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Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging
Journal of Colloid and Interface Science 321 (2008) 294–301 www.elsevier.com/locate/jcis
Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging Masashi Kamibayashi, Hironao Ogura, Yasufumi Otsubo ∗ Department of Urban Environment Systems, Faculty of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba-shi 263-8522, Japan Received 9 October 2007; accepted 14 February 2008 Available online 21 February 2008
Abstract The steady-shear viscosity, dynamic viscoelasticity, and stress relaxation behavior were measured for suspensions of silica nanoparticles dispersed in aqueous solutions of poly(ethylene oxide) (PEO). The suspensions of silica with diameters of 8–25 nm show striking shear-thickening profiles in steady shear and highly elastic responses under large strains in oscillatory shear. Since the silica particles are much smaller than the polymer coils, one molecule can extend through several particles by intrachain bridging. Each polymer coil may remain isolated as a floc unit and the silica particles hardly connect two flocs. Therefore, the flow of suspensions is Newtonian with low viscosity at low shear rates. When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. The shear-thickening flow may arise from the elastic forces of extended bridges. But, the polymer chain is easily detached from particle surface by thermal energy because of large curvature of particles. As a result, the network structures are reversibly broken down in a quiescent state and the suspensions behaves as viscoelastic fluids with the zero-shear viscosity. © 2008 Elsevier Inc. All rights reserved. Keywords: Bridging flocculation; Shear-thickening; Silica nanoparticle; Suspension
1. Introduction Because of large size and high flexibility, the adsorption of polymer coils onto a solid surface is different in many aspects from that of small molecules. The most significant feature is that a polymer chain is attached in sequence separated by segments which extend into solution. Although the conformation of adsorbed layers depends on the thermodynamic conditions among the polymer, the solvent, and the particle surface, most segments reside in loops and tails in many cases of practical interests [1]. When the long loops extending from particles come into contact with surface of bare particles, the bonds of polymer chains are formed between particles. The flocculation in which one polymer chain adsorbs onto two or more particles to bind them together is referred to as polymer bridging [2,3]. The primary parameter that influences the bridging conformation and bond strength between particles is the adsorption energy of a * Corresponding author.
E-mail address: [email protected] (Y. Otsubo). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.02.022
segment at the particle interface. Since the fraction of segments of an adsorbed chain in trains varies with particle diameter, one of the important factors controlling the bridging structure is the particle diameter [3,4]. The adsorption of polymer chain onto the surface of large particles may be stronger than that of smaller particles due to the difference in the segment fraction of trains. In addition, more than one polymer molecule is required to bridge large particles, whereas for small particles, only a small segment of a polymer chain is required, and thus one molecule can extend through many bridges. Owing to the weak adsorption affinity and long-range interactions, significant changes in flocculation structures and bulk properties can be observed when the particles are decreased to nanosizes. In previous papers [5–7], we have systematically studied the rheological properties of suspensions flocculated by polymer bridging as a function of the adsorption affinity and particle diameter. In general, polymer adsorption is essentially irreversible, because the polymer chain may attach to the surface at several points and may not be able to desorb simultaneously from all sites. The bridges between particles are not broken in a quiescent state. Therefore, the highly flocculated
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suspensions show elasticity at very low frequencies or plasticity with an infinite viscosity at low shear rates. When the polymer chains do not have strong affinity for the surface, the fraction of loops increases at the expense of trains and this causes the adsorption–desorption process to reversibly occur. In suspensions, the bridges are constantly forming and breaking by thermal energy. It has been clarified that the viscosity behavior of suspensions can be converted from shear-thinning to Newtonian profiles by the additions of surfactant because of the decrease in adsorption affinity of polymer. In ordinary bridging processes, the surface separation of particles is in the range of 10–30 nm. The decrease in particle diameter also drastically influences the suspension rheology. Due to the unique floc structures in which many particles are connected by one polymer chain with coil conformation, the suspensions of nanoparticles show interesting rheological behavior including viscosity reduction by intrachain bridging [8] and irreversible viscosity increase by shear-induced bridging [9]. Accordingly it is of interest to understand the bridging conformation of polymer chains on nanoparticles. In the present paper, the size effects on the rheological properties are studied for suspensions of silica nanoparticles dispersed in polymer solutions. 2. Experimental 2.1. Materials The suspensions were composed of silica, poly(ethylene oxide) (PEO), and water. The silica particles were Cataloid-S manufactured by Catalysts and Chemicals Industries Co., Ltd. (Japan), the diameters of which were 8, 11, 18, 25, and 46 nm. The Cataloid-S series were supplied in the form of aqueous suspensions which were electrostatically stabilized. The pH values of mother suspensions were about pH 9 for 8–25 nm silica and pH 10 for 46 nm silica. Three PEO samples having molecular weights of Mw = 2 × 105 and 1 × 106 from Polysciences, Inc., and of Mw = 5 × 105 from Wako Pure Chemical industries, Ltd., were used as received. The radius of gyration, Rg , of an isolated polymer coil in solution can be calculated from the intrinsic viscosity. The mean size, 2Rg , determined for PEO in aqueous solution are 28, 35, and 47 nm in order of increasing molecular weight. The water used as the medium was purified so that its conductivity was decreased to less than 1.0 × 10−4 S m−1 . By adding aqueous solutions of PEO to the mother suspensions, the sample suspensions were prepared at silica concentrations up to 12% by volume. The polymer concentrations were in the range of 0.2–0.8% by weight based on the water. The rheological measurements were carried out after the suspensions were stored at room temperature under gentle shear on a rolling device for more than 3 days.
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and the gap between two plates was 0.8 mm. The measuring shear rates were from 3.0×10−1 to 3.0×102 s−1 in steady-flow measurements. In stress relaxation experiments, the stress decay function was measured after cessation of steady shear at different constant shear rates. The dynamic viscoelastic functions (storage modulus G and loss modulus G ) were measured as a function of frequency at a constant stress and as a function of stress at a constant frequency. The frequencies were from 1.6 × 10−1 to 2.5×101 s−1 and stress amplitude was from 2.0×10−1 to 5.0 × 102 Pa. The temperature was 25 ◦ C for all runs. Concentrated suspensions and emulsions often cause slip at solid boundaries in rheometers. The errors due to wall slip can be corrected by a technique proposed by Yoshimura and Prud’homme [10]. Their technique involves two measurements on a parallel plate geometry with different gap settings. If the wall slip is generated, the curves of shear stress versus apparent shear rate for different gaps have different profiles. Since the curves were almost the same, significant wall slip was not observed in this study. 3. Results Fig. 1 shows the shear rate dependence of viscosity for suspensions of 8 nm silica in 0.5 wt% solution of PEO with a molecular weight of Mw = 5 × 105 (designated PEO500 k ) at different particle concentrations. The measurements were carried out for each sample in a cycle of increasing and decreasing shear rate. The shear rate was exponentially increased and decreased in the range of 0.3 and 300 s−1 in a measuring time of 10 min. Since significant difference are not observed between the up-curve and down-curve, the viscosity behavior showed no time dependence. The flow of polymer solution without particles is Newtonian with a viscosity of 3.5 mPa s. The additions of silica particles cause the viscosity increase over the entire range of shear rates. At a particle concentration of 3 vol%,
2.2. Methods Steady-shear viscosity, stress relaxation after cessation of steady shear, and dynamic viscoelasticity were measured using a parallel plate geometry on a stress-controlled rheometer (Haake Rheo-Stress RS100). The diameter of plates was 35 mm
Fig. 1. Shear rate dependence of viscosity during a cycle of increasing (open symbols) and decreasing (filled symbols) shear rates for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at different particle concentrations: 0 (!, "); 3 (1, 2); 5 (E, F); 8 (P, Q); 12 vol% (e, a).
