Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

TL;DR

This study uses molecular dynamics simulations to analyze how the diffusion behavior of interacting particles in quasi-one-dimensional channels transitions from single-file to two-dimensional regimes, depending on channel width and confinement profile.

Contribution

It reveals how the transition from single-file to 2D diffusion varies with confinement potential and channel shape, providing new insights into diffusion dynamics in confined geometries.

Findings

Transition depends on channel width and confinement profile.

Smooth transition for parabolic confinement; sharp for hard-wall confinement.

Distribution of particle density explains different transition behaviors.

Abstract

Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion (SFD) to the two-dimensional diffusion regime is investigated. This transition (regarding the calculation of the scaling exponent ($\alpha$) of the MSD $<\Delta x^{2}(t)>$ $\propto t^{\alpha}$) as a function of the width of the channel, is shown to change depending on the channel's confinement profile. In particular the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp/stepwise (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.