A structural indicator for water built upon potential energy considerations

Nanoscale water behavior and its impact on adsorption: A case study with CNTs and diclofenac

Water is a fundamental component of life, playing a critical role in regulating metabolic processes and facilitating the dissolution and transport of essential molecules. However, emerging contaminants, such as pharmaceuticals, pose significant challenges to water quality and safety. Nanomaterial-based technologies emerge as a promising solution for removing those contaminants from water. Nevertheless, interfacial water plays a major role in the adsorption of chemical compounds in nanomaterials-as it plays in biological processes such as protein folding, enzyme activity, and drug delivery. To understand this role, in this study, we employ molecular dynamics simulations to explore the adsorption dynamics of potassium diclofenac on single-walled carbon nanotubes (SWCNTs) and double-walled carbon nanotubes (DWCNTs), considering both dry and wet conditions. Our findings reveal that the structuring of water molecules around CNTs creates hydration layers that significantly influence the accessibility of active sites and the interaction strength between contaminants and adsorbents. Our analysis indicates higher energy barriers for adsorption in DWCNTs compared to SWCNTs, which is attributed to stronger water-surface interactions. This research highlights the importance of understanding nanoscale water behavior for optimizing the design and functionality of nanomaterials for water purification. These findings can guide the development of more efficient and selective nanomaterials, enhancing contaminant removal and ensuring safer water resources while contributing to a deeper understanding of fundamental biological interactions.

Toward mitigating the impact of non-bulk defects on describing water structure in salt aqueous solutions: Characterizing solution density with a network-based structural indicator

Structural indicators, also known as structural descriptors, including order parameters, have been proposed to quantify the structural properties of water to account for its anomalous behaviors. However, these indicators, mainly designed for bulk water, are not naturally transferrable to the vicinity of ions due to disruptions in the immediate neighboring space and a resulting loss of feature completeness. To address these non-bulk defects, we introduced a structural indicator that draws on the concept of clique number from graph theory and the criterion in agglomerative clustering, denoted as the average cluster number. This structural indicator aims to discern intrinsic structural characteristics within the water molecules regardless of the ions occupying the neighboring space, without requiring additional corrections. From molecular dynamics simulation results for neat water and salt aqueous solutions utilizing the TIP4P/2005 water model and the Madrid-2019 force field, we characterized the variations in densities with temperature using this network-based indicator, thereby demonstrating its practical utility. The findings suggest that at lower temperatures, the addition of ions disrupts the intrinsic structure of water molecules, with this effect diminishing as the temperature rises. Cations with larger charge density tend to induce stronger disruptions. This study highlights the importance of mitigating the impact of non-bulk defects before applying the indicators to analyze water's intrinsic structural properties in solutions. By doing so, the relationship between changes in water structure and solution behaviors can be more accurately assessed.

TIP 4 P 2005 Ice : Simulating water with two molecular states

Rigid, non-polarizable water models are very efficient from a computational point of view, and some of them have a great ability in predicting experimental properties. There is, however, little room for improvement in simulating water with this strategy, whose main shortcoming is that water molecules do not change their interaction parameters in response to the local molecular landscape. In this work, we propose a novel modeling strategy that involves using two rigid non-polarizable models as states that water molecules can adopt depending on their molecular environment. During the simulation, molecules dynamically transition from one state to another depending on a local order parameter that quantifies some local structural feature. In particular, molecules belonging to low- and high-tetrahedral order environments are represented with the TIP4P/2005 and TIP4P/Ice rigid models, respectively. In this way, the interaction between water molecules is strengthened when they acquire a tetrahedral coordination, which can be viewed as an effective way of introducing polarization effects. We call the resulting model TIP4P2005Ice and show that it outperforms either of the rigid models that build it. This multi-state strategy only slows down simulations by a factor of 1.5 compared to using a standard non-polarizable model and holds great promise for improving simulations of water and aqueous solutions.

Study of Protein Hydration Water with the V4S Structural Index: Focus on Binding Site Description

V4S, a new structural indicator for water specially designed to be suitable for hydration and nanoconfined contexts, has been recently introduced and preliminarily applied for water in contact with self-assembled monolayers and graphene-like systems. This index enabled an accurate detection of defective high local density water molecules (called HDA-like given their structural resemblance with the high-density amorphous ice, HDA). In the present work, we shall apply this new metric to characterize protein hydration water with particular interest in protein binding sites. As a first result, we shall find that protein hydration water has a higher concentration of HDA-like molecular arrangements compared to the bulk. Significantly, we shall show that the concentration of HDA-like molecules sharply decreases beyond the first hydration layer. Finally, we shall also reveal a highly nonuniform spatial distribution of the V4S values for the first hydration shell on the protein surface, where the higher hydrophobicity inherent to the ligand binding site will be evident from an enrichment in HDA-like molecules as compared to the population exhibited by the global protein surface.

