Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod

TL;DR

This paper develops a mesoscopic Perrin theory to accurately describe the anisotropic diffusion of strongly hindered rods in dense suspensions, matching Brownian dynamics simulations.

Contribution

It introduces a new mesoscopic model based on the exact solution of the Smoluchowski-Perrin equation for dense rod suspensions.

Findings

Quantitative agreement with Brownian dynamics simulations

Tube confinement characterized by a power law decay with exponent 1/2

Enhanced understanding of anisotropic diffusion in dense systems

Abstract

Slender rods in concentrated suspensions constitute strongly interacting systems with rich dynamics: transport slows down drastically and the anisotropy of the motion becomes arbitrarily large. We develop a mesoscopic description of the dynamics down to the length scale of the interparticle distance. Our theory is based on the exact solution of the Smoluchowski-Perrin equation; it is in quantitative agreement with extensive Brownian dynamics simulations in the dense regime. In particular, we show that the tube confinement is characterised by a power law decay of the intermediate scattering function with exponent 1/2.