Langmuir 1995,11, 1893-1898
1893
Rheology Control of Suspensions by Soluble Polymers Yasufumi Otsubo Center of Cooperative Research, Chiba University, Yayoi-cho 1-33,Inage-ku, Chiba-shi 263, Japan Received August 12, 1994. I n Final Form: February 6,199P The steady-flow and creep behavior was measured for suspensions flocculated by a soluble polymer. When a polymer chain attaches to the surface at several points, the adsorption is essentially irreversible. The suspensions flocculated by irreversible bridging are shear thinning over a wide range of shear rates. At low stresses, the deformation of bridges can accumulate elastic energy. As a result, the suspensions show viscoelastic responses with long relaxation times. The addition of surfactant decreases the fraction of segments adsorbed in trains and increases the reversibility of polymer adsorption. The bridges are constantly forming and breaking in a quiescent state. Since the polymer coils have the equilibrium conformation, the flow is Newtonian at low shear rates. When the surface is completely covered with surfactant, the nonadsorbing polymer coils give rise to depletion flocculationdue to attractive forces generated by exclusion of the free polymer from the interparticle space. The suspensions flocculated by depletion are also shear thinning. However, the particle bonds show little resistance with respect to the transverse bending force. Because of rapid dissipation of energy by the shear motion of particles, the suspensions behave as liquids with very weak elasticity. Thus, the rheologicalproperties of suspensions can be controlled by the affinity between the polymer chains and particle surface.
Introduction The addition of low concentrations of polymer often causes flocculation in colloidal suspensions by bridging, in which one polymer chain adsorbs onto two or more particles to bind them Polymer may attach to the surface a t several points along its chain. Since the displacement of segments is very slow and the chain may not be able to desorb simultaneously from all sites, polymer adsorption is essentially irreversible. The bridges between particles are not broken by thermal energy. Hence, the highly flocculated suspensions show elasticity a t very low frequencies or plasticity with an infinite viscosity a t low shear rate^.^-^ In high shear fields, the structural breakdown is progressively induced with increasing shear rate. The flow of suspensions flocculated by polymer bridging is shear thinning over a wide range of shear rates. The irreversibility of polymer adsorption arises from the multipoint attachment to the surface. When the particles are partially covered with surfactant, the fraction of loops which extend into the solution increases a t the expense of trains which are in direct contact with the surface. Since a surfactant molecule serves as a displacer, the adsorption-desorption can occur reversibly by Brownian motion. The reversibility is controlled by competition between polymer and surfactant adsorption. The reversible adsorption causes the polymer bridges to constantly form, break, and re-form in a quiescent state. In suspensions containing a soluble polymer of coil size comparable to the particle size, two particles can be connected by a deformable bridge. At shear rates where the time scale of coil extension in shear fields is longer than that of desorption, the flow becomes N e ~ t o n i a n . ~ ,The ' flow behavior of suspensions strongly depends on the adsorption-desorption kinetics which in turn is closely associated with the fraction of segments adsorbed in trains. Abstract published in Advance A C S Abstracts, May 15,1995. (1)Iler, R. K. J . Colloid Interface Sci. 1971,37,364. (2)Fleer, G.J.;Lyklema, J. J . Colloid Interface Sci. 1974,46,1. (3)Otsubo, Y.; Watanabe, K. J . Non-Newtonian Fluid Mech. 1987, 24,265. (4)Otsubo, Y.;Watanabe, K. J . Colloid Interface Sci. 1989,133,491. (5)Otsubo, Y.Langmuir 1990,6, 114. (6)Otsubo, Y.Langmuir 1992,8,2336. (7)Otsubo, Y.J . Rheol. 1993,37,799. @
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The most significant contribution of nonadsorbing polymer to the rheology is to increase the continuous phase viscosity. However, various theories8-10and experimental data1'-13 clearly indicate that under many conditions the flocculation of stabilized suspensions is induced by the free polymer in solution. The effect is referred to as depletion flocculation. When the concentration of free polymer exceeds some critical value, exclusion of the free polymer chains from the interparticle space into the bulk occurs. The concentration difference between the pure solvent in the gap and bulk solution produces an attractive potential between the particles, leading to flocculation. The suspensions flocculated by the depletion mechanism have been found to show shear-thinningflow a t low shear rates.14-16 An associative polymer, which consists of a nonadsorbing water-soluble backbone with grafted hydrocarbon arms, adsorbs onto the particles a t hydrophobic points along the chain. In the limit of very weak adsorbing groups, the associative polymer behaves as an nonadsorbing polymer. With many hydrophobes, a molecule behaves as a n adsorbing polymer and strong adsorption results in bridging attraction. The associative polymers may induce different interaction between particles, depending on the number of hydrophobes and adsorption strength. A statistical mechanical theory has been developed to predict the flocculation or phase separation of a colloidal suspension by associative polymer.17J8 The associative polymers have received increasing interest as rheology control agent^.'^!^^ (8) Asakura, S.; Oosawa, F.