The interplay between liquid-liquid and ferroelectric phase transitions in supercooled water

The distinctive characteristics of water, evident in its thermodynamic anomalies, have implications across disciplines from biology to geophysics. Considered a valid hypothesis to rationalize its unique properties, a liquid-liquid phase transition in water below the freezing point, in the so-called supercooled regime, has nowadays been observed in several molecular dynamics simulations and is being actively researched experimentally. The hypothesis of ferroelectric phase transition in supercooled water can be traced back to 1977, due to Stillinger. In this work, we highlight intriguing and far-reaching implications of water: The ferroelectric and liquid-liquid phase transitions can be designed as two facets of the same underlying phenomenon. Our results are based on the analysis of extensive molecular dynamics simulations and are explained in the context of a classical density functional theory in mean-field approximation valid for a polar liquid, where dipolar interaction is treated perturbatively. The theory underpins the potential role of ferroelectricity in promoting the liquid-liquid phase transition, being the density-polarization coupling inherent in the dipolar interaction potential. The existence of ferroelectric order in supercooled low-density liquid water is confirmed by the observation in molecular dynamics simulations of collective modes in space-time polarization correlation functions, traceable to spontaneous breaking of continuous rotational symmetry. Our work sheds light on water's supercooled behavior and opens the door to experimental investigations of the static and dynamic behavior of water's polarization.

Role of hydrogen-bond coordination defects in the structural relaxation of supercooled water

In this work, we shall study the role of threefold and fivefold coordination defects in the structure and dynamics of the hydrogen bond network of liquid water, with special emphasis on the glassy regime. A significant defect clusterization propensity will be made evident, with a prevalence of mixed pairs, that is, threefold- and fivefold-coordinated defects being first neighbors of each other. This structural analysis will enable us to determine the existence of defective and nondefective regions compatible with the high local density and low local density molecular states of liquid water, respectively. Hydrogen bond coordination defects will also be shown to promote water's structural relaxation, with the undercoordinated ones playing a main role in driving glassy relaxation dynamics. Moreover, we shall show that the three-foldcoordinated molecules together with their first neighbors present at the initial configuration act as markers of the dynamical heterogeneities that would emerge at later times commensurate with the structural relaxation of the supercooled system.

A structural determinant of the behavior of water at hydration and nanoconfinement conditions

The molecular nature of the phases that conform the two-liquid scenario is elucidated in this work in the light of a molecular principle governing water structuring, which unveils the relevance of the contraction and reorientation of the second molecular shell to allow for the existence of coordination defects in water's hydrogen bond network. In turn, such principle is shown to also determine the behavior of hydration and nanoconfined water while enabling to define conditions for wettability (quantifying hydrophobicity and predicting drying transitions), thus opening the possibility to unravel the active role of water in central fields of research.

Water at the nanoscale: From filling or dewetting hydrophobic pores and carbon nanotubes to "sliding" on graphene

In this work, we study the effect of nanoconfinement on the hydration properties of model hydrophobic pores and carbon nanotubes, determining their wetting propensity and the conditions for geometrically induced dehydration. By employing a recently introduced water structural index, we aim at two main goals: (1) to accurately quantify the local hydrophobicity and predict the drying transitions in such systems, and (2) to provide a molecular rationalization of the wetting process. In this sense, we will further discuss the number and strength of the interactions required by the water molecules to promote wetting. In the case of graphene-like surfaces, an explanation for their unexpectedly significant hydrophilicity will also be provided. On the one hand, the structural index will show that the net attraction to the dense carbon network that a water molecule experiences through several simultaneous weak interactions is sufficient to give rise to hydrophilic behavior. On the other hand, we will show that an additional effect is also at play: the hydrating water molecule is retained on the surface by a smooth exchange of such simultaneous weak interactions, as if "sliding" on graphene.

