# Brownian dynamics simulations of oblate and prolate colloidal particles in nematic liquid crystals

## TL;DR

This study uses Brownian dynamics simulations to analyze how shape anisotropy affects the diffusion of rod-like and disk-like particles in nematic liquid crystals, revealing anisotropic and shape-dependent diffusion behaviors.

## Contribution

It compares the dynamics of prolate and oblate particles with matched diffusion coefficients, highlighting shape-dependent diffusion anisotropy and timescale variations in nematic liquid crystals.

## Key findings

- Prolate particles diffuse faster than oblate particles at long times.
- Oblate particles are faster at short-to-intermediate times when matched by diffusion coefficients.
- Diffusion is anisotropic, with prolate particles diffusing faster along the nematic director and oblate particles faster perpendicular to it.

## Abstract

It is well known that understanding the transport properties of liquid crystals (LCs) is crucial to optimise their performance in a number of technological applications. In this work, we analyse the effect of shape anisotropy on the diffusion of rod-like and disk-like particles by Brownian dynamics simulations. To this end, we compare the dynamics of prolate and oblate nematic LCs incorporating particles with the same infinite-dilution translational or rotational diffusion coefficients. Under these conditions, which are benchmarked against the standard case of identical aspect ratios, we observe that prolate particles display faster dynamics than oblate particles at short and long timescales. Nevertheless, when compared at identical infinite-dilution translational diffusion coefficients, oblate particles are faster than their prolate counterparts at short-to-intermediate timescales, which extend over almost three time decades. Both oblate and prolate particles exhibit an anisotropic diffusion with respect to the orientation of the nematic director. More specifically, prolate particles show a fast diffusion in the direction parallel to the nematic director, while their diffusion in the direction perpendicular to it is slower. By contrast, the diffusion of oblate particles is faster in the plane perpendicular to the nematic director. Finally, in the light of our recent study on the long-time Gaussian and Fickian diffusion in nematic LCs, we map the decay of the autocorrelation functions and their fluctuations over the timescales of our simulations to ponder the existence of mobile clusters of particles and the occurrence of collective motion.