Phase Transition In Supercooled Water Research Articles

Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R2=90.7 % for diffusion coefficients and R2=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m−3∙s−1 at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R2= 99.9 %) and experimental results (R2 = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.

Phase transition of supercooled water confined in cooperative two-state domain

The question of ‘what is the structure of water?’ has been regarded as one of the major scientific conundrums in condensed-matter physics due to the complex phase behavior and condensed structure of supercooled water. Great effort has been made so far using both theoretical analysis based on various mathematical models and computer simulations such as molecular dynamics and first-principle. However, these theoretical and simulation studies often do not have strong evidences of condensed-matter physics to support. In this study, a cooperative domain model is formulated to describe the dynamic phase transition of supercooled water between supercooled water and amorphous ice, both of which are composed of low- and high-density liquid water. Free volume theory is initially employed to identify the working principle of dynamic phase transition and its connection to glass transition in the supercooled water. Then a cooperative two-state model is developed to characterize the dynamic anomalies of supercooled water, including density, viscosity and self-diffusion coefficient. Finally, the proposed model is verified using the experimental results reported in literature.

Discovering formation of ice 0 by low-frequency measurement data

In this work, low-frequency characteristics of wetted nanoporous silicate materials were measured, as well as the specimen’s own low-frequency electric fluctuations at the frequencies of 1…100 Hz. The measurements at low frequencies were conducted at different voltages of the probing signal. A capacity cell was used in making the measurements. In the experiments, at the temperatures below –25…–30 °C, non-linearity of the medium was discovered. The experiments on the study of the specimen’s own electric fluctuations at these temperatures revealed their essential increase. These temperatures are below the point of phase transition of supercooled water to recently discovered ferroelectric ice 0. Based on the measurements made, a conclusion was made regarding formation of this modification of ice in the nanosize pores of the wetted materials under study. Ice 0 is a ferroelectric; therefore, its formation from deeply supercooled water may have a significant impact on the electric parameters of wetted bodies at the temperatures below –23 °C. At the interface of such ice with another dielectric, a thin layer with practically metallic conductivity emerges. Such a layer influences not only the non-linear dependence of dielectric permittivity on the electric field but also increases attenuation of electromagnetic radiation in a medium.

Numerical investigation on impingement dynamics and freezing performance of micrometer-sized water droplet on dry flat surface in supercooled environment

In-flight icing usually occurs when supercooled droplets impact on the cold surface of an aircraft, which should be concerned for its adverse effects on aerodynamic performance. To fundamentally elucidate the detailed mechanism of aircraft icing, a mathematical model on the impingement dynamics and solidification of a supercooled water droplet was developed and further validated with previous experimental results. Considering the effects of surface tension, wall adhesion and contact line dynamics, the coupled volume of fluid and level-set method was used to track the air–water interface, with the solidification issue solved by the enthalpy-porosity method. The temporal evolutions of the water phase, flow velocity, temperature and heat flux distributions were tracked and analyzed after the phase transition of supercooled water occurred. High impact velocities and millimeter-sized droplets were considered in this study to make the results more applicable to in-flight icing. As concluded, the spreading ratios of the droplets mainly distribute in the range of 0.8 ± 0.1 corresponding to LWC = 1.0 g/m3. Besides, the transient heat transfer between the solid surface and droplets could be fitted by a logarithmic function after appropriate dimensionless processing, which was proportional to the 1.5th power of the liquid fraction. Contributions of this work could be an effort to understand the microphysical phenomenon in the aerodynamic icing process.

Surface tension of supercooled water nanodroplets from computer simulations.

We estimate the liquid-vapor surface tension from simulations of TIP4P/2005 water nanodroplets of size N = 100 to 2880 molecules over a temperature T range of 180 K-300 K. We compute the planar surface tension γp, the curvature-dependent surface tension γs, and the Tolman length δ, via two approaches, one based on the pressure tensor (the "mechanical route") and the other on the Laplace pressure (the "thermodynamic route"). We find that these two routes give different results for γp, γs, and δ although in all cases, we find that δ ≥ 0 and is independent of T. Nonetheless, the T dependence of γp is consistent between the two routes and with that of Vega and de Miguel [J. Chem. Phys. 126, 154707 (2007)] down to the crossing of the Widom line at 230 K for ambient pressure. Below 230 K, γp rises more rapidly on cooling than predicted from behavior for T ≥ 300 K. We show that the increase in γp at low T is correlated with the emergence of a well-structured random tetrahedral network in our nanodroplet cores and thus that the surface tension can be used as a probe to detect behavior associated with the proposed liquid-liquid phase transition in supercooled water.

