From random walk to single-file diffusion

TL;DR

This study experimentally investigates diffusion in a quasi-one-dimensional colloid suspension, confirming the validity of the hard rod single-file diffusion theory and linking it to a recent SFD theory by Kollmann.

Contribution

It provides the first experimental validation of the hard rod SFD theory for a Tonks gas and connects it with Kollmann's recent SFD theory.

Findings

Inverse mean squared displacement sums short and long time diffusion contributions.

Quantitative agreement with hard rod model for colloid concentration dependence.

Validation of the hard rod SFD theory for a Tonks gas.

Abstract

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. This ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the single-file 1D mobility on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann leads to the hard rod SFD theory for a Tonks gas.