Liquid-liquid Critical Point Research Articles

Liquid-liquid phase transition in a two-dimensional system with anomalous liquid properties

The phase diagram of the two-dimensional particles interacting through a smooth version of Stell-Hemmer interaction was studied using Monte Carlo computer simulations. By evaluating the pressure-volume isotherms, we observed liquid-liquid, liquid-gas phase transitions and three stable crystal phases. The model shows the liquid-liquid critical point in stable liquid phase and is confirmed by observing properties of other thermodynamic functions such as heat capacity and isothermal compressibility, for example. The liquid-gas and the liquid-liquid critical points were estimated within the thermodynamic limit.

Fragile to strong crossover at the Widom line in supercooled aqueous solutions of NaCl

We study by molecular dynamics simulations the dynamical properties of an aqueous solution of NaCl at a concentration of 0.67 mol/kg upon supercooling. In a previous study of the same ionic solution, we have located the liquid-liquid critical point (LLCP) and determined the Widom line connected to the liquid-liquid transition. We present here the results obtained from the study of the self-intermediate scattering function in a large range of temperatures and densities approaching the LLCP. The structural relaxation is in agreement with the mode coupling theory (MCT) in the region of mild supercooling. In the deeper supercooled region the α-relaxation time as function of temperature deviates from the MCT power law prediction showing a crossover from a fragile to a strong behavior. This crossover is found upon crossing the Widom line. The same trend was found in bulk water upon supercooling and it appears almost unchanged by the interaction with ions apart from a shift in the thermodynamic plane toward lower pressures and higher temperatures. These results show that the phenomenology of supercooled water transfers from bulk to solution where the study of the supercooled region is experimentally less difficult.

Heat capacity singularity of binary liquid mixtures at the liquid-liquid critical point

The critical anomaly of the isobaric molar heat capacity for the liquid-liquid phase transition in binary nonionic mixtures is explained through a theory based on the general assumption that their partition function can be exactly mapped into that of the Ising three-dimensional model. Under this approximation, it is found that the heat capacity singularity is directly linked to molar excess enthalpy. In order to check this prediction and complete the available data for such systems, isobaric molar heat capacity and molar excess enthalpy near the liquid-liquid critical point were experimentally determined for a large set of binary liquid mixtures. Agreement between theory and experimental results-both from literature and from present work-is good for most cases. This fact opens a way for explaining and predicting the heat capacity divergence at the liquid-liquid critical point through basically the same microscopic arguments as for molar excess enthalpy, widely used in the frame of solution thermodynamics.

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization

The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liquid phases--low-density liquid (LDL) and high-density liquid (HDL)--deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stability of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystallization after crystallites reach an estimated critical size of about 70 ± 10 molecules.

The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II

This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys. 135, 134503 (2011) and preprint arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light.

An analysis of fluctuations in supercooled TIP4P/2005 water

Large-scale, long-time molecular dynamics simulations are used to investigate fluctuations in the TIP4P/2005 water model in the supercooled region (240-190 K). Particular attention is focused in the vicinity of a previously reported liquid-liquid critical point [J. L. F. Abascal and C. Vega, J. Chem. Phys. 133, 234502 (2010)]. Water is viewed as an equimolar binary mixture with "species" defined based on a local tetrahedral order parameter. A Bhatia-Thornton fluctuation analysis is used to show that species concentration fluctuations couple to density fluctuations and completely account for the anomalous increase in the structure factor at small wave number observed under supercooled conditions. Although we find that both concentration and density fluctuations increase with decreasing temperature along the proposed critical isochore, we cannot confirm the existence of a liquid-liquid critical point. Our simulations suggest that the parameters previously reported are not a true liquid-liquid critical point and we find no evidence of two-phase coexistence in its vicinity. It is shown that very long simulations (on the order of 8 μs for 500 molecules) are necessary to obtain well converged density distributions for deeply supercooled water and this is especially important if one is seeking direct evidence of a two-phase region.

Thermal conductivity of supercooled water

The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.

