STATISTICAL-MECHANICS OF ANOMALOUS THERMAL EFFECTS IN MONOLAYERS

The monolayer is represented here by a two-dimensional lattice model in which a molecule in the singly bound state is a 'monomer' occupying one lattice site while a molecule in the doubly bound or 'extended' state is a 'dimer' occupying two neighbouring sites. There is an energy and an entropy of transition (both negative) from the former to the latter state. A series treatment of a lattice incompletely occupied by dimers, modified to allow for a monomer as well as a 'hole' or vacant-site species, is used. The three types of thermal anomaly can be represented by sets of theoretical surface-pressure/area isotherms in three reduced temperature ranges. A Flory-Huggins approximation is used to incorporate nearest-neighbour energies of interaction between the monolayer molecules and the three behaviour types are again reproduced.