Diffusion in a smectic liquid crystal with screw dislocations

Screw dislocations provide barrier-free pathways that enhance interlayer diffusion in smectic liquid crystals and other layered materials. To explore this contribution to interlayer diffusion we study a “random parking garage” model in which a random walker can move between layers only by circling a dislocation core. We find that in such a layered system with a density of ρ screw dislocations per unit area, with randomly chosen position, Burgers vector and phase, the ratio of interlayer to intralayer diffusion coefficients is D_‖/D_⊥=(ρb²/4π)lnR/a. Here b is the layer spacing, R is the layer radius, and a is the dislocation core size. Monte Carlo simulations are in agreement with this result. We discuss implications for both molecular simulation and experimental studies of diffusion in smectics.