Citation: HUGHES, A.P., THIELE, U. and ARCHER, A.J., 2015. Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling.Journal of Chemical Physics, 142 (7), 074702.Additional Information:• The contribution to the free energy for a film of liquid of thickness h on a solid surface due to the interactions between the solid-liquid and liquid-gas interfaces is given by the binding potential, g(h). The precise form of g(h) determines whether or not the liquid wets the surface. Note that differentiating g(h) gives the Derjaguin or disjoining pressure. We develop a microscopic density functional theory (DFT) based method for calculating g(h), allowing us to relate the form of g(h) to the nature of the molecular interactions in the system. We present results based on using a simple lattice gas model, to demonstrate the procedure. In order to describe the static and dynamic behaviour of non-uniform liquid films and drops on surfaces, a mesoscopic free energy based on g(h) is often used. We calculate such equilibrium film height profiles and also directly calculate using DFT the corresponding density profiles for liquid drops on surfaces. Comparing quantities such as the contact angle and also the shape of the drops, we find good agreement between the two methods. We also study in detail the effect on g(h) of truncating the range of the dispersion forces, both those between the fluid molecules and those between the fluid and wall. We find that truncating can have a significant effect on g(h) and the associated wetting behaviour of the fluid. C 2015 AIP Publishing LLC.[http://dx
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example, to calculate the density distribution of the molecules in the vicinity of a confining wall, the interfacial tension, the wetting behaviour and many other properties of nonuniform liquids. DFT can however be somewhat daunting to students entering the field, because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses and so students can quickly get to the stage of calculating density profiles, etc for themselves. We derive a simple DFT for the lattice-gas and present some typical results that can readily be calculated using the theory.
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). Here, the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential 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.
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