Confinement occurs naturally in many physical, chemical and biological systems such as nanotubes, porous rocks or crowded living cells. The effect of confinement on the properties of simple liquids has therefore been carefully studied with experiments  and simulations [2,3] showing a large variety of interesting phenomena. Even for the simplest case of hard spheres confined between parallel, hard walls one observes spatially inhomogeneous density profiles and diffusivities , anisotropic structure factors , multiple-reentrant glass transitions  and solid-to-solid transitions between different crystalline phases .
Here we calculate the phase diagram of a mixture of size-disperse hard spheres in confinement by computer simulations and a statistical mechanics theory . Despite the fact that this mixture is the prototypical model of a glass forming liquid, we find that when it is confined between walls, crystals form at densities significantly below the glass transition point. This crystallization is facilitated by fractionation, i.e., the demixing of particles based on their size. The numerical and theoretical results show semi-quantitative agreement, both featuring a novel honeycomb-shaped crystalline structure. We show that the crystallization can be exploited in a wedge geometry to demix particles of different sizes. Our findings could thus be exploited in the future as a purification technique.
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