title: 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 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.
authors: Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720-1462, United States. Electronic address: radke@berkeley.edu.
authors: C J
authors: CJ
authors: Radke
keywords: Conjoining/disjoining pressure; Film contact angle; Film model; Frumkin–Deryagin equation; Membrane model; Modified Young–Laplace relation; Molecular simulation; Square-gradient theory; Thin films; Thin-film Gibbs adsorption equation