Capillary ordering and layering transitions in two-dimensional hard-rod fluids

We calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In the first stage we study a semi-infinite system consisting of an isotropic fluid in contact with a single hard line. We have found complete wetting by the columnar phase at the wall-isotropic fluid interface. When the fluid is confined between two hard walls, capillary columnar ordering occurs via a first-order phase transition. For higher chemical potentials the system exhibits layering transitions even for very narrow slits (near the one-dimensional limit). The theoretical model used was a density-functional theory based on the fundamental-measure functional applied to a fluid of hard rectangles in the restricted-orientation approximation (Zwanzig model). The results presented here can be checked experimentally in two-dimensional granular media made of rods, where vertical motions induced by an external source and excluded volume interactions between the grains allow the system to explore those stationary states which entropically maximize packing configurations. We claim that some of the surface phenomena found here can be present in two-dimensional granular-media fluids.