  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.
