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

Abstract

Multiple numerical studies have unambiguously shown the existence of a liquid−liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of nearcritical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.

A Unified Description of the Liquid Structure, Static and Dynamic Anomalies, and Criticality of TIP4P/2005 Water by a Hierarchical Two-State Model

“…This order parameter ψ is often used to describe the second critical point. , Contrary to this, we have argued that the relevant order parameter should be the fraction of tetrahedral structures s . ,, Considering that locally favored tetrahedral structures are formed by the symmetry-selective directional interaction, i.e., hydrogen bonding, s should be the relevant order parameter of LLT. This problem concerning the nature of the order parameter has also recently been discussed in ref . We also point out the crucial difference between ψ and s : ψ is the conserved quantity since its change at a certain point inevitably involves the change of the surroundings, whereas s is the nonconserved quantity since tetrahedral structures can be created and annihilated independently .…”

“…Notably, the structural order parameter s (and s D ), representing the rotationally invariant angular order, can describe all water’s thermodynamic (and kinetic) anomalies and criticality. The two-order-parameter scenario can naturally allow a system to have two critical points, gas–liquid and liquid–liquid critical points. ,, Because of the strong correlation between ρ and s , we can hardly tell which of the ρ or s is the genuine order parameter of the LLT from thermodynamic measurements alone, as pointed out in ref . However, since s is a nonconserved order parameter while density is conserved, they are expected to show fundamentally different dynamic behavior. ,, Studying the dynamic critical phenomena associated with LLCP is an interesting topic for future study.…”

“…We can see that density has an almost one-to-one correlation to s in the vicinity of the critical point, consistent with recent calculations in the TIP4P/Ice model. 37 Nevertheless, we argue that the genuine order parameter of the LLT is the fraction of tetrahedral structures s and not the density ρ, and the density is subordinated to the order parameter s. Notably, the structural order parameter s (and s D ), representing the rotationally invariant angular order, can describe all water's thermodynamic (and kinetic) anomalies and criticality. The two-orderparameter scenario can naturally allow a system to have two critical points, gas−liquid and liquid−liquid critical points.…”

“…The existence of the LLT suggests that water has two different types of molecular arrangements in the liquid state. , Despite being controversial, increasing evidence strongly supporting the presence of two types of local structures (or two states) even above the critical point, reminiscent of LDL and HDL, has been accumulated both experimentally − and computationally. − The recent identification of the first diffraction peak in the partial oxygen X-ray structure factor for water is direct evidence for the presence of two microscopic states with distinct differences in the local structure and symmetry …”

“…Theoretically, many phenomenological two-state models, including the presence of LLCP, have been developed and quantitatively described water’s thermodynamic anomalies. ,− Some of these models have assumed the necessity of an additional order parameter besides density to describe water’s anomalies and the LLT and claimed that the order parameter governing the LLT is not the density ρ but the fraction of locally favored tetrahedral structures s . − ,− Unlike the density, the latter order parameter is a nonconserved quantity, which affects the dynamics but does not the thermodynamics. ,− Until now, there is no consensus on the nature of the order parameter describing the LLT of water (see, e.g., ref ).…”