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

Abstract

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.

Correlated Fluctuations of Structural Indicators Close to the Liquid–Liquid Transition in Supercooled Water

“…High values of NTC represent high connectivity and higher values of density. It must be noted that links in the network are defined on the basis of a simple geometric oxygen–oxygen distance criterion, so the resulting connectivity pattern does not coincide with the HB network. Another recent topological indicator is the centerline helicity scriptH c , a measure of the “degree of entangledness” in the HB network based on the identification of knots and ring structures Finally, we also present data based on a novel indicator, Ψ, introduced here for the first time.…”

“…Another recent topological indicator is the centerline helicity scriptH c , a measure of the “degree of entangledness” in the HB network based on the identification of knots and ring structures …”

“…In many numerical models of water, however, a LLT has been predicted to exist, ,− including models based on neural network potentials and models including quantum nuclear effects . In other models, the existence of a liquid–liquid critical point has been rigorously proven. − In silico, a liquid–liquid critical point has also been clearly identified in colloidal models mimicking, at the nano- and micron-scale, the tetrahedral binding of water. − …”

Two-Dimensional Structures Formed by Triblock Patchy Particles with Two Different Patches

“…When considering triblock patchy particles, which have two patches on their surfaces, more complicated structures than those created by single-patch particles are possible in both three-dimensional − and two-dimensional systems. − As an example of an open structure, a kagome lattice can be created in a two-dimensional system . When the two patch sizes are different from each other, − a ring-like structure and some chain-like structures are observed owing to the formation of a Y-shaped-bonding geometry, which is not observed in triblock patchy particles with uniformly sized patches.…”

“…When the two patch sizes are different from each other, − a ring-like structure and some chain-like structures are observed owing to the formation of a Y-shaped-bonding geometry, which is not observed in triblock patchy particles with uniformly sized patches. In three-dimensional systems, − open crystals are attractive materials, especially for use as photonic crystals, − and these are created effectively in particles with two patches with different sizes where the attractive interaction between the patches depends on the combination of patches. In the two-dimensional systems of triblock patchy particles, not only can structures be observed in experiments ,, but also other structures, which have yet to be experimentally observed, may also be created when the two patch areas are different and the attractive interaction strength is dependent on the patch types.…”