Harshad Pathak

Maxima in the thermodynamic response and correlation functions of deeply supercooled water

Pointing to a second critical point One explanation for the divergence of many of the thermodynamic properties of water is that there is a critical point in deeply supercooled water at some positive pressure. For bulk water samples, these conditions are described as “no mans land,” because ice nucleates before such temperatures can be reached. Kim et al. used femtosecond x-ray laser pulses to probe micrometer-sized water droplets cooled to 227 K (see the Perspective by Gallo and Stanley). The temperature dependence of the isothermal compressibility and correlation length extracted from x-ray scattering functions showed maxima at 229 K for H2O and 233 K for D2O, rather than diverging to infinity. These results point to the existence of the Widom line, a locus of maximum correlation lengths emanating from a critical point in the supercooled regime. Science, this issue p. 1589; see also p. 1543 Maxima in the isothermal compressibility and correlation length point to the existence of a second critical point in water. Femtosecond x-ray laser pulses were used to probe micrometer-sized water droplets that were cooled down to 227 kelvin in vacuum. Isothermal compressibility and correlation length were extracted from x-ray scattering at the low–momentum transfer region. The temperature dependence of these thermodynamic response and correlation functions shows maxima at 229 kelvin for water and 233 kelvin for heavy water. In addition, we observed that the liquids undergo the fastest growth of tetrahedral structures at similar temperatures. These observations point to the existence of a Widom line, defined as the locus of maximum correlation length emanating from a critical point at positive pressures in the deeply supercooled regime. The difference in the maximum value of the isothermal compressibility between the two isotopes shows the importance of nuclear quantum effects.

Freezing of Heavy Water (D2O) Nanodroplets

We follow the freezing of heavy water (D2O) nanodroplets formed in a supersonic nozzle apparatus using position resolved pressure trace measurements, Fourier transform infrared spectroscopy, and small-angle X-ray scattering. For these 3-9 nm radii droplets, freezing starts between 223 and 225 K, at volume based ice nucleation rates Jice,V on the order of 10(23) cm(-3) s(-1) or surface based ice nucleation rates Jice,S on the order of 10(16) cm(-2) s(-1). The temperatures corresponding to the onset of D2O ice nucleation are higher than those reported for H2O by Manka et al. [Manka, A.; Pathak, H.; Tanimura, S.; Wölk, J.; Strey, R.; Wyslouzil, B. E. Phys. Chem. Chem. Phys.2012, 14, 4505]. Although the values of Jice,S scale somewhat better with droplet size than values of Jice,V, the data are not accurate enough to state that nucleation is surface initiated. Finally, using current estimates of the thermophysical properties of D2O and the theoretical framework presented by Murray et al. [Murray, B. J.; Broadley, S. L.; Wilson, T. W.; Bull, S. J.; Wills, R. H.; Christenson, H. K.; Murray, E. J. Phys. Chem. Chem. Phys.2010, 12, 10380], we find that the theoretical ice nucleation rates are within 3 orders of magnitude of the measured rates over an ∼15 K temperature range.