Early prediction of spinodal-like relaxation events in supercooled liquid water

Several computational studies on different water models reported evidence of a phase transition in supercooled conditions between two liquid states of water differing in density: the high-density liquid (HDL) and the low-density liquid (LDL). Yet, conclusive experimental evidence of the existence of a phase transition between the two liquid water phases could not be obtained due to fast crystallization in the region where the phase transition should occur. For the same reason, the investigation of possible transition mechanisms between the two phases is committed to computational investigations. In this work, we simulate an out-of-equilibrium temperature-induced transition from the LDL to the HDL-like state in the TIP4P/2005 water model. To structurally characterize the system relaxation, we use the node total communicability (NTC) we recently proposed as an effective order parameter to discriminate the two liquid phases differing in density. We find that the relaxation process is compatible with a spinodal-like scenario. We observe the formation of HDL-like domains in the LDL phase and we characterize their fluctuating behavior and subsequent coarsening and stabilization. Furthermore, we find that the formation of stable HDL-like domains is favored in the regions where the early formation of small patches of highly connected HDL-like molecules (i.e., with very high NTC values) is observed. Besides characterizing the LDL- to HDL-like relaxation from a structural point of view, these results also show that the NTC order parameter can serve as an early-time predictor of the regions from which the transition process initiates.

Isotope effects in supercooled H2O and D2O and a corresponding-states-like rescaling of the temperature and pressure

Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H2O and D2O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations-with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a "corresponding-states-like" rescaling for water properties in three classical water models that all exhibit a liquid-liquid transition and critical point [Uralcan et al., J. Chem. Phys. 150, 064503 (2019)], the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H2O and D2O is investigated here. Utilizing previously published data and equations-of-state for H2O and D2O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid-liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water's anomalies.

Unraveling thermodynamic anomalies of water: A molecular simulation approach to probe the two-state theory with atomistic and coarse-grained water models

Thermodynamic and dynamic anomalies of water play a crucial role in supporting life on our planet. The two-state theory attributes these anomalies to a dynamic equilibrium between locally favored tetrahedral structures (LFTSs) and disordered normal liquid structures. This theory provides a straightforward, phenomenological explanation for water's unique thermodynamic and dynamic characteristics. To validate this two-state feature, it is critical to unequivocally identify these structural motifs in a dynamically fluctuating disordered liquid. In this study, we employ a recently introduced structural parameter (θavg) that characterizes the local angular order within the first coordination shell to identify these LFTSs through molecular dynamics simulations. We employ both realistic water models with a liquid-liquid critical point (LLCP) and a coarse-grained water model without an LLCP to study water's anomalies in low-pressure regions below 2 kbar. The two-state theory consistently describes water's thermodynamic anomalies in these models, both with and without an LLCP. This suggests that the anomalies predominantly result from the two-state features rather than criticality, particularly within experimentally accessible temperature-pressure regions.

Beyond Local Structures in Critical Supercooled Water through Unsupervised Learning

The presence of a second critical point in water has been a topic of intense investigation for the last few decades. The molecular origins underlying this phenomenon are typically rationalized in terms of the competition between local high-density (HD) and low-density (LD) structures. Their identification often requires designing parameters that are subject to human intervention. Herein, we use unsupervised learning to discover structures in atomistic simulations of water close to the liquid-liquid critical point (LLCP). Encoding the information on the environment using local descriptors, we do not find evidence for two distinct thermodynamic structures. In contrast, when we deploy nonlocal descriptors that probe instead heterogeneities on the nanometer length scale, this leads to the emergence of LD and HD domains rationalizing the microscopic origins of the density fluctuations close to criticality.

A water structure indicator suitable for generic contexts: Two-liquid behavior at hydration and nanoconfinement conditions and a molecular approach to hydrophobicity and wetting

In a recent work, we have briefly introduced a new structural index for water that, unlike previous indicators, was devised specifically for generic contexts beyond bulk conditions, making it suitable for hydration and nanoconfinement settings. In this work, we shall study this metric in detail, demonstrating its ability to reveal the existence of a fine-tuned interplay between the local structure and energetics in liquid water. This molecular principle enables the establishment of an extended hydrogen bond network, while simultaneously allowing for the existence of network defects by compensating for uncoordinated sites. By studying different water models and different temperatures encompassing both the normal liquid and the supercooled regime, this molecular mechanism will be shown to underlie the two-state behavior of bulk water. In addition, by studying functionalized self-assembled monolayers and diverse graphene-like surfaces, we shall show that this principle is also operative at hydration and nanoconfinement conditions, thus generalizing the validity of the two-liquid scenario of water to these contexts. This approach will allow us to define conditions for wettability, providing an accurate measure of hydrophobicity and a reliable predictor of filling and drying transitions. Hence, it might open the possibility of elucidating the active role of water in the broad fields of biophysics and materials science. As a preliminary step, we shall study the hydration structure and hydrophilicity of graphene-like systems (parallel graphene sheets and carbon nanotubes) as a function of the confinement dimensionality.

