Dependence of the Contact Angle on Adsorption at the Solid-Liquid Interface

A method for determining the surface tension of solid-fluid interfaces has been proposed. For a given temperature and fluid-solid combination, these surface tensions are expressed in terms of material properties that can be determined by measuring the amount of vapor adsorbed on the solid surface as a function of x^V, the ratio of the vapor-phase pressure to the saturation-vapor pressure. The thermodynamic concept of pressure is shown to be in conflict with that of continuum mechanics, but is supported experimentally. This approach leads to the prediction that the contact angle, θ, can only exist in a narrow pressure range and that in this pressure range, the solid-vapor surface tension is constant and equal to the surface tension of the liquid-vapor interface, γ^LV. The surface tension of the solid-liquid interface, γ^SL, may be expressed in terms of measurable properties, γ^LV and θ: γ^SL = γ^LV(1 − cosθ). The value of θ is predicted to depend on both the pressure in the liquid at the three-phase, line x₃^L, and the three-phase line curvature, C_cl. We examine these predictions using sessile water droplets on a polished Cu surface, maintained in a closed, constant volume, isothermal container. The value of θ is found to depend on the adsorption at the solid-liquid interface, n^SL = n^SL(x₃^L,C_cl). The predicted value of θ is compared with that measured, and found to be in close agreement, but no effect of line tension is found.