Liquid-liquid Critical Point Research Articles

Melting curves of ice polymorphs in the vicinity of the liquid-liquid critical point.

The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164-168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid-liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid-liquid critical point lies between the melting curves of ice III and ice V. We explore this conjecture using molecular dynamics simulations with a machine learning model based on abinitio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid-liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.

On the possible locus of the liquid-liquid critical point in real water from studies of supercooled water using the TIP4P/Ice model.

One of the most accepted hypothesis to explain the anomalous behavior of water is the presence of a critical point between two liquids, the liquid-liquid critical point (LLCP), buried within the deep supercooled regime. Unfortunately, such hypothesis is hard to be experimentally confirmed due to fast freezing. Here, we show that the TIP4P/Ice water potential shifted by 400 bar can reproduce with unprecedented accuracy the experimental isothermal compressibility of water and its liquid equation of state for a wide pressure and temperature range. We find, both by extrapolation of response function maxima and by a Maxwell construction, that the location of the model LLCP is consistent with previous calculations. According to the pressure shift needed to recover the experimental behavior of supercooled water, we estimate the experimental LLCP to be located around 1250 bar and 195K. We use the model to estimate the ice nucleation rate (J) in the vicinity of the hypothesized LLCP experimental location and obtain J = 1024 m-3 s-1. Thereby, experiments where the ratio between the cooling rate and the sample volume is equal or larger than the estimated nucleation rate could probe liquid-liquid equilibrium before freezing. Such conditions are not accessible in common experiments with microdroplets cooled at a few kelvin per second, but they could be, for instance, using nanodroplets of around 50nm radius observed in a millisecond timescale.

Phase Diagram of Aqueous Solutions of LiCl: a Study of Concentration Effects on the Anomalies of Water

We perform molecular dynamics simulations in order to study thermodynamics and the structure of supercooled aqueous solutions of lithium chloride (LiCl) at concentrations c = 0.678 and 2.034 mol/kg. We model the solvent using the TIP4P/2005 potential and the ions using the Madrid-2019 force field, a force field particularly suited for studying this solution. We find that, for c = 0.678 mol/kg, the behavior of the equation of state, studied in the P-T plane, indicates the presence of a liquid-liquid phase transition, similar to what was previously found for bulk water. We estimate the position of the liquid-liquid critical point to be at Tc ≈ 174 K, Pc ≈ 1775 bar, and ρc ≈ 1.065 g/cm3. When the concentration is tripled to c = 2.034 mol/kg, no critical point is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-ions structure in the two solutions, and we find that at the concentrations examined the effect of ions on the water-water structure is not strong, and all the features found in bulk water are preserved. We also calculate the hydration number of the Li and Cl ions, and in line with experiments, we find the value of 4 for Li+ and between 5.5 and 6 for Cl-, confirming the good performances of the Madrid-2019 force field.

Liquid–Liquid Criticality in TIP4P/2005 and Three-State Models of Water

Molecular dynamics simulations leading to the isothermal compressibility, the isobaric thermal expansivity, and the isobaric heat capacity of TIP4P/2005 water are found to be consistent with the coordinates of its second, liquid-liquid critical point reported recently by Debenedetti et al. [ Science 2020, 369, 289-292]. In accord with the theory of critical phenomena, we encounter that the rise in the magnitude of these response functions as temperature is lowered is especially marked along the critical isochore. Furthermore, response-function ratios provide a test for thermodynamic consistency at the critical point and manifest nonuniversal features sharply distinguishing liquid-liquid from standard gas-liquid criticality. The whole pattern of behavior revealed by simulations is qualitatively the same as the one of a three-state Ising model of water exhibiting a low-temperature liquid-liquid critical point. Exact solutions for the two-state components of such a three-state model are also provided.

Molecular Rotations, Multiscale Order, Hyperuniformity, and Signatures of Metastability during the Compression/Decompression Cycles of Amorphous Ices.