The stability-limit conjecture revisited.

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this re-entrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here, we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water which was first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si.

Water Is a Cagey Liquid.

Liquid water is considered poorly understood. How are water's physical properties encoded in its molecular structure? We introduce a statistical mechanical model (CageWater) of water's hydrogen-bonding (HB) and Lennard-Jones (LJ) interactions. It predicts the energetic and volumetric and anomalous properties accurately. Yet, because the model is analytical, it is essentially instantaneous to compute. This model advances our understanding beyond current molecular simulations and experiments. Water has long been regarded as a "2-density liquid": a dense LJ liquid and a looser HB one. Instead, we find here a different antagonism underlying water structure-property relations: HBs in water-water pairs drive density, while HBs in cooperative cages drive openness. The balance shifts strongly with temperature and pressure. This model interprets the molecular structures underlying the liquid-liquid phase transition in supercooled water. It may have value in geophysics, biomolecular modeling, and engineering of materials for water purification and green chemistry.

Time-of-Flight Neutron Imaging for the Distinction of Super-Cooled Water and Ice during PEFC Cold-Starts

The start-up of polymer electrolyte fuel cells (PEFCs) at sub-zero temperatures (cold-start) is a challenge for fuel cell designers and operators. The freezing of water in the cell can cause shutdown of the cell and severe damages to fuel cell components. However, water produced in the electrochemical reaction is pure enough to be present in the super-cooled state (liquid) at sub-zero temperatures (1). Methods that allow visualizing the location of freezing events during cold-starts help to understand which parameters influence the phase transitions. For this purpose our group has been using energy selective neutron imaging methods since 2013 (2). We exploit the fact that the attenuation for ice and super-cooled water differs at low neutron energies (wavelength > 4 Å) while it is identical for high energies (3). When water freezes in the pores of the catalyst and/or gas diffusion layer, its volume expands in all directions and the density decreases. To account for the density change, we record images in two different energy windows - one corresponding to high and the other to low energy neutrons – and obtain a relative attenuation image, which allows us to determine the state of aggregation. Energy selective neutron imaging with a neutron filter was successfully applied while operating a fuel cell with an active area of 50 cm2 for the detection of local freezing events (4). However, the obtained contrast between liquid water and ice was very low (1.6%), making the method particularly sensitive to biases. To increase the contrast, we use time-of-flight neutron imaging (TOF-NI), a method based on neutron pulses (either at a pulsed neutron source or with the help of a rotating chopper disk) where the neutron energy is determined by the time lag between the pulse and the moment the neutron reaches the detector. Compared to conventional TOF-NI, which uses short neutron pulses (duty cycles smaller than 1%), we use a chopper disk with broad slits making a duty cycle of approximately 30% and obtain a much higher neutron flux at the cost of lower energy resolution. Here, we will present experimental results obtained during isothermal cold-starts with a cell having an active area of 4.4 cm2. Simultaneously to neutron imaging, we measured the heat fluxes in and out of the cell with a setup described in other references (5). Figure 1 contains an example of the results obtained during a cold-start performed at -7.5°C. Figure 1 (a) depicts the evolution of voltage and heat flux over time during the cold-start while Fig. 1 (b) shows the relative attenuation (ratio between low and high energy attenuation) averaged over the whole active area (A), and over the channels B and C (the different areas are represented on Fig. 1 (e)). During phase I, larger accumulations of super-cooled water were present in the gas flow channels. The phase transition of super-cooled water to ice occurred 62 minutes after starting to draw current. This is visible from the voltage drop and the peak in heat flux due to the latent heat that is released during freezing of water [Fig 1 (a)]. Phase II corresponds to the time after the freezing event where the cell was not operated and its temperature was kept constant at -7.5°C. Figure 1 (c) and (d) depict the high energy attenuation images, from which the water thickness is retrieved by using the Beer-Lambert law. Those images are representative for classical transmission images without energy selectivity. The images representing the relative attenuation (attenuation at low energy divided by attenuation at high energy) are shown in Figure 1 (e) and (f). For clarity, only channel water is shown in these images. By comparing the classical attenuation based images [Fig 1 (c-d)] with the energy selective approach [Fig 1 (e-f)] it becomes evident that the high energy attenuation does not clearly differ for phase I and II. In contrast, the relative attenuation for ice measured in phase II [Fig 1 (b and f)] is – as expected – lower compared to the one measured for super-cooled water in phase I [Fig 1 (b and e)]. By using TOF-NI we could improve the contrast between super-cooled water and ice to reach approximately 5%. P. Oberholzer et. al, J. Electrochem. Soc., 159, B235 (2011). J. Biesdorf et. al, Phys. Rev. Lett., 112 (2014). L. Torres et. al, Nuc.l Instrum. Meth. B, 251, 304 (2006). P. Stahl et. al, J. Electrochem. Soc., 163, F1535 (2016). M. Cochet et. al, Submitted for publication (2018). Figure 1