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Fig. 2. Shear rate dependence of viscosity for suspensions of 8 nm silica at a particle concentration of 8 vol% in solutions of PEO with Mw = 5 × 105 at different polymer concentrations: 0.3 (!); 0.5 (2); 0.7 (E); 0.8 wt% (Q).
the suspension shows a Newtonian flow profile. However, in contrast to ordinary flocculated suspensions which are shearthinning in a wide range of shear rates and often shows plastic responses at very low shear rates, the flow behavior for the suspensions containing silica particles at concentrations of 5 vol% and above is quite different. The flow is Newtonian even at low shear rates and the suspension behaves as a fluid. As the shear rate is increased, the viscosity abruptly begins to increase, goes through a maximum, and then markedly decreases. The shear rate at which the shear-thickening flow begins decreases with increasing particle concentration. The transition boundary from Newtonian to shear-thickening profiles lies on a straight line with a slope of about −1. The critical shear rate is inversely proportional to the Newtonian viscosity. Beyond the peak viscosity, the viscosity rapidly decreases. It looks likely that the shear rates at the peak are also approximated by a straight line with a slope of −1. Presumably an important factor controlling the shear-thickening behavior is the shear stress. For completely dispersed suspensions consisting of noninteracting particles, the relative viscosity, defined as the viscosity of suspensions divided by that of the medium, is considerably small, and flow is Newtonian at low particle concentrations. Although the flow is Newtonian at low shear rates, the viscosity rapidly increases with increasing particle concentration. The drastic increase in viscosity indicates that the silica suspensions are highly flocculated by PEO polymer. Fig. 2 shows the shear rate dependence of viscosity for suspensions of 8 nm silica at a particle concentration of 8 vol% in PEO500 k solutions at different polymer concentrations. All suspensions show shear-thickening flow at high shear rates. With increasing polymer concentration, the Newtonian viscosity at low shear rates rapidly increases and the shear rate at the onset of shear-thickening flow is decreased. The concentration effect of polymer is very similar to that of particles. But the viscosity level beyond the maximum is not strongly affected by the polymer concentration. The flow of markedly shear-thickening suspensions are apparently plastic with a constant stress at high shear rates. Fig. 3 shows the frequency dependence of storage G and loss G moduli for suspensions of 8 nm silica in 0.5 wt% so-
Fig. 3. Frequency dependence of storage (open symbols) and loss (filled symbols) moduli for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at particle concentrations of 8 (P, Q) and 12 vol% (e, a).
lution of PEO500 k at particle concentrations of 8 and 12 vol%. The measurements were carried out at a constant stress of 2 Pa in the linear viscoelastic range. Both moduli rapidly decrease with decreasing frequency, and at low frequencies the loss modulus is predominant. It is well known that the viscoelastic function of ordinary flocculated suspensions shows a plateau at low frequencies [5,11,12]. The plateau has been explained by an additional relaxation process due to flocculated structure of particles. However, the plateau region was not observed for all suspensions studied. The rapid drop of moduli can be connected with the Newtonian profile in steady flow experiments. The suspensions are characterized as elastic liquids with short relaxation times. Many structuring fluids such as suspensions and polymer solutions show nonlinear viscoelasticity under large deformation. At very low strains, the storage and loss moduli show very little dependence on the strain. Under large strains, the moduli are drastically decreased. The rapid decrease of moduli can be analyzed in relation to the dynamic processes of structural breakdown. To examine the nonlinear behavior, the dynamic viscoelasticity was measured under large deformation. Fig. 4 shows the stress dependence of storage modulus at different frequencies for suspension of 8 nm silica in 0.5 wt% solution of PEO500 k at a particle concentration of 12 vol%. The storage modulus is constant and the viscoelastic responses are linear at low stresses. When the stress is increased above some critical level, the storage modulus shows a rapid increase. It is commonly accepted that the shear-thinning flow and sharp drop of storage modulus under large deformation which is observed for flocculated suspensions can be attributed to the structural rupture induced by shear. Therefore, the increase of storage modulus in oscillatory shear which is called strain hardening effect may express the same rheology as the shear thickening in steady shear. The nanoparticle suspensions flocculated by polymer are highly elastic under large strains. For better understanding of the detailed mechanism of shearthickening flow, it is helpful to analyze the elastic properties as
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Fig. 4. Stress dependence of storage modulus at different frequencies for 12 vol% suspension of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 : 1.3 (!); 1.6 (2); 3.1 (E); 6.3 s−1 (Q).
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Fig. 6. Viscosity (open symbols) and relaxation time (filled symbols) plotted against the shear rate for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at particle concentrations of 8 (P, Q) and 12 vol% (e, a).
Fig. 7. Effect of particle diameter on the viscosity behavior for suspensions at a particle concentration of 10 vol% prepared with 0.8 wt% solution of PEO with Mw = 5 × 105 : 8 (!); 11(2); 18(E); 25(Q); 46 nm (e). Fig. 5. Stress relaxation after cessation of steady shear at 10 (!) and 100 s−1 (2) for suspension of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at a particle concentration of 8 vol%.
a function of the relaxation time in nonlinear regions. Fig. 5 shows the stress relaxation behavior after cessation of steady shear for suspension of 8 nm silica in 0.5 wt% solution of PEO500 k at a particle concentration of 8 vol%. The ratio of stress to shear rate at the limit of t = 0 corresponds to the steady-shear viscosity. The accurate data of stress relaxation were not measured at low shear because of the limitation of rheometer. Since the stress decay curve can be approximated as a straight line at long times, the stress relaxation is governed by the longest relaxation mechanism and the time-dependent function is expressed by the following equation: σ ∝ exp(−t/τm ),
(1)
where τm is the longest relaxation time. Fig. 6 shows the viscosity and relaxation time plotted against the shear rate for suspensions of 8 nm silica in 0.5 wt% solution of PEO500 k at
particle concentrations of 8 and 12 vol%. In Newtonian region, the stress relaxation is rapidly completed and the relaxation time can be estimated to be less than 1 s. Once the shear thickening takes place above the critical shear rates, the relaxation time is drastically increased by a factor of more than 10. At the maximum viscosity, the values are about 20 and 60 s for 8 and 12 vol% suspensions, respectively. In high viscosity region, the relaxation time is almost constant, independent of shear rate. Fig. 7 shows the effect of particle diameter on the viscosity behavior for suspensions at a particle concentration of 10 vol% prepared with 0.8 wt% solution of PEO500 k . The flow is Newtonian at low shear rates, irrespective of particle diameter. The Newtonian viscosity decreases, passes though a minimum and then increases with increasing particle diameter and this size effect on the viscosity behavior is very unique. The general agreement is that the reduction of particle diameter results in the enhancement of suspension viscosity. In suspensions consisting of noninteracting particles, the dynamic structure in shear fields is governed by the balance between Brownian motion and hydrodynamic forces [13,14]. Since the viscosity curve of suspensions is scaled on the Péclet number which represents the
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Fig. 8. Effect of molecular weight of PEO on the viscosity behavior during a cycle of increasing (open symbols) and decreasing (filled symbols) shear rates for suspensions of 8 nm silica at a particle concentration of 8 vol% in 0.5 wt% polymer solutions: 2 × 105 (!, "); 5 × 105 (1, 2); 1 × 106 (P, Q).
