Mode-coupling theory of the glass transition for confined fluids
arXiv:1208.1929 · doi:10.1103/PhysRevE.86.021502
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.
16 pages; to be published in PRE
References in corpus (16)
- Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
- Layering and position-dependent diffusive dynamics of confined fluids
- Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
- Glass Transition in Confined Geometry
- Mixing effects for the structural relaxation in binary hard-sphere liquids
- Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
- Dynamic Glass Transition in Two Dimensions
- Glass transition of hard spheres in high dimensions
- Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
- Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
- Available states and available space: Static properties that predict dynamics of confined fluids
- Tests of mode-coupling theory in two dimensions
- Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory
- Space-resolved dynamics of a tracer in a disordered solid
- Glass transition of binary mixtures of dipolar particles in two dimensions
- Comment on "Mode-Coupling Theory as a Mean-Field Description of the Glass Transition"
Cited by in corpus (9)
- Multiple reentrant glass transitions in confined hard-sphere glasses
- Tagged-particle motion in a dense confined liquid
- Structural quantities of quasi-two-dimensional fluids
- Diverging time scale in the dimensional crossover for liquids in strong confinement
- Glassy dynamics in confinement: Planar and bulk limit of the mode-coupling theory
- Long-time limit of correlation functions
- Local structure-mobility relationships of confined fluids reverse upon supercooling
- Packing frustration in dense confined fluids
- Excess free energy of supercooled liquids at disordered walls