Obtaining the solid-liquid interfacial free energy via multi-scheme thermodynamic integration: Ag-ethylene glycol interfaces

The solid-liquid interfacial free energy γ s l is an important quantity in wetting, nucleation, and crystal growth. Although various methods have been developed to calculate γ s l with atomic-scale simulations, such calculations still remain challenging for multi-component interfaces between molecular fluids and solids. We present a multi-scheme thermodynamic integration method that is inspired by the “cleaving-wall” method and aimed at obtaining γ s l for such systems using open-source simulation packages. This method advances two aspects of its predecessor methods. First, we incorporate separate schemes to resolve difficulties when manipulating periodic boundary conditions of the supercell using open-source simulation packages. Second, we introduce a numerical approximation to obtain thermodynamic integrands for complex force fields when an analytical differentiation is not readily available. To demonstrate this method, we obtain γ s l for interfaces between Ag(100) and Ag(111) and ethylene glycol (EG). These interfacial free energies mirror interfacial potential energies for each facet. We also estimate entropies of interface formation and these are consistent with theoretical predictions in signs and trends. For the Ag-EG systems, we find that the largest contribution to γ s l is the free energy to create the bare metal surfaces. The second-largest contribution to γ s l is from the liquid-solid interaction. This user-friendly method will accelerate investigation in a broad range of research topics, such as the thermodynamic effect of structure-directing agents in solution-phase shape-controlled nanocrystal syntheses.