The Widom line and dynamical crossover in supercritical water: Popular water models versus experiments

Semiclassical thermodynamic geometry

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.

Fingerprints of the Crossing of the Frenkel and Melting Line on the Properties of High-Pressure Supercritical Water

Using molecular dynamics simulations in combination with the two-phase thermodynamic model, we reveal novel characteristic fingerprints of the crossing of the Frenkel and melting line on the properties of high-pressure water at a near-critical temperature (1.03T_c). The crossing of the Frenkel line at about 1.17 GPa is characterized by a crossover in the rotational and translational entropy ratio S^rot/S^trans, indicating a change in the coupling between translational and rotational motions which is also reflected in the shape of the rotational density of states. The observed isosbestic points in the translational and rotational density of states are also blue-shifted at density and pressure conditions higher than the ones corresponding to the Frenkel line. The first-order phase transition from a rigid liquid to a face-centered cubic plastic crystal phase at about 8.5 GPa is reflected in the discontinuous changes in the translational and rotational entropy, particularly in the significant increase of the ratio S^rot/S^trans. A noticeable discontinuous increase of the dielectric constant has also been revealed when crossing this melting line, which is attributed to the different arrangement of the water molecules in the plastic crystal phase. The reorientational dynamics in the plastic crystal phase is faster in comparison with the "rigid" liquid-like phase, but it remains unchanged upon a further pressure increase in the range of 8.5-11 GPa.

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.

Dynamical crossover and its connection to the Widom line in supercooled TIP4P/Ice water

We perform molecular dynamics simulations with the TIP4P/Ice water model to characterize the relationship between dynamics and thermodynamics of liquid water in the supercooled region. We calculate the relevant properties of the phase diagram, and we find that TIP4P/Ice presents a retracing line of density maxima, similar to what was previously found for atomistic water models and models of other tetrahedral liquids. For this model, a liquid-liquid critical point between a high-density liquid and a low-density liquid was recently found. We compute the lines of the maxima of isothermal compressibility and the minima of the coefficient of thermal expansion in the one phase region, and we show that these lines point to the liquid-liquid critical point while collapsing on the Widom line. This line is the line of the maxima of correlation length that emanates from a second order critical point in the one phase region. Supercooled water was found to follow mode coupling theory and to undergo a transition from a fragile to a strong behavior right at the crossing of the Widom line. We find here that this phenomenology also happens for TIP4P/Ice. Our results appear, therefore, to be a general characteristic of supercooled water, which does not depend on the interaction potential used, and they reinforce the idea that the dynamical crossover from a region where the relaxation mechanism is dominated by cage relaxation to a region where cages are frozen and hopping dominates is correlated in water to a phase transition between a high-density liquid and a low-density liquid.

Hysteresis in the temperature dependence of the IR bending vibration of deeply cooled confined water

Using Fourier Transform Infrared (FTIR) spectroscopy, we investigate the temperature dependence of the bending vibrations of water confined in the pores of a silica hydrogel in the temperature interval of 270-180 K. We also investigate the presence of thermal hysteresis by cooling and reheating temperature scans. The results clearly show the presence, at about 230 K, of a crossover in the temperature dependence of the IR spectra; moreover, the presence of hysteresis is clearly demonstrated. By comparing FTIR data with neutron diffraction data and previous calorimetric data on the same samples, we conclude that the crossover and the hysteretical behavior do not involve a water glass transition or crystallization but are related to a first-order-like liquid-liquid transition.

Investigation concerning the uniqueness of separatrix lines separating liquidlike from gaslike regimes deep in the supercritical phase of water with a focus on Widom line concepts

The supercritical phase of fluids has long been known to feature significantly different liquidlike and gaslike regimes. However, it is textbook knowledge that the supercritical state is a homogeneous fluid phase where properties change continuously. Nevertheless, there has been an increasing amount of evidence published that suggests that there might exist a unique line that rigorously separates different regimes in supercritical phases, particularly in the case of water. Here, we use the quasiexact IAPWS95 equation of state to rigorously assess the macroscopic thermodynamic properties of supercritical water without invoking any water model or related approximations. We focus on how these properties change deep in the supercritical phase, in particular if they allow one to introduce a unique "thermodynamic separatrix." Our rigorous thermodynamic analysis, which relies exclusively on accurate experimental data, makes clear that there is no unique separatrix in real supercritical water-such as the recently much-invoked "Widom line." A comparison to the van der Waals equation of state reproduces qualitatively all our findings for real water, thereby suggesting that our analysis should be transferable to other fluids and critical points. Topological analysis of the H-bond network structure of supercritical water, as obtained from molecular-dynamics simulations using a standard water model, demonstrates that also the percolation line does not provide a meaningful separatrix to rigorously distinguish liquidlike from gaslike regimes.

