(37c) Obtaining Solid-Liquid Interfacial Free Energy for Realistic Systems 

The solid-liquid interfacial free energy γ_sl is a critical quantity in understanding the thermodynamic aspects of shape-selective nanocrystal formation. Unlike the fluid-fluid interfacial free energy, the solid-liquid interfacial free energy is facet-specific and not identical to surface tension, which makes direct measurements with high enough resolution to resolve the anisotropy extremely challenging in experiments. Several simulation methods have been developed to obtain facet-specific γ_sl for systems with simple structures and potentials, but in the current stage, these methods are not applicable to systems with complicated configurations and complex force fields, and are also not compatible with commonly used open source simulation packages. Here we present a novel multi-scheme thermodynamic integration (TI) method that can be used to obtain γ_sl for real and complex systems using open source simulation packages. This is a six-step simulation method that obtains γ_sl by calculating the negative free energy change when transforming a solid-liquid coexistence to the individual bulk phases. This method is developed based on the previous â??cleaving wallâ? method [1, 2] and is advanced in two major aspects: two different TI schemes to deal with periodic boundary condition without locally modifying the simulation package, and a numerical approximation is introduced when the analytical form of the thermodynamic integrand is difficult to differentiate. These features successfully resolve simulation difficulties when using the previous methods, thus our method can be applied to a broad range of systems and force fields. To demonstrate its capability, we use our method to obtain γ_sl for Ag(100) and Ag(111) surfaces in contact with a solution used in shape-selective Ag nanocrystal synthesis â?? polyvinylpyrrolidone (PVP)-dissolved ethylene glycol (EG) solution. By having a higher binding affinity to Ag(100), PVP is an effective structure-directing agent (SDA) that helps to form {100}-faceted Ag nanocrystals, such as nanocubes and nanowires. Since bare Ag(111) surfaces are more thermodynamically stable than Ag(100) by possessing lower surface free energy, a hypothesis for observing {100}-faceted structures is that PVP can make γ_Ag(100) < γ_Ag(111) by tightly bound to Ag(100) surfaces and the produced {100}-faceted structures are thermodynamically favored. We obtain anisotropic γ_sl for Ag(100) and Ag(111) surfaces in contact with the PVP-EG solution using the multi-scheme TI method and show that although PVP can lower γ_Ag(100) to a larger extent than γ_Ag(111), it does not make γ_Ag(100) < γ_Ag(111). Combining with our findings in a previous â??relative deposition fluxâ? study [3], in which we quantified the relative deposition fluxes to these surfaces, we demonstrate that these {100}-faceted structure are not thermodynamic shapes and confirm the kinetic role of PVP in shape-selective Ag nanocrystal synthesis.