William B. Russel

Polymer-induced phase separations in nonaqueous colloidal suspensions

Abstract A theory based on statistical mechanics is developed to predict the destabilization or flocculation of nonaqueous colloidal suspensions by nonadsorbing polymer. The effective interaction potential between two colloidal particles is modeled via the volume restriction potential of Asakura and Oosawa. The free energy is calculated using second-order perturbation theory with the hard sphere system serving as the reference. A fluid—solid (as opposed to a fluid—fluid) phase separation emerges, indicating that the colloid-rich phase exhibits long range order. Phase diagrams are calculated which show the volume fraction of colloidal particles in each phase as a function of polymer concentration, polymer molecular weight, and colloidal particle size. The results agree well with the experimental observations of deHek and Vrij. The prediction of a fluid—solid phase separation remains to be verified experimentally, however, indicating the need for measurements of the colloid volume fraction in and structure of each phase.

Hard sphere colloidal dispersions: Viscosity as a function of shear rate and volume fraction

The viscosities of suspensions of sterically stabilized (hard) silica spheres in cyclohexane are reported as a function of shear rate (γ) and volume fraction (6×10−4<φ<0.6). The shear thinning scales according to (ηr−η∞)/(η0−η∞) =1/(1+1.31ηγa3/kT) with limiting low and high shear viscosities described up to φ∼0.35 by η0=1+5/2φ+(4±2)φ2+(42±10)φ3 , η∞=1+5/2φ+(4±2)φ2+(25±7)φ3 . At higher volume fractions the viscosity becomes more sensitive to φ and diverges at φm=0.63±0.02 (γ→0) , φm=0.70±0.02 (γ→∞) . The experimental results compare well with existing hard sphere theories and the data of Krieger (1972) for aqueous lattices. Even at the highest volume fraction neither yield stresses nor shear thickening are observed.

Crystallization of hard-sphere colloids in microgravity

The structure of, and transitions between, liquids, crystals and glasses have commonly been studied with the hard-sphere model, in which the atoms are modelled as spheres that interact only through an infinite repulsion on contact. Suspensions of uniform colloidal polymer particles are good approximations to hard spheres, and so provide an experimental model system for investigating hard-sphere phases. They display a crystallization transition driven by entropy alone. Because the particles are much larger than atoms, and the crystals are weakly bound, gravity plays a significant role in the formation and structure of these colloidal crystals. Here we report the results of microgravity experiments performed on the Space Shuttle Columbia to elucidate the effects of gravity on colloidal crystallization. Whereas in normal gravity colloidal crystals grown just above the volume fraction at melting show a mixture of random stacking of hexagonally close-packed planes (r.h.c.p.) and face-centred cubic (f.c.c.) packing if allowed time to settle,, those in microgravity exhibit the r.h.c.p. structure alone, suggesting that the f.c.c. component may be induced by gravity-induced stresses. We also see dendritic growth instabilities that are not evident in normal gravity, presumably because they are disrupted by shear-induced stresses as the crystals settle under gravity. Finally, glassy samples at high volume fraction which fail to crystallize after more than a year on Earth crystallize fully in less than two weeks in microgravity. Clearly gravity masks or alters some of the intrinsic aspects of colloidal crystallization.

Structure and breakup of flocs subjected to fluid stresses: I. Shear experiments

The structure and properties of flocculated suspensions were investigated experimentally using small-angle light scattering. Experiments monitoring the breakup resulting from uniform shear of flocculated 0.14 μm diameter polystyrene latices minimized kinetic effects, isolating the instantaneous breakup modeled in existing theories. The average number of particles per floc, 〈N〉, and mean radius of gyration cubed, 〈Rg2〉3/2, varied as γx, with x = −0.878 and −1.06, respectively. This shear dependence is weaker than predicted by the existing models. Comparison of the two relationships yields 〈N〉 ∝ 〈Rg2〉D/2, where the observed fractal dimensionality D = 2.48 indicates a nonuniform structure in conflict with the uniform porosity assumed in the models. Other methods for determining the fractal dimensionality yielded D = 1.6, 2.2, and 2.5, depending on the shear history of the samples. The effect of increasing electrolyte concentration was a slight weakening of the flocs for [NaCl] < 0.04 M followed by a significant strengthening above 0.04 M; DLVO theory successfully correlated this trend.

