A slope-dependent disjoining pressure for Lennard-Jones liquid films

A molecule in a bulk liquid is subject to intermolecular forces. A molecule in a thin liquid film may experience additional intermolecular forces, if the thin film thickness h is less than roughly 100 nm. The additional forces arise from the molecule\u27s proximity to different materials or phases sandwiching the thin film. The effect of these intermolecular forces at the continuum level is captured by disjoining pressure &Pi. Since dominates at small film thickness, it determines the stability and wettability of thin films. To leading order, Π = Π (h) because thin films are generally uniform. This form, however, can not be applied to films that end at the substrate with non-zero contact angles. Recently, a new procedure for deriving disjoining-pressure expressions has been developed (Wu and Wong 2004). In this approach, the total energy of a drop on a solid substrate is minimized. The total energy contains an interaction energy, which is found by pairwise summation of van der Waals potentials. Minimization of the total energy yields Π = Π (h,hx,hxx) . The current work extends the summation to the Lennard-Jones potential. Disjoning pressure Π = Π (h,hx,hxx) is also found, but the new expression accepts a much larger class of equilibrium drop and meniscus shapes. For example, a drop can have a precursor film of a finite or infinite extend and two drops can be connected by a precursor film and the unit repeats periodically. The last section discusses the stability of uniform films and the influence of intermolecular potential parameters