Critical Point Hypothesis Research Articles

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.

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.

Experimental estimation of the location of liquid-liquid critical point for polyol aqueous solutions.

To solve a mystery of low-temperature liquid water, a liquid-liquid critical point (LLCP) hypothesis that the two kinds of waters, low-density and high-density liquids (LDL and HDL), and a critical point relating to the two waters exist is thought to be the most realistic idea. However, there is no conclusive evidence showing the existence of LLCP. I measured the polyamorphic volume changes of the glassy dilute polyol (ethylene glycol, glycerol, meso-erythritol, xylitol, and D-sorbitol) aqueous solutions during the compression and decompression processes and estimated the location of LLCP for the polyol aqueous solution by a new analysis of the concentration dependence of polyamorphic transition. The LLCP of glycerol aqueous solution around 150 K is estimated to be around 0.045 GPa and around 0.135 molar fraction. This indicates that the solvent water in the glycerol aqueous solution at 1 atm changes continuously from the LDL-like state to the HDL-like state with the increase of solute concentration. The concentration region in which the crossover between LDL-like solvent water and HDL-like solvent water occurs is located near the region that the liquid-liquid transition line is extended to the concentration axis at 1 atm. Moreover, the formation of LDL-like solvent water relates deeply to the homogeneous nucleation of ice Ih in the polyol aqueous solution. This conclusion shows that the LLCP hypothesis of water has an important implication for understanding the dynamics of aqueous solution such as solubility, hydration, segregation, aggregation of solute, nucleation of ice Ih, glass formation, glass transition, and so on.

Perspective: Crossing the Widom line in no man's land: Experiments, simulations, and the location of the liquid-liquid critical point in supercooled water.

The origin of liquid water's anomalous behavior continues to be a subject of interest and debate. One possible explanation is the liquid-liquid critical point hypothesis, which proposes that supercooled water separates into two distinct liquids at low temperatures and high pressures. According to this hypothesis, liquid water's anomalies can be traced back to the critical point associated with this phase separation. If such a critical point actually exists, it is located in a region of the phase diagram known as No Man's Land (NML), where it is difficult to characterize the liquid using conventional experimental techniques due to rapid crystallization. Recently, however, experimentalists have managed to explore NML near the proposed location of the Widom line (i.e., the Kanno-Angell line), thereby providing valuable information concerning the liquid-liquid critical point hypothesis. In this perspective, we analyze these experimental results, in conjunction with molecular dynamics simulations based on the E3B3 water model and discuss their implications for the validity of the liquid-liquid critical point hypothesis and the possible location of water's second critical point.

Communication: Diffusion constant in supercooled water as the Widom line is crossed in no man's land.

According to the liquid-liquid critical point (LLCP) hypothesis, there are two distinct phases of supercooled liquid water, namely, high-density liquid and low-density liquid, separated by a coexistence line that terminates in an LLCP. If the LLCP is real, it is located within No Man's Land (NML), the region of the metastable phase diagram that is difficult to access using conventional experimental techniques due to rapid homogeneous nucleation to the crystal. However, a recent ingenious experiment has enabled measurement of the diffusion constant deep inside NML. In the current communication, these recent measurements are compared, with good agreement, to the diffusion constant of E3B3 water, a classical water model that explicitly includes three-body interactions. The behavior of the diffusion constant as the system crosses the Widom line (the extension of the liquid-liquid coexistence line into the one-phase region) is analyzed to derive information about the presence and location of the LLCP. Calculations over a wide range of temperatures and pressures show that the new experimental measurements are consistent with an LLCP having a critical pressure of over 0.6 kbar.

Experimental study of the polyamorphism of water. I. The isobaric transitions from amorphous ices to LDA at 4 MPa.

The existence of more than one solid amorphous state of water is an extraordinary feature. Since polyamorphism might be connected to the liquid-liquid critical point hypothesis, it is particularly important to study the relations amongst the different amorphous ices. Here we study the polyamorphic transformations of several high pressure amorphous ices to low-density amorphous ice (LDA) at 4 MPa by isobaric heating utilising in situ volumetry and ex situ X-ray diffraction. We find that very-high density amorphous ice (VHDA) and unannealed high density amorphous ice (HDA) show significant relaxation before transforming to LDA, whereby VHDA is seen to relax toward HDA. By contrast, expanded HDA shows almost no relaxation prior to the transformation. The transition to LDA itself obeys criteria for a first-order-like transition in all cases. In the case of VHDA, even macroscopic phase separation is observed. These findings suggest that HDA and LDA are two clearly distinct polyamorphs. We further present evidence that HDA reaches the metastable equilibrium at 140 K and 0.1 GPa but only comes close to that at 140 K and 0.2 GPa. The most important is the path independence of the amorphous phase reached at 140 K and 0.1 GPa.

