Extraction of the equilibrium pinning force on a contact line exerted from a wettability boundary of a solid surface through the connection between mechanical and thermodynamic routes.

By molecular dynamics (MD) simulations, we investigated the effects of chemical inhomogeniety of a wall surface on the equilibrium pinning behavior of a contact line (CL) of solid (S), liquid (L), and vapor (V) phases. We analyzed a quasi-two-dimensional LV-meniscus of Lennard-Jones fluid formed between two parallel flat solid walls, where the CL was located around the wetting boundary (WB) between lyophilic and lyophobic areas of the wall surface. Based on the relationship between the wall-tangential stress integral at the SL or SV interface and the corresponding thermodynamic work of adhesion WSL or WSV shown in our previous study [Y. Yamaguchi et al., J. Chem. Phys. 150, 044701 (2019)], the mechanical balance on the fluid around the CL was successfully described by the relation among WSL, WSV, the apparent contact angle, and the pinning force. In addition, the depinning force needed to move the CL across the WB was estimated as the difference between WSL values at lyophilic and lyophobic areas. Since the works of adhesion WSL and WSV can be easily calculated independently in simple systems through the thermodynamics integration, such a connection between the mechanical and thermodynamic routes provides a possible pathway toward the understanding of wetting including CL-pinning without the need of computationally demanding calculation of the local stress distributions.