New theory of equation of state for surface monolayer.

Abstract

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.