Glassy dynamics in confinement: Planar and bulk limit of the mode-coupling theory

Abstract

We demonstrate how the matrix-valued mode-coupling theory of the glass transition and glassy dynamics in planar confinement converges to the corresponding theory for two-dimensional (2D) planar and the three-dimensional bulk liquid, provided the wall potential satisfies certain conditions. Since the mode-coupling theory relies on the static properties as input, the emergence of a homogeneous limit for the matrix-valued intermediate scattering functions is directly connected to the convergence of the corresponding static quantities to their conventional counterparts. We show that the 2D limit is more subtle than the bulk limit, in particular, the in-planar dynamics decouples from the motion perpendicular to the walls. We investigate the frozen-in parts of the intermediate scattering function in the glass state and find that the limits time $t\to \infty$ and effective wall separation $L\to 0$ do not commute due to the mutual coupling of the residual transversal and lateral force kernels.

10 pages, published in PRE

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Cited by in corpus (9)

• Diverging time scale in the dimensional crossover for liquids in strong confinement
• Non-monotonic effect of confinement on the glass transition
• Nonergodicity parameters of confined hard-sphere glasses
• Mode-coupling theory of the glass transition for colloidal liquids in slit geometry
• Static properties of quasi-confined hard-sphere fluids
• Dynamical properties of densely packed confined hard-sphere fluids
• Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition
• Tagged-particle dynamics in confined colloidal liquids
• Tagged-particle motion in quasi-confined colloidal hard-sphere liquids