Phase behaviour of parallel hard rods in confinement: an Onsager theory study.

The effect of confinement on the positional ordering is examined in a system of parallel hard cylinders using the second virial theory of Onsager. Hard cylinders are arranged in a slit-like pore (two parallel planar hard walls) in such a way that the long axes of the particles are perpendicular to the surface of confining hard walls. We have incorporated the theories of the bulk and the confined systems into a single formalism, where a w(ij) kernel function provides the link between the bulk and confined systems. It is shown that the presence of hard walls inhibits the second order nematic-smectic A phase transition irrespective of the value of the wall-to-wall separation. Instead, due to accommodation problems of the cylinders into the pore, an infinite number of first order layering phase transitions appears. Coexisting curves, corresponding to the equilibrium between two phases having n and n + 1 smectic-like periods, are bounded with lower critical points. The gap between the average densities of the coexisting phases shrinks with increasing pore width, while the properties of the critical points monotonically move towards those of the nematic-smectic A phase transition of the bulk system (d --> ∞). The effect of only one hard wall is related to the bulk nematic-smectic A phase transition since a critical wetting transition of the wall induced layering takes place.