Brownian motion of interacting nonspherical tracer particles: General theory

A general theoretical framework is developed to describe the tracer-diffusion properties of nonspherical Brownian tracer particles that interact with the other particles in a multicomponent colloidal suspension of generally nonspherical particles, in the absence of hydrodynamic interactions. Here we present the derivation of the generalized Langevin equation (GLE) for the linear and angular velocity describing the Brownian motion of the tracer particle. In addition to the dissipative plus the random force and torque exerted by the solvent, this GLE contains the dissipative plus random force and torque due to the direct interactions with the other particles. An exact and general expression is derived for the time-dependent friction tensor that embodies the effects of the latter. Using a generalized Wertheim-Lovett's relation, this expression is cast in two alternative but equivalent forms. The long-time and short-time limits (in reference to the structural relaxation time τI) are also discussed.

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