On the Thermodynamics of Thin Films. The Frumkin Equation

The Frumkin equation—a fundamental law of the thermodynamics of thin films—relates the surface tension of an interfacial region, which includes a thin film, to its disjoining pressure and thickness. The study of the original work has shown that the first derivation of this relation published by A.N. Frumkin in 1938 is thermodynamically inconsistent. In this article, the way is shown in which the Frumkin equation should be correctly derived, interpreted, and used. The following approaches are discussed: the finite-thickness layer method; the Gibbs methods with one, two, and three dividing surfaces; and the gravitational-field method.