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

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).

This is the published version of the paper, minor modification, few more references added

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