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.

Crossovers in supercooled solvation water: Effects of hydrophilic and hydrophobic interactions

Systematic 8 ns ab initio molecular dynamics (AIMD) were performed to study the structure and dynamics of water in bulk and close to hydrophobic (CH3) and hydrophilic (carbonyl) groups of tetramethylurea (TMU). Dynamical behaviour showed two crossovers: The first around the hydrophobic group at , and the second at related to the relative strengths of water-water and water-carbonyl hydrogen bonds (HBs). For bulk water, relaxation times appear to diverge at , rendering support to the liquid-liquid critical point hypothesis. To identify the effects due to the hydrophilic carbonyl group, systems of water with one methane molecule were used as references. Our findings are related to the structural and thermodynamic transitions reported for proteins in solution and may play a role in cold denaturation.

The structure of water; from ambient to deeply supercooled

Here we discuss the structure of water in terms of a temperature-dependent balance between two classes of hydrogen-bonded structures. At high and down to mildly supercooled temperatures most molecules favor a closer packing than tetrahedral, with strongly distorted hydrogen bonds. This allows the quantized librational modes to be excited and contribute to the entropy while the loss of enthalpy due to breaking hydrogen bonds is compensated by enhanced van der Waals interactions. Tetrahedral hydrogen bonding is of lower enthalpy resulting in tetrahedrally bonded water patches appearing, but only as fluctuations with size and life-time increasing at lower temperatures. Measurements of the structure at deeply supercooled conditions show a continuous increase in tetrahedrality which becomes accelerated below the temperature of homogeneous ice nucleation. The two local structures are connected to the liquid–liquid critical point (LLCP) hypothesis in supercooled water and correspond to high density liquid (HDL) and low density liquid (LDL). We propose that both HDL and LDL behave as normal liquids and that the anomalous properties of water result from the transition between them, which occurs over a wide temperature range at ambient pressure. The key issue is the competition between incompatible conditions for maximizing the entropy, favored in HDL, and minimizing the enthalpy, favored in LDL, which leads to the instability in the liquid and is the fundamental origin of the proposed LLCP.

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.

Perspective on the structure of liquid water

We present a picture that combines discussions regarding the thermodynamic anomalies in ambient and supercooled water with recent interpretations of X-ray spectroscopy and scattering data of water in the ambient regime. At ambient temperatures most molecules favor a closer packing than tetrahedral, with strongly distorted hydrogen bonds, which allows the quantized librational modes to be excited and contribute to the entropy, but with enthalpically favored tetrahedrally bonded water patches appearing as fluctuations, i.e. a competition between entropy and enthalpy. Upon cooling water the amount of molecules participating in tetrahedral structures and the size of the tetrahedral patches increase. The two local structures are connected to the liquid–liquid critical point hypothesis in supercooled water corresponding to high density liquid and low density liquid. We will discuss the interpretation of X-ray absorption spectroscopy, X-ray emission spectroscopy, wide and small angle X-ray scattering and molecular dynamics simulations in light of the current debate.

Experimental observation of increased fluctuations in an order parameter before epochs of extended brain synchronization

The identification of epileptic seizure precursors has potential clinical relevance. It is conjectured that seizures may be represented by dynamical bifurcations and that an adequate order parameter to characterize brain dynamics is the phase difference in the oscillatory activity of neural systems. In this study, the critical point hypothesis that seizures, or more generally periods of widespread high synchronization, represent bifurcations is empirically tested by monitoring the growth of fluctuations in the putative order parameter of phase differences between magnetoencephalographic and electroencephalographic signals in nearby brain regions in patients with epilepsy and normal subjects during hyperventilation. Implications of the results with regard to epileptic phenomena are discussed.

Failure as a critical phenomenon in a progressive damage model

The critical point hypothesis for fracture is tested using a progressive damagemodel. The advantage of the present model, based on continuum mechanics, is thepossibility of tracking the approach to final failure in terms either of discrete events(the avalanches) or of the resulting continuous strain field. Different but actuallyclosely linked phenomena are reported. In terms of damage avalanches, power lawdistributions of avalanche sizes and energies are observed associated with a finitesize scaling. The finite size scaling is also observed for the spatial correlations ofdamage events. A divergence of the correlation length is reported in the vicinity offinal failure, from a correlation analysis of discrete events and from a scalinganalysis of the continuous strain rate field. We also show that multifractal propertiesof the deformation emerge from the long-range elastic interactions that occurnear final failure. All of these results argue for a critical point interpretation offailure. Finally, we discuss the implications of our results for the criticality offracture and deformation of geophysical objects, and for associated precursoryphenomena.

