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Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
Open AccessArticle

Ice-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension. Part I: Theoretical Foundation

1
Leibniz Institute for Tropospheric Research (TROPOS), Permoserstraße 15, D-04318 Leipzig, Germany
2
Institute of Physics, University of Rostock, Albert-Einstein-Straße 23-25, D-18059 Rostock, Germany
3
Leibniz Institute for Baltic Research (IOW), Seestraße 15, D-18119 Rostock-Warnemünde, Germany
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(1), 50; https://doi.org/10.3390/e22010050
Received: 15 September 2019 / Revised: 17 December 2019 / Accepted: 19 December 2019 / Published: 30 December 2019
(This article belongs to the Special Issue Crystallization Thermodynamics)
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 T K = 116 K , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to p K = 212 MPa , 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. View Full-Text
Keywords: classical nucleation theory; crystallization thermodynamics; homogeneous freezing; thermodynamic driving force of nucleation; ice–water surface tension; Kauzmann temperature and pressure; TEOS-10 classical nucleation theory; crystallization thermodynamics; homogeneous freezing; thermodynamic driving force of nucleation; ice–water surface tension; Kauzmann temperature and pressure; TEOS-10
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Hellmuth, O.; Schmelzer, J.W.P.; Feistel, R. Ice-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension. Part I: Theoretical Foundation. Entropy 2020, 22, 50.

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