J. Chem. Phys. 1954,22,1255. (9)Vrij, A. Pure Appl. Chem. 1976,48,471. (10)Gast, A. P.; Hall, C . K.; Russel, W. B. J . Colloid Interface Sci. 1983,96,251. (11)Patel, P. D.;Russel, W. B. J . Rheol. 1987,31,599. (12)Vincent, B.;Luckham, P. F.; Waite, F. A. J . Colloid Interface Sci. 1980,73,508. (13)deHek, H.; Vrij, A. J . Colloid Interface Sci. 1981,84,409. (14)Patel, P. D.;Russel, W. B. Colloids Surf. 1988,31,355. Tadros, Th. F. Faraday Discuss. Chem. SOC. 1983,76, (15)Heath, D.; 203. (16)Speny, P. R.;Hopfenberg, H. B.; Thomas, N. L. J . Colloid Interface Sci. 1981,82,62. (17)Santore,M.M.; Russel,W. B.; Prud'homme, R. K.Macromolecules 1989,22,1317. (18)Santore, M. M.; Russel, W. B.; Prud'homme, R. K.Macromolecules 1990,23,3821.
0 1995 American Chemical Society
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1894 Langmuir, Vol. 11, No. 6, 1995
The flow behavior of suspensions varies with types of flocculation mechanisms which are determined by the conformation of polymer chains. The important factor to control the rheology for suspensions containing a soluble polymer is the affinity between the polymer chains and particle surface.z1 The adsorption affinity can be controlled by the addition of small amounts of surfactant. A previous paperzz discussed the effects of surfactant adsorption on the rheological properties of suspensions in relation to the bridging conformation. The rheological properties have been explained by the dynamics of flocs constructed by permanent bridges due to irreversible adsorption and temporary bridges due to reversible adsorption. The present study is designed to provide more insight into the flocculation induced by soluble polymer chains. The attention is focused to the rheology control of suspensions by a soluble polymer.
