Abstract
A recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice-water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10-based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice-water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice-water system was found to amount , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to , suggesting favor of homogeneous freezing on exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.
Highlights
In the last decade highly accurate equations of state (EoS) for water and ice became available, which are based on data from the experimentally accessible parts of the phase diagram of water: (i) for stable water (Wagner and Pruß [70], Wagner et al [71], Guder [72]); (ii) for seawater (Feistel and Hagen [73], Feistel [74,75], Feistel et al [76]) (iii) for hexagonal ice (Feistel and Hagen [77,78], Feistel and Wagner [79,80,81,82], IAPWS R10-06 [83]), (iii) for undercooled water (Holten et al [84,85,86])
Adopting the closure conditions pβ = p and Tβ = T, assuming that pressure and temperature in the ambient phase are given, and having at one’s disposal the knowledge of the chemical potentials of the considered component in both macrophases, the chemical equilibrium given by Equation (3) provides a condition for the direct determination of pα = pα(p, T) and therewith for the thermodynamic driving force of nucleation, ∆gd(bf,uclk) according to Equation (1)
The crystal–melt interface energy has a large impact on the thermodynamic energy barrier for homogeneous freezing, because it enters the expression of the critical formation work by the power to three, i.e., ∆Gc(cluster) ∝ σα3β
Summary
The outstanding importance of homogeneous freezing for a variety of natural and technical processes such as the microphysical evolution of atmospheric clouds This consequence of Gibbs’ theory gives the foundation of one of the main approximations of CNT in application to crystal nucleation, namely the identification of the bulk properties of the critical crystallites with the properties of the evolving macroscopic crystalline phase (Schmelzer and Abyzov [105]) In line with such approximation, the surface tension in between melt and critical crystal can be identified with the respective value for a planar equilibrium coexistence of the respective liquid and crystalline phases. Alternative approaches have been advanced in recent decades based on generalizations of the classical Gibbs’ approach going beyond these simplest approximations (Gutzow and Schmelzer [99], Schmelzer et al [106], Schmelzer and Abyzov [107]) These methods allow one to describe and in this way to account for variations of the bulk properties of critical clusters in dependence on the degree of deviation from equilibrium. At least as a first estimate, CNT based on Gibbs’ classical method of description will be retained in future to serve as a valuable tool in treating experimental data
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