Mechanical and thermodynamic routes to the liquid–liquid interfacial tension and mixing free energy by molecular dynamics

In this study, we carried out equilibrium molecular dynamics (EMD) simulations of the liquid-liquid (LL) interface between two different Lennard-Jones components with varying miscibility, where we examined the relation between the interfacial tension and the free energy to completely isolate the two liquids using both a mechanical and thermodynamic approach. Using the mechanical approach, we obtained a stress distribution around a quasi-one-dimensional EMD system with a flat LL interface. From the stress distribution, we calculated the LL interfacial tension based on Bakker's equation, which uses the stress anisotropy around the interface, and measured how it varied with miscibility. The second approach uses thermodynamic integration by enforcing quasi-static isolation of the two liquids to calculate the free energy. This uses the same EMD systems as the mechanical approach, with both extended dry-surface and phantom-wall (PW) schemes applied. When the two components were immiscible, the mechanical interfacial tension and isolation free energy were in good agreement. When the components were miscible, the values were significantly different. From the result of PW for the case of completely mixed liquids, the difference was attributed to the additional free energy required to separate the binary mixture into single components against the osmotic pressure prior to the complete detachment of the two components. This provides a new route to obtain the free energy of mixing.