Perspectives

Supercooled water reveals its secrets

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Science  22 Dec 2017:
Vol. 358, Issue 6370, pp. 1543-1544
DOI: 10.1126/science.aar3575

When a substance remains liquid below its melting point, it is said to be in a metastable supercooled state. In the region where the substance can be supercooled, the crystal is still the stable state, but crystallization can be avoided if the cooling occurs fast enough. The supercooled phase diagram of water has received particular attention (1). The anomalous thermodynamic properties of water point to the possible existence of two different liquid phases—one with high density and the other with low density—that become identical at a liquid-liquid critical point in the supercooled phase (C′, see the figure). But whereas mild supercooling of water is moderately easy to achieve, the deeply supercooled region has been out of the reach of experiments. On page 1589 of this issue, Kim et al. (2) use an evaporative cooling technique to cool micrometer-sized water droplets to deeply supercooled temperatures and provide evidence for the postulated critical point.

It was 25 years ago that Poole et al. (3) proposed, on the basis of computer simulations, the existence of two coexisting forms of liquid water—a high-density liquid (HDL) and a low-density liquid (LDL)—with a well-defined coexistence line in the pressure-temperature plane terminating in a second liquid-liquid critical point in the supercooled state. The second-order nature of this liquid-liquid critical point has been demonstrated in simulations, and the border between HDL and LDL has been shown to be a coexistence line separating the two phases (4).

This hypothesis is consistent with the experimental fact that thermodynamic quantities such as the isothermal compressibility, the isobaric specific heat, and the coefficient of thermal expansion display anomalous increases upon cooling and that, at low temperature, two forms of amorphous solid water exist: one with high density and one with low density.

Several potentials for water show a liquid-liquid critical point and a Widom line above the critical point (5, 6). To understand the meaning of the Widom line, we must first consider a fundamental property of liquids. Below the critical point, the two phases (gas and liquid, or HDL and LDL) are well separated, with a coexistence line that marks the sharp change from one phase to another (see the figure). Above the critical point, these phases merge into a single phase. If a substance is in this one-phase region and gets close enough to the critical point, bubbles of one phase start to form inside the other, giving rise to strong density fluctuations. Because of these fluctuations, in the one-phase region, thermodynamic quantities such as the isothermal compressibility (which is proportional to the mean square density fluctuations) display maxima that merge on a single line terminating at the critical point. This line is made by the maxima of the correlation length, a quantity that measures the maximum distance for which the fluctuations in two regions of the space of interest are correlated. The correlation length diverges at the critical point.

It is this line that is called the Widom line, named after the chemist Benjamin Widom, who emphasized that one cannot take data at the critical point, but only nearby. To recognize the critical point, one can detect the locus of maxima of correlation length by measuring the locus of maxima of a quantity, such as compressibility, and then extrapolate to the location of the critical point. A useful metaphor might be to imagine locating Mount Everest when its top is cloud-covered. If we are close enough and find a path that is the local maximum, for example, a ridge, and follow this path upward, we will move toward the summit.

When water goes supercooled

Scientists have long predicted the existence of two different liquid states of supercooled water. Kim et al. now provide experimental evidence for their existence.

GRAPHIC: C. BICKEL/SCIENCE

In water, the Widom line exists in the one-phase region above the liquid-gas critical point (7) (see the figure), but no convincing experimental evidence had been reported to date for a Widom line in supercooled water. Xu et al. (5) have argued that if such evidence were found, it would point to the existence of the hypothesized liquid-liquid transition terminating in a liquid-liquid critical point. The Widom line is also connected to dynamics, because the diffusive behavior changes upon crossing the Widom line (5, 7, 8).

Extensive computer simulations for a wide range of models of liquid water largely confirm the picture from the initial studies. The nature of the two phases, the LDL and HDL, continues to be probed by sophisticated experiments and detailed simulations.

Kim et al. now present experimental data for a region of the supercooled-water phase diagram that was not accessible to experiments before. The authors cooled their droplets down to 227.7 K for water (H2O) and 232.5 K for heavy water (D2O). These two temperatures are below the temperatures of homogeneous nucleation for the respective liquids. By probing the droplets with femtosecond x-ray scattering, the authors measured both the structure and the maxima in isothermal compressibility and correlation length. Because a maximum in the correlation length is a feature of the Widom line, they unambiguously prove the existence of this line and, hence, of a second-order critical point. These results not only pave the way for the full exploration of the forbidden region of supercooled water, but are also important for fields such as cryopreservation, astrobiology, and the food industry where crystallization must be avoided.

The basis for the liquid-liquid transition in water lies in its intermolecular interactions, which are distinguished by two characteristic length scales of interaction. Two pentamers—that is, the tetrahedral structure formed by a water molecule and its four neighbors—can approach each other in two distinct fashions: a “handshake” configuration, where two corners of one pentamer approach two corners of another pentamer, and a “tango” configuration, where one pentamer is rotated 90° with respect to the other (see the figure). This reasoning suggests the possibility that a liquid-liquid phase transition might also occur in other liquids with local tetrahedral structure. This interesting idea is being explored in simulations and experiments on a number of liquids, including the common materials silicon and silicon dioxide (912) and colloids (13).

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