Dynamics of hard colloidal cuboids in nematic liquid crystals

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.