We review the effect of water anomalies on the properties of low temperature water. When supercooled, liquids dynamical properties change drastically. Supercooled liquids undergo an at least exponential decrease of their diffusion coefficient when temperature decreases while their structure merely does not change. We discuss how that still unexplained change of dynamical properties at low temperatures affect water differently from other liquids and what can be deduced from it.
The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn upon testing the validities of some variants of the SE relation rather than its original form, and it appears conflicting with the fact that supercooled water is in its local equilibrium. In this work, we show by molecular dynamics simulation that both the Einstein and Stokes relations are indeed conserved in supercooled water. The inconsistency between the original SE relation and its variants comes from two facts: (1) the substitutes of the shear viscosity in the …
The viscosity of supercooled water has been a subject of intense study, in particular with respect to its temperature dependence. Much less is known, however, about the influence of dynamical effects on the viscosity in its supercooled state. Here we address this issue for the first time, using molecular dynamics simulations to investigate the shear-rate dependence of the viscosity of supercooled water as described by the TIP4P/Ice model. We show the existence of a distinct cross-over from Newtonian to non-Newtonian behavior characterized by a power-law shear-thinning regime. The viscosity red…
We use molecular dynamics simulations to study the behavior of supercooled water subject to different stimuli from a diluted azobenzene hydrophobic probe. When the molecular motor does not fold, it acts as a passive probe, modifying the structure of water around it, while when the motor is active, it induces elementary diffusion processes inside the medium acting mainly on the dynamics. We study two particular densities, the density of ambient water and a lower density around the ambient pressure ice density, chosen to favor high density liquid and low density liquid (LDL) water, respectively.…
The temperature dependence (10-290 K) of the low-frequency (20-150 cm-1) Raman-active phonon modes of supercooled confined water in L,L-diphenylalanine micro/nanotubes was analysed. The isolated dynamics of a specific geometry of water cluster (pentamer) in supercooled confined regime was studied in detail. A particular mode concerning water-nanotube interaction was also probed. A fragile-to-strong transition at 204 K was observed and related to the crossing of the Widom line. The critical exponent analyses of the relaxation rate data based on mode-coupling theory indicated perfect agreement a…
Water displays breakdown of the Stokes-Einstein relation at low temperatures. We hypothesize that the breakdown is a result of the structural changes and a sharp rise in dynamic heterogeneities that occurs low T upon crossing the Widom line.
Water is the most familiar liquid, and arguably the most complex. Anomalies of supercooled water have been measured during decades, and competing interpretations proposed. Yet, a decisive experiment remains elusive, because of unavoidable crystallization into ice. We investigate the state of water that is both supercooled and under mechanical tension, or negative pressure. Liquids under negative pressure can be found in plants or fluid inclusions in minerals. Using such water inclusions in quartz, we report the first measurements on doubly metastable water down to $-15^\circ\mathrm{C}$ and aro…
Small angle neutron scattering (SANS) is used to measure the density of heavy water contained in 1-D cylindrical pores of mesoporous silica material MCM-41-S-15, with pores of diameter of 15+-1 A. In these pores the homogenous nucleation process of bulk water at 235 K does not occur and the liquid can be supercooled down to at least 160 K. The analysis of SANS data allows us to determine the absolute value of the density of D2O as a function of temperature. We observe a density minimum at 210+-5 K with a value of 1.041+-0.003 g/cm3. We show that the results are consistent with the predictions …
We perform extensive molecular dynamics simulations of the TIP4P/2005 model of water to investigate the origin of the Boson peak reported in experiments on supercooled water in nanoconfined pores, and in hydration water around proteins. We find that the onset of the Boson peak in supercooled bulk water coincides with the crossover to a predominantly low-density-like liquid below the Widom line $T_W$. The frequency and onset temperature of the Boson peak in our simulations of bulk water agree well with the results from experiments on nanoconfined water. Our results suggest that the Boson peak i…
