Microscopic Theories of the Rheology of Stable Colloidal Dispersions.

Here we employ statistical mechanics for predicting the nonequilibrium structure and rheology of concentrated colloidal dispersions, with particular attention to the interparticle potential and polymeric additives. The outcome is a hicrsrchical theory for spherical particles characterized by radius, number density, pair potential, and thickness and density of any adsorbed polymer layer. From that the equilibrium dynamics and pair hydrodynamic functions are constructed. These, along with the applied shear field, enter the conservation equation governing the nonequilibrium pair probability. To approximate the effect of pairwise additive coupling with a third particle, we implement a series of increasingly sophisticated closures. The conservation equation is solved numerically by perturbing from the equilibrium fluid state to determine the nonequilibrium structure and linear viscoelastic properties.

For the present, comparison of extensive calculations for a variety of interaction potentials and hydrodynamic conditions establishes quantitative accuracy in the high frequency limit and qualitatively correct results for steady shear. For the latter the error with the most sophisticated closure is systematic and can be normalized by examining ratios of properties or trends. We demonstralc this with a variety of repulsive interparticle potentials and complications such as adsorbed or grafted polymer layers and polydispersity. The current formulation is especially useful for mechanistic studies of changes in dispersion behavior with modifications to either the interparticle potential or the size distribution. We also have confidence in the applicability of the. theory to systems with attractive interactions as long as the dispersion remains fluid (i.e. lacks a yield stress).

Calculations at the lowest or pair level yield semiquantitative results for rel- atively short range potentials and monodispersions. More accurate closures that account explicitly for many body couplings are required to capture the effects of polydispersity and longer range interactions.