Mode-coupling theory of the glass transition for colloidal liquids in slit geometry

TL;DR

This paper derives mode-coupling equations for colloidal liquids confined between parallel walls, extending the theory to slit geometries and confirming the universality of the glass transition across different microscopic dynamics.

Contribution

It introduces irreducible memory kernels for relaxation channels and extends the projection operator technique to confined colloidal systems.

Findings

Mode-coupling functional has the same form as in Newtonian systems.

Universality of the glass-transition singularity is confirmed.

Extended theoretical framework for colloids in slit geometry.

Abstract

We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection operator technique to colloidal liquids in slit geometry. Investigating both the collective dynamics as well as the tagged-particle motion, we prove that the mode-coupling functional assumes the same form as in the Newtonian case corroborating the universality of the glass-transition singularity with respect to the microscopic dynamics.