The statistics of an adsorbed monolayer with repulsive interaction between the adsorbed particles

• Published in: Physica 1956, Vol.22 (1), p.397-407
• Main Author: Kasteleijn, P.W.
• Format: Article
• Language: English
• ISSN: 0031-8914
• DOI: 10.1016/S0031-8914(56)80054-2

The properties of a monolayer of particles adsorbed on a surface with a two-sublattice structure, within which there is a positive interaction energy (repulsive force) between neighbouring particles, are investigated by means of a method developed in a previous paper for ferro- and antiferromagnetism. The grand partition function of the monolayer is expressed in terms of the effective energy V e of a pair of neighbouring lattice sites, which is of a very simple form. By making an assumption about V e analogous to the assumption of constant effective coupling in an Ising spin system the constant coupling approximation is obtained, which is equivalent to the quasi-chemical, or Bethe-Peierls approximation. On the basis of this approximation it is shown that for temperatures lower than a certain critical temperature the monolayer can exist in two phases, namely a disordered phase in which the two sublattices are equally covered by adsorbed particles, and an ordered phase in which there are more particles in one sublattice than in the other. The latter phase is realized only if the pressure p of the gas with which the monolayer is in equilibrium lies between two limits, p − and p +, which depend on the temperature. For p ⩽ p − and for p ⩾ p + the system is in the disordered phase, and both at p = p − and at p = p + a phase transition occurs. The energy E and the fraction Θ of the lattice covered with atoms are continuous in these two transition points, but there is a jump in the derivatives ∂ E/∂ Θ and ∂ Θ/∂ p. The adsorption isotherms are studied in detail, and the heat of adsorption is calculated as a function of Θ.