Ordering of hard rectangles in strong confinement

Abstract

Using transfer operator and fundamental measure theories, we examine the structural and thermodynamic properties of hard rectangles confined between two parallel hard walls. The side lengths of the rectangle ($L$ and $D$, $L>D$) and the pore width ($H$) are chosen such that maximum two layers are allowed to form in planar order ($L$ is parallel to the wall), while only one in homeotropic order ($D$ is parallel to the wall). We observe three different structures: (i) a low density fluid phase with parallel alignment to the wall, (ii) an intermediate and high density fluid phase with two layers and planar ordering and (iii) a dense single fluid layer with homeotropic ordering. The appearance of these phases and the change in the ordering direction with density is a consequence of the varying close packing structures with $L$ and $H$. Interestingly, even three different structures can be observed with increasing density if $L$ is close to $H$.

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• Ordering transitions of weakly anisotropic hard rods in narrow slit-like pores
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• The columnar-disorder phase boundary in a mixture of hard squares and dimers
• Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: one or two phase transitions?
• Three stable phases and thermodynamic anomaly in a binary mixture of hard particles
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes
• Confinement effects on the random sequential adsorption packings of elongated particles in a slit
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• Highly confined mixtures of parallel hard squares: A Density Functional Theory study