Liquid-Liquid Crossover in Water Model: Local Structure vs Kinetics of Hydrogen Bonds

In equilibrium and supercooled liquids, polymorphism is manifested by thermodynamic regions defined in the phase diagram, which are predominantly of different short- and medium-range order (local structure). It is found that on the phase diagram of the water model, the thermodynamic region corresponding to the equilibrium liquid phase is divided by a line of the smooth liquid-liquid crossover. In the case of the water model TIP4P/2005, this crossover is revealed by various local order parameters and corresponds to pressures on the order of 3150 ± 350 atm at ambient temperature. In the vicinity of the crossover, the dynamics of water molecules change significantly, which is reflected, in particular, in the fact that the self-diffusion coefficient reaches its maximum values. In addition, changes in the structure also manifest themselves in changes in the kinetics of hydrogen bonding, which are captured by values of such quantities as the average lifetime of hydrogen bonding, the average lifetimes of different local coordination numbers, and the frequencies of changes in different local coordination numbers. An interpretation of the hydrogen bond kinetics in terms of the free energy landscape concept in the space of possible coordination numbers is proposed.

Liquid-Liquid Criticality in the WAIL Water Model

The hypothesis that the anomalous behavior of liquid water is related to the existence of a second critical point in deeply supercooled states has long been the subject of intense debate. Recent, sophisticated experiments designed to observe the transformation between the two subcritical liquids on nano- and microsecond time scales, along with demanding numerical simulations based on classical (rigid) models parametrized to reproduce thermodynamic properties of water, have provided support to this hypothesis. A stronger numerical proof requires demonstrating that the critical point, which occurs at temperatures and pressures far from those at which the models were optimized, is robust with respect to model parameterization, specifically with respect to incorporating additional physical effects. Here we show that a liquid-liquid critical point can be rigorously located also in the WAIL model of water [J. Chem. Phys. 137, 014510 (2012)], a model parameterized using ab-initio calculations only. The model incorporates two features not present in many previously-studied water models: it is both flexible and polarizable, properties which can significantly influence the phase behavior of water. The observation of the critical point in a model in which the water-water interaction is estimated using only quantum ab-initio calculations provides strong support to the viewpoint according to which the existence of two distinct liquids is a robust feature in the free energy landscape of supercooled water.

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

Evidence of a liquid-liquid phase transition in H[Formula: see text]O and D[Formula: see text]O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H[Formula: see text]O and D[Formula: see text]O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density [Formula: see text], isothermal compressibility [Formula: see text], and self-diffusion coefficients D(T) of H[Formula: see text]O and D[Formula: see text]O are in excellent agreement with available experimental data; the isobaric heat capacity [Formula: see text] obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H[Formula: see text]O and D[Formula: see text]O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H[Formula: see text]O and D[Formula: see text]O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H[Formula: see text]O, from PIMD simulations, is located at [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D[Formula: see text]O is estimated to be [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of [Formula: see text] for D[Formula: see text]O and, particularly, H[Formula: see text]O suggest that improved water models are needed for the study of supercooled water.

Finite-size scaling and thermodynamics of model supercooled liquids: long-range concentration fluctuations and the role of attractive interactions

We compute partial structure factors, Kirkwood-Buff integrals (KBIs) and chemical potentials of model supercooled liquids with and without attractive interactions. We aim at investigating whether relatively small differences in the tail of the radial distribution functions result in contrasting thermodynamic properties. Our results suggest that the attractive potential favours the nucleation of long-range structures. Indeed, upon decreasing temperature, Bathia-Thornton structure factors display anomalous behaviour in the k→0 limit. KBIs extrapolated to the thermodynamic limit confirm this picture, and excess coordination numbers identify the anomaly with long-range concentration fluctuations. By contrast, the purely repulsive system remains perfectly miscible for the same temperature interval and only reveals qualitatively similar concentration fluctuations in the crystalline state. Furthermore, differences in both isothermal compressibilities and chemical potentials show that thermodynamics is not entirely governed by the short-range repulsive part of the interaction potential, emphasising the nonperturbative role of attractive interactions. Finally, at higher density, where both systems display nearly identical dynamical properties and repulsive interactions become dominant, the anomaly disappears, and both systems also exhibit similar thermodynamic properties.

