Volume crossover in deeply supercooled water adiabatically freezing under isobaric conditions

Abstract

The irreversible return of a supercooled liquid to stable thermodynamic equilibrium often begins as a fast process which adiabatically drives the system to solid-liquid coexistence. Only at a later stage will solidification proceed with the expected exchange of thermal energy with the external bath. In this paper we discuss some aspects of the adiabatic freezing of metastable water at constant pressure. In particular, we investigated the thermal behavior of the isobaric gap between the molar volume of supercooled water and that of the warmer ice-water mixture which eventually forms at equilibrium. The available experimental data at ambient pressure, extrapolated into the metastable region within the scheme provided by the reference IAPWS-95 formulation, show that water ordinarily expands upon (partially) freezing under isenthalpic conditions. However, the same scheme also suggests that, for increasing undercoolings, the volume gap is gradually reduced and eventually vanishes at a temperature close to the currently estimated homogeneous ice nucleation temperature. This behavior is contrasted with that of substances which do not display a volumetric anomaly. The effect of increasing pressures on the alleged volume crossover from an expanded to a contracted ice-water mixture is also discussed.

Many-body Approaches at Different Scales

“…On cooling, a crossover temperature can be eventually reached at which the volume of the metastable system is equal to the volume of the stable phase that is formed under adiabatic conditions [24]. This is what happens to OTP, as indicated in the upper panel of Fig.…”

“…In this respect, a candidate threshold would be the Kauzmann temperature [3] at which the entropies of the metastable liquid and of the thermodynamically stable crystalline solid become equal. However, it has been argued that the hypothetical coexistence of a liquid and a solid phase would not be possible at a temperature lower than the equilibrium coexistence temperature [29,24]. In fact, whenever a supercooled liquid escapes from metastability and freezes, it does so irreversibly and adiabatically with an increase of both entropy and temperature as a consequence of the release of heat.…”

“…In order to take explicitly into account this crucial aspect, we assumed that the relaxation of the temperature-dependent molar specific heat of our model system, as observed in a typical differential scanning calorimetry experiment, can be represented by the expression [26,27]: 0.17 The cusp singularity at T solid ≈ 280 K marks the boundary between two different outcomes of the irreversible transition eventually undergone by supercooled liquid OTP: for T > T solid the nucleated phase is a solid-liquid mixture at the freezing/melting temperature T m , whereas for lower temperatures the equilibrium phase is a pure crystalline solid whose temperature decreases with (while still keeping higher than) that of the parent liquid, and whose volume is correspondingly larger than that of the solid (blue continuous line) at T m (for more details see [24]). Lower panel: temperature of the asymptotic metastable phase to which the liquid, originally undercooled to a temperature T , would relax at isoenthalpic conditions (black continuous line); for graphical convenience, we also plot the temperature of the metastable supercooled liquid as a red line -the dashed part being the linear extrapolation below T g of the higher-temperature experimental datawhich, by construction, coincides with the first quadrant bisector; the green continuous line (also expanded in the inset) represents the temperature T eq of the metastable state that would be reached asymptotically by the glass as calculated through Eq.…”

Supercooled water escaping from metastability

“…Recently, it has been argued that the widely adopted scheme describing the nucleation of a solid phase from a supercooled liquid as an isothermal process can be fundamentally wrong since it disregards any enthalpy contribution282930. In fact, solid nucleation always occurs exothermically on a local scale, which implies that the liquid warms up while (partially) solidifying31.…”

“…A comparison between the enthalpy content of homogeneous supercooled water and that of its corresponding heterogeneous stable state at the melting temperature shows that the adiabatic description is indeed well suited for any experiment performed at ambient pressure (see the Supplementary Information). In an adiabatic setup the mole fraction of ice produced by the decay of a metastable fluid supercooled down to a given temperature T is2932: where C P is the isobaric heat capacity of the liquid, L m ( P ) is the latent heat of fusion, and T m is the melting temperature.…”