We model, via large-scale molecular dynamics simulations, the isothermal compression of low-density amorphous ice (LDA) to generate high-density amorphous ice (HDA) and the corresponding decompression extending to negative pressures to recover the low-density amorphous phase (LDAHDA). Both LDA and HDA are nearly hyperuniform and are characterized by a dynamical HBN, showing that amorphous ices are nonstatic materials and implying that nearly hyperuniformity can be accommodated in dynamical networks. In correspondence with both the LDA-to-HDA and the HDA-to-LDAHDA phase transitions, the (partial) activation of rotational degrees of freedom activates a cascade effect that induces a drastic change in the connectivity and a pervasive reorganization of the HBN topology which, ultimately, break the samples' hyperuniform character. Key to this effect is the rapid rate at which changes occur, and not their magnitude. The inspection of structural properties from the short- to the long-range shows that signatures of metastability are present at all length-scales, hence providing further solid evidence in support of the liquid-liquid critical point scenario. LDA and LDAHDA differ in terms of HBN and structural properties, implying that they are distinct low-density glasses. Our work unveils the role of molecular rotations in the phase transitions between amorphous ices and shows how the unfreezing of rotational degrees of freedom generates a cascade effect that propagates over multiple length-scales. Our findings greatly improve our basic understanding of water and amorphous ices and can potentially impact the field of molecular network-forming materials at large.

Solid-amorphous transition is related to the waterlike anomalies in a fluid without liquid-liquid phase transition.

The most accepted origin for the water anomalous behavior is the phase transition between two liquids (LLPT) in the supercooled regime connected to the glassy first order phase transition at lower temperatures. Two length scale potentials are an effective approach that has long been employed to understand the properties of fluids with waterlike anomalies and, more recently, the behavior of colloids and nanoparticles. These potentials can be parameterized to have distinct shapes, as a pure repulsive ramp, such as the model proposed by de Oliveira et al. [J. Chem. Phys. 124, 64901 (2006)]. This model has waterlike anomalies despite the absence of LLPT. To unravel how the waterlike anomalies are connected to the solid phases, we employ molecular dynamics simulations. We have analyzed the fluid-solid transition under cooling, with two solid crystalline phases, BCC and HCP, and two amorphous regions being observed. We show how the competition between the scales creates an amorphous cluster in the BCC crystal that leads to amorphization at low temperatures. A similar mechanism is found in the fluid phase, with the system changing from a BCC-like to an amorphous-like structure in the point where a maxima in kT is observed. With this, we can relate the competition between two fluid structures with the amorphous clusterization in the BCC phase. These findings help to understand the origins of waterlike behavior in systems without the liquid-liquid critical point.

Phase behavior of metastable water based on fully ab initio simulations

Based on the strongly constrained and appropriately normed (SCAN) functional, phase behavior of metastable water is studied by ab initio molecular dynamics simulations. A clear van der Waals loop or two-phase coexistence line is observed in the simulated isotherms from 230 to 380 K, providing ab initio evidence for a first-order phase transition. The stability limit line formed by connecting the calculated spinodal points is observed to be a continuous reentrant curve, and the liquid-liquid critical point appears to be hidden at its minimum. The line of maximum density also tends to end at this minimum. These results suggest that the phase behavior of metastable water favors a critical-point-free scenario. Due to the potential limitations of the SCAN functional itself and the failure to take nuclear quantum effects into account, it remains to be further investigated whether the phase behavior of real water remains as predicted in the present work.

Equation of State of Liquid Water Written by Simple Experimental Polynomials and the Liquid–Liquid Critical Point

Experimental and theoretical evidence has been accumulating to support the liquid-liquid critical point (LLCP) hypothesis for water. However, no agreement has yet been reached on the pressure and temperature of LLCP. Here we made simple experimental equations that reproduced the volume of liquid water measured over a wide pressure-temperature range. They were polynomials that calculate pressure using volume and temperature as variables, and coefficients were determined by the method of least-squares. We analyzed the polynomials by changing the volume data and the number of terms in the polynomials and extrapolated them slightly to low temperatures. Consequently, the available experimental volume of liquid water indicated (but did not prove) the existence of LLCP at low temperature. Representative polynomials suggested that LLCP locates around 105 ± ∼ 9 MPa, 207 ± ∼ 5 K, and 0.993 ± ∼ 0.009 cm3/g.

Anomalous Concentration Dependence of Surface Tension and Concentration-Concentration Correlation Functions of Binary Non-Electrolyte Solutions.

The concentration dependence of the surface tension of several binary mixtures of non-electrolytes has been measured at 298.15 K. The mixtures have been chosen since they presented a so-called "W-shape" concentration dependence of the excess constant pressure heat capacity and high values of the concentration-concentration correlation function. This behavior was interpreted in terms of the existence of anomalously high concentration fluctuations that resemble those existing in the proximities of critical points. However, no liquid-liquid phase separation has been found in any of these mixtures over a wide temperature range. In this work, we have extended these studies to the liquid-air interfacial properties. The results show that the concentration dependence of the surface tension shows a plateau and the mixing surface tension presents a "W-shape" behavior. To the best of our knowledge, this is the first time that this behavior is reported. The weak anomalies of the surface tension near a liquid-liquid critical point suggest that the results obtained cannot be considered far-from-critical effects. The usual approach of substituting the activity by the concentration in the Gibbs equation for the relative surface concentration has been found to lead to large errors and the mixtures to have a fuzzy and thick liquid/vapor interface.

Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature.

This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.

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.

The effect of intra-molecular bonds on the liquid-liquid critical point in modified-WAC models.

To obtain a better understanding of liquid-liquid critical points (LLCPs) in one-component liquids, we extend the modified-WAC model by E. Lascaris, Phys. Rev. Lett. 116, 125701 (2016) which is known to have a LLCP. The original WAC model is a model for silica (SiO2) and consists of a mixture of non-bonded Si and O ions. By adding explicit intra-molecular Si-O bonds to the model, we are able to study how several parameters (Si-O bond length, O-Si-O angle, and bond stiffness) affect the existence and location of the LLCP. We find that for this model, only the Si-O bond length has a strong effect on the LLCP, while the bond angle and bond stiffness have no significant effect on the LLCP. An analysis of the relevant coordination numbers indicates that increasing the bond length decreases the ratio RSi/O of additional Si ions per additional O ion in the first coordination shell of the Si, which causes the LLCP to move to higher, more accessible temperatures. The behavior of the RSi/O parameter shows a strong correlation with the behavior of the LLCP and might be a useful tool to determine if a LLCP exists at low, hard-to-reach temperatures in other models.

Water's Unusual Thermodynamics in the Realm of Physical Chemistry.

While it is known since the early work by Edsall, Frank and Evans, Kauzmann, and others that the thermodynamics of solvation of nonpolar solutes in water is unusual and has implications for the thermodynamics of protein folding, only recently have its connections with the unusual temperature dependence of the density of solvent water been illuminated. Such density behavior is, in turn, one of the manifestations of a nonstandard thermodynamic pattern contemplating a second, liquid-liquid critical point at conditions of temperature and pressure at which water exists as a deeply supercooled liquid. Recent experimental and computational work unambiguously points toward the existence of such a critical point, thereby providing concrete answers to the questions posed by the 1976 pioneering experiments by Speedy and Angell and the associated "liquid-liquid transition hypothesis" posited in 1992 by Stanley and co-workers. Challenges of this phenomenology to the branch of Statistical Mechanics remain.

Origin of the anomalous properties in supercooled water based on experimental probing inside “no-man's land”

Austen Angell conducted pioneering work that opened up the field of supercooled water by observing the temperature dependent divergence of the thermodynamic response functions. Many different scenarios have been proposed as the origin of the anomalous properties and now it has become possible to test the various hypotheses in experimental studies of bulk supercooled water at conditions where ice crystallization becomes extremely rapid. Through the usage of x-ray lasers, ultrafast measurements could be conducted, as the sample is rapidly brought to the extreme conditions on time scales preceding ice formation. In particular the experimental observation of the existence of a liquid-liquid transition at positive pressure, one phase behavior at atmospheric conditions at temperatures down to 228 K, and the existence of maxima in several properties at 230 K indicative of a Widom line, are only consistent with the proposed liquid-liquid critical point model as the origin of the anomalous properties. • Unexpected behavior of the heat capacity started the field of supercooled water. • Experimental exploration of no-man's land tests hypotheses. • The liquid-liquid transition and critical point scenario consistent with the data.

Low- and High-Density Unknown Waters at Ice-Water Interfaces.

Experimental confirmation of liquid polymorphs of water, high-density liquid (HDL) and low-density liquid (LDL), is desired for understanding not only the liquid state of matter but also the origin of the mysterious properties of water. However, this remains challenging because the liquid-liquid critical point of water lies in experimentally inaccessible supercooling conditions known as "no man's land". Here, we show by in situ optical microscopy that droplets and layers of low- and high-density unknown waters (LDUW and HDUW) appear macroscopically depending upon ice polymorphs at non-equilibrium interfaces between water and ices under experimentally accessible (de)pressurization conditions. These unknown waters were found to have characteristic velocities (about 20 and 100 m/s for LDUW and HDUW, respectively) different from water (about 40 m/s) and quasi-liquid layers (QLLs) (about 2 and 0.2 m/s for droplet and layer forms of QLLs, respectively). Our discoveries provide insight on liquid polymorphism of water.