We have developed a scaled parametric equation of state to describe and predict thermodynamic properties of supercooled water. The equation of state, built on the growing evidence that the critical point of supercooled liquid-liquid water separation exists, is universal in terms of theoretical scaling fields and is shown to belong to the Ising-model class of universality. The theoretical scaling fields are postulated to be analytical combinations of the physical fields, pressure and temperature. The equation of state enables us to accurately locate the "Widom line" (the locus of stability mini…
The supercooled state of bulk water is largely hidden by unavoidable crystallization, which creates an experimentally inaccessible temperature regime - a 'no man's land'. We address this and circumvent the crystallization problem by systematically studying the supercooled dynamics of hydrogen bonded oligomeric liquids (glycols), where water corresponds to the chain-ends alone. This novel approach permits a 'dilution of water' by altering the hydrogen bond concentration via variations in chain length. We observe a dynamic crossover in the temperature dependence of the structural relaxation time…
Dielectric permittivity of supercooled volume water has been measured in the range of temperatures from $-20\,^{\circ}$C to $-60\,^{\circ}$C at the frequencies $7.6$~GHz and $9.7$~GHz. The measurements have been made using microwave resonators and wetted silicate sorbents. From the data obtained, the temperature dependences of the relaxation frequencies were updated for the Debye model with two relaxation frequencies. The updated formulae for dielectric permittivity of cold water may be applied to the frequency range $7\ldots200$~GHz.
The anomalous properties of water in the supercooled state are numerous and well-known. Particularly striking are the strong changes in dynamic properties that appear to display divergences at temperatures close to -- but beyond -- the lowest temperatures attainable either experimentally or in computer simulations. Recent work on slow or glassy dynamics in water suggests analogies with simple liquids not previously appreciated, and at the same time highlights some aspects that remain peculiar to water. A comparison of the behavior of water with normal liquids, with respect to its dynamic, ther…
The paper provides data on measuring electrical properties of supercooled water in nanoporous silica MCM-41 with 3.5 nm diameter cylindrical pores, using the methods of dielectric spectroscopy and measuring proper electrical fluctuations at low frequencies. Occurrence of non-linear media properties at the temperatures below -35 C was determined, which was revealed in the form of registered cell capacity dependence on voltage amplitude in it, as well as noise increase close to -40 C. The effects observed are supposed to be related to the earlier predicted ferroelectric phase transition.
Supercooled water is a metastable phase of liquid water below the melting temperature. An interesting discussion recently developed on the relationship between crystallization rate and the time scales of equilibration within the liquid phase. Calculations using a coarse grained monatomic model of water, the mW model, suggested that equilibration of the liquid below the temperature of homogeneous nucleation $T_H\approx225$ K is slower than ice nucleation. Here, a 3 $μ$s long molecular dynamics simulation of the TIP4P-Ew water model is presented to investigate the relaxation properties of an ato…
We investigate the properties of water along the liquid/vapor coexistence line in the supercooled regime down to the no-man's land. Extensive molecular dynamics simulations of the TIP4P/2005 liquid/vapor interface in the range 198 -- 348 K allow us to locate the second surface tension inflection point with high accuracy at 283$\pm$5 K, close to the temperature of maximum density (TMD). This temperature also coincides with the appearance of a density anomaly at the interface known as the apophysis. We relate the emergence of the apophysis to the observation of HDL water adsorption in the proxim…
Bulk water presents a large number of crystalline and amorphous ices. Hydrophobic nanoconfinement is known to affect the tendency of water to form ice and to reduce the melting temperature. However, a systematic study of the ice phases in nanoconfinement is hampered by the computational cost of simulations at very low temperatures. Here we develop a coarse-grained model for a water monolayer in hydrophobic nanoconfinement and study the formation of ice by Mote Carlo simulations. We find two ice phases: low-density-crystal ice at low pressure and high-density hexatic ice at high pressure, an in…
