Density and bond-orientational relaxations in supercooled water

ABSTRACT

Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.     

Liquid-liquid phase transition in water

Water shows anomalies different from most of other materials.Different sceniaros have been proposed to explain water anomalies,among which the liquid-liquid phase transition(LLPT)is the most discussed one.It attributes water anomalies to the existence of a hypothesized liquid-liquid critical point(LLCP)buried deep in the supercooled region.We briefly review the recent experimental and theoretical progresses on the study of the LLPT in water.These studies include the discussion on the existence of the first order LLPT in supercooled water and the detection of liquid-liquid critical point.Simulational results of different water models for LLPT and the experimental evidence in confined water are also discussed.     

The Boson peak in confined water: An experimental investigation of the liquid-liquid phase transition hypothesis

The Boson peak (BP) of deeply cooled confined water is studied by using inelastic neutron scattering (INS) in a large interval of the (P, T) phase plane. By taking into account the different behavior of such a collective vibrational mode in both strong and fragile glasses as well as in glass-forming materials, we were able to determine the Widom line that characterizes supercooled bulk water within the frame of the liquid-liquid phase transition (LLPT) hypothesis. The peak frequency and width of the BP correlated with the water polymorphism of the LLPT scenario, allowing us to distinguish the “low-density liquid” (LDL) and “high-density liquid” (HDL) phases in deeply cooled bulk water.Moreover, the BP properties afford a further confirmation of theWidom line temperature T_W as the (P, T) locus in which the local structure of water transforms from a predominately LDL form to a predominately HDL form.     

Spatial heterogeneity in liquid–liquid phase transition

Molecular dynamics simulations are performed to investigate the liquid–liquid phase transition(LLPT) and the spatial heterogeneity in Al–Pb monotectic alloys. The results reveal that homogeneous liquid Al–Pb alloy undergoes an LLPT,separating into Al-rich and Pb-rich domains, which is quite different from the isocompositional liquid water with a transition between low-density liquid(LDL) and high-density liquid(HDL). With spatial heterogeneity becoming large, LLPT takes place correspondingly. The relationship between the cooling rate, relaxation temperature and percentage of Al and the spatial heterogeneity is also reported. This study may throw light on the relationship between the structure heterogeneity and LLPT, which provides novel strategies to control the microstructures in the fabrication of the material with high performance.     

液体-液体相变与反常特性

绝大多数物质的液态密度随温度降低而增大,即常见的热胀冷缩现象.但存在一类物质,如水及第四主族的硅、锗等,其液态密度在一定温度范围内随温度的升高而增大,即密度反常现象.此外,该类物质还存在动力学反常(密度越大粒子运动越快)、热力学反常(热力学量的涨落随温度降低而升高)等其他反常特性.这类材料的化学性质千差万别,但却具有相似的物理反常特性.进一步的理论研究发现部分材料具有两种液态,即高密度液态和低密度液态,两者之间存在一级相变.因此,反常特性与液体-液体相变是否有直接关联是一个值得深入研究的课题.本文主要介绍了具有液体-液体相变的一类材料及其反常特性,包括高温高压下氢的液体-液体相变及其超临界现象,镓的反常特性及其与液体-液体相变的关联等.     

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.     

A computational investigation of the thermodynamics of the Stillinger-Weber family of models at supercooled conditions

The existence of metastable liquid-liquid phase transitions (LLPTs) in tetrahedral liquids such as water, silicon, and silica has been the subject of vigorous scientific debate. Because high crystallization rates hinder experimental investigation at deeply supercooled conditions, computer simulation has been widely employed to investigate the existence of LLPTs in molecular models of tetrahedral liquids. The Stillinger-Weber (SW) model of silicon (and more generally, the SW family of models) has been actively studied along these lines. Whereas some studies observe evidence of an LLPT in this model, others report that only a single metastable liquid exists under deeply supercooled conditions. Here, we perform extensive state-of-the-art free energy calculations to investigate the possibility of an LLPT in the SW model of silicon. A similar analysis is also presented for the generalized SW family of models constructed by varying the strength of the three-body energetic term. Our analysis does not show any evidence of an LLPT in SW silicon nor in the generalized family of SW models over the parameter ranges studied. Explanations for the aforementioned discrepancies between previous studies are provided, along with explicit demonstrations of how these discrepancies may have occurred. Outstanding ambiguities and directions for future work are also discussed.     