Understanding Static and Dynamic Heterogeneities in Confined Water

Abstract We report recent efforts to understand the new MIT-Messina experimental discovery of a dynamic crossover at low temperatures in confined water. Preliminary calculations are not inconsistent with one tentative interpretation of this dynamic crossover as resulting from the system passing from the high-temperature high-pressure "HDL" side of the Widom line (where the liquid might display fragile behavior) to the low-temperature low-pressure "LDL" side of the Widom line (where the liquid might display strong behavior). The Widom line - defined to be the line in the pressure-temperature plane where the correlation length has its maximum - arises only if there is a critical point. Hence interpreting the MIT experiments in terms of a Widom line is of potential relevance to testing experimentally, for confined water, the liquid-liquid critical point hypothesis.

Polyamorphism in Water and the Second Critical Point Hypothesis

Polyamorphism in Water and the Second Critical Point Hypothesis

NMR evidence of a sharp change in a measure of local order in deeply supercooled confined water

Using NMR, we measure the proton chemical shift delta, of supercooled nanoconfined water in the temperature range 195 K < T < 350 K. Because delta is directly connected to the magnetic shielding tensor, we discuss the data in terms of the local hydrogen bond geometry and order. We argue that the derivative -( partial differential ln delta/ partial differentialT)(P) should behave roughly as the constant pressure specific heat C(P)(T), and we confirm this argument by detailed comparisons with literature values of C(P)(T) in the range 290-370 K. We find that -( partial differential ln delta/ partial differentialT)(P) displays a pronounced maximum upon crossing the locus of maximum correlation length at approximately 240 K, consistent with the liquid-liquid critical point hypothesis for water, which predicts that C(P)(T) displays a maximum on crossing the Widom line.

Proposed high-pressure calorimetric experiment to probe theoretical predictions on the liquid-liquid critical point hypothesis

A high-pressure calorimetric experiment to test the validity of a water model's prediction, regarding the behavior of the heat capacity in the liquid-liquid critical point and singularity-free scenarios, is proposed in this paper. The response of the specific heat at high pressure is different depending on the existence, or not, of a second critical point. If the model presents a second critical point, there is a nondivergent maximum in the specific heat at a temperature T approximately T(c) for any pressure P > P(c) (T(c) and P(c) being the temperature and pressure of the model's second critical point). This maximum does not appear for the model with a singularity free scenario.

液‐液臨界点による「水の不思議」の解釈

According to liquid-liquid critical point hypothesis of water, liquid separates into low- and high-density liquid phases at low temperature and high pressure, and these liquid phases become known low- and high-density amorphous ices below their glass transition temperatures. An accumulation of experimental and theoretical results seems to support this hypothesis, and this hypothesis may virtually explain the mysteries of water including density maximum at 277 K. Aqueous solutions and confined appear to be readily interpreted on hypothesis.

Parallel 3-D Simulation of a Fault Gouge Using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.

Computational Earthquake Physics PART I: Introduction

Large earthquakes are terrible natural disasters which usually cause massive casualties and huge property loss. In the beginning of the new century, large earthquakes violently struck the world, especially the Asia-Pacific region. Nearly 300,000 people were killed by the magnitude 9.0 Northern Sumatra earthquake and tsunami, and the magnitude 7.8 Pakistan earthquake of October 8th, 2005 resulted in 90,000 deaths. In the meantime, there has been great progress in computational earthquake physics. New understanding of earthquake processes, numerous ideas on earthquake dynamics and complexity, new numerical models and methods, higher performance super-computers, and new data and analysis methods are emerging. These include the LSM (Lattice Solid particle simulation Model) Australian Computational Earth Systems Simulator (ACcESS), Japan’s Earth Simulator, GeoFEM, GeoFEST, QuakeSim, SERVO grid, iSERVO, LURR (Load-Unload Response Ratio), PI (Pattern Informatics), Critical Sensitivity, earthquake Critical Point Hypothesis, the friction law and seismicity, tremor, the Virtual California model, interaction between faults and the conversation of earthquakes, ROC (Relative Operating Characteristic), MFEM (Multiscale Finite-Element Model), etc. Most of these are the outcome of ACES-related research and activities, and will be presented in this volume.