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 freeenergy 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.