Experimental evidence of the ferroelectric nature of the λ-point transition in liquid water

We studied the dielectric properties of nano-sized liquid water samples confined in polymerized silicates MCM-41 characterized by pore sizes 3–10 nm. Freezing temperature suppression in nanopores helps keep the water samples in liquid form at temperatures well below 0°C and thus effectively study the properties of supercooled liquid water. We report the first direct measurements of the dielectric constant by the dielectric spectroscopy method and demonstrate very clear signatures of the second-order phase transition of ferroelectric nature at temperatures next to the λ-point in the supercooled bulk water in full agreement with the recently developed model of the polar liquid.     

Anomalous scattering in supercooled ST2 water

ABSTRACT

Large-scale molecular dynamics (MD) simulations of systems containing up to 256,000 molecules were performed to investigate the scattering behaviour of the ST2 water model at deeply supercooled conditions. The simulations reveal that ST2 exhibits anomalous scattering, reminiscent of that observed in experiment, which is characterised by an increase in the static structure factor at low wavenumbers. This unusual behaviour in ST2 is linked with coupled fluctuations in density and local tetrahedral order in the liquid. The Ornstein–Zernike correlation length estimated from the anomalous scattering component exhibits power-law growth upon cooling, consistent with the existence of a liquid–liquid critical point (LLCP) in the ST2 model at ca. 245 K. Further, spontaneous liquid–liquid phase separation is observed upon thermally quenching a large system with 256,000 water molecules below the predicted critical temperature into the two-phase region. The large-scale MD simulations therefore confirm the existence of a metastable liquid–liquid phase transition in ST2 and support findings from previous computational studies performed using smaller systems containing only a few hundred molecules. We anticipate that our analysis may prove useful in interpreting recent scattering experiments that have been performed to search for an LLCP in deeply supercooled water.     

Large decrease of fluctuations for supercooled water in hydrophobic nanoconfinement

Using Monte Carlo simulations, we study a coarse-grained model of a water layer confined in a fixed disordered matrix of hydrophobic nanoparticles at different particle concentrations c. For c=0, we find a first-order liquid-liquid phase transition (LLPT) ending in one critical point at low pressure P. For c>0, our simulations are consistent with a LLPT line ending in two critical points at low and high P. For c=25%, at high P and low temperature, we find a dramatic decrease of compressibility, thermal expansion coefficient, and specific heat. Surprisingly, the effect is present also for c as low as 2.4%. We conclude that even a small presence of hydrophobic nanoparticles can drastically suppress thermodynamic fluctuations, making the detection of the LLPT more difficult.     

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.     

Liquid-liquid phase transition in elemental carbon: a first-principles investigation

It has been recently suggested that elemental carbon may be a promising candidate to exhibit a liquid-liquid phase transition (LLPT). We report the results of first-principles molecular dynamics simulations showing no evidence of LLPT in carbon, in the same temperature and pressure range where such a transition was found using empirical calculations. Our simulations indicate a continuous evolution from a primarily sp-bonded liquid to an sp(2)-like and an sp(3)-like fluid, as a function of pressure, above the graphite melting line. The discrepancy between quantum and classical simulations is attributed to the inability of empirical potentials to describe complex electronic effects in condensed carbon phases.     

Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive V_R and a density-dependent attractive V_A part.     

Density fluctuations in liquid water

The density distributions and fluctuations in grids of varying size in liquid water at ambient pressure, both above the freezing point and in the supercooled state, are analyzed from the trajectories obtained from large-scale molecular dynamics simulations. It is found that the occurrence of low- and high-density regions (LDL and HDL) is transient and their respective residence times are dependent on the size of the simulated system. The spatial extent of density-density correlation is found to be within 7 ? or less. The temporal existence of LDL and HDL arises as a result of natural density fluctuations of an equilibrium system. The density of bulk water at ambient conditions is homogenous.     

