Prediction of the wetting condition from the Zeta adsorption isotherm

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 gamma(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 gamma(SV) from the surface tension of the substrate in the absence of adsorption, gamma(SO), to that at the wetting condition. The wetting hypothesis indicates that gamma(SV) at wetting, x(W)(V), is equal gamma(LV), the surface tension of the liquid-vapour interface. For water vapour adsorbing on silica, adsorption lowers gamma(SV) to gamma(LV) at x(W)(V) equal unity, but for the hydrocarbons heptane, octane and toluene adsorbing on silica x(W)(V) is found to be 1.40, 1.30 and 1.32 respectively.