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

TL;DR

This study reveals that in smectic phases, non-commensurate guest particles diffuse faster and exhibit more homogeneous dynamics than host particles, with the Self-van Hove function providing detailed insights into their heterogeneous behavior.

Contribution

The paper demonstrates the effectiveness of the Self-van Hove function in detecting heterogeneous dynamics and highlights differences in diffusion behavior between host and guest particles in smectic phases.

Findings

Guest particles diffuse faster than host particles.

Self-van Hove functions reveal heterogeneous dynamics post phase transition.

Gaussian behavior of guest particles persists up to smectic-B phase.

Abstract

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