A Local Gradient Theory for Structural Forces in Thin Fluid Films

The gradient theory is applied to a thin liquid film between two flat surfaces. In the spirit of the gradient theory, the free energy functional is written in terms of the order parameter (φ). A lattice model is used to physically interpret the model parameters. The approach enables us to consider a generalization of the Marcelja and Radic (Chem. Phys. Lett. 42, 129 (1976)) and Cahn (J. Chem. Phys. 66, 3667 (1977)) models. We assume that the bulk free energy is an arbitrary function without inflection points (the possibility of a phase transition is excluded), and the short-range interactions between solids and fluid are considered. The model presented is shown to have an exact solution in implicit form. The qualitative behavior of the solution in the interlayer region is illustrated through the phase plane method, and the corresponding dependence of the pressure acting on both surfaces is derived. When the film thickness is much larger than the intermolecular separation distance, we develop an asymptotically exact technique for obtaining explicit relations between various thermodynamic parameters. In this limit, the disjoining pressure decays exponentially with film thickness. The parameter in the exponent term is the correlation radius of bulk liquid, and the preexponent factor includes the properties of the bounding surfaces and also takes into account the deviation of the bulk free energy from a quadratic form. It is shown that the disjoining pressure can be either positive or negative. Conditions for sign reversal are obtained in terms of the lattice model parameters for multicomponent liquids.