The liquid and supercooled states of water show a series of anomalies whose nature is debated. A key role is attributed to the formation of structural aggregates induced by critical phenomena occurring deep in the supercooled region; the nature of the water anomalies and of the hidden critical processes remains elusive. Here we report a time-resolved optical Kerr effect investigation of the vibrational dynamics and relaxation processes in supercooled bulk water. The experiment measures the water intermolecular vibrations and the structural relaxation process in an extended temperature range, a…
The temperature scale of simple water models in general does not coincide with the natural one. Therefore, in order to make a meaningful evaluation of different water models a temperature rescaling is necessary. In this paper we introduce a rescaling using the melting temperature and the temperature corresponding to the maximum of the heat capacity to evaluate four common water models (TIP4P-Ew, TIP4P-2005, TIP5P-Ew and Six-Sites) in the supercooled regime. Although all the models show the same general qualitative behavior, the TIP5P-Ew appears as the best representation of the supercooled reg…
By confining water in nano-pores of silica glass, we can bypass the crystallization and study the pressure effect on the dynamical behavior in deeply supercooled state using neutron scattering. We observe a clear evidence of a cusp-like fragile-to-strong (F-S) dynamic transition. Here we show that the transition temperature decreases steadily with an increasing pressure, until it intersects the homogenous nucleation temperature line of bulk water at a pressure of 1600 bar. Above this pressure, it is no longer possible to discern the characteristic feature of the F-S transition. Identification …
The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) li…
We calculate the configurational entropy S_conf for the SPC/E model of water for state points covering a large region of the (T,rho) plane. We find that (i) the (T,rho) dependence of S_conf correlates with the diffusion constant and (ii) that the line of maxima in S_conf tracks the line of density maxima. Our simulation data indicate that the dynamics are strongly influenced by S_conf even above the mode-coupling temperature T_MCT(rho).
Deeply supercooled water exhibits complex dynamics with large density fluctuations, ice coarsening and characteristic time scales extending from picoseconds to milliseconds. Here, we discuss implications of these time scales as they pertain to two-phase coexistence and to molecular simulations of supercooled water. Specifically, we argue that it is possible to discount liquid-liquid criticality because the time scales imply that correlation lengths for such behavior would be bounded by no more than a few nanometers. Similarly, it is possible to discount two-liquid coexistence because the time …
To study the coexistence of two liquid states of water within one simulation box, we implement an equilibrium sedimentation method--which involves applying a gravitational field to the system and measuring/calculating the resulting density profile in equilibrium. We simulate a system of particles interacting via the ST2 potential, a model for water. We detect the coexistence of two liquid phases at low temperature.
In this article we study in detail the Q-vector dependence of the collective dynamics in simulated deeply supercooled SPC/E water. The evolution of the system has been followed for 250 ns at low T, allowing a clear identification of a two step relaxation process. We present evidence in favor of the use of the mode coupling theory for supercooled liquid as framework for the description of the slow alpha-relaxation dynamics in SPC/E water, notwithstanding the fact that the cage formation in this system is controlled by the formation of an open network of hydrogen bonds as opposed to packing cons…
We develop a series of molecular dynamics computer simulations of liquid water, performed with a polarizable potential model, to calculate the spinodal line and the curve of maximum density inside the metastable supercooled region. After analysing the structural properties,the liquid spinodal line is followed down to T=210 K. A monotonic decrease is found in the explored region. The curve of maximum density bends on approaching the spinodal line. These results, in agreement with similar studies on non polarizable models of water, are consistent with the existence of a second critical point for…
