Tagged-particle dynamics in confined colloidal liquids

TL;DR

This paper uses mode-coupling theory to analyze the dynamics of colloidal particles in confined geometries, revealing how confinement influences relaxation, diffusion, and velocity correlations near the glass transition.

Contribution

It provides new theoretical predictions for localization length, diffusion scaling, and VACF behavior in confined colloidal liquids, supported by numerical and simulation results.

Findings

Confinement affects low-frequency susceptibility spectra similarly regardless of microscopic dynamics.

Derived analytical expressions match Brownian dynamics simulations for scattering functions.

Identified a transition in VACF scaling from unconfined to confined regimes.

Abstract

We present numerical results for the tagged-particle dynamics by solving the mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show that neither the microscopic dynamics nor the type of intermediate scattering function qualitatively changes the asymptotic dynamics in vicinity of the glass transition. In particular, we find similar characteristics of confinement in the low-frequency susceptibility spectrum which we interpret as footprints of parallel relaxation. We derive predictions for the localization length and the scaling of the diffusion coefficient in the supercooled regime and discover a pronounced non-monotonic dependence on the confinement length. For dilute liquids in the hydrodynamic limit we calculate an analytical expression for the intermediate scattering functions, which is in perfect agreement with event-driven Brownian dynamics simulations. From this, we derive an expression for persistent anti-correlations in the velocity autocorrelation function (VACF) for confined motion. Using numerical results of the cMCT equations for the VACF we also identify a cross-over between different scalings corresponding to a transition from unconfined to confined behaviour.