Effects of nanoparticle heating on the structure of a concentrated aqueous salt solution

The effects of a rapidly heated nanoparticle on the structure of a concentrated aqueous salt solution are studied using molecular dynamics simulations. A diamond-like nanoparticle of radius 20 Å is immersed in a sodium-chloride solution at 20% above the experimental saturation concentration and equilibrated at T = 293 K and P = 1 atm. The nanoparticle is then rapidly heated to several thousand degrees Kelvin, and the system is held under isobaric-isoenthalpic conditions. It is observed that after 2-3 ns, the salt ions are depleted far more than water molecules from a proximal zone 15-25 Å from the nanoparticle surface. This leads to a transient reduction in molality in the proximal zone and an increase in ion clustering in the distal zone. At longer times, ions begin to diffuse back into the proximal zone. It is speculated that the formation of proximal and distal zones, and the increase in ion clustering, plays a role in the mechanism of nonphotochemical laser-induced nucleation.

Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations

Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.

EDTA aggregates induce SYPRO orange-based fluorescence in thermal shift assay

Ethylenediaminetetraacetic acid (EDTA) is widely used in the life sciences as chelating ligand of metal ions. However, formation of supramolecular EDTA aggregates at pH > 8 has been reported, which may lead to artifactual assay results. When applied as a buffer component at pH ≈ 10 in differential scanning fluorimetry (TSA) using SYPRO Orange as fluorescent dye, we observed a sharp change in fluorescence intensity about 20°C lower than expected for the investigated protein. We hypothesized that this change results from SYPRO Orange/EDTA interactions. TSA experiments in the presence of SYPRO Orange using solutions that contain EDTA-Na+ but no protein were performed. The TSA experiments provide evidence that suggests that at pH > 9, EDTA4- interacts with SYPRO Orange in a temperature-dependent manner, leading to a fluorescence signal yielding a "denaturation temperature" of ~68°C. Titrating Ca2+ to SYPRO Orange and EDTA solutions quenched fluorescence. Ethylene glycol tetraacetic acid (EGTA) behaved similarly to EDTA. Analytical ultracentrifugation corroborated the formation of EDTA aggregates. Molecular dynamics simulations of free diffusion of EDTA-Na+ and SYPRO Orange of in total 27 μs suggested the first structural model of EDTA aggregates in which U-shaped EDTA4- arrange in an inverse bilayer-like manner, exposing ethylene moieties to the solvent, with which SYPRO Orange interacts. We conclude that EDTA aggregates induce a SYPRO Orange-based fluorescence in TSA. These results make it relevant to ascertain that future TSA results are not influenced by interference between EDTA, or EDTA-related molecules, and the fluorescent dye.

Evidence for a liquid-liquid critical point in supercooled water within the E3B3 model and a possible interpretation of the kink in the homogeneous nucleation line

Supercooled water exhibits many thermodynamic anomalies, and several scenarios have been proposed to interpret them, among which the liquid-liquid critical point (LLCP) hypothesis is the most commonly discussed. We investigated Widom lines and the LLCP of deeply supercooled water, by using molecular dynamics simulation with a newly reparameterized water model that explicitly includes three-body interactions. Seven isobars are studied from ambient pressure to 2.5 kbar, and Widom lines are identified by calculating maxima in the coefficient of thermal expansion and the isothermal compressibility (both with respect to temperature). From these data we estimate that the LLCP of the new water model is at 180 K and 2.1 kbar. The oxygen radial distribution function is calculated along the 2 kbar isobar. It shows a steep change in the height of its second peak between 180 and 185 K, which indicates a transition between the high-density liquid and low-density liquid phases and which is consistent with the ascribed location of the critical point. The good agreement of the height of the second peak of the radial distribution function between simulation and experiment at 1 bar, as a function of temperature, supports the validity of the model. The location of the LLCP within the model is close to the kink in the experimental homogeneous nucleation line. We use existing experimental data to argue that the experimental LLCP is at 168 K and 1.95 kbar and speculate how this LLCP and its Widom line might be responsible for the kink in the homogeneous nucleation line.

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.