Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [Sauer, E.; Gross, J. Ind. Eng. Chem. Res. 56, 2017, 4119-4135] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77 degrees.