption, the flocculation mechanism is the polymer bridging. The flow of flocculated suspensions becomes shear-thinning in a wide range of shear rates. (2) For latex suspensions flocculated by associating polymer, the overall effect of surfactant is the reduction of viscosity. However, the surfactant molecule behaves as a displacer to desorb the polymer chains from the particle surfaces and at the same time enhances the micellar formation between the adsorbed chains. Therefore, the flow becomes shear-thickening in the presence of surfactant. Since the deformable flocs are built up by multichain bridges, the extended bridges can result in high resistance to flow due to the elastic effects. Fig. 9. Effect of surfactant concentration on the viscosity behavior for complex suspensions with a mixing ratio of W S =1/1 in 0.5 wt% HEUR solution: 0( ), 0.5( ), 1.0 wt%( ). (3) The viscosity of silica suspensions flocculated by associating polymer is increased by small amounts of surfactant. The associating polymer may adopt a chain conformation with water-soluble backbone attached to the surfaces on the silica particles. The viscosity increase may be attributed to enhancement of micellar formation between hydrophobes extending from the chains adsorbed onto different particles by surfactant. (4) By mixing the silica and latex suspensions which are highly flocculated by associating polymer, the viscosity is substantially reduced and the flow becomes nearly Newtonian. Since the hydrophobes are adsorbed onto the hydrophobic surfaces and water-soluble chains onto the hydrophilic surfaces, the associating polymer in complex suspensions acts as binder between the silica and latex particles. The hetero-flocculation which leads to the formation of composite particles may be responsible for the viscosity reduction of complex suspensions. REFERENCES 1) Jenkins RD, Silebi CA, El-Aasser MS, ACS Symp Ser, 462, 222 (1991). 2) Wang L, Tiu C, T, Liu TJ, Colloid Polym Sci, 274, 138 (1996). 3) Jiménez-Regalado E, Selb J, Candau F, Langmuir, 16, 8611 (2000). 4) Sperry PR, Thibeault JC, Kastanek EC, Adv Org Coatings Sci Technol, 9, 1 (1987). 5) Huldén M, Colloids Surf, 88, 207 (1994). 6) Pham QT, Russel WB, Lau W, J Rheol, 42, 159 (1998). 7) Antunes FE, Thuresson K, Lindman B, Miguel MG, Colloids Surf A, 215, 87 (2003). 8) Santore MM, Russel WB, Prud homme RK, Macromolecules, 23, 3821 (1990). 9) Santore MM, Russel WB, Prud homme RK, Faraday Discuss Chem Soc, 90, 323 (1990). 10) Asakura S, Oosawa F, J Chem Phys, 22, 1255 (1954). 11) Asakura S, Oosawa F, J Polym Sci, 37, 183 (1958). 12) Horigome M, Otsubo Y, Langmuir, 18, 1968 (2002). 13) Otsubo Y, Horigome M, Korea-Australia Rheol J, 15, 27 (2003). 14) Otsubo Y, Horigome M, Korea-Australia Rheol J, 15, 179 (2003). 15) Iliopoulos I, Wang TK, Audebert R, Langmuir, 7, 617 (1991). 16) Aubry T, Moan M, J Rheol, 40, 441 (1996). 17) Panmai S, Prud homme RK, Peiffer DG, Colloids Surf A, 147, 3 (1999). 18) Li Y, Kwak CT, Colloids Surf A, 225, 169 (2003). 19) Kamibayashi M, Ogura H, Otsubo Y, J Colloid Interface Sci, 290, 592 (2005). 33

8 Nihon Reoroji Gakkaishi Vol ) Kamibayashi M, Ogura H, Otsubo Y, J Rheol, (2006) in press. 21) Otsubo Y, Langmuir, 10, 1018 (1994). 22) Otsubo Y, Langmuir, 6, 114 (1990). 23) Iler RK, J Colloid Interface Sci, 37, 364 (1971). 24) Fleer GJ, Lyklema J, J Colloid Interface Sci, 46, 1 (1974). 25) Otsubo Y, J Colloid Interface Sci, 153, 584 (1992). 26) Vrahopoulou EP, McHugh AJ, J Rheol, 31, 371 (1987). 27) Otsubo Y, Langmuir, 8, 2336 (1992). 28) Otsubo Y, Langmuir, 15, 1960 (1999). 34

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