Single-file dynamics of colloids in circular channels: time scales, scaling laws and their universality

TL;DR

This paper investigates the complex time-dependent behavior of colloidal particles confined in circular channels, revealing universal scaling laws and identifying four distinct dynamical regimes through experiments, simulations, and theoretical analysis.

Contribution

It introduces a comprehensive analysis of single-file colloidal dynamics in circular confinement, deriving universal scaling laws and crossover times validated by experiments and simulations.

Findings

Four temporal regimes identified: diffusion, sub-diffusion, rotational diffusion, saturation.

Analytical expressions for mean-square angular displacement and crossover times derived.

Universal scaling laws accurately predict long-time dynamics across systems.

Abstract

In colloidal systems, Brownian motion emerges from the massive separation of time and length scales associated to characteristic dynamics of the solute and solvent constituents. This separation of scales produces several temporal regimes in the colloidal dynamics when combined with the effects of the interaction between the particles, confinement conditions, and state variables, such as density and temperature. Some examples are the short- and long-time regimes in two- and three-dimensional open systems and the diffusive and sub-diffusive regimes observed in the single-file dynamics along a straight line. This work studies the way in which a confining geometry induces new time scales. We report on the dynamics of interacting colloidal particles moving along a circle by combining a heuristic theoretical analysis of the involved scales, Brownian Dynamics computer simulations, and video-microscopy experiments with paramagnetic colloids confined to lithographic circular channels subjected to an external magnetic field. The systems display four temporal regimes in this order: one-dimensional free diffusion, single-file sub-diffusion, free-cluster rotational diffusion, and the expected saturation due to the confinement. We also report analytical expressions for the mean-square angular displacement and crossover times obtained from scaling arguments, which accurately reproduce both experiments and simulations. Our generic approach can be used to predict the long-time dynamics of many other confined physical systems.