Comment on "Maxima in the thermodynamic response and correlation functions of deeply supercooled water".

Kim et al recently measured the structure factor of deeply supercooled water droplets (Reports, 22 December 2017, p. 1589). We raise several concerns about their data analysis and interpretation. In our opinion, the reported data do not lead to clear conclusions about the origins of water's anomalies.

Compressibility Anomalies in Stretched Water and Their Interplay with Density Anomalies.

Water keeps puzzling scientists because of its numerous properties which behave oppositely to those of usual liquids: for instance, water expands upon cooling, and liquid water is denser than ice. To explain this anomalous behavior, several theories have been proposed, with different predictions for the properties of supercooled water (liquid at conditions where ice is stable). However, discriminating between those theories with experiments has remained elusive because of spontaneous ice nucleation. Here we measure the sound velocity in liquid water stretched to negative pressure and derive an experimental equation of state, which reveals compressibility anomalies. We show by rigorous thermodynamic relations how these anomalies are intricately linked with the density anomaly. Some features we observe are necessary conditions for the validity of two theories of water.

Deriving Second Osmotic Virial Coefficients from Equations of State and from Experiment.

The osmotic virial coefficients, which are measures of the effective interactions between solute molecules in dilute solution, may be obtained from expansions of the osmotic pressure or of the solute activity in powers of the solute concentration. In these expansions, the temperature is held fixed, and one additional constraint is imposed. When the additional constraint is that of fixed chemical potential of the solvent, the coefficient of the second-order term yields directly the second osmotic virial coefficient itself. Alternative constraints, such as fixed pressure, fixed solvent density, or the specification of liquid-vapor equilibrium, yield alternative measures of the solute-solute interaction, different from but related to the osmotic virial coefficient. These relations are summarized and, where new, are derived here. The coefficient in question may be calculated from equations of state in which the parameters have been obtained by fitting to other experimental properties. Alternatively, the coefficients may be calculated from direct experimental measurements of the deviations from Henry's law based on measurements of the activity of the solute in a coexisting gas phase. It is seen for propane in water as a test case that with the latter method, even with what appear to be the best available experimental data, there are still large uncertainties in the resulting second osmotic virial coefficient. With the former method, by contrast, the coefficient may be obtained with high numerical precision but then depends for its accuracy on the quality of the equation of state from which it is derived.

Behavior of supercooled aqueous solutions stemming from hidden liquid-liquid transition in water.

A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid-liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid-liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H2O-NaCl and H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid-liquid transition. We elucidate the non-conserved nature of the order parameter (extent of "reaction" between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases.

Two-state thermodynamics of the ST2 model for supercooled water.

Thermodynamic properties of the ST2 model for supercooled liquid water exhibit anomalies similar to those observed in real water. A possible explanation of these anomalies is the existence of a metastable, liquid-liquid transition terminated by a critical point. This phenomenon, whose possible existence in real water is the subject of much current experimental work, has been unambiguously demonstrated for this particular model by most recent simulations. In this work, we reproduce the anomalies of two versions of the ST2 model with an equation of state describing water as a non-ideal "mixture" of two different types of local molecular order. We show that the liquid-liquid transition in the ST2 water is energy-driven. This is in contrast to another popular model, mW, in which non-ideality in mixing of two alternative local molecular orders is entropy-driven, and is not sufficiently strong to induce a liquid-liquid transition.

Nature of the anomalies in the supercooled liquid state of the mW model of water.

The thermodynamic properties of the supercooled liquid state of the mW model of water show anomalous behavior. Like in real water, the heat capacity and compressibility sharply increase upon supercooling. One of the possible explanations of these anomalies, the existence of a second (liquid-liquid) critical point, is not supported by simulations for this model. In this work, we reproduce the anomalies of the mW model with two thermodynamic scenarios: one based on a non-ideal "mixture" with two different types of local order of the water molecules, and one based on weak crystallization theory. We show that both descriptions accurately reproduce the model's basic thermodynamic properties. However, the coupling constant required for the power laws implied by weak crystallization theory is too large relative to the regular backgrounds, contradicting assumptions of weak crystallization theory. Fluctuation corrections outside the scope of this work would be necessary to fit the forms predicted by weak crystallization theory. For the two-state approach, the direct computation of the low-density fraction of molecules in the mW model is in agreement with the prediction of the phenomenological equation of state. The non-ideality of the "mixture" of the two states never becomes strong enough to cause liquid-liquid phase separation, also in agreement with simulation results.

Thermal conductivity of supercooled water.

The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.