Review of the Role of Colloidal Forces in the Rheology of Suspensions

Experimental and theoretical work defining the effects of Brownian motion and dispersion, steric, and electrostatic forces on the rheology of suspensions is reviewed. Data from well‐characterized monodisperse systems are interpreted through analyses, primarily of pair interactions, which relate the bulk stress to the suspension microstructure. The magnitudes of the interparticle forces relative to Brownian motion determine the nature of the microstructure at rest: neutrally stable, stable due to strong electrostatic or steric repulsions, or flocculated by strong attractive forces. The rheological behavior varies correspondingly from moderately shear thinning with Newtonian low‐ and high‐shear viscosities for hard sphere interactions to solidlike in the low‐shear limit when multiparticle attractive or repulsive forces dominate Brownian motion.

Electrophoresis of spherical polymer-coated colloidal particles

Abstract The motion of a spherical polymer-coated colloidal particle in a steady electric field is studied via “exact” numerical solutions of the electrokinetic equations. The hydrodynamic influence of the polymer is represented by a distribution of Stokes resistance centers. With neutral polymer, charge resides on the underlying bare particle, whereas for polyelectrolytes, the charge is distributed throughout the coating. The coatings may be brush-like or have long tails. As expected, neutral coatings lower the mobility because of increased drag and a decrease in the effective charge behind the shear surface. For polyelectrolyte coatings, the behavior is more complex. For example, the mobility becomes independent of the ionic strength and particle size when Donnan equilibrium prevails inside the coating and the coating is thick relative to the Brinkman screening length (square root of the coating permeability). In this limit, the mobility follows from a simple balance of forces within the coating and, therefore, becomes proportional to the fixed charge density and the coating permeability. If the permeability is sufficiently high, the mobility of a polyelectrolyte-coated particle may exceed that of its bare counterpart with the same net charge. In general, the effects of polarization and relaxation are as important for coated particles as they are for bare particles.

Structure and breakup of flocs subjected to fluid stresses: II. Theory

Abstract An improved model for the breakup of an isolated floc in a shear flow is developed, similar in concept to previous versions but generalized to consider a spatial variation of the internal volume fraction of the form ϕ ∝ rD−3. Assumptions of linear elasticity and the Mises criterion for yield, with moduli and critical stress varying with volume fraction as φn, produce a relationship between floc radius R and shear rate γ of the form R ∼ γ (D−1) 2n(D−3) in the nondraining limit. Our experimental results for floc breakup are correlated with D = 2.48 and n = 4.45, in good agreement with independent measures of D from the floc mass and n from the elasticity of flocculated networks. The maximum strain at rupture is estimated to be ∼5%, in accord with the limit of linearity in the elasticity experiments. More general theoretical results are also presented to facilitate comparison with future experiments.

Simple Ordering in Complex Fluids

Ordering and the formation of crystals have long fascinated mankind. The reverence bestowed on gem‐stones and the fantastic properties attributed to crystalline matter arise from the unique optical, geometric and physical properties of the ordered state. Although scientific inquiry has focused mostly on molecular and atomic crystals, much also can be learned from the study of super‐molecular and colloidal arrays.

An experimental and theoretical study of phase transitions in the polystyrene latex and hydroxyethylcellulose system

Abstract We present an experimental study of phase transitions induced in polystyrene latices by hydroxyethylcellulose and interpret the results by applying perturbation theory from statistical mechanics to an interaction potential derived from the volume exclusion mechanism of Akasura and Oosawa. The predictions agree semiquantitatively with the measured colloidal phase densities and the critical polymer concentration above which flocculation occurs for a wide range of ionic strengths. The theory also predicts the type of phase transition, i.e., fluid-solid or fluid-fluid, observed by Sperry. The agreement between experiment and theory demonstrates the predictive capability of the perturbation theory for weakly aggregating colloidal suspensions.

Disorder-to-order transition in settling suspensions of colloidal silica: X-ray measurements

Dispersions of colloidal particles exhibit thermodynamic properties similar to those of molecular systems, including a hard sphere disorder-to-order transition. In experiments with organophilic silica in cyclohexane, gravity settling was used to concentrate the particles. With small particles the slow sedimentation permits rearrangement into the iridescent ordered phase, but larger particles form amorphous sediments instead. Scanning electron microscopy of the crystalline sediment indicates hexagonally closepacked layers. X-ray attenuation measurements reveal a discontinuity coincident with the observed boundary between iridescent and opaque regions. Sediments accumulating faster than the maximum rate of crystallization produce a glass, in accord with the classical theory for crystal growth.