The mode-coupling glass transition in a fluid confined by a periodic potential

TL;DR

This study demonstrates that a fluid confined by a periodic potential can undergo a glass transition at lower densities than in bulk, using mode-coupling theory and one-dimensional modeling to explore the effects of confinement.

Contribution

The paper introduces a mode-coupling theory analysis of glass transition in confined fluids with periodic potentials, highlighting the influence of confinement wavelength and revealing complex relaxation behaviors.

Findings

Glass transition occurs at lower densities under confinement.

Observation of three-step relaxation and glass-glass transition.

Results suggest similar phenomena in higher-dimensional systems.

Abstract

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory (MCT) at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behaviour expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S.H. Krishnan, PhD thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J-ST 189, 135-139 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack, PRE 75, 031503 (2007) and Lang et al., PRL 105, 125701 (2010).