Materials and Methods Materials. The suspensions were composed of styrenemethyl acrylate copolymer particles, poly(viny1alcohol),Triton X-100,and water. The pH value was adjusted with hydrochloric acid to pH 2. The diameter and density of copolymer particles were 240 nm and 1.13 x 103 kg m-3, respectively. Triton X-100 surfactant (Union Carbide Co.) is an ethoxylated octylphenol. Poly(viny1alcohol) (PVA)with a molecular weight of M, = 1 x 105obtained from Kanto ChemicalCo. was used as received.The radius of gyration of the polymer coil, Rg, is about 15 nm in aqueoussolutionat pH 2. The samplesuspensionswere prepared at a concentration of 30%by volume. The PVA and surfactant concentrations were in the range of 0-1.0% and 0-2.0%, respectively, by weight based on the water. The rheological measurements were carried out for the suspensionsstored at 25 "C for 1 day. Methods. Steady-flow properties were measured using a Couette geometry on a Rheometrics RFS I1 rheometer. The diameter of the bob and cup were 30 and 32 mm, respectively. The immersion length of the bob was 30 mm. The measuring t o 2.7 x lo2 s-l. Creep and shear rates p were from 1.7 x recovery were measured with a cone-and-plategeometry on a Haake RSlOO rheometer. The cone diameter was 60 mm, and the gap angle between the cone and plate was 4'. The stress was applied instantaneously, maintained for 60 s, and suddenly removed. The applied stresses were from 0.05to 2.0 Pa. All the measurements were carried out at 25 "C. Adsorption of PVA on the particle surface was measured with suspensions which contain surfactant. To determine the concentration of nonadsorbing polymer, the particles or flocs were separated by centrifugation at ZOOOg, and the viscosity of supernatant solution was measured. At high concentrationsof surfactant, the supernatant solutions were slightly turbid. On the assumption that the supernatant solution has the same mixing ratio of surfactant and polymer as the initial solution, the amount of adsorbedpolymer was calculatedfrom the residual polymer concentration. The final sedimentation volume gives the concentrationof the dispersedphase, from which the surface separation between particles can be estimated. Results and Discussion Figure 1 shows the shear rate dependence of viscosity for suspensions in 0.3 wt % PVA solutions containing surfactant at different concentrations. The 30 vol % suspensionwithout additives is electrostatically stabilized Pa s. The and Newtonian with a viscosity of 3.5 x addition of PVA causes a n increase in the viscosity, especially at low shear rates, and the flow is shear thinning. The shear-thinning flow can be explained by (19) Sperry, P. R.; Thibeault, J. C.; Kostansek, E. C. Adu. Org. Coatings Sci. Technol. Ser. 1985,9 , 1. (20) Santore, M. M.; Russel, W. B.; Prud'homme, R. K. Faraday Discuss. Chem. Soc. 1990,90, 323. (21) Ploehn, H. J.; Russel, W. B. Adu. Chem. Eng. 1990,15, 137. (22) Otsubo, Y. Langmuir 1994,10, 1018.
.-
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Figure 1. Shear rate dependence of viscosity for suspensions in 0.3 wt % PVA solutions containing surfactant at different concentrations: 0 (01,0.4 (01,0.7 (e),0.8 (01,1.0 (01,and 2.0 wt % (0).
I V
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Figure 2. Shear rate dependenceof viscosity for suspensions in 0.5 wt % PVA solutions containing surfactant at different concentrations: 0 (01,0.5 (01,0.7 (e),1.0 (01,1.5 (e),and 2.0 wt % (0).
the shear-induced breakdown offlocs connected by polymer bridges. When the particles are thoroughly covered with surfactant molecules, the polymer adsorption cannot occur. Since the suspensions can be dispersed to noninteracting particles, the flow becomes Newtonian at high surfactant concentrations. At intermediate concentrations of surfactant, the number of bridges connecting particles decreases with increasing surface coverage of particles with surfactant. This can reach a n inference that the surfactant adsorption causes the viscosity reduction over the entire range of shear rates. However, the effect of surfactant adsorption on the viscosity curve is not simple. The viscosity at a given shear rate increases, passes a maximum, and then decreases with increasing surfactant concentration. The most interesting feature is that the viscosity behavior at low shear rates changes from shear thinning to Newtonian when the surfactant concentration is increased above 0.7 wt %. Figure 2 shows the shear rate dependence of viscosity for suspensions in 0.5 wt % PVA solutions containing surfactant at different concentrations. At surfactant concentrations of 0.5 and 0.7 wt %, the suspension has a higher viscosity than that without surfactant. The
Langmuir, Vol. 11, No. 6, 1995 1895
Control of Suspensions by Soluble Polymers 1o2 h
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Figure 3. Shear rate dependence of viscosity for suspensions in 1.0wt % PVA solutions containing surfactant at different concentrations: 0 (O), 0.3 ((b), 0.7 (e),1.0 (a),1.5 (01,and 2.0 wt % (0).
