Shape-Driven Caging Dynamics of Hard Polygons

TL;DR

This paper investigates the unique caging dynamics of nearly-hard polygonal particles in fluids, revealing intermediate-time behaviors and developing a coupled translational-rotational Langevin model that predicts these phenomena.

Contribution

It introduces a novel study of shape-driven caging in anisotropic particles and extends Langevin theory to include secondary cross-correlations for better dynamic predictions.

Findings

Identification of shape-dependent caging at intermediate densities

Development of a coupled translational-rotational Langevin model

Prediction of relaxation times incorporating secondary correlations

Abstract

The fundamentals of Brownian motion have been largely well understood since the early 20th century, with most recent additions focusing on understanding anomalous diffusion via rescaling of drag coefficents. That focus emphasizes long-time dynamic behavior, but recent results indicate that additional, secondary modes are also present at short and intermediate times in fluids of anisotropic particles. Here, we study the dynamics of a representative family of nearly-hard n-gons. Using molecular dynamics simulations, we study a distinct form of caging only present in anisotropic systems. We show that this caging behavior emerges in the mean squared displacement of n-gons at intermediate particle volume fractions. We then develop an extended Langevin theory directly coupling translational and rotational motion as a function of the relative anisotropy for different n-gons that predicts the observed caging behavior. Extending our theory to incorporate secondary, off-phase cross-correlations between particles further enables the prediction of both translational and rotational relaxation times of the system.