Structural characteristics of low-density environments in liquid water

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at ∼109.5^{∘}, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water

We perform path-integral molecular dynamics (PIMD) simulations of H₂O and D₂O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H₂O and D₂O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient α_P(T), isothermal compressibility κ_T(T), isobaric heat capacity C_P(T), and static dielectric constant ε(T). While these properties are in excellent [α_P(T) and κ_T(T)] or semi-quantitative agreement [C_P(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in C_P(T) and κ_T(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κ_T(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in C_P(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H₂O and D₂O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with C_P(T), D(T), and structural properties being the only (expected) exceptions.

Enhancement and maximum in the isobaric specific-heat capacity measurements of deeply supercooled water using ultrafast calorimetry

Knowledge of the temperature dependence of the isobaric specific heat (C_p) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in C_p exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid-liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in C_p, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The C_p maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the C_p measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

The anomalies and criticality of liquid water

The origin of water's anomalies has been a matter of long-standing debate. A two-state model, dating back to Röntgen, relies on the dynamical coexistence of two types of local structures-locally favored tetrahedral structure (LFTS) and disordered normal-liquid structure (DNLS)-in liquid water. Phenomenologically, this model not only explains water's thermodynamic anomalies but also can rationalize the existence of a liquid-liquid critical point (LLCP) if there is a cooperative formation of LFTS. We recently found direct evidence for the coexistence of LFTS and DNLS in the experimental structure factor of liquid water. However, the existence of the LLCP and its impact on water's properties has remained elusive, leaving the origin of water's anomalies unclear. Here we propose a unique strategy to locate the LLCP of liquid water. First, we make a comprehensive analysis of a large set of experimental structural, thermodynamic, and dynamic data based on our hierarchical two-state model. This model predicts that the two thermodynamic and dynamical fluctuation maxima lines should cross at the LLCP if it exists, which we confirm by hundred-microsecond simulations for model waters. Based on recent experimental results of the compressibility and diffusivity measurements in the no man's land, we reveal that the two lines cross around 184 K and 173 MPa for real water, suggesting the presence of the LLCP around there. Nevertheless, we find that the criticality is almost negligible in the experimentally accessible region of liquid water because it is too far from the LLCP. Our findings would provide a clue to settle the long-standing debate.

Decoding a Percolation Phase Transition of Water at ∼330 K with a Nanoparticle Ruler

Liquid water, despite its simple molecular structure, remains one of the most fascinating and complex substances. Most notably, many questions continue to exist regarding the phase transitions and anomalous properties of water, which are subtle to observe experimentally. Here, we report a sharp transition in water at 330 K unveiled through experimental measurements of the instantaneous Brownian velocity of NaYF₄:Yb/Er upconversion nanoparticles in water. Our experimental investigations, corroborated by molecular dynamics simulations, elucidate a geometrical phase transition where a low-density liquid (LDL) clusters become percolated below 330 K. Around this critical temperature, we find the sizes of the LDL clusters to be similar to those of the nanoparticles, confirming the role of the upconversion nanoparticle as a powerful ruler for measuring the extensiveness of the LDL hydrogen-bond network and nanometer-scale spatial changes (20-100 nm) in liquids. Additionally, a new order parameter that unequivocally classifies water molecules into two local geometric states is introduced, providing a new tool for understanding and modeling water's many anomalous properties and phase transitions.

The nano-structural inhomogeneity of dynamic hydrogen bond network of TIP4P/2005 water

A method for studying the time dependence of the short-range molecular order of water has been proposed. In the present study, water is considered as a dynamic network between molecules at distances not exceeding 3.2 Å. The instantaneous configurations obtained with the molecular dynamics method have been sequentially analyzed. The mutual orientation of each molecule with its neighboring molecules has been studied and the interaction energy of each pair of neighbor molecules has been calculated. The majority of mutual orientation angles between molecules lie in the interval [0°; 20°]. More than 85% of the molecular pairs in each instantaneous configuration form H-bonds and the H-bond network includes all water molecules in the temperature range 233-293 K. The number of H-bonds fluctuates near the mean value and increases with decreasing temperature, and the energy of the vast majority of such bonds is much higher than the thermal energy. The interaction energy of 80% of the H-bonding molecular pairs lies in the interval [-7; -4] kcal/mol. The interaction energy of pairs that do not satisfy the H-bond angle criterion lies in the interval [-5; 4] kcal/mol; the number of such bonds does not exceed 15% and decreases with decreasing temperature. For the first time it has been found that in each instantaneous configuration the H-bond network contains built-in nanometric structural heterogeneities formed by shorter H-bonds. The fraction of molecules involved in the structural heterogeneities increases from 40% to 60% with a temperature decrease from 293 K to 233 K. Each heterogeneity has a finite lifetime and changeable structure, but they are constantly present during the entire simulation time.