We determine the phase diagram of liquid supercooled water by extensive computer simulations using the TIP5P-E model [J. Chem. Phys. {\bf 120}, 6085 (2004)]. We find that the transformation of water into a low density liquid in the supercooled range strongly enhances the solubility of hydrophobic particles. The transformation of water into a tetrahedrally structured liquid is accompanied by a minimum in the hydration entropy and enthalpy. The corresponding change in sign of the solvation heat capacity indicates a loss of one characteristic signature of hydrophobic hydration. The observed behav…
Glass formers exhibit a viscoelastic behavior: at the laboratory timescale, they behave like (glassy) solids at low temperatures, and like liquids at high temperatures. Based on this observation, elastic models relate the long time supercooled dynamics to short time elastic properties of the supercooled liquid. In the present work, we assess the validity of elastic models for the shear viscosity and the $α$-relaxation time of supercooled water, using molecular dynamics simulations with the TIP4P/2005f force field over a wide range of temperatures. We show that elastic models provide a good des…
Properties of water have been well elucidated for temperatures above $\sim$230 K and yet mysteries remain in the deeply supercooled region. By performing extensive molecular dynamics simulations on this supercooled region, we find that structural and dynamical instabilities are hidden in the experimentally inaccessible region between 235 K and 150 K. We find a hitherto undiscovered fragmentation from 220 K to 190 K, which is the break-up of large clusters consisting of molecules with locally distorted tetrahedral structure into small pieces with one or two isolated defects. The fragmentation l…
Liquid-liquid and liquid-vapor coexistence regions of various water models were determined by MC simulations of isotherms of density fluctuation restricted systems and by Gibbs ensemble MC simulations. All studied water models show multiple liquid-liquid phase transitions in the supercooled region: we observe two transitions of the TIP4P, TIP5P and SPCE model and three transitions of the ST2 model. The location of these phase transitions with respect to the liquid-vapor coexistence curve and the glass temperature is highly sensitive to the water model and its implementation. We suggest, that t…
Liquid water exhibits anomalous behavior in the supercooled region. A popular hypothesis to explain supercooled water's anomalies is the existence of a metastable liquid-liquid transition terminating at a critical point. The hypothesized phase transition is not directly accessible in a bulk experiment because it is expected to occur in "no-man's" region below the kinetic stability limit of the liquid phase at about 235 K, the temperature of homogeneous ice formation. Therefore, verifications of this hypothesis are usually based on extrapolations from the experimentally accessible region. In th…
Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models - based on the assumption of the existence of two types of competing local states (or, structures) in liquid water - have been extremely successful in describing water's thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a geometrical order parameter-free approach to unambiguously identify the two types of competing local states -- entropically and energet…
The loss factor of supercooled water at the frequencies 11...180 GHz has been measured. A measuring technique has been proposed, in which wetted nanoporous silicate materials, silica gels, with the mean diameter of the pores being 6-9 nm, were used to obtain deeply supercooled water. Results have been obtained for the loss factor of supercooled water, close to volume water for its properties, when cooled down to -45 °C. To ascertain the mechanism of pore water losses, measurements have been made in the range of temperatures 0...-90 °C. The results obtained have demonstrated the existence of si…
We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different appr…
According to the Random First Order Transition (RFOT) theory of glasses, the barriers for activated dynamics in supercooled liquids vanish as the temperature of a viscous liquid approaches the dynamical transition temperature from below. This occurs due to a decrease of the surface tension between local meta-stable molecular arrangements much like at a spinodal. The dynamical transition thus represents a crossover from the low $T$ activated bevavior to a collisional transport regime at high $T$. This barrier softening explains the deviation of the relaxation times, as a function of temperature…
We propose a unified model combining the first-order liquid-liquid and the second-order ferroelectric phase transitions models and explaining various features of the $λ$-point of liquid water within a single theoretical framework. It becomes clear within the proposed model that not only does the long-range dipole-dipole interaction of water molecules yield a large value of dielectric constant $ε$ at room temperatures, our analysis shows that the large dipole moment of the water molecules also leads to a ferroelectric phase transition at a temperature close to the lambda-point. Our more refined…
