Film and membrane-model thermodynamics of free thin liquid films

Abstract

In spite of over 7 decades of effort, the thermodynamics of thin free liquid films (as in emulsions and foams) lacks clarity. Following a brief review of the meaning and measurement of thin-film forces (i.e., conjoining/disjoining pressures), we offer a consistent analysis of thin-film thermodynamics. By carefully defining film reversible work, two distinct thermodynamic formalisms emerge: a film model with two zero-volume membranes each of film tension γf and a membrane model with a single zero-volume membrane of membrane tension 2γm. In both models, detailed thermodynamic analysis gives rise to thin-film Gibbs adsorption equations that allow calculation of film and membrane tensions from measurements of disjoining-pressure isotherms. A modified Young–Laplace equation arises in the film model to calculate film-thickness profiles from the film center to the surrounding bulk meniscus. No corresponding relation exists in the membrane model.Illustrative calculations of disjoining-pressure isotherms for water are presented using square-gradient theory. We report considerable deviations from Hamaker theory for films less than about 3nm in thickness. Such thin films are considerably more attractive than in classical Hamaker theory. Available molecular simulations reinforce this finding.