An Empirical Isotherm for Multilayer Physisorption

An empirical isotherm is presented for the physisorption of multilayers in the pressure range from the saturated vapor pressure to the pressure corresponding to monolayer coverage. The isotherm equation is θ = V/V m ((2n − 1)ψ)/(1 − ψ))1/ n , where V is the amount adsorbed and V m is the amount adsorbed in a monolayer, ψ = p/p s (p is the pressure and p s is the saturated vapor pressure), and n lies between 2.5 and 4.5 in most cases. It is shown than this empirical isotherm approaches the Frenkel−Halsey−Hill or MacMillan−Teller isotherms for ψ > 0.7 and approaches the Brunauer−Emmett−Teller (BET) isotherm for ψ < 0.3. The empirical isotherm is compared with published experimental data for the adsorption of N2, Ar, H2O, and neopentane on several nonporous solids; the agreement is good from θ = 1 to 3 in most cases and in some cases to θ = 10. A method is outlined for deriving monolayer coverage from a plot of log V against log ψ /(1 − ψ). For several sets of experimental data for the adsorption of the above gases on nonporous surfaces the monolayer coverage so determined is in agreement with that measured by the BET method to better than 10%.