Mode-coupling theory of the glass transition for confined fluids

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.

Excess free energy of supercooled liquids at disordered walls

“…It is plau-sible, therefore, that this behavior of γ with respect to the temperature, is correlated to the relaxation time of the supercooled liquid near the wall, which as previous works have shown, decreases in the neighborhood of the wall as temperature increases [4]. It is to be noted that for glass-forming systems strongly confined by parallel flat walls, a Mode-coupling theory has been developed recently to explain the slowing down of the relaxation dynamics [16]. However, no such microscopic theories exist for supercooled liquids in contact with disordered walls.…”

Long-time limit of correlation functions

“…Matrix-valued correlation functions occur for example considering mixtures of different species [2,3,12]. Several relaxation channels emerge naturally for molecular fluids [14,15] or in confined geometry [13,16,17] and yield a different mathematical structure, nevertheless it appears feasible to demonstrate the existence of the long-time limit also for this case.…”

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

“…Relying on this set of distinguished variables the equations of motion have been derived within the Zwanzig-Mori projection operator formalism [44,114,119]. As a peculiarity of the confinement there appear now two different relaxation channels corresponding to currents parallel and perpendicular to the walls, thereby changing the mathematical structure of the theory with respect to bulk systems.…”

“…Alternatively, confinement can also introduce such competing mechanisms. To describe dense liquids in such confinement the MCT has been extended [44,114] relying on symmetry-adapted modes that account for the broken translational symmetry perpendicular to the walls. A striking prediction of the MCT in slit geometry has been the emergence of a multiple reentrant glass transition in the nonequilibrium state diagram as a function of the slit width along lines of constant packing fraction [44,115,116].…”