Unified icing theory based on phase transition of supercooled water on a substrate

Lack of knowledge on substrate icing hinders us from predicting the effects of typical substrate properties in icing and anti-icing research. The pattern formation and tip shape of icing on a substrate must be explored to understanding the physics of icing on a substrate. In this paper, the pattern, velocity and tip shape of ice on substrates with different thermal conductivities and surface energies are evaluated in a series of experiments. Experimental results show that as supercooling and thermal conductivity increase, the ice on substrate evolves from a single-needle dendrite to a smooth ice film. In contrast, for free icing the same evolution process can be completed at a higher supercooling than substrate icing. Experimental results on hydrophilic and Plexiglas surfaces demonstrate an abruptly decrease of velocity and Peclet number of ice occurs at approximately 271.6 K, whereas the tip shape of ice does not change obviously; while for free icing this phenomenon is not found. Furthermore, a theoretical analysis on phase transition of substrate icing is performed. It shows that the surface energy of substrates can increase the size of metastable cubic ice and reduce the temperature on the ice tip by 1.5 K compared to free ice, thereby causing the decrease in the velocity and Peclet number of ice. Also the heat conduction of substrates decrease the heat flux in ice growth direction and lead to absolute stability of substrate icing in lower supercooling compared to free icing. In terms of the comparison between free icing and substrate icing, a unified icing theory is proposed to describe the equilibrium icing mode, the non-equilibrium growth state, and the corresponding growth equations. Using this theory, the velocity and pattern of substrate icing with different supercooling, thermal conductivity, and surface energy can be predicted well, as well as these results of free icing.

Low-temperature dielectric measurements of confined water in porous granites

The dielectric behavior of rocks affected by the known phase transition of supercooled water is the main problem we analyzed. Three different granitic rocks were used to perform dielectric measurements in the frequency range from 100 Hz to 1 MHz and temperatures 100–350 K. Thin cylindrical samples were prepared, and circular electrodes were established using silver conductive paint. A clear change in the dielectric measurements appears at [Formula: see text] for one of the samples. This coincides with the known phase transition of supercooled water. Tightly bounded water confined in the pores of the rock do not crystallize at 273 K, but form a metastable liquid down to 200–220 K maintaining water polarization. Below this temperature, water molecules solidify and polarizability decreases. The rock presenting the most sizable change has a very low specific surface area of [Formula: see text], has connected porosity of [Formula: see text], and has the smallest degree of alteration. In addition, geochemical analyzes reveal a low percentage of hydration water in its structure confirming the role of pore water in this change. A comparison between water-saturated, oven-dried, and vacuum-dried samples was done. Finally, a logarithmic dependency of the critical temperature for the supercooled water phase transition with the measuring frequency was found.

III-1 細孔中の水のダイナミクス 過冷却水の相転移

中性子準弾性散乱や中性子スピンエコー法により180K～298KにわたりMCM-41細孔(内径2.1nm)内の毛管凝縮水や単層吸着水のダイナミクスが研究された。毛管凝縮水の緩和時間は，222Kより高温側でVogel-Tamman-Fulcher式に従い，一方低温側ではArrhenius型の挙動を示し，222K付近に動的クロスオーバーが存在した。一方，単層吸着水ではArrhenius型の振る舞いのみを示した。また，動的クロスオーバーは制限空間水の高密度水―低密度水転移に対応している。

Liquid–liquid transition in supercooled water suggested by microsecond simulations

The putative liquid-liquid phase transition in supercooled water has been used to explain many anomalous behaviors of water. However, no direct experimental verification of such a phase transition has been accomplished, and theoretical studies from different simulations contradict each other. We investigated the putative liquid-liquid phase transition using the Water potential from Adaptive Force Matching for Ice and Liquid (WAIL). The simulation reveals a first-order phase transition in the supercooled regime with the critical point at ~207 K and 50 MPa. Normal water is high-density liquid (HDL). Low-density liquid (LDL) emerges at lower temperatures. The LDL phase has a density only slightly larger than that of the ice-Ih and shows more long-range order than HDL. However, the transformation from LDL to HDL is spontaneous across the first-order phase transition line, suggesting the LDL configuration is not poorly formed nanocrystalline ice. It has been demonstrated in the past that the WAIL potential provides reliable predictions of water properties such as melting temperature and temperature of maximum density. Compared with other simple water potentials, WAIL is not biased by fitting to experimental properties, and simulation with this potential reflects the prediction of a high-quality first-principle potential energy surface.