Diffusive dynamics during the high-to-low density transition in amorphous ice

Significance The importance of a molecular-level understanding of the properties, structure, and dynamics of liquid water is recognized in many scientific fields. It has been debated whether the observed high- and low-density amorphous ice forms are related to two distinct liquid forms. Here, we study experimentally the structure and dynamics of high-density amorphous ice as it relaxes into the low-density form. The unique aspect of this work is the combination of two X-ray methods, where wide-angle X-ray scattering provides the evidence for the structure at the atomic level and X-ray photon-correlation spectroscopy provides insight about the motion at the nanoscale, respectively. The observed motion appears diffusive, indicating liquid-like dynamics during the relaxation from the high-to low-density form. Water exists in high- and low-density amorphous ice forms (HDA and LDA), which could correspond to the glassy states of high- (HDL) and low-density liquid (LDL) in the metastable part of the phase diagram. However, the nature of both the glass transition and the high-to-low-density transition are debated and new experimental evidence is needed. Here we combine wide-angle X-ray scattering (WAXS) with X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry to probe both the structural and dynamical properties during the high-to-low-density transition in amorphous ice at 1 bar. By analyzing the structure factor and the radial distribution function, the coexistence of two structurally distinct domains is observed at T = 125 K. XPCS probes the dynamics in momentum space, which in the SAXS geometry reflects structural relaxation on the nanometer length scale. The dynamics of HDA are characterized by a slow component with a large time constant, arising from viscoelastic relaxation and stress release from nanometer-sized heterogeneities. Above 110 K a faster, strongly temperature-dependent component appears, with momentum transfer dependence pointing toward nanoscale diffusion. This dynamical component slows down after transition into the low-density form at 130 K, but remains diffusive. The diffusive character of both the high- and low-density forms is discussed among different interpretations and the results are most consistent with the hypothesis of a liquid–liquid transition in the ultraviscous regime.

The structural validity of various thermodynamical models of supercooled water.

The thermodynamic response functions of water exhibit an anomalous increase upon cooling that becomes strongly amplified in the deeply supercooled regime due to structural fluctuations between disordered and tetrahedral local structures. Here, we compare structural data from recent x-ray laser scattering measurements of water at 1 bar and temperatures down to 227 K with structural properties computed for several different water models using molecular dynamics simulations. Based on this comparison, we critically evaluate four different thermodynamic scenarios that have been invoked to explain the unusual behavior of water. The critical point-free model predicts small variations in the tetrahedrality with decreasing temperature, followed by a stepwise change at the liquid-liquid transition around 228 K at ambient pressure. This scenario is not consistent with the experimental data that instead show a smooth and accelerated variation in structure from 320 to 227 K. Both the singularity-free model and ice coarsening hypothesis give trends that indirectly indicate an increase in tetrahedral structure with temperature that is too weak to be consistent with experiment. A model that includes an apparent divergent point (ADP) at high positive pressure, however, predicts structural development consistent with our experimental measurements. The terminology ADP, instead of the commonly used liquid-liquid critical point, is more general in that it focuses on the growing fluctuations, whether or not they result in true criticality. Extrapolating this model beyond the experimental data, we estimate that an ADP in real water may lie around 1500 ± 250 bars and 190 ± 6 K.

How Cubic Can Ice Be

Using an X-ray laser, we investigated the crystal structure of ice formed by homogeneous ice nucleation in deeply supercooled water nanodrops (r ≈ 10 nm) at ∼225 K. The nanodrops were formed by condensation of vapor in a supersonic nozzle, and the ice was probed within 100 μs of freezing using femtosecond wide-angle X-ray scattering at the Linac Coherent Light Source free-electron X-ray laser. The X-ray diffraction spectra indicate that this ice has a metastable, predominantly cubic structure; the shape of the first ice diffraction peak suggests stacking-disordered ice with a cubicity value, χ, in the range of 0.78 ± 0.05. The cubicity value determined here is higher than those determined in experiments with micron-sized drops but comparable to those found in molecular dynamics simulations. The high cubicity is most likely caused by the extremely low freezing temperatures and by the rapid freezing, which occurs on a ∼1 μs time scale in single nanodroplets.

Co-condensation of nonane and D2O in a supersonic nozzle

We study the unary and binary nucleation and growth of nonane-D2O nanodroplets in a supersonic nozzle. Fourier Transform Infrared spectroscopy measurements provide the overall composition of the droplets and Small Angle X-ray Scattering experiments measure the size and number density of the droplets. The unary nucleation rates Jmax of nonane, 9.4 × 10(15) < Jmax /cm(-3) s(-1) < 2.0 × 10(16), and those of D2O, 2.4 × 10(17) < Jmax /cm(-3) s(-1) < 4.1 × 10(17), measured here agree well with previous results. In most of the binary condensation experiments new particle formation is dominated by D2O, but the observed nucleation rates are decreased by up to a factor of 6 relative to the rates measured for pure D2O, an effect that can be partly explained by non-isothermal nucleation theory. The subsequent condensation of D2O is inhibited both by the increased temperature of the binary droplets relative to the pure D2O droplets, and because the binary droplet surface is expected to be comprised largely of nonane. For the one case where nonane appears to initiate condensation, we find that the nucleation rate is about 50% higher than that observed for pure nonane at comparable pv0, consistent with significant particle formation driven by D2O.