relative importance of shearing forces to Brownian diffusion, the viscosity at a given shear rate becomes higher for smaller particles. The colloidal interactions rapidly increase when the diameter is reduced to the order of nanometer. It is usually difficult to prepare the highly stabilized suspensions of nanoparticles [15–18]. In the sample suspensions, the lowest viscosity is obtained for the silica with diameters of 11 and 18 nm. With respect to the diameter effect on suspension rheology, the most interesting point is that the suspensions which give the lowest viscosity in Newtonian range show remarkable shear-thickening behavior. Although an indication of shear-thickening flow is observed for suspensions of silica with 8 and 25 nm diameters, the overall flow profiles are characterized as shear-thinning in a similar manner to suspension of 46 nm silica. The particle– particle interactions can be drastically changed at about 15 nm in nanoparticle suspensions flocculated by soluble polymers. Fig. 8 shows the effect of molecular weight of PEO on the viscosity behavior for suspensions of 8 nm silica at a particle concentration of 8 vol% prepared with 0.5 wt% polymer solutions. The viscosity behavior is obtained in a cycle of increasing and decreasing shear rate. The suspension prepared with PEO200 k solution is Newtonian with low viscosity. Presumably the flocculation level is very low. On the other hand, the suspensions prepared with PEO200 k and PEO1 M solutions show striking shear-thickening flow. For suspension prepared with PEO1 M solution, the accurate values of viscosity above shear rates of 10 s−1 were not measured, because the sample was expelled from the parallel-plate gap due to the normal stress effect. In addition, this suspension showed the hysteresis behavior and the measurements were repeated twice in the procedure that the maximum shear rate was increased. In the first cycle, the
shear rate was stepwise increased and decreased in the range of 0.2 and 2 s−1 in a shearing time of 30 s at each shear rate. Although the data are not shown in the figure, significant differences are not observed between the up-curve and down-curve. In the second cycle, the maximum shear rate is increased to 10 s−1 . The up-curve has almost the same profile as the viscosity curve below 2 s−1 in the first cycle. However, the viscosity of down-curve is increased as shown by filled circles in Fig. 8 and the hysteresis appears between two curves. When the suspension is kept at rest for more than 20 min after the viscosity measurements, the effects of shear history disappears and the initial viscosity curves are regained. The time-dependent behavior of viscosity suggests that the suspension containing PEO with very high molecular weights should have the long relaxation time. From Figs. 1–8, the effect of polymers on the suspension rheology can be summarized as follows: (a) The addition of small amounts of PEO causes an increase in viscosity and dynamic viscoelastic functions of silica suspensions. The PEO polymers act as flocculants. (b) The suspensions are Newtonian in the limit of zero shear rate and behave as liquids, irrespective of degree of flocculation. (c) When the silica particles with diameters of 8–25 nm are dispersed in aqueous solutions of PEO with molecular weights of 5 × 105 –1 × 106 , the suspensions show striking shear-thickening behavior in steady shear and strain hardening in oscillatory shear. 4. Discussion The shear-thickening flow can be observed for several types of suspensions. The highly concentrated suspensions consisting of particles without colloidal interactions show the shearthickening behavior followed by a discontinuous jump of viscosity or flow instability beyond a certain shear rate. In shear fields, the anisotropic structures are induced by twodimensional layering. However, the layered arrangement is unstable and is disrupted above a critical shear rate. Hoffman [19,20] has shown that the discontinuous viscosity jump arises from the structural breakdown of two-dimensional hexagonal packing to random arrangement. An alternate mechanism of shear-thickening flow for concentrated suspensions of noninteracting particles is the formation of large anisotropic aggregates induced by hydrodynamic forces [21,22]. This theory has been proposed through optical measurements based on a fact that the dichroism remains relatively constant during thickening processes. Therefore, the mechanisms of shear thickening are of two types: two-dimensional layering and hydrodynamic clustering. The latex suspensions flocculated by polymer bridging can generate the viscosity jump [23,24]. When the polymer adsorption reversibly takes place owing to the weak affinity for the particle surface, the polymer bridges are constantly forming, breaking and reforming by thermal energy. The suspensions flocculated by reversible bridging are Newtonian in the limit of zero shear rate. Because the particles can be bridged by a flexible polymer coil, the deformable flocs are built up over the systems. On the application of shear fields where the flexible
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bridges are highly extended within the lifetime, the extended bridges can lead to high resistance to flow due to the restoring forces. Hence, the flow becomes shear-thickening. In oscillatory shear, the storage modulus at a constant frequency shows a rapid increase when the strain is increased above a critical level. The shear-thickening behavior can be explained in connection with the nonlinear elasticity of flexible bridges [25]. The rheological properties of silica suspensions studied in the present work are very similar to those of latex suspensions flocculated by reversible bridging. So, the bridging flocculation may be a possible mechanism. To explain the shearthickening flow, the attention is focused on the polymer adsorption on nanoparticles and particle–particle interactions. Since the polymer adsorption is regarded as irreversible, the polymer bridges between particles are not broken down by thermal energy. Many authors have reported that the suspensions flocculated by irreversible bridging show shear-thinning flow in a wide range of shear rates. However, the diameters of particles employed in previous work on suspension rheology are larger than 50 nm. In the present paper we have observed the striking shear-thickening behavior for particles with diameters of 8–25 nm. One of the most important factor controlling the bridging structure and the resultant rheology is the particle diameter. In polymer adsorption on a solid surface, the thickness of the adsorbed layer is roughly in the range of 20–30 nm. When the particle diameter is decreased to 20 nm and below, one polymer chain can extend through many bridges. To provide more insight into the bridging conformation between nanoparticles, the discussion will be expanded by the use of shear-thickening suspension consisting of 8 nm silica at 8 vol% in 0.5 wt% solution of PEO500 k . The mean size of polymer coil in aqueous solution is about 35 nm and is much larger than that of particles. When the bridging flocculation is induced, the average number of particles which are bound by one polymer chain is estimated to be 6.2. Because of large curvatures of particles, the floc structures can be expressed by a model in which the particles are entrapped in polymer coils with spherical conformation. From the concentration dependence of viscosity, the overlapping concentration is estimated to be 1.2 wt% for aqueous solutions of PEO500 k . At 0.5 wt%, the silica particles hardly connect two polymer coils, but each polymer coil unit may remain isolated as a floc in the suspension. To support this explanation, the viscosity measurements were carried out for suspensions prepared with dilute polymer solution. Fig. 9 shows the concentration dependence of viscosity for suspensions of 8 nm silica in 0.3 wt% solution of PEO500 k . Generally the suspension viscosity monotonously increases with increasing particle concentration. But the viscosity of sample suspensions decreases at first, shows a minimum and rapidly increases. It must be stressed that the suspension viscosity at low concentrations is lower than that of medium. According to Einstein theory of suspension rheology, the increase in viscosity is attributed to the distortion of the velocity field in the vicinity of each particle. The addition of particles inevitably causes a viscosity increase of the liquid. Hence it seems difficult to explain the reduction of suspension viscosity by the previously established mechanisms such as hydrodynamic in-
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Fig. 9. Concentration dependence of viscosity for suspensions of 8 nm silica in 0.3 wt% solution of PEO with Mw = 5 × 105 . The broken line shows the Einstein prediction.
