Diffusion of Classical Particles in a Random Medium I. Linear Response of a Single Particle

Abstract

A kinetic theory of diffusion of a single classical particle with a large frictional damping is developed in the presence of a random array of medium particles which behave as obstructions or traps. Starting from Langevin-type equations of motion, a formalism to calculate the frequency-dependent mobility μ^* and self diffusion coefficient D^* is constructed. Through a given radial distribution function, the distribution of medium particles is taken into account and many body effects due to interactions between diffusing and medium particles are considered on the basis of the superposition approximation for the three-particle distribution function. Model calculations are carried out for hard-sphere, soft-sphere and attractive Gaussian core systems and an important role of short-range order between medium particles is clarified. The frequency dependence of μ^* and D^* shows existence of the broad distribution of relaxation times in hard-sphere systems.