Multiple liquid-liquid critical points and density anomaly in core-softened potentials

The relation between liquid-liquid phase transitions and waterlike density anomalies in core-softened potentials of fluids was investigated in an exactly solvable one-dimensional lattice model and in a three-dimensional fluid with a Fermi-like potential, the latter by molecular dynamics. Both systems were shown to present three liquid phases, two liquid-liquid phase transitions closely connected to two distinct regions of anomalous density increase. We propose that an oscillatory behavior observed on the thermal expansion coefficient as a function of pressure can be used as a signature of the connection between the liquid-liquid phase transition and density anomaly.

Free energy surface of ST2 water near the liquid-liquid phase transition

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function of two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.

Deeply-cooled water under strong confinement: neutron scattering investigations and the liquid–liquid critical point hypothesis

We present an overview of recent experimental investigations into the properties of strongly-confined water below the bulk freezing temperature. Under strong confinement, the crystallization of water is completely suppressed and the behavior of the confined liquid state can be measured at temperatures and pressures that are inaccessible to the bulk liquid. We focus on two phenomena that have recently been discovered in strongly confined water: the density minimum and the fragile-to-strong dynamic crossover. All experimental results seem to indicate that confined water undergoes a unique kind of transition below the bulk homogeneous nucleation limit. Much of the recent work on deeply-cooled water under strong confinement has been motivated by the liquid-liquid critical point (LLCP) hypothesis. We discuss this hypothesis in the context of the various experimental findings.

Cold and supercooled water: A novel supercritical-fluid solvent

Peculiar properties of fluid mixtures in the vicinity of the critical point of the pure solvent are commonly used in supercritical-fluid technologies, such as fluid extraction, enhanced oil recovery, supercritical chromatography, and micronization. These properties are linked to critical-point anomalies, in particular, very large compressibility and very low interfacial tension. Water, near its vapor-liquid critical point, as a supercritical solvent, is well studied, in contrast to supercooled water. However, more recently, many scientists have started to believe that deep in supercooled region, not directly accessible to bulk-water experiments, there exists a critical point of liquid-liquid separation (“liquid water polyamorphism”). If the water liquid-liquid critical point exists, the addition of a solute will generate critical lines emanating from the pure-water critical point. The phenomenon would be conceptually similar to what is known near the vapor-liquid critical point and what is commonly exploited in supercritical-fluid science and technology. This new idea has not yet been elaborated. The investigation of aqueous systems below the freezing temperature of pure water would not only shed light on the nature of plausible water polyamorphism, but also could open the way for utilizing cold water as a novel and unusual supercritical-fluid solvent.

Effect of pressure on the anomalous response functions of a confined water monolayer at low temperature

We study a coarse-grained model for a water monolayer that cannot crystallize due to the presence of confining interfaces, such as protein powders or inorganic surfaces. Using both Monte Carlo simulations and mean field calculations, we calculate three response functions: the isobaric specific heat C(P), the isothermal compressibility K(T), and the isobaric thermal expansivity α(P). At low temperature T, we find two distinct maxima in C(P), K(T), and ∣α(P)∣, all converging toward a liquid-liquid critical point (LLCP) with increasing pressure P. We show that the maximum in C(P) at higher T is due to the fluctuations of hydrogen (H) bond formation and that the second maximum at lower T is due to the cooperativity among the H bonds. We discuss a similar effect in K(T) and ∣α(P)∣. If this cooperativity were not taken into account, both the lower-T maximum and the LLCP would disappear. However, comparison with recent experiments on water hydrating protein powders provides evidence for the existence of the lower-T maximum, supporting the hypothesized LLCP at positive P and finite T. The model also predicts that when P moves closer to the critical P the C(P) maxima move closer in T until they merge at the LLCP. Considering that other scenarios for water are thermodynamically possible, we discuss how an experimental measurement of the changing separation in T between the two maxima of C(P) as P increases could determine the best scenario for describing water.