viscosity increase suggests that the addition of a small amount of surfactant enhances the flocculating power of PVA. At 1.5wt % surfactant, each particle independently remains as a flow unit in shear fields, because the suspension is Newtonian with a low viscosity. It is considered that no colloidal attraction acts between particles. However, further addition of surfactant leads to a viscosity increase a t low shear rate, and the flow becomes shear thinning. It seems likely that the flocculation is induced when the surfactant concentration is increased to 2.0 wt %. Figure 3 shows the shear rate dependence of viscosity for suspensions in 1.0 wt % PVA solutions containing surfactant at different concentrations. In the range of 0.3-1.0 wt %, the increase in surfactant concentration causes a viscosity decrease a t low shear rates and a n increase at high shear rates. As a result, the viscosity behavior is converted from shear thinning to Newtonian profiles without a viscosity change at a shear rate of 1.5 s-l. Although the viscosity is drastically decreased at 1.5 wt % surfactant, further addition of surfactant induces striking shear-thinning flow a t low shear rates. It is obvious that the suspensions with surfactant a t high concentrations are flocculated systems. From Figures 1-3, the effect of surfactant on the flow behavior of suspensions flocculated by polymer bridging can be summarized as follows: (a) The viscosity is increased by the addition of a small amount of surfactant over the entire range of shear rates. (b)At intermediate concentrations, the increase in surfactant causes a viscosity decrease a t low shear rates and a n increase at high shear rates. The viscosity behavior changes from shear thinning to Newtonian. (c)When the surfactant is added beyond the concentration a t which the minimum viscosity is achieved, the viscosity a t low shear rates begins to increase and the flow becomes shear thinning. It can be accepted that, with increasing surfactant concentration, the sites available for polymer adsorption decrease and the polymer chains are forced to desorb from the particle surfaces. However, the overall effect of surfactant adsorption is to reduce the fraction of segments of a n adsorbed polymer in trains. The conformation and mobility of adsorbed polymer are affected by the surface coverage of particles with surfactant. The sedimentation and adsorption experiments will provide useful information about bridging conformation and floc structure.
0
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Surfactant con cent rat ion ( w t %)
Figure 4. Amount of adsorbed polymer plotted against surfactant concentration: 30 vol % suspensions in 1.0 wt % PVA solutions (0) and at saturation (0). Figure 4 shows the effect of surfactant concentration on the amount of adsorbed polymer for suspensions in 1.0 wt % PVA solutions. If the polymer chains completely adsorbed onto the particles in 30 vol % suspension, the adsorbed amount per unit surface area is 0.9 mg m-2 and in good agreement with the plateau level at low surfactant concentrations. Although all the polymer chains adsorb onto particles, the degree of bridging does not reach saturation. Using a 15 vol % suspension without surfactant, the saturated value of the adsorbed amount was determined to be 1.6 mg m-2. It must be stressed that the equilibrium adsorbance at saturation monotonously decreases with increasing surfactant concentration. However, since the amount of adsorbed polymer is not strongly affected by the addition of very small concentrations of surfactant for 30 vol % suspensions in a 1.0 wt % PVA solution, the viscosity change is small. For suspensions containing PVA a t lower concentrations, the viscosity is markedly increased a t surfactant concentrations of 0.4-0.7 wt %. When the degree of bridging is low, the small coverage of surface with surfactant leads to a striking increase in viscosity. It is important to understand the relation between the surface coverage and bridging structure. Figure 5 shows the coverage of particles with PVA and surface separation plotted against the surfactant concentration for suspensions containing 0.5 wt % PVA. The coverage is given by the ratio of the amount of adsorbed PVA to the adsorbance at saturation. If the adsorption process is irreversible, the values less than unity indicate that all the polymer chains adsorb onto the particles and the concentration of nonadsorbing polymer in the solution phase is zero. The surface separation H , which corresponds to the bridging distance of adsorbed polymer in flocculated suspensions, is determined from the mean distance between particle surfaces by the equation
where d is the particle diameter (=240 nm), C, the maximum particle concentration for random sphere
