Wilhelmy equation revisited: A lightweight method to measure liquid-vapor, solid-liquid, and solid-vapor interfacial tensions from a single molecular dynamics simulation.

We have given theoretical expressions for the forces exerted on a so-called Wilhelmy plate, which we modeled as a quasi-2D flat and smooth solid plate immersed in a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line, and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. The force expressions were derived by a purely mechanical approach, which is exact and ensures the force balance on the control volumes arbitrarily set in the system, and are valid as long as the solid-liquid (SL) and solid-vapor (SV) interactions can be described by mean-fields. In addition, we revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γSL and γSV, and this was verified through the comparison with the SL and SV works of adhesion obtained by the thermodynamic integration (TI). From these results, it has been confirmed that γSL and γSV as well as the liquid-vapor interfacial tension γLV can be extracted from a single equilibrium MD simulation without the computationally demanding calculation of the local stress distributions and the TI.