Entropy-driven liquid-liquid separation in supercooled water

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Abstract

Twenty years ago Poole et al. (Nature 360, 324, 1992) suggested that the anomalous properties of supercooled water may be caused by a critical point that terminates a line of liquid-liquid separation of lower-density and higher-density water. Here we present an explicit thermodynamic model based on this hypothesis, which describes all available experimental data for supercooled water with better quality and with fewer adjustable parameters than any other model suggested so far. Liquid water at low temperatures is viewed as an 'athermal solution' of two molecular structures with different entropies and densities. Alternatively to popular models for water, in which the liquid-liquid separation is driven by energy, the phase separation in the athermal two-state water is driven by entropy upon increasing the pressure, while the critical temperature is defined by the 'reaction' equilibrium constant. In particular, the model predicts the location of density maxima at the locus of a near-constant fraction (about 0.12) of the lower-density structure.

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Water modeled as an intermediate element between carbon and silicon.

Valeria Molinero, Emily Moore (2009)

Water and silicon are chemically dissimilar substances with common physical properties. Their liquids display a temperature of maximum density, increased diffusivity on compression, and they form tetrahedral crystals and tetrahedral amorphous phases. The common feature to water, silicon, and carbon is the formation of tetrahedrally coordinated units. We exploit these similarities to develop a coarse-grained model of water (mW) that is essentially an atom with tetrahedrality intermediate between carbon and silicon. mW mimics the hydrogen-bonded structure of water through the introduction of a nonbond angular dependent term that encourages tetrahedral configurations. The model departs from the prevailing paradigm in water modeling: the use of long-ranged forces (electrostatics) to produce short-ranged (hydrogen-bonded) structure. mW has only short-range interactions yet it reproduces the energetics, density and structure of liquid water, and its anomalies and phase transitions with comparable or better accuracy than the most popular atomistic models of water, at less than 1% of the computational cost. We conclude that it is not the nature of the interactions but the connectivity of the molecules that determines the structural and thermodynamic behavior of water. The speedup in computing time provided by mW makes it particularly useful for the study of slow processes in deeply supercooled water, the mechanism of ice nucleation, wetting-drying transitions, and as a realistic water model for coarse-grained simulations of biomolecules and complex materials.

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THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS

L.D. Landau, E.M. Lifshitz (1980)

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Structural transformation in supercooled water controls the crystallization rate of ice

Valeria Molinero, Emily Moore (2011)

One of water's unsolved puzzles is the question of what determines the lowest temperature to which it can be cooled before freezing to ice. The supercooled liquid has been probed experimentally to near the homogeneous nucleation temperature TH{\approx}232 K, yet the mechanism of ice crystallization - including the size and structure of critical nuclei - has not yet been resolved. The heat capacity and compressibility of liquid water anomalously increase upon moving into the supercooled region according to a power law that would diverge at Ts{\approx}225 K,(1,2) so there may be a link between water's thermodynamic anomalies and the crystallization rate of ice. But probing this link is challenging because fast crystallization prevents experimental studies of the liquid below TH. And while atomistic studies have captured water crystallization(3), the computational costs involved have so far prevented an assessment of the rates and mechanism involved. Here we report coarse-grained molecular simulations with the mW water model(4) in the supercooled regime around TH, which reveal that a sharp increase in the fraction of four-coordinated molecules in supercooled liquid water explains its anomalous thermodynamics and also controls the rate and mechanism of ice formation. The simulations reveal that the crystallization rate of water reaches a maximum around 225 K, below which ice nuclei form faster than liquid water can equilibrate. This implies a lower limit of metastability of liquid water just below TH and well above its glass transition temperature Tg{\approx}136 K. By providing a relationship between the structural transformation in liquid water, its anomalous thermodynamics and its crystallization rate, this work provides a microscopic foundation to the experimental finding that the thermodynamics of water determines the rates of homogeneous nucleation of ice.(5)