The thermodynamics of adsorption at the surface of solutions

Abstract

In Gibbs’ thermodynamic theory of surfaces, the general equations governing equilibrium at interfaces were given, including equations governing adsorption. He pointed out, that in order to assign definite numerical values to the surface excess Г of each component, it is necessary to choose a definite position for a certain mathematical surface, placed parallel to, and within, or near to, the inhomogeneous region between the two bulk phases. Gibbs’ most general equations apply to any possible position of this surface, but the particular equation commonly known as "Gibbs' adsorption equation” was deduced by the aid of a particular choice of the position of this mathematical surface, such that the surface excess of one of the components vanished. The object of this paper is to examine the form taken by Gibbs’ general equations, when other conventions relating to the position of this dividing surface are chosen, and to establish the quantitative relations between the values of the surface excess of each component, obtained on the various conventions used. Our aim in doing this is to attempt to remove some of the confusion which has arisen, when interpreting the results of calculations of the Г in terms of the physical structure of the surface. The particular convention relating to the position of the dividing surface used by Gibbs suffers from the disadvantage that it is not easily visualised in terms of the physical structure of the surfaces, and is also unsymmetrical in respect of the components of the solution. Some of the alternative conventions examined here seem to us more convenient in both these respects, and the values of Г obtained by their aid are no more difficult to calculate from surface tension and vapour pressure data on solutions.