THE EFFECTIVE TRANSLATIONAL SELF-DIFFUSION COEFFICIENT OF SMALL MOLECULES IN COLLOIDAL CRYSTALS OF SPHERICAL-PARTICLES

The effective translational self-diffusion coefficient of small molecules in colloidal crystals of spherical particles is calculated. The colloidal crystal is modeled as a two-phase system. The colloidal particles are treated as immobile spheres with their centers located on the lattice points of a cubic array. The diffusing molecule under consideration is characterized by both a self-diffusion coefficient and a concentration inside the colloidal particle as well as a self-diffusion coefficient and a concentration in the continuous phase. We have analyzed the results for three different cubic lattice types. For low volume fractions of colloidal particles (<0.3) the calculated self-diffusion coefficient is found to be independent of the lattice type and shows quantitative agreement with a simple cell model. (B. Jonsson, H. Wennerstrom, P. G. Nilsson, and P. Linse, Colloid Polym. Sci. 264, 77, 1986). The results of this study therefore support the analysis of experimental data on self-diffusion of small hydrophobic molecules in latex dispersions for low-volume fractions by the cell model (M. H. Blees and J. C. Leyte, J. Colloid Interface Sci. 157, 355, 1993). For higher volume fractions the behavior is found to be rather different. The self-diffusion coefficient is found to depend on the specific lattice structure of the colloidal particles, and significant deviations from the cell model result are found. Both sign and magnitude of the deviations are found to depend on the ratio of the transport coefficient of the diffusing molecule in the colloidal particles and the transport coefficient in the continuous phase. (C) 1994 Academic Press, Inc.