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arXiv · 1208.1929

Mode-coupling theory of the glass transition for confined fluids

Simon Lang·Rolf Schilling·Vincent Krakoviack·Thomas Franosch
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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.

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Simon Lang, Rolf Schilling, Vincent Krakoviack, Thomas Franosch. 2012-08-09. Mode-coupling theory of the glass transition for confined fluids. https://doi.org/10.1103/physreve.86.021502

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