Non-Fickian single-file pore transport

TL;DR

This study investigates how binding kinetics influence single-file pore transport, revealing a non-Fickian regime with flux scaling as 1/L^3 in short channels, modeled effectively by a two-state system.

Contribution

It demonstrates the emergence of a non-Fickian transport regime in short channels due to slow binding kinetics, modeled by a two-state stochastic process.

Findings

Flux scales as 1/L^3 in the non-Fickian regime

A two-state model accurately describes the system dynamics

Longer channels tend to be in low-flux states

Abstract

Single file diffusion (SFD) exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short pore-like channels using a symmetric exclusion process (SEP) with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux $\langle \Phi \rangle \sim 1/L^3$, where $L$ is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with $\langle \Phi \rangle \sim 1/L$. Longer systems are more often in a low flux state, leading to the non-Fickian behavior.