Liquid polyamorphism: Possible relation to the anomalous behaviour of water

We present evidence from experiments and computer simulations supporting the hypothesis that water displays polyamorphism, i.e., water separates into two distinct liquid phases. This concept of a new liquid-liquid phase transition is finding application to other liquids as well as water, such as silicon and silica. Specifically, we investigate, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point in (i) Two models of water, TIP5P and ST2, which display a first order liquid-liquid phase transition at low temperatures; (ii) the Jagla model, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions; and (iii) A Hamiltonian model of water where the idea of two length/energy scales is built in. This model also displays a first order liquid-liquid phase transition at low temperatures besides the first order liquid-gas phase transition at high temperatures. We find a correlation between the dynamic fragility crossover and the locus of specific heat maxima C_P^max (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesised liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between C_P^max and the dynamic crossover is not limited to the case of water, a hydrogen bonded network liquid, but is a more general feature of crossing the Widom line, an extension of the first-order coexistence line in the supercritical region. Dedicated to Armin Bunde on the occasion of his 60th birthday.     

Dynamics of supercooled confined water measured by deep inelastic neutron scattering

In this paper, we present the results of deep inelastic neutron scattering (DINS) measurements on supercooled water confined within the pores (average pore diameter ~ 20 Å) of a disordered hydrophilic silica matrix obtained through hydrolysis and polycondensation of the alkoxide precursor Tetra-Methyl-Ortho-Silicate via the sol-gel method. Experiments were performed at two temperatures (250 K and 210 K, i.e., before and after the putative liquid–liquid transition of supercooled confined water) on a “wet” sample with hydration h ~ 40% w/w, which is high enough to have water-filled pores but low enough to avoid water crystallization. A virtually “dry” sample at h ~ 7% was also investigated to measure the contribution of the silica matrix to the neutron scattering signal. As is well known, DINS measurements allow the determination of the mean kinetic energy and the momentum distribution of the hydrogen atoms in the system and therefore, allow researchers to probe the local structure of supercooled confined water. The main result obtained is that at 210 K the hydrogen mean kinetic energy is equal or even slightly higher than at 250 K. This is at odds with the predictions of a semiempirical harmonic model recently proposed to describe the temperature dependence of the kinetic energy of hydrogen in water. This is a new and very interesting result, which suggests that at 210 K, the water hydrogens experience a stiffer intermolecular potential than at 250 K. This is in agreement with the liquid–liquid transition hypothesis.     

Detection of early stage precursor during formation of plastic crystal ethanol from the supercooled liquid state: a simultaneous dielectric spectroscopy with neutron diffraction study

Transformation of deuterated ethanol from supercooled liquid into a plastic crystal or rotator phase is investigated by means of a particular experimental setup combining simultaneously dielectric spectroscopy with neutron diffraction techniques. We demonstrate that, previous to the growth of the bcc lattice of the plastic crystal phase, the formation of a precursor or intermediate phase through a liquid-liquid phase separation takes place. Once this precursor phase is formed, subsequent (plastic) crystalline nucleation and growth is expected to develop.     

Metal-to-semimetal transition in supercooled liquid silicon

Computer simulations, using the Stillinger-Weber potential, have previously been employed to demonstrate a liquid-liquid transition in supercooled silicon near 1060 K. From calculations of electronic structure using an empirical psuedopotential, we show that silicon undergoes an associated metal to semimetal transition with a resistivity jump of roughly 1 order of magnitude. We show that the electronic states near the Fermi energy become localized in the low temperature phase, and that changes in electronic structure between the two phases arise from a change in atomic structure, and not from a change in density.     

Liquid-liquid phase transformation in silicon: evidence from first-principles molecular dynamics simulations

We report results of first principles molecular dynamics simulations that confirm early speculations on the presence of liquid-liquid phase transition in undercooled silicon. However, we find that structural and electronic properties of both low-density liquid (LDL) and high-density liquid (HDL) phases are quite different from those obtained by empirical calculations, the difference being more pronounced for the HDL phase. The discrepancy between quantum and classical simulations is attributed to the inability of empirical potentials to describe changes in chemical bonds induced by density and temperature variations.