The Structure of Supercooled Water and the Mechanism of Homogeneous Nucleation of Ice Ih

Abstract The mechanism of the phase transition of supercooled water to ice Ih at −36 ºC is discussed on a molecular level. The structure of liquid water is described by the interstitial model first proposed by Samoilov. It is consistent with the results of X-Ray and neutron scattering and the experimental results on the diverse properties of liquid water. In order to illustrate our reflections several numerical calculations have been performed using exclusively experimental data. From the temperatur dependence of the nucleation rate the minimum number of water molecules, which constitute the critical germ, and the volume of the critical germ are determined. The occupation numbers of the regular tridymite lattice and the vacancies of the interstitial lattice are evaluated. The negative entropy of nucleation is discussed. It can be split in two contributions. They refer to the change of the statistics by the the transition from the protonucleus to the nucleus and the changes of the degrees of freedom of motion. Considering the simple model, the calculated value fits well to the experimental value of the nucleation entropy. The transition state, which is a key point in the classical nucleation theory, is discussed on a molecular level. It has a lifetime of 0.57 × 10−12 s. The nucleation volume is of the order nm3. One can expect that in this small volume density fluctuations exist in which especially the molecules in interstitial positions are involved. They are rich in energy and easily moveable. Statistical calculations deliver the deviation ±5 from the average value 23 of the number of molecules at interstitial positions in the nucleation volume. Corresponding density fluctuations have been observed by Huang et al. by very fast measurements of small angle X-ray scattering.

Laser induced breakdown spectroscopy on soils and rocks: Influence of the sample temperature, moisture and roughness

ExoMars, ESA's next mission to Mars, will include a combined Raman/LIBS instrument for the comprehensive in-situ mineralogical and elemental analyses of Martian rocks and soils. It is inferred that water exists in the upper Martian surface as ice layers, “crystal” water or adsorbed pore water. Thus, we studied Laser Induced Breakdown Spectroscopy (LIBS) on wet and dry rocks under Martian environmental conditions in the temperature range − 60 °C to + 20 °C and in two pressure regimes, above and below the water triple point. Above this point, the LIBS signals from the rock forming elements have local minima that are accompanied by hydrogen (water) emission maxima at certain temperatures that we associate with phase transitions of free or confined water/ice. At these sample temperatures, the plasma electron density and its temperature are slightly lowered. In contrast to powder samples, a general increase of the electron density upon cooling was observed on rock samples. By comparing the LIBS signal behavior from the same rock with different grades of polishing, and different rocks with the same surface treatment, it was possible to distinguish between the influence of surface roughness and the bulk material structure (pores and grains). Below the triple point of water, the LIBS signal from the major sample elements is almost independent of the sample temperature. However, at both considered pressures we observed a hydrogen emission peak close to − 50 °C, which is attributed to a phase transition of supercooled water trapped inside bulk pores.

Effect of confinement on the liquid-liquid phase transition of supercooled water

We report on an observation of the phase transition between two liquid phases of supercooled confined water in simulations. The temperature of the liquid-liquid transition of water at zero pressure slightly decreases due to confinement in the hydrophobic pore. The hydrophilic confinement affects this temperature in the opposite direction and shifts the critical point of the liquid-liquid transition to a higher pressure. As a result, in a strongly hydrophilic pore the liquid-liquid phase transition becomes continuous at zero pressure, indicating the shift of its critical point from negative to a positive pressure. These findings indicate that experimental studies of water confined in the pores of various hydrophobicity/hydrophilicity may clarify the location of the liquid-liquid critical point of bulk water.

