Density profiles of concentrated colloidal suspensions in sedimentation equilibrium

Abstract

Sedimentation equilibria in concentrated colloidal suspensions are studied within the framework of density functional theory for inhomogeneous fluids. The density profile in the gravitational field is calculated exactly for the one-dimensional model of hard rods. The predictions of the local density approximation agree very well with coarse-grained density profiles derived from extensive Monte Carlo simulations of three-dimensional systems of hard spheres and charge-stabilized colloidal particles. The simulations show that the shape of the density profiles is very sensitive to the nature of the interactions between colloidal particles, and allow a direct test of a simple inversion procedure, which extracts the osmotic equation of state of colloidal suspensions from a measurement of their density profile. The method is sufficiently sensitive to allow the crystal-fluid tie line to be located at high colloid concentrations. The local density approximation is generalized to calculate density profiles of bidisperse hard sphere suspensions; the competition between gravity and entropy leads to nonmonotonic density profiles which are sensitive to the mass ratio, for a given size ratio. The density functional approach and Monte Carlo simulations are finally extended to study the effect of interparticle attractions on the density profiles, which exhibit a region of rapid variation corresponding to the ‘‘liquid-gas’’ interface for sufficiently strong attractive interactions.