Otsubo
1896 Langmuir, Vol. 11, No. 6, 1995
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Surfactant concentration (wt O L ) Figure 6. Coverage of PVA and surface separation plotted against the surfactant concentration. packing, and C the particle concentration in the sediment. An increase in the surfactant concentration causes an
increase in the coverage, because the PVA adsorbance at saturation is decreased by surfactant adsorption. On the other hand, the surface separationincreases at first, passes a maximum, and decreases. When the attractive force between polymer chain and particle surface is strong, the chain lies flat on the surface. With decreasing polymer-surface interactions, the fraction of loops increases at the expenseof trains. The volume occupied by polymer coils at the surface and hence the bridging distance are increased by surfactant adsorption. A long loop extending from one particle easily adsorbs onto a particle in the other floc. Since the adsorbed chains with long loops efficiently make bridges, the flocculation can be promoted by surfactant adsorption, especially for suspensions in which the coverage of particle surface with PVA is relatively low. The viscosity increase a t low surfactant concentrations may be attributed to enhanced flocculation. In polymer bridging, the highly developed flocculation is not necessarily induced by strong interactions between polymer chains and particle surface. The maximum bridging distance is comparableto the diameter of an isolated polymer chain in solution. The polymer coils have the equilibrium conformationand the particles can be bridged by flexible coils. In the suspension with 1.0 wt % surfactant, the bridges are constantly forming and breaking by thermal energy. The Newtonian flow of flocculated suspensions arises from the reversible bridging. The adsorption affinity play an important role in controlling the bridging conformation and flow behavior. When the particle surfaces are thoroughly covered with surfactant, the polymer bridges are completely broken down and the viscosity shows a drastic drop. However, the viscosity data clearly indicate that further addition of surfactant gives rise to flocculation of suspension without polymer adsorption. When two particles approach a distance of separation less than twice the radius ofgyration of the free polymer chains in solution, the interparticle space is occupied by the pure solvent. The exclusion of the polymer chains from the interparticle space produces an attractive force between particles, which is proportional to the osmotic pressure of the polymer solution. When the volume concentration .of the free polymer exceeds a certain limiting value, depletion flocculation is induced. Since this destabilization process is essentially phase separation, the dense solid phase shows iridescence characteristic of an ordered ~ t r u c t u r e . ~ ~ - ~ ~ (23) Sperry, P.R. J . Colloid Interface Sci. 1982,87, 375. (24) Sperry, P.R. J . Colloid Interface Sci. 1984,99, 97.
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2.0 Surfactant concentration (wt %) Figure 6. Phase separation boundary for 30 vol % suspensions: phase-separated system, the bottom of which shows iridescence (0);system with two layers consisting of sediment of flocs and supernatant solution ( x 1. To clarify the flocculation mechanism at high surfactant concentrations, the phase separation behavior was examined for suspensions stored in a quiescent state for more than 6 months. Figure 6 shows the phase separation boundary for 30 vol % suspensions. The suspensions, in which the iridescent phase appears a t the bottom of systems, are regarded as phase separated. The phase separation occurs when both the particle and polymer concentrations exceed some critical values. In depletion flocculation by nonadsorbing polymer, the suspension results in phase separation into particle-rich and polymerrich phases. However, the PVA chains have weak affinity for the surface of copolymer particles. Therefore, the suspensions containing surfactant at low concentrations can be separated into three layers: the iridescent solid, opaque and viscous liquid, and very slightly turbid solution. Irrespective of initial composition, the particle concentration of the iridescent phase is about 55 ~ 0 1 % . The opaque liquid consists of the sediment of flocculated particles, the concentration of which is about 30 vol %. Since the suspensions are flocculated by two different mechanisms, the phase separation and sedimentation processes are very complicated. Pate1 and Russell1have determined the phase diagram for suspensions of polystyrene particles with a diameter of 240 nm in a solution of dextran polymer