# The effect of soft repulsive interactions on the diffusion of particles in quasi-one-dimensional channels: A hopping time approach

## TL;DR

This study develops a transition state theory to predict hopping times for particles in quasi-one-dimensional channels, revealing how soft repulsive interactions influence diffusion crossover and how channel width affects particle dynamics.

## Contribution

It introduces a quantitative transition state theory approach to predict hopping times in confined soft particle systems, accounting for particle softness and channel width effects.

## Key findings

- Free energy barrier peaks at intermediate particle softness.
- Hopping times are influenced by channel width and particle softness.
- Maximum free energy barrier shifts with channel narrowing.

## Abstract

Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping events are rare, the diffusion coefficient in the long time limit can be related to a hopping time that measures the average time it takes a particle to escape the local cage formed by its neighbours. In this work, we show that a transition state theory that calculates the free energy barrier for two particles attempting to pass each other in the small system isobaric ensemble is able to quantitatively predict the hopping time in a system of two-dimensional soft repulsive discs [$U(r_{ij})=(\sigma/r_{ij})^{\alpha}$] confined to a hard walled channel over a range of channel radii and degrees of particle softness measured in terms of $1/\alpha$. The free energy barrier exhibits a maximum at intermediate values of $\alpha$ that moves to smaller values of $1/\alpha$ (harder particles) as the channel becomes narrower. However, the presence of the maximum is only observed in the hopping times for wide channels because the interaction potential dependence of the kinetic prefactor plays an increasingly important role for narrower channels. We also begin to explore how our transition state theory approach can be used to optimize and control dynamics in confined quasi-one-dimensional fluids.