Liquid drops on surfaces: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling

For a film of liquid on a solid surface, the binding potential g(h) gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure Π = −∂g/∂h. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of g(h). Several different methods based on density functional theory (DFT) for calculating g(h) are described. The first is the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015), 146, 064705 (2017)], that self-consistently calculates an effective fictitious external potential that stabilises films with non-equilibrium value of h. A second method is to calculating g(h) using a Nudged Elastic Band (NEB) approach [Buller et al., J. Chem. Phys. 147, 024701 (2017)]. A third approach is to use an overdamped nonconserved pseudo-dynamics that finds g(h) as the trajectory through the free energy landscape. We also show that all three methods generate identical results for g(h). We illustrate these methods by presenting results from a simple discrete lattice-gas model and also for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures g(h) decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.