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

Abstract

The effect of confinement on the positional ordering is examined in a system of parallelhard cylinders using the second virial theory of Onsager. Hard cylinders are arranged in aslit-like pore (two parallel planar hard walls) in such a way that the long axes of theparticles are perpendicular to the surface of confining hard walls. We have incorporated thetheories of the bulk and the confined systems into a single formalism, where awij kernel function provides the link between the bulk and confined systems. It is shown thatthe presence of hard walls inhibits the second order nematic–smectic A phase transitionirrespective of the value of the wall-to-wall separation. Instead, due to accommodation problemsof the cylinders into the pore, an infinite number of first order layering phase transitionsappears. Coexisting curves, corresponding to the equilibrium between two phases havingn andn + 1 smectic-like periods, are bounded with lower critical points. The gap between theaverage densities of the coexisting phases shrinks with increasing pore width,while the properties of the critical points monotonically move towards those ofthe nematic–smectic A phase transition of the bulk system (). The effect of only one hard wall is related to the bulk nematic–smectic A phasetransition since a critical wetting transition of the wall induced layering takes place.