Identification of local structures in water from supercooled to ambient conditions

Studies of water thermodynamics have long been tied to the identification of two distinct families of local structures, whose competition could explain the origin of the many thermodynamic anomalies and the hypothesized liquid-liquid critical point in water. Despite the many successes and insights gained, the structural indicators proposed throughout the years were not able to unequivocally identify these two families over a wide range of conditions. We show that a recently introduced indicator, Ψ, which exploits information on the hydrogen bond network connectivity, can reliably identify these two distinct local environments over a wide range of thermodynamic conditions (188-300 K and 0-13 kbar) and that close to the liquid-liquid critical point, the spatial correlations of density fluctuations are identical to those of the Ψ indicator. Our results strongly support the idea that water thermodynamic properties arise from the competition between two distinct and identifiable local environments.

Influence of docosahexaenoic acid on the interfacial behavior of cholesterol-containing lipid membranes: Interactions with small amphiphiles and hydration properties

Cholesterol is known to significantly modify both the structural and the dynamical properties of lipid membranes. On one side, the presence of free cholesterol molecules has been determined to stiffen the membrane bilayer by stretching the hydrophobic tails. Additionally, recent experimental and computational findings have made evident the fact that cholesterol also alters the dynamics and the hydration properties of the polar head groups of DPPC model lipid membranes. In turn, we have recently shown that the Omega-3 fatty acid docosahexaenoic acid, DHA, counteracts the effect of cholesterol on DPPC membrane's mechanical properties by fluidizing the bilayer. However, such behavior represents in fact a global outcome dominated by the larger lipid hydrophobic tails that neither discriminates between the different parts of the membrane nor elucidates the effect on membrane hydration and binding properties. Thus, we now perform molecular dynamics simulations to scrutinize the influence of DHA on the interfacial behavior of cholesterol-containing lipid membranes by characterizing their hydration properties and their binding to amphiphiles. We find that while cholesterol destabilizes interactions with amphiphiles and slightly weakens the lipid's hydration layer, the incorporation of DHA practically restores the interfacial behavior of pure DPPC.

A statistical mechanical model of supercooled water based on minimal clusters of correlated molecules

In this paper, we apply a theoretical model for fluid state thermodynamics to investigate simulated water in supercooled conditions. This model, which we recently proposed and applied to sub- and super-critical fluid water [Zanetti-Polzi et al., J. Chem. Phys. 156(4), 44506 (2022)], is based on a combination of the moment-generating functions of the enthalpy and volume fluctuations as provided by two gamma distributions and provides the free energy of the system as well as other relevant thermodynamic quantities. The application we make here provides a thermodynamic description of supercooled water fully consistent with that expected by crossing the liquid-liquid Widom line, indicating the presence of two distinct liquid states. In particular, the present model accurately reproduces the Widom line temperatures estimated with other two-state models and well describes the heat capacity anomalies. Differently from previous models, according to our description, a cluster of molecules that extends beyond the first hydration shell is necessary to discriminate between the statistical fluctuation regimes typical of the two liquid states.

Turning an energy-based defect detector into a multi-molecule structural indicator for water

Recent studies have provided conclusive evidence for the existence of a liquid-liquid critical point in numerical models of water. Such a scenario implies the competition between two local molecular arrangements of different densities: a high-density liquid (HDL) and a low-density liquid (LDL). Within this context, the development of accurate structural indicators to properly characterize the two interconverting local structures is demanded. In a previous study, we introduced a reliable energy-based structural descriptor that properly discriminates water molecules into tetrahedrally arranged molecules (T molecules) and distorted molecules (D molecules). The latter constitute defects in terms of hydrogen bond (HB) coordination and have been shown to represent a minority component, even at high temperatures above the melting point. In addition, the D molecules tend to form high-quality HBs with three T molecules and to be surrounded by T and D molecules at further distances. Thus, it became evident that, while the LDL state might consist of a virtually pure T state, the HDL state would comprise mixed molecular arrangements including the D molecules. Such a need to abandon the single-molecule description requires the investigation of the degree of structural information to be incorporated in order to build an appropriate multi-molecule indicator. Hence, in this work, we shall study the effect of the local structural constraints on the water molecules in order to discriminate the different molecular arrangements into two disjoint classes. This will enable us to build a multi-molecule structural indicator for water whose performance will then be investigated within the water's supercooled regime.

