Mode-coupling theory of the glass transition for confined fluids

Simon Lang, Rolf Schilling, Vincent Krakoviack, and Thomas Franosch
Phys. Rev. E 86, 021502 – Published 10 August 2012

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.

  • Received 23 March 2012

DOI:https://doi.org/10.1103/PhysRevE.86.021502

©2012 American Physical Society

Authors & Affiliations

Simon Lang1, Rolf Schilling2, Vincent Krakoviack3, and Thomas Franosch1

  • 1Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
  • 2Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany
  • 3Laboratoire de Chimie, UMR CNRS 5182, École Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 7, France

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Issue

Vol. 86, Iss. 2 — August 2012

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