We consider and compare the structural properties of bulk TIP4P water and of a sodium chloride aqueous solution in TIP4P water with concentration c = 0.67 mol/kg, in the metastable supercooled region. In a previous paper [D. Corradini, M. Rovere and P. Gallo, J. Chem. Phys. 132, 134508 (2010)] we found in both systems the presence of a liquid-liquid critical point (LLCP). The LLCP is believed to be the end point of the coexistence line between a high density liquid (HDL) and a low density liquid (LDL) phase of water. In the present paper we study the different features of water-water structure…
Numerical simulations for a number of water models have supported the possibility of a metastable liquid-liquid critical point (LLCP) in the deep super-cooled region. Here we consider a theoretical model for a supercooled liquid water monolayer and its mathematical mapping onto a percolation problem. The mapping allows us to identify the finite-size clusters at any state-point, and the infinite cluster at the critical point, with the regions of correlated hydrogen bonds (HBs). We show that the percolation line coincides with the first-order liquid-liquid phase transition ending at the LLCP. At…
Some experiments have witnessed increasing decoupling of viscosity from the translational self-diffusion of supercooled water with decreasing temperature. While theory and computer simulation studies indicated the jump translation of the molecules as a probable origin of the above decoupling, a precise quantitative estimation is still lacking. Through a molecular dynamics (MD) simulation study, along with careful consideration of translational jump motion, we have found the most definite proof of increasing relevance of translational jump diffusion in the above decoupling phenomena. By separat…
We measured electron paramagnetic resonance (EPR) spectra of 14N- and 15N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various radical concentrations. By fitting the EPR spectra to spectral shape functions based on the modified Bloch equations, we obtained concentration dependences of EPR parameters of radicals at each measured temperature. From concentration dependences of the EPR parameters quantifying spin dephasing, coherence transfer, and hyperfine splitting, we determined linear concentration coefficients, whose values depend on the relative motion of radical…
One of water's unsolved puzzles is the question of what determines the lowest temperature to which it can be cooled before freezing to ice. The supercooled liquid has been probed experimentally to near the homogeneous nucleation temperature TH{\approx}232 K, yet the mechanism of ice crystallization - including the size and structure of critical nuclei - has not yet been resolved. The heat capacity and compressibility of liquid water anomalously increase upon moving into the supercooled region according to a power law that would diverge at Ts{\approx}225 K,(1,2) so there may be a link between w…
Nanofluidics is an emerging field offering innovative solutions for energy harvesting and desalination. The efficiency of these applications depends strongly on liquid-solid slip, arising from a favorable ratio between viscosity and interfacial friction. Using molecular dynamics simulations, we show that wall slip increases strongly when water is cooled below its melting point. For water on graphene, the slip length is multiplied by up to a factor of five and reaches $230$nm at the lowest simulated temperature, $T \sim 225$K; experiments in nanopores can reach much lower temperatures and could…
Dynamical mechanical analysis (DMA)(f=0.2 - 100 Hz) is used to study the dynamics of confined water in mesoporous Gelsil (2.6 nm and 5 nm pores) and Vycor (10 nm) in the temperature range from T=80 K to 300 K. Confining water into nanopores partly suppresses crystallization and allows us to perform measurements of supercooled water below 235 K, i.e. in water's so called "no man's land", in parts of the pores. Two distinct relaxation peaks are observed around T1 = 145 K (P1) and T2 = 205 K (P2) for Gelsil 2.6 nm and Gelsil 5 nm at 0.2 Hz. Both peaks shift to higher T with increasing pore size d…
We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analysing a million particle simulated system we provide evidence of the existence, upon supercooling, of a significant enhancement of spatially localized dynamic fluctuations stemming from regions of correlated mobile molecules. We show that both the magnitude of the departure from the value expected for the system-size dependence of an uncorrelated system and the molecular siz…