teractions and floc formation by colloidal forces. The 8 nm silica particles have an extremely large specific surface and can adsorb a large amount of polymer in suspension. As a first approach, a possible mechanism of viscosity reduction can be the decrease of polymer concentration in the solution phase by adsorption. However, the viscosity behavior is not scaled on the specific surface of particles, but the silica size is confirmed to be a primarily important factor in the viscosity reduction. In polymer solutions, the gross molecular structure is represented by a flexible coil with a radius of gyration Rg . The viscosity reduction in the presence of nanoparticles implies the decrease in radius of gyration of polymer coils. The silica nanoparticles act as binders, resulting in a contraction of the polymer coil. Fig. 9 is helpful to understand the floc model constructed by intrachain bridging. Now we will discuss the shear-thickening behavior of nanoparticle suspensions flocculated by polymer bridging. Although the nanoparticles are entrapped, the polymer coils may be flexible and the loops of adsorbed chain in an extended conformation. The interaction energy very rapidly increases as the separation between coils is decreased. Further flocculation in a quiescent state is retarded by steep repulsion and the viscosity of suspensions is very low at low shear rates. However, the flocs formed by intrachain bridging will be easily extended and compressed during rotation and collision in high shear fields. When enough kinetic energy is given to flocs by shear, the loops adsorbed on the particle comes into contact with the surface of favorably situated particle in the other floc and the floc–floc bonds can be formed by bridging. Due to the mechanical activation energy, the bridging flocculation is promoted in shear fields. Cabane et al. [26] have analyzed the shear-induced gelation of aqueous suspensions of silica nanoparticles in the presence of soluble polymer. Trough small angle neutron scattering, it is confirmed that the necklaces consisting a few particles bound to one polymer chain is stretched and the connections are formed between them in shear fields. On the basis of this
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explanation, the shear-induced bridging of nanoparticles may be acceptable. But the adsorption affinity of polymer on the nanoparticle surface is weak in this work. Since the bridging interactions between flocs is reversible in a quiescent state, the resultant structure in shear fields may be transient. The polymer chain is easily detached from particle surface by thermal energy and the decrease in shear rates gives no hysteresis for viscosity behavior. The shear-thickening flow without time dependence for nanoparticle suspensions is originated from flocculation by the shear-induced reversible bridging. The reversible bridges constructed in high shear fields are broken down in a quiescent state. The desorption of polymer chains from the particle surfaces governs the stress relaxation. The relaxation time determined from the stress decay curve after cessation of steady shear is considered to reflect the time scale of adsorption– desorption process in flocculated suspensions. The associating polymers are hydrophilic long-chain molecules which contain a small amount of hydrophobic groups. In aqueous solution, the hydrophobes tend to aggregate and create a bond between polymer chains by reversible associating interactions. When the polymer concentration is increased beyond some critical levels, a three-dimensional structure of transient network is constructed over the system. Due to intrachain and interchain associations, the aqueous solutions of associating polymers often show unusual rheological behavior [27,28]. One of the most interesting features is a shearthickening flow profile [29–32]. Shear flow serves to elongate the polymer chains and break some of the intrachain associations, forming interchain associations. Similarly, in the suspensions studied, the flow may increase the number of interchain bridging at the expense of intrachain bridging. The statistical mechanical network model for polymer solutions has shown [33,34] that the shear-thickening flow is induced by the decrease in entropy of polymer chain in the network during extension by shear. Referring to these models, the three-dimensional network structure of flocs must be developed to span the system for shear-thickening behavior of suspensions. The threedimensional structures can transmit the forces through the polymer bridges over the system. Therefore, the elastic responses observed for shear-thickening suspensions can be coupled with the network structure of infinite flocs. Although the elasticity arises only from bridge between two coils which contain several particles, the development of three-dimensional network is required for appearance of elasticity as bulk responses. Since the mechanical properties of flexible bridges are analogous to the rubbery elasticity, the storage modulus markedly increases in extended states as shown in Fig. 4. The nonlinear elasticity of polymer bridges plays an important role in controlling the shear-thickening flow. The importance of extensional behavior of polymer chains is demonstrated for suspensions of noninteracting particles in polymer solutions. Scirocco et al. [35] have shown that the strong extensional flow of thin liquid layer between particles contributes to shear-thickening flow even at low particle concentrations. The stress-controlled nature of shearthickening flow can be explained by the extensional properties of polymer solution. The high extensional viscosity due to chain extension is also reported for suspension of nanoparticles in
Fig. 10. Photographs of shear-thickening suspension in a quiescent state (a) and right after violent shaking in horizontal direction (b), and the corresponding structural models. The fluid with low viscosity is converted to gel-like paste by structural changes from discrete flocs to three-dimensional network in shear fields.
polymer solutions. Wang et al. [36] have confirmed through tubeless siphon technique that the additions of nanoparticles to polymer solutions give rise to the enhancement of extensional viscosity, because the extension of polymer bridges between particle markedly increase the resistance to flow. To summarize the macroscopic shear-thickening behavior and interpretation of mechanism, Fig. 10 shows the photographs of suspensions in a quiescent state and right after shaking, and the corresponding structural models. The suspensions are converted from liquids with low viscosity to gel-like pastes on the application of violent shear. The shear-induced formation of transient network is responsible for the shear-thickening flow for nanoparticle suspensions flocculated by polymer bridging. 5. Conclusions (1) The suspensions of silica particles with diameters of 8– 25 nm in aqueous solutions of PEO with molecular weights of 5 × 105 –1 × 106 are Newtonian in the limit of zero shear rate and become shear-thickening at high shear rates. (2) The relaxation time determined from the stress decay process after cessation of steady shear drastically increases in the shear-thickening regions. The storage modulus at a constant frequency shows a rapid increase when the stress is increased above some critical levels. The elastic component plays an important role in controlling the overall rheology. (3) The basic mechanism of interesting rheological behavior is the bridging flocculation. Because of size effect, several particles are connected by intrachain bridging of one polymer coil. The Newtonian flow with low viscosity implies that interactions between coils are very weak. (4) When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. Due to the restoring forces of extended bridges, the suspension shows striking shear-thickening and highly elastic effects.
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R.L. Hoffman, Trans. Soc. Rheol. 16 (1972) 155. R.L. Hoffman, J. Colloid Interface Sci. 46 (1974) 491. J.W. Bender, N.J. Wagner, J. Colloid Interface Sci. 172 (1995) 171. P. D’Haene, J. Mewis, G.G. Fuller, J. Colloid Interface Sci. 156 (1993) 350. Y. Otsubo, Langmuir 8 (1992) 2336. Y. Otsubo, J. Rheol. 37 (1993) 799. Y. Otsubo, Langmuir 15 (1999) 1960. B. Cabane, K. Wong, P. Lindner, F. Lafuma, J. Rheol. 41 (1997) 531. T. Annable, R. Buscall, R. Ettelaie, D. Whittletone, J. Rheol. 37 (1993) 695. C. Esquenet, P. Terech, F. Boué, E. Buhler, Langmuir 20 (2004) 3583. T.A. Witten, M.H. Cohen, Macromolecules 18 (1985) 1915. D.J. Lundberg, J.E. Glass, R.R. Eley, J. Rheol. 35 (1991) 1255. R.J. English, H.S. Gulati, R.D. Jenkins, S.A. Khan, J. Rheol. 41 (1997) 427. H. Tan, K.C. Tam, R.D. Jenkins, Langmuir 16 (2000) 5600. E.P. Vrahopoulou, A.J. McHugh, J. Rheol. 31 (1987) 371. T. Annable, R. Buscall, R. Ettelaie, D. Whittlestone, J. Rheol. 37 (1993) 695. R. Scirocco, J. Vermant, J. Mewis, J. Rheol. 49 (2005) 551. J. Wang, R. Bai, D.D. Joseph, J. Fluid Mech. 516 (2004) 335.
Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging Masashi Kamibayashi, Hironao Ogura, Yasufumi Otsubo ∗ Department of Urban Environment Systems, Faculty of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba-shi 263-8522, Japan Received 9 October 2007; accepted 14 February 2008 Available online 21 February 2008
Abstract The steady-shear viscosity, dynamic viscoelasticity, and stress relaxation behavior were measured for suspensions of silica nanoparticles dispersed in aqueous solutions of poly(ethylene oxide) (PEO). The suspensions of silica with diameters of 8–25 nm show striking shear-thickening profiles in steady shear and highly elastic responses under large strains in oscillatory shear. Since the silica particles are much smaller than the polymer coils, one molecule can extend through several particles by intrachain bridging. Each polymer coil may remain isolated as a floc unit and the silica particles hardly connect two flocs. Therefore, the flow of suspensions is Newtonian with low viscosity at low shear rates. When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. The shear-thickening flow may arise from the elastic forces of extended bridges. But, the polymer chain is easily detached from particle surface by thermal energy because of large curvature of particles. As a result, the network structures are reversibly broken down in a quiescent state and the suspensions behaves as viscoelastic fluids with the zero-shear viscosity. © 2008 Elsevier Inc. All rights reserved. Keywords: Bridging flocculation; Shear-thickening; Silica nanoparticle; Suspension
1. Introduction Because of large size and high flexibility, the adsorption of polymer coils onto a solid surface is different in many aspects from that of small molecules. The most significant feature is that a polymer chain is attached in sequence separated by segments which extend into solution. Although the conformation of adsorbed layers depends on the thermodynamic conditions among the polymer, the solvent, and the particle surface, most segments reside in loops and tails in many cases of practical interests [1]. When the long loops extending from particles come into contact with surface of bare particles, the bonds of polymer chains are formed between particles. The flocculation in which one polymer chain adsorbs onto two or more particles to bind them together is referred to as polymer bridging [2,3]. The primary parameter that influences the bridging conformation and bond strength between particles is the adsorption energy of a * Corresponding author.
E-mail address: [email protected] (Y. Otsubo). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.02.022
segment at the particle interface. Since the fraction of segments of an adsorbed chain in trains varies with particle diameter, one of the important factors controlling the bridging structure is the particle diameter [3,4]. The adsorption of polymer chain onto the surface of large particles may be stronger than that of smaller particles due to the difference in the segment fraction of trains. In addition, more than one polymer molecule is required to bridge large particles, whereas for small particles, only a small segment of a polymer chain is required, and thus one molecule can extend through many bridges. Owing to the weak adsorption affinity and long-range interactions, significant changes in flocculation structures and bulk properties can be observed when the particles are decreased to nanosizes. In previous papers [5–7], we have systematically studied the rheological properties of suspensions flocculated by polymer bridging as a function of the adsorption affinity and particle diameter. In general, polymer adsorption is essentially irreversible, because the polymer chain may attach to the surface at several points and may not be able to desorb simultaneously from all sites. The bridges between particles are not broken in a quiescent state. Therefore, the highly flocculated
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suspensions show elasticity at very low frequencies or plasticity with an infinite viscosity at low shear rates. When the polymer chains do not have strong affinity for the surface, the fraction of loops increases at the expense of trains and this causes the adsorption–desorption process to reversibly occur. In suspensions, the bridges are constantly forming and breaking by thermal energy. It has been clarified that the viscosity behavior of suspensions can be converted from shear-thinning to Newtonian profiles by the additions of surfactant because of the decrease in adsorption affinity of polymer. In ordinary bridging processes, the surface separation of particles is in the range of 10–30 nm. The decrease in particle diameter also drastically influences the suspension rheology. Due to the unique floc structures in which many particles are connected by one polymer chain with coil conformation, the suspensions of nanoparticles show interesting rheological behavior including viscosity reduction by intrachain bridging [8] and irreversible viscosity increase by shear-induced bridging [9]. Accordingly it is of interest to understand the bridging conformation of polymer chains on nanoparticles. In the present paper, the size effects on the rheological properties are studied for suspensions of silica nanoparticles dispersed in polymer solutions. 2. Experimental 2.1. Materials The suspensions were composed of silica, poly(ethylene oxide) (PEO), and water. The silica particles were Cataloid-S manufactured by Catalysts and Chemicals Industries Co., Ltd. (Japan), the diameters of which were 8, 11, 18, 25, and 46 nm. The Cataloid-S series were supplied in the form of aqueous suspensions which were electrostatically stabilized. The pH values of mother suspensions were about pH 9 for 8–25 nm silica and pH 10 for 46 nm silica. Three PEO samples having molecular weights of Mw = 2 × 105 and 1 × 106 from Polysciences, Inc., and of Mw = 5 × 105 from Wako Pure Chemical industries, Ltd., were used as received. The radius of gyration, Rg , of an isolated polymer coil in solution can be calculated from the intrinsic viscosity. The mean size, 2Rg , determined for PEO in aqueous solution are 28, 35, and 47 nm in order of increasing molecular weight. The water used as the medium was purified so that its conductivity was decreased to less than 1.0 × 10−4 S m−1 . By adding aqueous solutions of PEO to the mother suspensions, the sample suspensions were prepared at silica concentrations up to 12% by volume. The polymer concentrations were in the range of 0.2–0.8% by weight based on the water. The rheological measurements were carried out after the suspensions were stored at room temperature under gentle shear on a rolling device for more than 3 days.
