Statistical Thermodynamic Theory for Adsorption Isotherms

Abstract

It is shown that the natural expansion parameter in the grand canonical ensemble for monolayer surface coverage is the expansion of the logarithm of the number of adsorbed molecules, ln ${\overline{N}}_a$ , as a polynomial expansion in ln ${\mathrm{z/z}}_0=\ln {\mathrm{\hspace{0.17em}P/P}}_0{\mathrm{=(\mu -\mu }}_0\mathrm{)/\; kT}$ . For the heterogeneous localized site model this expansion truncates after the squared term in the expansion, and the linear dependence of the monolayer surface coverage adsorption isotherms, as a function of ${\mathrm{(\mu -\mu }}_0{)}^2\mathrm{=\; (kT}\ln {\mathrm{\hspace{0.17em}P/P}}_0{)}^2$ , has a natural explanation.