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.

两个不同密度的四面体网络之间的一阶相变——作为解释深度过冷水的某些热力学性质的异常行为的假设而被引入——近年来得到了越来越多的工作的大力支持。在这里，我们表明四面体网络中的这种液-液相转变可以描述为未纠缠的低密度液体和纠缠的高密度液体之间的转变，后者包含一组拓扑复杂的基序。我们首先在合理设计的水胶体类似物中揭示了这种区别。我们表明，这种胶体水模型显示了众所周知的水热力学异常以及液-液临界点。然后，我们使用两种广泛使用的分子模型研究水，