A molecular dynamics study of the equation of state and the structure of supercooled aqueous solutions of methanol

We perform molecular dynamics computer simulations in order to study the equation of state and the structure of supercooled aqueous solutions of methanol at methanol mole fractions x(m) = 0.05 and x(m) = 0.10. We model the solvent using the TIP4P/2005 potential and the methanol using the OPLS-AA force field. We find that for x(m) = 0.05 the behavior of the equation of state, studied in the P - T and P - ρ planes, is consistent with the presence of a liquid-liquid phase transition, reminiscent of that previously found for x(m) = 0. We estimate the position of the liquid-liquid critical point to be at T = 193 K, P = 96 MPa, and ρ = 1.003 g/cm(3). When the methanol mole fraction is doubled to x(m) = 0.10 no liquid-liquid transition is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-methanol structure in the two solutions. We find that down to low temperature methanol can be incorporated into the water structure for both x(m) = 0.05 and x(m) = 0.10.

Ising Universality Class for the Liquid-Liquid Critical Point of a One Component Fluid: A Finite-Size Scaling Test

We present a finite-size scaling study of the liquid-liquid critical point in the Jagla model, a prototype model for liquids that present the same thermodynamic anomalies which characterize liquid water. Performing successive umbrella sampling grand canonical Monte Carlo simulations, we evaluate an accurate density of states for different system sizes and determine the size-dependent critical parameters. Extrapolation to infinite size provides estimates of the bulk critical values for this model. The finite-size study allows us to establish that critical fluctuations are consistent with the Ising universality class and to provide definitive evidence for the existence of a liquid-liquid critical point in the Jagla potential. This finding supports the possibility of the existence of a genuine liquid-liquid critical point in anomalous one-component liquids like water.

Mode coupling and fragile to strong transition in supercooled TIP4P water

We consider one of the most used model for water, the rigid four site TIP4P potential, and we study by molecular dynamics simulation the dynamical properties of the liquid upon supercooling. In the previous studies of the thermodynamics of the TIP4P model a liquid-liquid critical point (LLCP) located at the end of the coexistence between the low density liquid (LDL) and the high density liquid (HDL) of water was found. We present here the analysis of the self intermediate scattering functions in a large range of temperatures and densities and we show that the structural relaxation in the region of mild supercooling is in agreement with the predictions of the mode coupling theory. In the more deep supercooled region we observe that the α-relaxation time deviates from the mode coupling theory (MCT) trend and a crossover takes place from a fragile to a strong behavior upon crossing the Widom line emanating from the LLCP. The HDL and the LDL phases are associated with the fragile and the strong behavior, respectively.

Phase diagram of a two-dimensional system with anomalous liquid properties

Using Monte Carlo simulation techniques, we calculate the phase diagram for a square-shoulder square-well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas, and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.

Nanoscale Dynamics of Phase Flipping in Water near its Hypothesized Liquid-Liquid Critical Point

One hypothesized explanation for water's anomalies imagines the existence of a liquid-liquid (LL) phase transition line separating two liquid phases and terminating at a LL critical point. We simulate the classic ST2 model of water for times up to 1000 ns and system size up to N = 729. We find that for state points near the LL transition line, the entire system flips rapidly between liquid states of high and low density. Our finite-size scaling analysis accurately locates both the LL transition line and its associated LL critical point. We test the stability of the two liquids with respect to the crystal and find that of the 350 systems simulated, only 3 of them crystallize and these 3 for the relatively small system size N = 343 while for all other simulations the incipient crystallites vanish on a time scales smaller than ≈ 100 ns.

Fragile-to-strong crossover coupled to the liquid-liquid transition in hydrophobic solutions

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density-high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.

The critical behavior of the refractive index near liquid-liquid critical points

The nature of the critical behavior in the refractive index n is revisited in the framework of the complete scaling formulation. A comparison is made with the critical behavior of n as derived from the Lorentz-Lorenz equation. Analogue anomalies to those predicted for the dielectric constant ε, namely, a leading |t|(2β) singularity in the coexistence-curve diameter in the two-phase region and a |t|(1-α) along the critical isopleth in the one phase region, are expected in both cases. However, significant differences as regards the amplitudes of both singularities are obtained from the two approaches. Analysis of some literature data along coexistence in the two-phase region and along the critical isopleth in the one-phase region provide evidence of an intrinsic effect, independent of the density, in the critical anomalies of n. This effect is governed by the shift of the critical temperature with an electric field, which is supposed to take smaller values at optical frequencies than at low frequencies in the Hz to MHz range.

Thermodynamics of supercooled water

We review the available experimental information on the thermodynamic properties of supercooled water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are also discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.