When bigger is faster: A self-Van Hove analysis of the enhanced self-diffusion of non-commensurate guest particles in smectics

We investigate the anomalous dynamics in smectic phases of short host rods where, counter-intuitively, long guest rod-shaped particles diffusive faster than ones, due to their precise size mismatch. In addition previously reported mean-square displacement, we analyze time evolution Self-van Hove functions G(r,t), as this probability density function uncovers intrinsic heterogeneous dynamics. Through analysis, show that parallel director becomes non-gaussian and therefore after nematic-to-smectic-A phase transition, even though it exhibits a nearly behavior according its displacement. contrast, non-commensurate display Gaussian motion, up transition smectic-B phase. Thus, is very sensitive probe account for instantaneous our system, should be more widely considered quantitative complementary approach classical displacement characterization diffusion processes.