Relaxation dynamics in the columnar liquid crystal phase of hard platelets

We perform Monte Carlo simulations to analyze the equilibrium dynamics and the long-time structural relaxation decay of columnar liquid crystals of disk-like colloidal particles. In the wake of recent studies on the columnar mesophase of hard calamitic (rod-like) colloids, we now focus on the diffusion of their discotic counterparts, here modeled as oblate hard spherocylinders. These systems exhibit a non-Gaussian column-to-column diffusion due to the combined action of transient cages and periodic free-energy barriers. We find that at fixed packing fraction the barrier height increases with decreasing particle thickness, resulting into a more heterogeneous and non-Gaussian dynamics for thinner platelets, and reducing the inter-column diffusion coefficient. Moreover, we observe the characteristic two-step relaxation decay of the structure in the plane perpendicular to the column axis. By contrast, the in-column dynamics is similar to the typical single-file diffusion of one-dimensional dense fluids, with a relatively fast decay of the correlation functions.