Mode-coupling theory of the glass transition for confined fluids

TL;DR

This paper develops a microscopic mode-coupling theory for the glass transition in confined fluids between parallel walls, accounting for broken translational symmetry and anisotropic correlations.

Contribution

It introduces a novel mode-coupling framework tailored for slab geometries, extending bulk theories to confined systems with explicit wall effects.

Findings

Derivation of symmetry-adapted correlation functions.

Proof of covariance properties in nonergodicity equations.

Framework applicable to confined glass-forming liquids.

Abstract

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.