Phase transition, equation of state, and limiting shear viscosities of hard sphere dispersions

Abstract

Despite an interparticle potential consisting of only an infinite repulsion at contact, the thermodynamics and dynamics of concentrated dispersions of hard spheres are not yet fully understood. Colloidal poly-(methyl methacrylate) spheres with a grafted layer of poly-(12-hydroxy stearic acid) (PMMA-PHSA) comprise a common model for investigating structural, dynamic, and rheological properties. These highly monodisperse spheres can be index matched in nonaqueous solvents, reducing van der Waals forces and allowing characterization via light scattering. In this work, we test the behavior of these dispersions against expectations for hard spheres through observations of the phase behavior, x-ray densitometry of equilibrium sediments, and Zimm viscometry. We set the effective hard sphere volume fraction by the disorder-order transition, thereby accounting for the polymer layer, any swelling due to the solvent, and polydispersity. The melting transition then occurs close to the expected value and the equation of state for the fluid phase, extracted from the equilibrium sediment with x-ray densitometry, conforms to the Carnahan-Starling equation. However, the osmotic pressure of the crystalline phase lies slightly above that calculated for a single fcc crystal even after accounting for polydispersity. Likewise the high shear viscosity of the fluid compares well with other hard sphere dispersions, but the low shear viscosity for PMMA-PHSA hard spheres exceeds those for polystyrene and silica hard spheres, e.g., a relative viscosity of 45±3 at $\phi =0.50\mathrm{}$ rather than 24. Our low shear viscosities are consistent with other PMMA-PHSA data after rescaling for both the polymer layer thickness and polydispersity, and may represent the true hard sphere curve. We anticipate that the equation of state for the crystal deviates due to polycrystallinity or a direct effect of polydispersity.