A topological entanglement model for metastable water undergoing liquid-liquid phase transition

Due to the coexistence of two distinct states, namely low-density liquid (LDL) and high-density liquid (HDL), water exhibits many anomalous properties and has a unique liquid-liquid phase transition (LLPT) behavior. However, the underlying mechanism is not well understood owing to the complex evolution and entanglements of the condensed structures during this LLPT. This study proposes a new topological model to study the LLPTs of LDL and HDL in the metastable water and describe its condensed structures utilizing theoretical models of topological unlink, entanglement and sub-entanglement of the condensed structures. Topological unlinks and topological entangled Hopf links are firstly used to describe the topological characteristics of the LDL and HDL, respectively, where there is no configurational entropy for the LDL owing to its intra-entanglement in a single molecule chain. Moreover, the sub-entanglement model is developed to formulate the inter-entanglement dynamics and describe the inter-molecular interactions between LDL and HDL during the LLPT. This model is then extended using the free-volume theory and Adam-Gibbs model to establish constitutive relationships among volume, density, viscosity, diffusion coefficient, glass transition temperature and hydrodynamic radius for the metastable water. Finally, effectiveness of the proposed model is verified by molecular dynamics (MD) simulations and experimental data of the metastable water reported in literature. The proposed topological entanglement model is expected to provide a topological entanglement model to understand the liquid-liquid phase transitions of the metastable water.