Measurements of the low-shear viscosity eta(o) with a Zimm-Crothers viscometer for dispersions of colloidal hard spheres are reported as a function of volume fraction phi up to 0.56. Nonequilibrium theories based on solutions to the two-particle Smoluchoski equation or ideal mode coupling approximations do not capture the divergence. However, the nonhydrodynamic contribution to the relative viscosity Deltaeta(o) is correlated over a wide range of volume fractions by the Doolittle and Adam-Gibbs equations, indicating an exponential divergence at phi(m)=0.625+/-0.015. The data extend the previously proposed master curve, providing a test for improved theories for the many-body thermodynamic and hydrodynamic interactions that determine the viscosity of hard-sphere dispersions.

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We use simple models and molecular dynamics simulations to determine the effects of polydispersity δ on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction φ increases, particularly for φ>0.60. Mean field theory predicts a higher osmotic pressure with increasing polydispersity, but the effects are only significant for δ>0.10. Molecular dynamics simulations with δ=0.05 bound the equation of state between a metastable disordered upper limit and a crystalline organized polydisperse (possibly) lower limit. The pressure for the PMMA-PHSA spheres lies close to the organized polydisperse limit, indicating a preference for a crystalline ordered arrangement where smaller particles surround larger ones. Thus, the higher osmotic pressure seen in the equation of state of PMMA-PHSA spheres is a direct effect of polydispersity, manifest as a pronounced reduction in the crystalline close packed volume fraction from φmax(FCC, δ=0)=0.7404 to φmax(FCC, δ=0.1)=0.665. The random close packing φmax(RCP) is almost independent of polydispersity. This leads to a crossing of values of φmax(FCC) and φmax(RCP) and hence a possible terminal polydispersity of 0.12±0.01, consistent with other simulations, theories, and experiments. Since our results do not include size fractionation of the liquid and solid, the exact meaning of this crossing is unclear and its agreement with previously reported terminal polydispersities may be coincidental.

We present measurements of the high-frequency shear modulus and dynamic viscosity for nonaqueous hard sphere colloidal crystals both in normal and microgravity environments. All experiments were performed on a multipurpose PHaSE instrument. For the rheological measurements, we detect the resonant response to oscillatory forcing with a dynamic light scattering scheme. The resonant response for colloidal crystals formed in normal and microgravity environments was similar, indicating that the bulk rheological properties are unaffected by differing crystal structure and crystallite size within the experimental error. Our high-frequency shear modulus seems reasonable, lying close to Frenkel and Ladd's predictions [Phys. Rev. Lett. 59, 1169 (1987)] for the static modulus of hard sphere crystals. Our high-frequency dynamic viscosity, on the other hand, seems high, exceeding Shikata and Pearson [J. Rheol. 38, 601 (1994)] and van der Werff et al.'s measurements [Phys. Rev. A 39, 795 (1989)] on the high-frequency dynamic viscosity for metastable fluids. The measurements are in the linear regime for the shear modulus but may not be for the dynamic viscosity as Frith et al. [Powder Technol. 51, 27 (1987)] report that the dynamic viscosity passes through a maximum with strain amplitude.