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and the gap between two plates was 0.8 mm. The measuring shear rates were from 3.0×10−1 to 3.0×102 s−1 in steady-flow measurements. In stress relaxation experiments, the stress decay function was measured after cessation of steady shear at different constant shear rates. The dynamic viscoelastic functions (storage modulus G and loss modulus G ) were measured as a function of frequency at a constant stress and as a function of stress at a constant frequency. The frequencies were from 1.6 × 10−1 to 2.5×101 s−1 and stress amplitude was from 2.0×10−1 to 5.0 × 102 Pa. The temperature was 25 ◦ C for all runs. Concentrated suspensions and emulsions often cause slip at solid boundaries in rheometers. The errors due to wall slip can be corrected by a technique proposed by Yoshimura and Prud’homme [10]. Their technique involves two measurements on a parallel plate geometry with different gap settings. If the wall slip is generated, the curves of shear stress versus apparent shear rate for different gaps have different profiles. Since the curves were almost the same, significant wall slip was not observed in this study. 3. Results Fig. 1 shows the shear rate dependence of viscosity for suspensions of 8 nm silica in 0.5 wt% solution of PEO with a molecular weight of Mw = 5 × 105 (designated PEO500 k ) at different particle concentrations. The measurements were carried out for each sample in a cycle of increasing and decreasing shear rate. The shear rate was exponentially increased and decreased in the range of 0.3 and 300 s−1 in a measuring time of 10 min. Since significant difference are not observed between the up-curve and down-curve, the viscosity behavior showed no time dependence. The flow of polymer solution without particles is Newtonian with a viscosity of 3.5 mPa s. The additions of silica particles cause the viscosity increase over the entire range of shear rates. At a particle concentration of 3 vol%,
2.2. Methods Steady-shear viscosity, stress relaxation after cessation of steady shear, and dynamic viscoelasticity were measured using a parallel plate geometry on a stress-controlled rheometer (Haake Rheo-Stress RS100). The diameter of plates was 35 mm
Fig. 1. Shear rate dependence of viscosity during a cycle of increasing (open symbols) and decreasing (filled symbols) shear rates for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at different particle concentrations: 0 (!, "); 3 (1, 2); 5 (E, F); 8 (P, Q); 12 vol% (e, a).
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Fig. 2. Shear rate dependence of viscosity for suspensions of 8 nm silica at a particle concentration of 8 vol% in solutions of PEO with Mw = 5 × 105 at different polymer concentrations: 0.3 (!); 0.5 (2); 0.7 (E); 0.8 wt% (Q).
the suspension shows a Newtonian flow profile. However, in contrast to ordinary flocculated suspensions which are shearthinning in a wide range of shear rates and often shows plastic responses at very low shear rates, the flow behavior for the suspensions containing silica particles at concentrations of 5 vol% and above is quite different. The flow is Newtonian even at low shear rates and the suspension behaves as a fluid. As the shear rate is increased, the viscosity abruptly begins to increase, goes through a maximum, and then markedly decreases. The shear rate at which the shear-thickening flow begins decreases with increasing particle concentration. The transition boundary from Newtonian to shear-thickening profiles lies on a straight line with a slope of about −1. The critical shear rate is inversely proportional to the Newtonian viscosity. Beyond the peak viscosity, the viscosity rapidly decreases. It looks likely that the shear rates at the peak are also approximated by a straight line with a slope of −1. Presumably an important factor controlling the shear-thickening behavior is the shear stress. For completely dispersed suspensions consisting of noninteracting particles, the relative viscosity, defined as the viscosity of suspensions divided by that of the medium, is considerably small, and flow is Newtonian at low particle concentrations. Although the flow is Newtonian at low shear rates, the viscosity rapidly increases with increasing particle concentration. The drastic increase in viscosity indicates that the silica suspensions are highly flocculated by PEO polymer. Fig. 2 shows the shear rate dependence of viscosity for suspensions of 8 nm silica at a particle concentration of 8 vol% in PEO500 k solutions at different polymer concentrations. All suspensions show shear-thickening flow at high shear rates. With increasing polymer concentration, the Newtonian viscosity at low shear rates rapidly increases and the shear rate at the onset of shear-thickening flow is decreased. The concentration effect of polymer is very similar to that of particles. But the viscosity level beyond the maximum is not strongly affected by the polymer concentration. The flow of markedly shear-thickening suspensions are apparently plastic with a constant stress at high shear rates. Fig. 3 shows the frequency dependence of storage G and loss G moduli for suspensions of 8 nm silica in 0.5 wt% so-
Fig. 3. Frequency dependence of storage (open symbols) and loss (filled symbols) moduli for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at particle concentrations of 8 (P, Q) and 12 vol% (e, a).
lution of PEO500 k at particle concentrations of 8 and 12 vol%. The measurements were carried out at a constant stress of 2 Pa in the linear viscoelastic range. Both moduli rapidly decrease with decreasing frequency, and at low frequencies the loss modulus is predominant. It is well known that the viscoelastic function of ordinary flocculated suspensions shows a plateau at low frequencies [5,11,12]. The plateau has been explained by an additional relaxation process due to flocculated structure of particles. However, the plateau region was not observed for all suspensions studied. The rapid drop of moduli can be connected with the Newtonian profile in steady flow experiments. The suspensions are characterized as elastic liquids with short relaxation times. Many structuring fluids such as suspensions and polymer solutions show nonlinear viscoelasticity under large deformation. At very low strains, the storage and loss moduli show very little dependence on the strain. Under large strains, the moduli are drastically decreased. The rapid decrease of moduli can be analyzed in relation to the dynamic processes of structural breakdown. To examine the nonlinear behavior, the dynamic viscoelasticity was measured under large deformation. Fig. 4 shows the stress dependence of storage modulus at different frequencies for suspension of 8 nm silica in 0.5 wt% solution of PEO500 k at a particle concentration of 12 vol%. The storage modulus is constant and the viscoelastic responses are linear at low stresses. When the stress is increased above some critical level, the storage modulus shows a rapid increase. It is commonly accepted that the shear-thinning flow and sharp drop of storage modulus under large deformation which is observed for flocculated suspensions can be attributed to the structural rupture induced by shear. Therefore, the increase of storage modulus in oscillatory shear which is called strain hardening effect may express the same rheology as the shear thickening in steady shear. The nanoparticle suspensions flocculated by polymer are highly elastic under large strains. For better understanding of the detailed mechanism of shearthickening flow, it is helpful to analyze the elastic properties as
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Fig. 4. Stress dependence of storage modulus at different frequencies for 12 vol% suspension of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 : 1.3 (!); 1.6 (2); 3.1 (E); 6.3 s−1 (Q).
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Fig. 6. Viscosity (open symbols) and relaxation time (filled symbols) plotted against the shear rate for suspensions of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at particle concentrations of 8 (P, Q) and 12 vol% (e, a).
Fig. 7. Effect of particle diameter on the viscosity behavior for suspensions at a particle concentration of 10 vol% prepared with 0.8 wt% solution of PEO with Mw = 5 × 105 : 8 (!); 11(2); 18(E); 25(Q); 46 nm (e). Fig. 5. Stress relaxation after cessation of steady shear at 10 (!) and 100 s−1 (2) for suspension of 8 nm silica in 0.5 wt% solution of PEO with Mw = 5 × 105 at a particle concentration of 8 vol%.
