The lippmann equation and the characterization of black lipid films

Abstract

An optically black lipid film in aqueous media approximates closely to an ideally polarizable system and, in this respect, can be described by a form of the Lippmann equation. This equation is derived and integrated assuming the film capacitance to be independent of applied potential. Measurements of the contact angle and of the bulk interfacial tension are used to find accurate values of the film tension and it is shown that, for a range of lipid films, the integrated equation is obeyed for potential differences up to approximately 100 mV. Various ways are then described in which the Lippmann equation may be used to find film properties not readily accessible by other methods. Thus, for phospholipid films the accurate measurement of both film and bulk interface tensions presents difficulties, but these can be overcome if the specific capacitance is known. In this way the specific free energy of thinning of the film may be obtained. Conversely, for films in media of low conductivity or in systems in which film area measurements are difficult the determination of the specific capacitance is not readily achieved. A knowledge of the tension of the Plateau-Gibbs border together with the contact angle at different applied potentials, however, circumvents this problem. Finally it is pointed out that the use of the Lippmann equation provides an independent means of finding the interfacial tension between bulk oil and water phases and hence of checking the accuracy of the nonabsolute direct methods, such as the drop-volume technique, which have to be employed in such systems.