Derivation of a theoretical equation for the Brownian motion of interacting particles

Abstract

A theoretical equation for the Brownian motion of interacting particles is derived on the basis of the Langevin equation. The mean-square displacement of a Brownian particle is given by 〈Δr²(t)〉= 6D[graphic omitted] which corresponds to the experimental equation proposed by Pusey. The values of α and λ are given by [graphic omitted] where 〈N〉, K and ζ are the average number of particles interacting with one particle, the force constant of the interaction and the friction coefficient of the particle, respectively.