Nonisothermal Droplet Growth in the Free Molecular Regime

The growth rates of nonane and D2O nanodroplets produced in supersonic expansions are characterized using small angle X-ray scattering (SAXS) and pressure trace measurements (PTM). The experimental growth rates are compared to the predictions of a Hertz–Knudsen model that assumes either isothermal or nonisothermal droplet growth in the free molecular regime. For nonane, the predicted growth rates are insensitive to both droplet temperature and the evaporation coefficient, and agree well with the experimentally measured growth rates assuming a condensation coefficient of 1. For D2O, droplet growth rates are quite sensitive to droplet temperature, and the best agreement between experiments and theory are achieved for a condensation coefficient of 1 and an evaporation coefficient in the range from 0.5 to 1. Under our experimental conditions, incorporating coagulation is important to match the measured D2O growth rates but not those of nonane. Copyright 2013 American Association for Aerosol Research

The structure of D2O-nonane nanodroplets

We study the internal structure of nanometer-sized D2O-nonane aerosol droplets formed in supersonic nozzle expansions using a variety of experimental techniques including small angle X-ray scattering (SAXS). By fitting the SAXS spectra to a wide range of droplet structure models, we find that the experimental results are inconsistent with mixed droplets that form aqueous core-organic shell structures, but are quite consistent with spherically asymmetric lens-on-sphere structures. The structure that agrees best with the SAXS data and Fourier transform infra-red spectroscopy measurements is that of a nonane lens on a sphere of D2O with a contact angle in the range of 40°-120°.

Binary nucleation rates for ethanol/water mixtures in supersonic Laval nozzles: analyses by the first and second nucleation theorems.

We performed pressure trace measurements and small angle x-ray scattering measurements to determine the vapor-liquid nucleation rates of EtOH/H2O mixtures including pure EtOH and pure H2O in two supersonic Laval nozzles with different expansion rates. The nucleation rates varied from 0.9 × 10(17) to 16 × 10(17) cm(-3) s(-1) over the temperature range of 210 K to 230 K, EtOH activity range of 0 to 11.6, and H2O activity range of 0 to 124. The first and second nucleation theorems were applied to the nucleation rates to estimate the sizes, compositions, and excess energies of the critical clusters. The critical clusters contained from 4 to 15 molecules for pure H2O and EtOH/H2O clusters, and from 16 to 23 molecules for pure EtOH clusters. Comparing the excess energies of the pure H2O critical clusters with the results of a quantum-chemistry calculation suggested that the pre-factor of the theoretical nucleation rate is almost constant regardless of the monomer concentration. One possible explanation for this result is that cooling of the critical clusters limits the nucleation rate under the highly supersaturated conditions. The results of the analyses also yielded the relation between the surface energy and the composition of the critical clusters, where the latter are predicted to consist only of surface molecules. Applying this relationship to the EtOH/H2O bulk liquid mixtures, we estimated the EtOH mole fraction in the surface layer and found it is higher than that derived from the surface tension based on the Gibbs adsorption equation when the EtOH mole fraction in the liquid is higher than about 0.2 mol/mol. This discrepancy was attributed to the existence of the EtOH depletion layer just below the surface layer of the liquid.

Response to Comment on “Maxima in the thermodynamic response and correlation functions of deeply supercooled water”

Caupin et al. have raised several issues regarding our recent paper on maxima in thermodynamic response and correlation functions in deeply supercooled water. We show that these issues can be addressed without affecting the conclusion of the paper.