Topological nature of the liquid–liquid phase transition in tetrahedral liquids

The first-order phase transition between two tetrahedral networks of different density-introduced as a hypothesis to account for the anomalous behaviour of certain thermodynamic properties of deeply supercooled water-has received strong support from a growing body of work in recent years. Here we show that this liquid-liquid phase transition in tetrahedral networks can be described as a transition between an unentangled, low-density liquid and an entangled, high-density liquid, the latter containing an ensemble of topologically complex motifs. We first reveal this distinction in a rationally designed colloidal analogue of water. We show that this colloidal water model displays the well-known water thermodynamic anomalies as well as a liquid-liquid critical point. We then investigate water, employing two widely used molecular models, to demonstrate that there is also a clear topological distinction between its two supercooled liquid networks, thereby establishing the generality of this observation, which might have far-reaching implications for understanding liquid-liquid phase transitions in tetrahedral liquids.Supercooled water undergoes a liquid-liquid phase transition. The authors show that the two phases have distinct hydrogen-bond networks, differing in their degree of entanglement, and thus the transition can be described by the topological changes of the network.