Electrical instabilities in organic semiconductors caused by trapped supercooled water

It is reported that the electrical instability known as bias stress is caused by the presence of trapped water in the organic layer. Experimental evidence as provided by the observation of an anomaly occurring systematically at around 200K. This anomaly is observed in a variety of materials, independent of the deposition techniques and remarkably coincides with a known phase transition of supercooled water. Confined water does not crystallize at 273K but forms a metastable liquid. This metastable water behaves electrically as a charge trap, which causes the instability. Below 200K the water finally solidifies and the electrical traps disappear.

Water activity as the determinant for homogeneous ice nucleation in aqueous solutions

The unique properties of water in the supercooled (metastable) state are not fully understood. In particular, the effects of solutes and mechanical pressure on the kinetics of the liquid-to-solid phase transition of supercooled water and aqueous solutions to ice have remained unresolved. Here we show from experimental data that the homogeneous nucleation of ice from supercooled aqueous solutions is independent of the nature of the solute, but depends only on the water activity of the solution--that is, the ratio between the water vapour pressures of the solution and of pure water under the same conditions. In addition, we show that the presence of solutes and the application of pressure have a very similar effect on ice nucleation. We present a thermodynamic theory for homogeneous ice nucleation, which expresses the nucleation rate coefficient as a function of water activity and pressure. Recent observations from clouds containing ice are in good agreement with our theory and our results should help to overcome one of the main weaknesses of numerical models of the atmosphere, the formulation of cloud processes.

水に二状態が存在する！？

Water has two amorphous solid states at low temperatures: the low-density and high-density amorphous ices. These two amorphous solids may be related to liquid water at high temperatures. We review experiments and simulations on liquid and amorphous solid water, and discuss the possibility of the existence of a liquid-liquid phase transition in supercooled water.

Effect of oscillatory shear on the fluid–solid phase transition of supercooled water

The present study aims at the methodological improvement of the electrofreezing of supercooled water by applying oscillatory shear along with a homogeneous electric field in non-equilibrium molecular dynamics simulations of simple water models (such as TIP4P and SPC/E). The application of a planar Couette flow field accounts for a moderate speedup in the phase transition. Since the system goes through a nonergodic glassy state in the course of the process, it is not surprising that a macroscopic manifestation of the Lyapunov instability inherent in the equations of motion is observed. The formation of a conjectured high-density ice polymorph (ice XII) has been studied in terms of the applied electric and oscillatory flow fields. The threshold value of the electric field for the crystallization has been determined. The method of applying the oscillatory flow field was also investigated in detail.

Psychophysical study of stinging pain evoked by brief freezing of superficial skin and ensuing short-lasting changes in sensations of cool and cold pain

Psychophysical methods were used to investigate pain in human subjects elicited by controlled freezing of the skin using a novel vortex thermode. When cooling stimuli delivered with a small thermode (7 mm diameter) exceeded the normal cold pain threshold into the sub-zero temperature range (−5 to −11°C), all subjects reported an intense, sharp stinging pain sensation which occurred suddenly and was readily differentiated from normal cold pain. The onset of this stinging `freezing' pain was closely correlated with a sudden increase in skin temperature beneath the thermode of 4.77±0.86°C (±SD) associated with the phase transition of supercooled water to ice. The mean intensity of freezing pain was rated as 1.7 times as intense as cold pain at threshold. Subjects' mean reaction-time latency to signal stinging pain following the onset of phase transition on the volar forearm was 687±220 ms, which was slower than that for mechanically evoked impact pain. Freezing pain is suggested to be mediated by A-delta fibers, based on estimates of conduction velocity and on the observation that the freezing pain took on a burning quality of slower onset during an A-fiber pressure block of nerve fibers. We also investigated changes in skin sensation following the freezing stimulus, and found that freezing led to (a) an immediate, significant decrease in the cold pain threshold (to higher temperatures), which recovered to baseline in <16 min, (b) a concomitant change in the quality of cold pain from dull to burning, (c) a significant, parallel increase in the threshold for the perception of cooling (to lower temperatures) which frequently manifested as a complete loss of cold sensation, and (d) a mild heat pain hyperalgesia which was still present 24 h later. The changes in thermal sensitivity were not accompanied by consistent changes in mechanical sensitivity. These results indicate that a characteristic sharp, stinging pain is reliably evoked abruptly at the phase transition of supercooled skin water to ice The ensuing brief decrease in cold pain threshold with burning quality, coupled with decreased sensitivity to cold, are speculated to reflect a central disinhibition of C-fiber nociceptor input due to reduced cold fiber activity. These effects may be relevant to frostbite, and distinguish themselves from the more pronounced thermal and mechanical hyperalgesia seen following intense freeze lesion of the skin.