with a radius of gyration of 15.8 nm. At a particle concentration of 30 vol %, the calculated value of the limiting free polymer concentration at which the phase separation occurs is about 17 ~ 0 1 % This . corresponds to 0.3 wt % PVA in the suspensions studied. Since the phase separation takes place at 0.3 wt % PVAfor suspensions in which the particle surface is completely covered with surfactant, the experimental result in the present study agrees with the prediction. However, the iridescent phase is formed below the full coverage of surface with surfactant. Under conditions where the adsorption and desorption of polymer chains reversibly take place by Brownian motion, the attractive force between two particles is generated once the polymer coil is excluded from the interparticle space. We consider the phase separation behavior in connection with the depletion free energy for suspensions flocculated by bridging. As a simplified approach, the depletion free energy of attraction Gdepcan be given by the expression*Sz6 (25) Gast, A. P.; Hall, C. K.; Russel, W. B.J . Colloid Interface Sci. 1986,109, 161. (26) Asakura, S.;Oosawa, F.J . Polym. Sci. 1968,37,183.
Control of Suspensions by Soluble Polymers
GdedkT= -(xN412)(2Rg- HI2(3d + 4Rg + H)
Langmuir, Vol. 11, No. 6,1995 1897 (2)
where kT is thermal energy, Npthe number density of polymer molecules. The suspension containing 1.0 wt % PVA and 0.7 wt % surfactant is phase-separated, although the flow is nearly plastic at low shear rates due to irreversible bridging. The concentration of nonadsorbing polymer is about 0.35 wt % from Figure 4. The surface separation H being taken as 20 nm, the Gdepis estimated to be about 0.3 kT. T a d r o ~have ~ ~ discussed ,~~ the relation between the Bingham yield stress tg and depletion free energy for suspensions flocculated by depletion through the following equation
(3) where @ is the volume fraction of particles and z the coordination number. Assuming two values of z of 8 and 6, the yield stresses are determined as 0.20 and 0.15 Pa, respectively. The flow curve with a slope of -1 a t low shear rates gives the yield stress of about 0.2Pa. Although the flocs are partially constructed by irreversible bridging, the stress induced by depletion is comparable to that required to break the permanent bridges. Therefore, the phase separation is possible for suspensions flocculated by bridging when the attractive forces are reduced by surfactant adsorption. Although both the suspensions flocculated by irreversible bridging and depletion are shear thinning at low shear rates, the mechanical properties of bond connecting two particles are quite different. Creep and recovery experiments provide understanding the deformation of flocs and force transmission between particles. Figure 7 shows the creep and recovery curves at shear stresses of 0.1, 0.2, and 0.5 Pa for a suspension in a 1.0 wt % PVA solution. The strain curve comprises three regions: instantaneous, retardation, and constant rate. At the longest times, the strain linearly increases with time. The constant rate is due to viscous flow. The instantaneous deformation on the application or removal of stress is a manifestation of elasticity. The suspension behaves as a n elastic liquid. For the same suspension, the creep and recovery curves a t shear stresses of 1.0 and 2.0 Pa are shown in Figure 8. At high stresses, the strain rapidly increases. Although the instantaneous recovery appears after the removal of stress, the elastic effect is very weak. With increasing shear stress, the behavior becomes more liquidlike with a dominating viscous contribution to the total strain. The viscoelastic responses of suspensions flocculated by irreversible bridging are markedly nonlinear even at low stresses. Figure 9 shows the creep and recovery curves a t shear stresses of 0.1 and 0.2 Pa for a suspension containing 1.0 wt % PVA and 0.7 wt % surfactant. The recovery is very small, and the suspension is characterized as a liquid with weak elasticity. The differencebetween two curves implies the changes of the flow mechanism. From Figure 3, the suspension is shear thinning a t low shear rates and nearly Newtonian a t high shear rates. The flocs may be constructed by temporary bridges due to reversible adsorption and permanent bridges due to irreversible adsorption. The pemanent bridges are broken down on the application of shear, resulting in shear thinning, whereas the temporary bridges are responsible for Newtonian flow. When subjected to high shear fields, the irreversible bridges are broken down to a great extent. The resistance to flow a t 0.2 Pa arises from the flocs (27) Tadros, "h.F. Langmuir 1990,6, 28. (28) Tadros, Th. F.; Zsednai, A. Colloids Su$. 1990,49,103.
