Where adsorption affects the contact angle: Wetting and condensation transitions

The effect of adsorption on the contact angle of a fluid on a smooth, homogeneous surface is often neglected, but all of the adsorption isotherms that account for multi-layer adsorption suggest the amount adsorbed at the solid-vapor interface becomes unboundedly large when the pressure, PV approaches the saturation vapor pressure, PS. The Gibbs adsorption equation indicates that strong adsorption at this interface would decrease the solid-vapor surface tension, and the Young equation indicates that a decrease in this surface tension would increase the value of the contact angle. However, neither adsorption nor its effect on the contact angle has been previously investigated experimentally in the limit of PV approaching P S. The expression for the adsorption equation (alpha-isotherm) is obtained by approximating a solid surface as consisting of M adsorption sites at each of which a molecular cluster consisting of an arbitrary number of molecules may adsorbed when the solid surface is exposed to the vapor phase of a fluid. Each molecular cluster is approximated as a quantum mechanical harmonic oscillator with a zero-point energy and frequency that depend on the number of molecules in the cluster. The canonical ensemble is used to derive the expression for the chemical potential of a molecule in a cluster. The alpha-isotherm is similar to the BET isotherm in functional form. If alpha is set equal to unity, they become equivalent, but the physical models on which their derivations are based are very different. Hill introduced the model leading to the BET equation, but characterized it as "physically unrealistic". In the BET model, the solid surface was also viewed as consisting of M adsorption sites, but at a given site the adsorbed molecules were assumed to be in a "vertical pile".; A similar procedure is used to obtain the adsorption alpha-isotherm at the solid surface when it is exposed to the liquid phase of the fluid. When the two isotherm relations are combined with the Gibbs adsorption and Young equations, one finds an expression for the contact angle of an equilibrium system consisting of both the liquid and vapor phases of a fluid held in a container with smooth and homogeneous surfaces. This expression is in terms of the temperature and the ratio of the pressure at the three-phase line to the saturation vapor pressure, x3. The parameters appearing in this expression have been evaluated for water and for formamide adsorbing on borosilicate (Pyrex(TM)7740) glass at temperatures of 5, 10, 20, 40 and 80°C.; The values of the interfacial properties and the ellipsometric measurements of adsorbed film thickness are used with the isotherm expression to examine the wetting transition and the transition in adsorbate occurring in the limit of the pressure approaching the saturation pressure, PS. The contact angle relation indicates that below a limiting value of x3, denoted as xw, the contact angle has a value of zero (wetting), but for xw ≤ x3 < alpha-1 the contact angle increases sharply with x3, where alpha is parameter appearing in the isotherm relation that has a value near unity. As x3 approaches alpha-1, the mass density of the clusters approaches that of the liquid phase.