Liquid-liquid phase transitions in tetrahedrally coordinated fluids via Wertheim theory

Network interpenetration has been proposed as a mechanism for generating liquid−liquid phase transitions in one component systems. We introduce a model of four coordinated particles, which explicitly treats the system as a mixture of two interacting interpenetrating networks that can freely exchange particles. This model can be solved within Wertheim’s theory for associating fluids and shows liquid−liquid phase separations (in addition to the gas−liquid) for a wide range of model parameters. We find that originating a liquid−liquid transition requires a small degree of interpenetrability and a preference for intranetwork bonding. Physically, these requirements can be seen as controlling the softness of the particle−particle interaction and the bond flexibility, in full agreement with recent findings [Smallenburg, F.; Filion, L.; Sciortino, F. Nat. Phys. 2014, 10, 653].