a function of the relaxation time in nonlinear regions. Fig. 5 shows the stress relaxation behavior after cessation of steady shear for suspension of 8 nm silica in 0.5 wt% solution of PEO500 k at a particle concentration of 8 vol%. The ratio of stress to shear rate at the limit of t = 0 corresponds to the steady-shear viscosity. The accurate data of stress relaxation were not measured at low shear because of the limitation of rheometer. Since the stress decay curve can be approximated as a straight line at long times, the stress relaxation is governed by the longest relaxation mechanism and the time-dependent function is expressed by the following equation: σ ∝ exp(−t/τm ),
(1)
where τm is the longest relaxation time. Fig. 6 shows the viscosity and relaxation time plotted against the shear rate for suspensions of 8 nm silica in 0.5 wt% solution of PEO500 k at
particle concentrations of 8 and 12 vol%. In Newtonian region, the stress relaxation is rapidly completed and the relaxation time can be estimated to be less than 1 s. Once the shear thickening takes place above the critical shear rates, the relaxation time is drastically increased by a factor of more than 10. At the maximum viscosity, the values are about 20 and 60 s for 8 and 12 vol% suspensions, respectively. In high viscosity region, the relaxation time is almost constant, independent of shear rate. Fig. 7 shows the effect of particle diameter on the viscosity behavior for suspensions at a particle concentration of 10 vol% prepared with 0.8 wt% solution of PEO500 k . The flow is Newtonian at low shear rates, irrespective of particle diameter. The Newtonian viscosity decreases, passes though a minimum and then increases with increasing particle diameter and this size effect on the viscosity behavior is very unique. The general agreement is that the reduction of particle diameter results in the enhancement of suspension viscosity. In suspensions consisting of noninteracting particles, the dynamic structure in shear fields is governed by the balance between Brownian motion and hydrodynamic forces [13,14]. Since the viscosity curve of suspensions is scaled on the Péclet number which represents the
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Fig. 8. Effect of molecular weight of PEO on the viscosity behavior during a cycle of increasing (open symbols) and decreasing (filled symbols) shear rates for suspensions of 8 nm silica at a particle concentration of 8 vol% in 0.5 wt% polymer solutions: 2 × 105 (!, "); 5 × 105 (1, 2); 1 × 106 (P, Q).
relative importance of shearing forces to Brownian diffusion, the viscosity at a given shear rate becomes higher for smaller particles. The colloidal interactions rapidly increase when the diameter is reduced to the order of nanometer. It is usually difficult to prepare the highly stabilized suspensions of nanoparticles [15–18]. In the sample suspensions, the lowest viscosity is obtained for the silica with diameters of 11 and 18 nm. With respect to the diameter effect on suspension rheology, the most interesting point is that the suspensions which give the lowest viscosity in Newtonian range show remarkable shear-thickening behavior. Although an indication of shear-thickening flow is observed for suspensions of silica with 8 and 25 nm diameters, the overall flow profiles are characterized as shear-thinning in a similar manner to suspension of 46 nm silica. The particle– particle interactions can be drastically changed at about 15 nm in nanoparticle suspensions flocculated by soluble polymers. Fig. 8 shows the effect of molecular weight of PEO on the viscosity behavior for suspensions of 8 nm silica at a particle concentration of 8 vol% prepared with 0.5 wt% polymer solutions. The viscosity behavior is obtained in a cycle of increasing and decreasing shear rate. The suspension prepared with PEO200 k solution is Newtonian with low viscosity. Presumably the flocculation level is very low. On the other hand, the suspensions prepared with PEO200 k and PEO1 M solutions show striking shear-thickening flow. For suspension prepared with PEO1 M solution, the accurate values of viscosity above shear rates of 10 s−1 were not measured, because the sample was expelled from the parallel-plate gap due to the normal stress effect. In addition, this suspension showed the hysteresis behavior and the measurements were repeated twice in the procedure that the maximum shear rate was increased. In the first cycle, the
shear rate was stepwise increased and decreased in the range of 0.2 and 2 s−1 in a shearing time of 30 s at each shear rate. Although the data are not shown in the figure, significant differences are not observed between the up-curve and down-curve. In the second cycle, the maximum shear rate is increased to 10 s−1 . The up-curve has almost the same profile as the viscosity curve below 2 s−1 in the first cycle. However, the viscosity of down-curve is increased as shown by filled circles in Fig. 8 and the hysteresis appears between two curves. When the suspension is kept at rest for more than 20 min after the viscosity measurements, the effects of shear history disappears and the initial viscosity curves are regained. The time-dependent behavior of viscosity suggests that the suspension containing PEO with very high molecular weights should have the long relaxation time. From Figs. 1–8, the effect of polymers on the suspension rheology can be summarized as follows: (a) The addition of small amounts of PEO causes an increase in viscosity and dynamic viscoelastic functions of silica suspensions. The PEO polymers act as flocculants. (b) The suspensions are Newtonian in the limit of zero shear rate and behave as liquids, irrespective of degree of flocculation. (c) When the silica particles with diameters of 8–25 nm are dispersed in aqueous solutions of PEO with molecular weights of 5 × 105 –1 × 106 , the suspensions show striking shear-thickening behavior in steady shear and strain hardening in oscillatory shear. 4. Discussion The shear-thickening flow can be observed for several types of suspensions. The highly concentrated suspensions consisting of particles without colloidal interactions show the shearthickening behavior followed by a discontinuous jump of viscosity or flow instability beyond a certain shear rate. In shear fields, the anisotropic structures are induced by twodimensional layering. However, the layered arrangement is unstable and is disrupted above a critical shear rate. Hoffman [19,20] has shown that the discontinuous viscosity jump arises from the structural breakdown of two-dimensional hexagonal packing to random arrangement. An alternate mechanism of shear-thickening flow for concentrated suspensions of noninteracting particles is the formation of large anisotropic aggregates induced by hydrodynamic forces [21,22]. This theory has been proposed through optical measurements based on a fact that the dichroism remains relatively constant during thickening processes. Therefore, the mechanisms of shear thickening are of two types: two-dimensional layering and hydrodynamic clustering. The latex suspensions flocculated by polymer bridging can generate the viscosity jump [23,24]. When the polymer adsorption reversibly takes place owing to the weak affinity for the particle surface, the polymer bridges are constantly forming, breaking and reforming by thermal energy. The suspensions flocculated by reversible bridging are Newtonian in the limit of zero shear rate. Because the particles can be bridged by a flexible polymer coil, the deformable flocs are built up over the systems. On the application of shear fields where the flexible
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bridges are highly extended within the lifetime, the extended bridges can lead to high resistance to flow due to the restoring forces. Hence, the flow becomes shear-thickening. In oscillatory shear, the storage modulus at a constant frequency shows a rapid increase when the strain is increased above a critical level. The shear-thickening behavior can be explained in connection with the nonlinear elasticity of flexible bridges [25]. The rheological properties of silica suspensions studied in the present work are very similar to those of latex suspensions flocculated by reversible bridging. So, the bridging flocculation may be a possible mechanism. To explain the shearthickening flow, the attention is focused on the polymer adsorption on nanoparticles and particle–particle interactions. Since the polymer adsorption is regarded as irreversible, the polymer bridges between particles are not broken down by thermal energy. Many authors have reported that the suspensions flocculated by irreversible bridging show shear-thinning flow in a wide range of shear rates. However, the diameters of particles employed in previous work on suspension rheology are larger than 50 nm. In the present paper we have observed the striking shear-thickening behavior for particles with diameters of 8–25 nm. One of the most important factor controlling the bridging structure and the resultant rheology is the particle diameter. In polymer adsorption on a solid surface, the thickness of the adsorbed layer is roughly in the range of 20–30 nm. When the particle diameter is decreased to 20 nm and below, one polymer chain can extend through many bridges. To provide more insight into the bridging conformation between nanoparticles, the discussion will be expanded by the use of shear-thickening suspension consisting of 8 nm silica at 8 vol% in 0.5 wt% solution of PEO500 k . The mean size of polymer coil in aqueous solution is about 35 nm and is much larger than that of particles. When the bridging flocculation is induced, the average number of particles which are bound by one polymer chain is estimated to be 6.2. Because of large curvatures of particles, the floc structures can be expressed by a model in which the particles are entrapped in polymer coils with spherical conformation. From the concentration dependence of viscosity, the overlapping concentration is estimated to be 1.2 wt% for aqueous solutions of PEO500 k . At 0.5 wt%, the silica particles hardly connect two polymer coils, but each polymer coil unit may remain isolated as a floc in the suspension. To support this explanation, the viscosity measurements were carried out for suspensions prepared with dilute polymer solution. Fig. 9 shows the concentration dependence of viscosity for suspensions of 8 nm silica in 0.3 wt% solution of PEO500 k . Generally the suspension viscosity monotonously increases with increasing particle concentration. But the viscosity of sample suspensions decreases at first, shows a minimum and rapidly increases. It must be stressed that the suspension viscosity at low concentrations is lower than that of medium. According to Einstein theory of suspension rheology, the increase in viscosity is attributed to the distortion of the velocity field in the vicinity of each particle. The addition of particles inevitably causes a viscosity increase of the liquid. Hence it seems difficult to explain the reduction of suspension viscosity by the previously established mechanisms such as hydrodynamic in-
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Fig. 9. Concentration dependence of viscosity for suspensions of 8 nm silica in 0.3 wt% solution of PEO with Mw = 5 × 105 . The broken line shows the Einstein prediction.
