The effective self-diffusion coefficient of solvent molecules in colloidal crystals

Abstract

An analysis is given of the self-diffusion of solvent molecules in a colloidal crystal. The effective self-diffusion coefficient of the solvent molecules is calculated, by solving the Laplace equation, as a function of the volume fraction of the colloidal particles. Using an expansion of the probability distribution for a given solvent molecule in terms of solid spherical harmonics it is possible to obtain the exact value for the effective self-diffusion coefficient for all volume fractions up to dense packing. It is found that contrary to earlier predictions (1–3), the self-diffusion coefficient changes from a convex decreasing function to a concave decreasing function of the volume fraction at a volume fraction about 50% of close packing. Experimental results obtained using the 1-H NMR pulsed field gradient technique are also discussed in this paper and confirm the change from convex to concave behavior.