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Figure 8. Creep behavior at stresses of 1.0 and 2.0 Pa for suspension in a 1.0 wt % PVA solution.
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constructed through temporary bridges. With increasing conversion of permanent bridges into temporary ones by surfactant adsorption, the elastic effect is diminished. Figure 10 shows the creep behavior a t 0.05 Pa for suspensions containing 1.0 wt % PVA and surfactant at concentrations of 1.0 and 2.0 wt %. From Figure 3, the flow of suspension with 1.0 wt % surfactant is Newtonian a t low shear rates because the particles are connected only by the temporary bridges. At 2.0 wt % surfactant, the complete desorption of PVA gives rise to depletion flocculation and the flow becomes shear thinning. Although the flow profiles in steady shear are different, the creep curves are ofthe same type. Since the strain linearly increases with time and does not show instantaneous recovery, the suspensions are purely viscous fluids without
Otsubo
1898 Langmuir, Vol. 11, No. 6, 1995
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.-= 2
2
5 ; 1
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t
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Figure 10. Creep behavior at a stressof0.05 Pa for suspensions containing 1.0 w t % PVA and surfactant at different concentrations: 1.0 (-1 and 2.0 wt % (- -1.
elasticity. The deformation of flocs in low shear fields can hardly accumulate the elastic energy. The factor determining the creep and flow behavior in the zero shear limit is the lifetime and vector nature of the bond. In reversible adsorption, the bridges are constantly forming and breaking in a quiescent state. The coil connecting two particles is extended in shear fields and contributes to energy storage. However, the Newtonian flow suggests that the time scale of coil extension by shear is much longer than that of desorption. Because of short relaxation time, the rheological response of suspensions flocculated by reversible bridging is purely viscous. In irreversible bridging, the chain lies flat on the surface and the polymer coil forms a rigid bridge. The flocs behave as solids with high modulus. Therefore, the suspensions flocculated by irreversible bridging show
typical viscoelasticresponses. In the elastic flocs the bonds transmit central and transverse forces. The local elastic constant of the bond is given as a set of central and transverse elastic constants. In depletion flocculation, the attractive force between particles is generated by the osmotic pressure. The bonds show little resistance with respect to transverse bending forces. Indeed, the lack of energy barrier for transverse motion is essential in development of a n ordered lattice. Since the strain energy is rapidly dissipated by the transverse or shear motion of the particles, the suspensions flocculated by depletion are liquids with very weak elasticity. The difference in creep behavior between two shear-thinning suspensions may be attributed to the difference in elastic properties for bond bending.
Conclusions The flow of suspensions flocculated by irreversible bridging is shear thinning over a wide range of shear rates. At low stresses, the deformation of bridges can accumulate the elastic energy. The suspensions show viscoelastic responses with long relaxation times. The addition of a small amount of surfactant enhances the reversibility of polymer adsorption. Since the bridges are constantly forming and breaking by Brownian motion, the flow becomes Newtonian. When the surface is completely covered with surfactant, the nonadsorbing polymer coils give rise to depletion flocculation. The flocculated suspensions are shear thinning. However, the particle bonds show little resistance with respect to transverse bending forces. Since the strain energy is rapidly dissipated by the shear motion of particles, the suspensions flocculated by depletion are viscous liquids with very weak elasticity. LA9407323
