Surface Tension and Adsorption without a Dividing Surface

The ingenious concept of a dividing surface of zero thickness that was introduced by Gibbs is the basis of the theory of surface tension and adsorption. However, some fundamental questions, mainly those related to the location of the dividing surface and the proper definition of relative adsorption, have remained open over the years. To avoid these questions, the present paper proposes to analyze an interfacial phase by defining a thermodynamic system of constant, but nonzero thickness. The interfacial phase is analyzed as it really is, namely a nonuniform three-dimensional entity. The current analysis redevelops the equation for calculating surface tension, though with different assumptions. However, the main point in the proposed model is that the thermodynamic interfacial system, due to its fixed thickness, conforms to the requirement of first-order homogeneity of the internal energy. This property is the key that allows using the Gibbs adsorption isotherm. It is also characteristic of the Gibbs dividing surface model, but has not always been discussed with regard to subsequent models. The resulting equation leads to a simple, "natural" expression for the relative adsorption. This expression may be compared with simulations and sophisticated surface concentration measurements, and from which the dependence of interfacial tension on the solution composition can be derived. Finally, it is important to point out that in order to calculate the interfacial tension as well as the relative adsorption from data on the properties of the interfacial phase, there is no need to know its exact thickness, as long as it is bigger than the actual thickness but sufficiently small.