Film and membrane-model thermodynamics of free thin liquid films.

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 γ(f) and a membrane model with a single zero-volume membrane of membrane tension 2γ(m). 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 3 nm in thickness. Such thin films are considerably more attractive than in classical Hamaker theory. Available molecular simulations reinforce this finding.