Model of freezing behavior of liquid monolayers adsorbed in cylindrical pores

Freezing behavior of liquid monolayers adsorbed in extremely narrow tubes is studied by a lattice model that can be mapped to the Ising magnet. The model assumes an m × ∞ square net with cylindrical geometry with m cells in the circular direction, each cell being occupied by a molecule with q orientations. First we examine how the freezing behavior of the model monolayer varies with increasing m, i.e., increasing the pore diameter. It is shown that the behavior in two dimensions (m → ∞) is nearly achieved with small values ofm(m ∼ 8). Second we study an extended model that has anisotropic intermolecular interaction. When the anisotropic interaction energies are those with which the corresponding Ising model has antiferromangetic interactions in the axial direction and ferromagnetic interactions in the circular direction, a semiordered phase appears in a temperature regime between those of solid and liquid states.