Role of Interfacial Free Energy in Non-classical Nucleation of Polyhedral Nanoparticles

Direct measurements of the interfacial free energy between disordered & ordered phases of hard nanoparticles were conducted via cleaving walls method with Monte Carlo simulations. At the disordered-ordered phase coexistence, hard cubes are found to have an unusually low interfacial free energy relative to other shapes. A law of mass action model is constructed to describe the relation between the concentration of ordered nuclei & interfacial free energy. For a low enough interfacial free energy, as in the case of hard cubes, the model predicts a high concentration of ordered nuclei in the disordered phase. This aligns with previous observations for hard cubes, where ripening among concentrated pre-critical nuclei leads to non-classical bulk phase transition. Simulations of hard truncated cubes reveal a similar phase transition, albeit with a much higher free energy barrier than hard cubes, a difference that can be ascribed to a higher interfacial free energy. Interfacial free energies were obtained for various crystal planes, which in case of hard gyrobifastigia accurately predict the shape & interfacial free energy of the nucleus via Wulff construction. Results indicate a general correlation of roughness of the interface with its interfacial free energy.