Cargando…

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

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that...

Descripción completa

Detalles Bibliográficos
Autor principal: Schmelzer, Jürn W. P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514492/
http://dx.doi.org/10.3390/e21121147
_version_ 1783586600318402560
author Schmelzer, Jürn W. P.
author_facet Schmelzer, Jürn W. P.
author_sort Schmelzer, Jürn W. P.
collection PubMed
description Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that is valid not only for one-component but generally for multi-component systems. In this analysis, one basic assumption of classical nucleation theory is utilized. In addition, commonly employed in application to crystallization, it is supposed that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)], also relying widely on the standard classical approach in the description of crystal nucleation, holds for multi-component systems as well. The general form of the nucleation theorem derived by us is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, expressions recently developed by us for the curvature dependence of the surface tension, respectively, its dependence on pressure and/or temperature are employed. The basic assumption of classical nucleation theory mentioned above is, however, in general, not true. The bulk and surface properties of the critical crystal clusters may differ considerably from the properties of the evolving macroscopic phases. Such effects can be incorporated into the theoretical description by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem, as derived based on classical nucleation theory, holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.
format Online
Article
Text
id pubmed-7514492
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-75144922020-11-09 Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results Schmelzer, Jürn W. P. Entropy (Basel) Article Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that is valid not only for one-component but generally for multi-component systems. In this analysis, one basic assumption of classical nucleation theory is utilized. In addition, commonly employed in application to crystallization, it is supposed that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)], also relying widely on the standard classical approach in the description of crystal nucleation, holds for multi-component systems as well. The general form of the nucleation theorem derived by us is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, expressions recently developed by us for the curvature dependence of the surface tension, respectively, its dependence on pressure and/or temperature are employed. The basic assumption of classical nucleation theory mentioned above is, however, in general, not true. The bulk and surface properties of the critical crystal clusters may differ considerably from the properties of the evolving macroscopic phases. Such effects can be incorporated into the theoretical description by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem, as derived based on classical nucleation theory, holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for. MDPI 2019-11-25 /pmc/articles/PMC7514492/ http://dx.doi.org/10.3390/e21121147 Text en © 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Schmelzer, Jürn W. P.
Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title_full Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title_fullStr Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title_full_unstemmed Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title_short Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results
title_sort application of the nucleation theorem to crystallization of liquids: some general theoretical results
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514492/
http://dx.doi.org/10.3390/e21121147
work_keys_str_mv AT schmelzerjurnwp applicationofthenucleationtheoremtocrystallizationofliquidssomegeneraltheoreticalresults