Prediction of the wetting condition from the Zeta adsorption isotherm

Abstract

We use the Zeta adsorption isotherm and propose a method for determining the conditions at which an adsorbed vapour becomes an adsorbed liquid. This isotherm does not have a singularity when vapour phase pressure, P^V, is equal to the saturation-vapour pressure, P_s, and is empirically supported by earlier studies for P^V < P_s. We illustrate the method using water and three hydrocarbon vapours adsorbing on silica. When the Zeta isotherm is combined with Gibbsian thermodynamics, an expression for γ^SV, the surface tension of the solid–vapour interface as a function of x^V(≡P^V/P_s) is obtained, and it is predicted that adsorption lowers γ^SV from the surface tension of the substrate in the absence of adsorption, γ^S0, to that at the wetting condition. The wetting hypothesis indicates that γ^SV at wetting, x^V_w, is equal γ^LV, the surface tension of the liquid–vapour interface. For water vapour adsorbing on silica, adsorption lowers γ^SV to γ^LV at x^V_w equal unity, but for the hydrocarbons heptane, octane and toluene adsorbing on silica x^V_w is found to be 1.40, 1.30 and 1.32 respectively.