Correlations between defect propensity and dynamical heterogeneities in supercooled water

A salient feature of supercooled liquids consists in the dramatic dynamical slowdown they undergo as temperature decreases while no significant structural change is evident. These systems also present dynamical heterogeneities (DH): certain molecules, spatially arranged in clusters, relax various orders of magnitude faster than the others. However, again, no static quantity (such as structural or energetic measures) shows strong direct correlations with such fast-moving molecules. In turn, the dynamic propensity approach, an indirect measure that quantifies the tendency of the molecules to move in a given structural configuration, has revealed that dynamical constraints, indeed, originate from the initial structure. Nevertheless, this approach is not able to elicit which structural quantity is, in fact, responsible for such a behavior. In an effort to remove dynamics from its definition in favor of a static quantity, an energy-based propensity has also been developed for supercooled water, but it could only find positive correlations between the lowest-energy and the least-mobile molecules, while no correlations could be found for those more relevant mobile molecules involved in the DH clusters responsible for the system's structural relaxation. Thus, in this work, we shall define a defect propensity measure based on a recently introduced structural index that accurately characterizes water structural defects. We shall show that this defect propensity measure provides positive correlations with dynamic propensity, being also able to account for the fast-moving molecules responsible for the structural relaxation. Moreover, time dependent correlations will show that defect propensity represents an appropriate early-time predictor of the long-time dynamical heterogeneity.

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

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 near-critical 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.

Manifestations of the structural origin of supercooled water’s anomalies in the heterogeneous relaxation on the potential energy landscape

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models—based on the assumption of the existence of two types of competing local states (or, structures) in liquid water—have been extremely successful in describing water’s thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a predefined structural order parameter-free approach to unambiguously identify two types of competing local states—entropically and energetically favored—with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water’s thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Structure and dynamics of nanoconfined water and aqueous solutions

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

Manifestations of metastable criticality in the long-range structure of model water glasses

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index; water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids.

The subtle connections between water’s supercooled liquid and glassy states are difficult to characterize. Gartner et al. suggest with MD simulations that the long-range structure of glassy water may reflect signatures of water’s debated second critical point in the supercooled liquid.

Structural and topological changes across the liquid-liquid transition in water

It has recently been shown that the TIP4P/Ice model of water can be studied numerically in metastable equilibrium at and below its liquid-liquid critical temperature. We report here simulations along a subcritical isotherm, for which two liquid states with the same pressure and temperature but different density can be equilibrated. This allows for a clear visualization of the structural changes taking place across the transition. We specifically focus on how the topological properties of the H-bond network change across the liquid-liquid transition. Our results demonstrate that the structure of the high-density liquid, characterized by the existence of interstitial molecules and commonly explained in terms of the collapse of the second neighbor shell, actually originates from the folding back of long rings, bringing pairs of molecules separated by several hydrogen-bonds close by in space.

Structural aspects of an energy-based water classification index and the structure-dynamics link in glassy relaxation

An energy-based structural indicator for water, [Formula: see text], has been recently introduced by our group. In turn, in this work we aim at: (1) demonstrating that [Formula: see text] is indeed able to correctly classify water molecules between locally structured tetrahedral (T) and locally distorted (D) ones, circumventing the usual problem of certain previous indicators of overestimating the distorted state; (2) correlating [Formula: see text] with dynamic propensity, a measure of the molecular mobility tendency, in order to seek for the existence of a connection between structure and dynamics within the supercooled regime. More specifically, in the first part of this work we will show that [Formula: see text] accurately discriminates between merely thermally deformed local molecular arrangements and truly distorted molecules (defects). This fact will be made evident not only from radial distribution function results but also from the dynamic propensity distributions of the different kinds of molecules. In turn, we shall devote the second part of this work to finding correlations between T and D molecules with low- and high-dynamic-propensity molecules, respectively, thus revealing the existence of a link between local structure and dynamics, while also making evident the dominant role of the D molecules (defects) in the structural relaxation. Moreover, the availability of a proper molecular classification technique will enable us to study the timescale of such influence of structure on dynamics by defining a modified dynamic propensity measure and by applying it to the structured and unstructured water molecular states.