Remarks on the Gibbs adsorption equation and the van der Waals, Cahn-Hilliard theory of interfaces

The common statements of the Gibbs adsorption equation, and a phenomenological theory of interfaces (van der Waals, Cahn-Hilliard theory), are summarized, and then two remarks are made. The first is that only certain identifications of the local energy and entropy densities are admissible in the phenomenological theory if it is to be consistent with the adsorption equation. The second is a generalization to any of the relative adsorptions Γi(j) in a c-component system, of a microscopic interpetation that Leng, Rowlinson, and Thompson recently gave to Γ2(1) in a one-component system, where 2 and 1 refer to the densities of energy and matter, respectively.