BROWNIAN-MOTION OF INTERACTING NONSPHERICAL TRACER PARTICLES - GENERAL-THEORY

A general theoretical framework is developed to describe the tracer-di ffusion properties of nonspherical Brownian tracer particles that inte ract with the other particles in a multicomponent colloidal suspension of generally nonspherical particles, in the absence of hydrodynamic i nteractions. Here we present the derivation of the generalized Langevi n equation (GLE) for the linear and angular velocity describing the Br ownian motion of the tracer particle. In addition to the dissipative p lus the random force and torque exerted by the solvent, this GLE conta ins the dissipative plus random force and torque due to the direct int eractions with the other particles. An exact and general expression is derived for the time-dependent friction tensor that embodies the effe cts of the latter. Using a generalized Wertheim-Lovett's relation, thi s expression is cast in two alternative but equivalent forms. The long -time and short-time limits (in reference to the structural relaxation time tau(I)) are also discussed.