Tagged-particle motion in a dense confined liquid

TL;DR

This paper develops a theoretical framework to analyze the motion of a tagged particle in a dense, confined liquid, accounting for interactions and lack of translational symmetry, and derives microscopic expressions for diffusion parallel to the walls.

Contribution

It introduces a generalized mode-coupling approach for confined liquids and provides a microscopic expression for in-plane diffusion of a tagged particle.

Findings

Derived an equation of motion for the incoherent scattering function in confined geometry.

Provided a microscopic expression for the diffusion coefficient parallel to the walls.

Enabled systematic analysis of how particle size and interactions affect dynamics in confinement.

Abstract

We investigate the dynamics of a tagged particle embedded in a strongly interacting confined liquid enclosed between two opposing flat walls. Using the Zwanzig-Mori projection operator formalism we obtain an equation of motion for the incoherent scattering function suitably generalized to account for the lack of translational symmetry. We close the equations of motion by a self-consistent mode-coupling ansatz. The interaction of the tracer with the surrounding liquid is encoded in generalized direct correlation functions. We extract the in-plane dynamics and provide a microscopic expression for the diffusion coefficient parallel to the walls. The solute particle may differ in size or interaction from the surrounding host-liquid constituents offering the possibility of a systematic analysis of dynamic effects on the tagged-particle motion in confinement.