Here, we investigate the hypothesis that despite the existence of at least two high-density amorphous ices, only one high-density liquid state exists in water. We prepared a very-high-density amorphous ice (VHDA) sample and rapidly increased its temperature to around 205 ± 10 K using laser-induced isochoric heating. This temperature falls within the so-called “no-man’s land” well above the glass-liquid transition, wherein the IR laser pulse creates a metastable liquid state. Subsequently, this high-density liquid (HDL) state of water decompresses over time, and we examined the time-dependent structural changes using short x-ray pulses from a free electron laser. We observed a liquid–liquid transition to low-density liquid water (LDL) over time scales ranging from 20 ns to 3 μs, consistent with previous experimental results using expanded high-density amorphous ice (eHDA) as the initial state. In addition, the resulting LDL derived both from VHDA and eHDA displays similar density and degree of inhomogeneity. Our observation supports the idea that regardless of the initial annealing states of the high-density amorphous ices, the same HDL and final LDL states are reached at temperatures around 205 K.

Recent experiments continue to find evidence for a liquid-liquid phase transition (LLPT) in supercooled water, which would unify our understanding of the anomalous properties of liquid water and amorphous ice. These experiments are challenging because the proposed LLPT occurs under extreme metastable conditions where the liquid freezes to a crystal on a very short time scale. Here, we analyze models for the LLPT to show that coexistence of distinct high-density and low-density liquid phases may be observed by subjecting low-density amorphous (LDA) ice to ultrafast heating. We then describe experiments in which we heat LDA ice to near the predicted critical point of the LLPT by an ultrafast infrared laser pulse, following which we measure the structure factor using femtosecond x-ray laser pulses. Consistent with our predictions, we observe a LLPT occurring on a time scale < 100 ns and widely separated from ice formation, which begins at times >1 μs.

The phase transition between water and ice is ubiquitous and one of the most important phenomena in nature. Here, we performed time-resolved x-ray scattering experiments capturing the melting and recrystallization dynamics of ice. The ultrafast heating of ice I is induced by an IR laser pulse and probed with an intense x-ray pulse which provided us with direct structural information on different length scales. From the wide-angle x-ray scattering (WAXS) patterns, the molten fraction, as well as the corresponding temperature at each delay, were determined. The small-angle x-ray scattering (SAXS) patterns, together with the information extracted from the WAXS analysis, provided the time-dependent change of the size and the number of liquid domains. The results show partial melting (similar to 13%) and superheating of ice occurring at around 20 ns. After 100 ns, the average size of the liquid domains grows from about 2.5 nm to 4.5 nm by the coalescence of approximately six adjacent domains. Subsequently, we capture the recrystallization of the liquid domains, which occurs on microsecond timescales due to the cooling by heat dissipation and results to a decrease of the average liquid domain size.

Using time-resolved wide-angle X-ray scattering, we investigated the early stages (10 μs–1 ms) of crystallization of supercooled water, obtained by the ultrafast heating of high- and low-density amorphous ice (HDA and LDA) up to a temperature T = 205 K ± 10 K. We have determined that the crystallizing phase is stacking disordered ice (I_sd), with a maximum cubicity of χ = 0.6, in agreement with predictions from molecular dynamics simulations at similar temperatures. However, we note that a growing small portion of hexagonal ice (I_h) was also observed, suggesting that within our timeframe, I_sd starts annealing into I_h. The onset of crystallization, in both amorphous ice, occurs at a similar temperature, but the observed final crystalline fraction in the LDA sample is considerably lower than that in the HDA sample. We attribute this discrepancy to the thickness difference between the two samples. 

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å⁻¹, which covered the principal doublet of the x-ray structure factor of water. The oxygen–oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen–oxygen structure factor (q₂). We found that q₂ exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q2 shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen–oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling. 

Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

We study the structural dynamics of liquid water by time-resolved anisotropic x-ray scattering under the optical Kerr effect condition. In this way, we can separate the anisotropic scattering decay of 160 fs from the delayed temperature increase of similar to 0.1 K occurring at 1 ps and quantify transient changes in the O-O pair distribution function. Polarizable molecular dynamics simulations reproduce well the experiment, indicating transient alignment of molecules along the electric field, which shortens the nearest-neighbor distances. In addition, analysis of the simulated water local structure provides evidence that two hypothesized fluctuating water configurations exhibit different polarizability.

The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power law all the way to the maximum values with best-fit exponents of gamma = 0.40 +/- 0.01 for the isothermal compressibility and nu = 0.26 +/- 0.03 for the correlation length. The ratio between these exponents is close to a value of approximate to 0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of gamma obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.

Wide angle x-ray scattering of supercooled water down to 234.8 K was studied using high energy x rays at the European Synchrotron Radiation Facility. The oxygen-oxygen pair distribution function (PDF) was calculated from the scattering pattern out to the 5th peak at an intermolecular distance, r approximate to 11 angstrom. We observe that the 4th peak and the 5th peak in the PDF increase in height upon supercooling. We also observe that the 4th peak position (r(4)) shifts to shorter distances upon supercooling consistent with previous studies, but we see a more rapid change at the lowest temperature. The running oxygen-oxygen coordination number is calculated for 5 different temperatures, and an isosbestic point at r(iso) = 3.31 +/- 0.05 angstrom was found corresponding to a coordination number of 4.39 +/- 0.15. The comparison of the PDF of the coldest water with that of amorphous ice shows distinct differences. We propose that there are 5-member pentamer rings in low density liquid-like structures giving rise to the sharp correlations at r approximate to 9 angstrom and r approximate to 11 angstrom.

We study the temperature behavior of the first four peaks of the oxygen-oxygen radial distribution function of water, simulated by the TIP4P/2005, MB-pol, TIP5P, and SPC/E models and compare to experimental X-ray diffraction data, including a new measurement which extends down to 235 K [H. Pathak et al., J. Chem. Phys. 150, 224506 (2019)]. We find the overall best agreement using the MB-pol and TIP4P/2005 models. We observe, upon cooling, a minimum in the position of the second shell simulated with TIP4P/2005 and SPC/E potentials, located close to the temperature of maximum density. We also calculated the two-body entropy and the contributions coming from the first, second, and outer shells to this quantity. We show that, even if the main contribution comes from the first shell, the contribution of the second shell can become important at low temperature. While real water appears to be less ordered at short distance than obtained by any of the potentials, the different water potentials show more or less order compared to the experiments depending on the considered length-scale.