We numerically investigate the metastable equilibrium structure of deep supercooled and glassy water under pressure, covering the range of densities corresponding to the experimentally produced high-density and very-high-density amorphous phases. At $T = 188$ K, a continuous increase in density is observed on varying pressure from $2.5$ to $13$ kbar, with no signs of first-order transitions. Exploiting a recently proposed approach to the analysis of the radial distribution function -- based on topological properties of the hydrogen-bond network -- we are able to identify well-defined local geo…
By confining water in nanopores, so narrow that the liquid cannot freeze, it is possible to explore its properties well below its homogeneous nucleation temperature TH ~ 235 K. In particular, the dynamical parameters of water can be measured down to 180 K approaching the suggested glass transition temperature Tg ~ 165 K. Here we present experimental evidence, obtained from Nuclear Magnetic Resonance and Quasi-Elastic Neutron Scattering spectroscopies, of a well defined decoupling of transport properties (the self-diffusion coefficient and the average translational relaxation time), which impli…
The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ~1 nm from the interface. While these structural changes are well established it is, in contrast, less clear how an interface perturbs the dynamics of water molecules within the liquid. Here, through an extensive set of molecular dynamics simulations of supercooled bulk and interfacial water films and nano-droplets, we observe the formation of persistent, spatially extended dynamical domains …
Within the so-called "no-man's land" between about 150 and 235 K, crystallization of bulk water is inevitable. The glasslike freezing and a liquid-to-liquid transition of water, predicted to occur in this region, can be investigated by confining water in nanometer-sized pores. Here we report the molecular dynamics of water within the pores of a metal-organic framework using dielectric spectroscopy. The detected temperature-dependent dynamics of supercooled water matches that of bulk water as reported outside the borders of the no-man's land. In confinement, a different type of water is formed,…
We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhi…
Dynamical Heterogeneity in Supercooled Water and its Spectroscopic Fingerprints
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；SISSA – Scuola Internazionale Superiore di Studi Avanzati（国际高等研究学校）；Politecnico di Torino（都灵理工大学）；The Abdus Salam Centre for Theoretical Physics（阿卜杜斯·萨拉姆理论物理中心）；Consiglio Nazionale delle Ricerche – Istituto Officina dei Materiali, SISSA Unit（国家研究委员会-材料研究所，SISSA分部）
We use systematic 8 ns ab initio molecular dynamics (AIMD) to study the structure and dynamics of water in bulk, and close to both hydrophobic and hydrophilic (carbonyl) groups of tetramethylurea (TMU). We observe crossovers in the dynamical behavior around the hydrophobic group at $T_X = 256 \pm 4$K and another one at $265 \pm 5$K related to the relative strength of water-water and water-carbonyl hydrogen bonds (HBs). For bulk water, the temperature of the apparent divergence in relaxation times is located at $T_c = 210 \pm 10$K. To better identify the effects arising from the hydrophilic car…
Heterogeneous ice growth exhibits a maximum in freezing rate arising from the competition between kinetics and the thermodynamic driving force between the solid and liquid states. Here, we use molecular dynamics simulations to elucidate the atomistic details of this competition, focusing on water properties in the interfacial region along the secondary prismatic direction. The crystal growth velocity is maximized when the efficiency of converting interfacial water molecules to ice, collectively known as the attachment kinetics, is greatest. We find water molecules that contact the intermediate…
We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a Seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mole per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations we combine Seeding with the direc…
Motivated by an experimental finding on the density of supercooled water at high pressure [O. Mishima, J. Chem. Phys. 133, 144503 (2010)] we performed atomistic molecular dynamics simulations study of bulk water in the isothermal-isobaric ensemble. Cooling and heating cycles at different isobars and isothermal compression at different temperatures are performed on the water sample with pressures that range from 0 to 1.0 GPa. The cooling simulations are done at temperatures that range from 40 K to 380 K using two different cooling rates, 10 K/ns and 10 K/5 ns. For the heating simulations we use…
