An approximate adsorption isotherm for physical adsorption. I. Lattice gas

Abstract

The matrix method of statistical mechanics has been used to obtain an approximate adsorption isotherm for a lattice gas in the presence of a wall which interacts with adjoining sites. The excess number adsorbed per surface site has the form [ρII(z′)−ρIII(z)](1 +∂ ln α/∂ ln z), where the densities ρII and ρIII are two- and three-dimensional (bulk) functions of activity z; α is defined by ρII(α2z)=ρIII(z); and z′ =z⋅α⋅exp(−βεB). Here, εB is the interaction energy of a particle with the wall. Surface viral coefficients were calculated as a test of the theory. For nearest neighbor lattice gases, the first and second coefficients are exact. The third coefficient is exact in the special case of a hard wall, and it is also exact for a hard core gas with coordination number 12 in three dimensions and 6 on the surface layer (corresponding to the geometry of the closest packed spheres). The isotherm was also applied to the continuum model of hard spheres against a hard wall. Virial coefficients indicate results slightly inferior to scaled particle theory.