Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard mode-coupling theory equations in bulk and in two dimensions as limiting cases and requires as input solely the equilibrium density profile and the structure factors of the fluid in confinement. We evaluate the phase diagram as a function of the distance of the plates for the case of a hard sphere fluid and obtain an oscillatory behavior of the glass transition line as a result of the structural changes related to layering.

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.

Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro-and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition. A thorough understanding of the slowing down of transport by orders of magnitude upon approaching the glass transition is one of the grand challenges of condensed matter theory [1][2][3][4][5]. A recent focus in the study of glasses has been to introduce competing mechanisms that lead to glass transition phase diagrams exhibiting non-monotonic behaviour. Reentrant scenarios have been uncovered, for example, upon adding a short-range attraction to colloidal particles [6][7][8], by competing near ordering in binary mixtures [9,10], or by inserting the liquid in a frozen disordered host structure [11][12][13]. However, instead of changing the structure of the liquid directly, one may also affect its properties by purely geometric means, via an increase of its confinement [14][15][16][17][18][19][20][21][22][23][24]. Depending on the ratio of the characteristic confinement length (e.g., the wall separation) to particle diameter, this can either lead to an increase or decrease of the first peak of the pair distribution function-the latter being a measure of the "stiffness" of the local packing structure [18]. As long as crystallization is kinetically hindered, this is expected to have a strong impact on the dynamics of the liquid and the glass transition. Earlier simulation studies and experiments of the confinement effects on the glass transition were mainly concerned with wall-to-wall separations of the order of several particle diameters or larger (see, e.g., [14][15][16][17][18][19] and references therein). Recently, however, the case of stronger confinement has received growing attention [20][21][22][23]. Here we focus on this latter regime of strong confinement, where only a few particle layers fit into the space between the walls. The problem of crystallization is circumvented by introducing size-dispersity [25] into our simulations, which leads to a geometric frustration. We evaluate the diffusion coefficient to assess the slowing-down of the dynamics and to establish a glass-transition state diag...