teractions and floc formation by colloidal forces. The 8 nm silica particles have an extremely large specific surface and can adsorb a large amount of polymer in suspension. As a first approach, a possible mechanism of viscosity reduction can be the decrease of polymer concentration in the solution phase by adsorption. However, the viscosity behavior is not scaled on the specific surface of particles, but the silica size is confirmed to be a primarily important factor in the viscosity reduction. In polymer solutions, the gross molecular structure is represented by a flexible coil with a radius of gyration Rg . The viscosity reduction in the presence of nanoparticles implies the decrease in radius of gyration of polymer coils. The silica nanoparticles act as binders, resulting in a contraction of the polymer coil. Fig. 9 is helpful to understand the floc model constructed by intrachain bridging. Now we will discuss the shear-thickening behavior of nanoparticle suspensions flocculated by polymer bridging. Although the nanoparticles are entrapped, the polymer coils may be flexible and the loops of adsorbed chain in an extended conformation. The interaction energy very rapidly increases as the separation between coils is decreased. Further flocculation in a quiescent state is retarded by steep repulsion and the viscosity of suspensions is very low at low shear rates. However, the flocs formed by intrachain bridging will be easily extended and compressed during rotation and collision in high shear fields. When enough kinetic energy is given to flocs by shear, the loops adsorbed on the particle comes into contact with the surface of favorably situated particle in the other floc and the floc–floc bonds can be formed by bridging. Due to the mechanical activation energy, the bridging flocculation is promoted in shear fields. Cabane et al. [26] have analyzed the shear-induced gelation of aqueous suspensions of silica nanoparticles in the presence of soluble polymer. Trough small angle neutron scattering, it is confirmed that the necklaces consisting a few particles bound to one polymer chain is stretched and the connections are formed between them in shear fields. On the basis of this
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explanation, the shear-induced bridging of nanoparticles may be acceptable. But the adsorption affinity of polymer on the nanoparticle surface is weak in this work. Since the bridging interactions between flocs is reversible in a quiescent state, the resultant structure in shear fields may be transient. The polymer chain is easily detached from particle surface by thermal energy and the decrease in shear rates gives no hysteresis for viscosity behavior. The shear-thickening flow without time dependence for nanoparticle suspensions is originated from flocculation by the shear-induced reversible bridging. The reversible bridges constructed in high shear fields are broken down in a quiescent state. The desorption of polymer chains from the particle surfaces governs the stress relaxation. The relaxation time determined from the stress decay curve after cessation of steady shear is considered to reflect the time scale of adsorption– desorption process in flocculated suspensions. The associating polymers are hydrophilic long-chain molecules which contain a small amount of hydrophobic groups. In aqueous solution, the hydrophobes tend to aggregate and create a bond between polymer chains by reversible associating interactions. When the polymer concentration is increased beyond some critical levels, a three-dimensional structure of transient network is constructed over the system. Due to intrachain and interchain associations, the aqueous solutions of associating polymers often show unusual rheological behavior [27,28]. One of the most interesting features is a shearthickening flow profile [29–32]. Shear flow serves to elongate the polymer chains and break some of the intrachain associations, forming interchain associations. Similarly, in the suspensions studied, the flow may increase the number of interchain bridging at the expense of intrachain bridging. The statistical mechanical network model for polymer solutions has shown [33,34] that the shear-thickening flow is induced by the decrease in entropy of polymer chain in the network during extension by shear. Referring to these models, the three-dimensional network structure of flocs must be developed to span the system for shear-thickening behavior of suspensions. The threedimensional structures can transmit the forces through the polymer bridges over the system. Therefore, the elastic responses observed for shear-thickening suspensions can be coupled with the network structure of infinite flocs. Although the elasticity arises only from bridge between two coils which contain several particles, the development of three-dimensional network is required for appearance of elasticity as bulk responses. Since the mechanical properties of flexible bridges are analogous to the rubbery elasticity, the storage modulus markedly increases in extended states as shown in Fig. 4. The nonlinear elasticity of polymer bridges plays an important role in controlling the shear-thickening flow. The importance of extensional behavior of polymer chains is demonstrated for suspensions of noninteracting particles in polymer solutions. Scirocco et al. [35] have shown that the strong extensional flow of thin liquid layer between particles contributes to shear-thickening flow even at low particle concentrations. The stress-controlled nature of shearthickening flow can be explained by the extensional properties of polymer solution. The high extensional viscosity due to chain extension is also reported for suspension of nanoparticles in
Fig. 10. Photographs of shear-thickening suspension in a quiescent state (a) and right after violent shaking in horizontal direction (b), and the corresponding structural models. The fluid with low viscosity is converted to gel-like paste by structural changes from discrete flocs to three-dimensional network in shear fields.
polymer solutions. Wang et al. [36] have confirmed through tubeless siphon technique that the additions of nanoparticles to polymer solutions give rise to the enhancement of extensional viscosity, because the extension of polymer bridges between particle markedly increase the resistance to flow. To summarize the macroscopic shear-thickening behavior and interpretation of mechanism, Fig. 10 shows the photographs of suspensions in a quiescent state and right after shaking, and the corresponding structural models. The suspensions are converted from liquids with low viscosity to gel-like pastes on the application of violent shear. The shear-induced formation of transient network is responsible for the shear-thickening flow for nanoparticle suspensions flocculated by polymer bridging. 5. Conclusions (1) The suspensions of silica particles with diameters of 8– 25 nm in aqueous solutions of PEO with molecular weights of 5 × 105 –1 × 106 are Newtonian in the limit of zero shear rate and become shear-thickening at high shear rates. (2) The relaxation time determined from the stress decay process after cessation of steady shear drastically increases in the shear-thickening regions. The storage modulus at a constant frequency shows a rapid increase when the stress is increased above some critical levels. The elastic component plays an important role in controlling the overall rheology. (3) The basic mechanism of interesting rheological behavior is the bridging flocculation. Because of size effect, several particles are connected by intrachain bridging of one polymer coil. The Newtonian flow with low viscosity implies that interactions between coils are very weak. (4) When the polymer coils containing several nanoparticles are subjected to high shear fields, three-dimensional network is developed over the system. Due to the restoring forces of extended bridges, the suspension shows striking shear-thickening and highly elastic effects.
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