Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 4 November 2019 / Approved: 4 November 2019 / Online: 4 November 2019 (11:07:48 CET)

How to cite: Schmelzer, J.W. Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results. Preprints 2019, 2019110038 (doi: 10.20944/preprints201911.0038.v1). Schmelzer, J.W. Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results. Preprints 2019, 2019110038 (doi: 10.20944/preprints201911.0038.v1).

Abstract

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 and assuming that the basic assumptions of classical nucleation theory commonly employed in application to crystallization hold, a general form of the nucleation theorem can be formulated valid not only for one-component but generally for multi-component systems. This result 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, recently developed by us expressions for the curvature dependence of the surface tension, respectively, the dependence of the surface tension on pressure and/or temperature are employed. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)] holds also for multi-component systems as far as mentioned above assumptions are fulfilled. In the application of classical nucleation theory to crystallization processes it is assumed as one of its basic ingredients that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. This assumption is, however, in general, it is not true. This limitation of the theoretical description can be overcome 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.

Subject Areas

general theory of phase transitions; nucleation; thermodynamics of nucleation in physical chemistry and chemical physics; theory and models of crystal growth; glasses

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