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

Abstract

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

Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

“…The liquid is treated grand canonically because the vapour above the drop acts as a reservoir with chemical potential µ, with which the system can exchange particles, allowing the number of liquid particles in the system to vary over time. This is achieved by periodically setting the density of the top layer of the system to the low density result ρ i ≈ e βµ /(1 + e βµ ) [20,40]. This enables the removal of particles from the system as the liquid drop evaporates.…”

“…The influence on the wetting behaviour of truncating the range of the interactions is discussed in Refs. [20,21].…”

“…Generally MD is computationally infeasible even for moderate system sizes due to the long time scales over which the evaporative drying occurs. Similarly, classical density functional theory (DFT) [12][13][14] and dynamical DFT [15][16][17][18] can describe in great detail the density profile of the liquid at the interface and the structure down to the scale of individual particles [13,14,[19][20][21] but the level of detail makes this also computationally very expensive.…”

Nudged elastic band calculation of the binding potential for liquids at interfaces

“…9 for more on the behavior at the wetting transition. We emphasize that at large adsorption values, both methods yield the power law decay g(Γ) ∼ Γ −2 expected in a system with long-range interactions 1,4,5,9,24 (here the interaction with the wall), cf. the inset of Fig.…”

“…Then, the binding potential is a useful tool to bridge the scales from a quantitative microscopic description to a corresponding mesoscopic coarse grained description where it enters the effective interface Hamiltonian or mesoscopic free energy. In particular, binding potentials have been extracted from molecular dynamics (MD) computer simulations 7,8 , from lattice density functional theory (DFT) 9 and continuum DFT 1 .…”