THE LATTICE DYNAMICS OF COLLOIDAL CRYSTALS

Colloidal crystals are ordered arrays of highly charged microspheres in water that exhibit spectacular optical diffraction effects by virtue of a large lattice parameter. The microspheres perform Brownian motion that is influenced by the interparticle and fluid forces. The purpose of this study was to understand the nature of the collective motions in colloidal crystals in terms of classical lattice dynamics.;Intensity autocorrelation spectroscopy was used to probe the lattice dynamics by measuring the phonon dispersion curves. A thin-film cell was used to reduce multiple scattering to acceptable levels. An experiment to measure wall effects on Brownian motion was necessary to determine the decrease in diffusion rate inherent in the thin-film geometry. The wall effects were found to agree with macroscopic hydrodynamics. An additional experiment measured the elastic anisotropy of the crystal lattice from the thermal diffuse scattering. The theoretical dispersion curves were found to agree well with the measured curves.;In the theoretical analysis, the particle displacements due to Brownian motion were formally decomposed into phonon-like lattice disturbances analogous to the phonons in atomic and molecular solids except that they are heavily damped. The analysis was based on a harmonic solid model with special attention paid to the hydrodynamic interaction between particles. A hydrodynamic model using the Oseen interaction was worked for a three-dimensional lattice but it failed in two important respects: it overestimated the friction factor for long wavelength modes and did not predict a previously observed propagating transverse mode. Both of these failures were corrected by a hydrodynamic model based on periodic solutions to the Stokes equation. In addition, the effects of fluid inertia and constraining walls were considered.