Evidence of a liquid\u2013liquid phase transition in H_2O and D_2O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H_2O and D_2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density rho (T), isothermal compressibility kappa _T(T), and self-diffusion coefficients D(T) of H_2O and D_2O are in excellent agreement with available experimental data; the isobaric heat capacity C_P(T) 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_2O and D_2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H_2O and D_2O 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_2O, from PIMD simulations, is located at P_c = 167 pm 9 MPa, T_c = 159 pm 6 K, and rho _c = 1.02 pm 0.01 g/cm^3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D_2O is estimated to be P_c = 176 pm 4 MPa, T_c = 177 pm 2 K, and rho _c = 1.13 pm 0.01 g/cm^3. 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, P_c = 203 pm 4 MPa, T_c = 175 pm 2 K, and rho _c = 1.03 pm 0.01 g/cm^3). 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 T_c for D_2O and, particularly, H_2O suggest that improved water models are needed for the study of supercooled water.

A Metastable Amorphous Intermediate Is Responsible for Laser-Induced Nucleation of Glycine.

Laser-induced crystal nucleation through optical tweezing, and in particular polymorph selection through laser polarization, promises unprecedented control over crystallization. However, in the absence of a nearby liquid-liquid critical point or miscibility gap, the origin of the required mesoscale clusters remains unclear. A number of recent studies of so-called nonclassical nucleation have suggested the presence of large amorphous clusters. Here, we show that supersaturated aqueous glycine solutions form metastable intermediate particles that are off the direct path to crystal nucleation. Laser-induced crystal nucleation only occurs when the laser "activates" one of these particles. In situ low-frequency Raman spectroscopy is used to demonstrate their amorphous or partially ordered character and transformation to various crystal polymorphs. The requirement for solution aging in many previously reported laser-induced crystal nucleation experiments strongly suggests that the presence of amorphous intermediates is a general requirement.

Decompression dynamics of high density amorphous ice above and below the liquid-liquid critical point

We investigate via numerical simulations of the TIP4P/Ice model the isothermal decompression of high density amorphous ice (HDA) mirroring the experimental protocol followed by recent experiments [H. K. Kim, et al., Science 370 , 978, 2020]. Taking advantage of the recent determination of the TIP4P/Ice liquid-liquid critical point, we decompress our samples at temperatures both below and above the critical temperature. We follow the crossover between high and low density, complementing the time evolution of the structure factor with the time evolution of microscopic descriptors. Our results support the interpretation of the experimental pathway as a structural change from high to low density states through a first-order transition line. In the simulation study we do not observe nucleation events, but rather a spinodal-like non-equilibrium transformation, which offers an explanation on why the decompression process even at sub-critical temperatures may result in a continuous time evolution of the density and of the microscopic descriptors.

Surface densities prewet a near critical membrane

Recent work has highlighted roles for thermodynamic phases in cellular processes. Proteins and nucleic acids can phase separate into three-dimensional liquid droplets in the cytoplasm and nucleus and the plasma membrane of some cells appears tuned close to a two-dimensional liquid-liquid critical point. In some examples, cytoplasmic proteins aggregate as ‘surface densities’ at plasma membrane domains, forming structures such as the post-synaptic density and diverse signaling clusters. We examine the physics of surface densities with a minimal Monte-Carlo model and Landau theory calculations.

Direct observation of reversible liquid–liquid transition in a trehalose aqueous solution

Water forms two glassy waters, low-density and high-density amorphs, which undergo a reversible polyamorphic transition with the change in pressure. The two glassy waters transform into the different liquids, low-density liquid (LDL) and high-density liquid (HDL), at high temperatures. It is predicted that the two liquid waters also undergo a liquid-liquid transition (LLT). However, the reversible LLT, particularly the LDL-to-HDL transition, has not been observed directly due to rapid crystallization. Here, I prepared a glassy dilute trehalose aqueous solution (0.020 molar fraction) without segregation and measured the isothermal volume change at 0.01 to 1.00 GPa below 160 K. The polyamorphic transition and the glass-to-liquid transition for the high-density and low-density solutions were examined, and the liquid region where both LDL and HDL existed was determined. The results show that the reversible polyamorphic transition induced by the pressure change above 140 K is the LLT. That is, the transition from LDL to HDL is observed. Moreover, the pressure hysteresis of LLT suggests strongly that the LLT has a first-order nature. The direct observation of the reversible LLT in the trehalose aqueous solution has implications for understanding not only the liquid-liquid critical point hypothesis of pure water but also the relation between aqueous solution and water polyamorphism.