It is well known that understanding the transport properties of liquid crystals is crucial to optimize their performance in a number of technological applications. In this work, we analyze the effect of shape anisotropy on the diffusion of rodlike and disklike particles by Brownian dynamics simulations. To this end, we compare the dynamics of prolate and oblate nematic fluids 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 time scales. Nevertheless, when compared at identical infinite-dilution translational diffusion coefficients, oblate particles are faster than their prolate counterparts at short-to-intermediate time scales, 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 systems, we map the decay of the autocorrelation functions and their fluctuations over the time scales of our simulations to ponder the existence of mobile clusters of particles and the occurrence of collective motion.

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