Two-state free-volume model for anomalous dynamics in supercooled water macromolecules undergoing liquid–liquid phase transition

Modelling anomalous dynamics of complex liquid water is a huge challenge due to its various condensed molecular structures and the associated liquid–liquid phase transitions (LLPTs). In this study, we considered, for the first time, the influences of free volume and entropy on LLPTs for both low-density liquid (LDL) and high-density liquid (HDL) waters. Firstly, we proposed a two-state free-volume model and combined with the Adam-Gibbs models to investigate the dynamic equilibria with free diffusion coefficient, viscosity, glass transition temperature and the anomalous dynamics in the two-state water. Free-energy equation was then developed to explore the constitutive relationships of free volume, entropy and anomalously dynamic behaviors. Finally, analytical results of the proposed two-state free-volume model were compared with the experimental data of two-state water reported in literature, and good agreements between them were demonstrated. This study offers a new physical insight into free volume for the anomalous dynamics and LLPTs in the two-state water.