General Concepts of Crystallization: Some Recent Results and Possible Future Developments
Classical nucleation theory is till now the major tool in the interpretation of crystal nucleation and growth processes in a variety of liquids. For its application, the knowledge of the thermodynamic driving force and the dependence of the surface tensio
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Abstract Classical nucleation theory is till now the major tool in the interpretation of crystal nucleation and growth processes in a variety of liquids. For its application, the knowledge of the thermodynamic driving force and the dependence of the surface tension on pressure and temperature, respectively, the knowledge of relations describing the curvature dependence of the surface tension is required. New developments in this direction are summarized in the first part of the present chapter. Based on these results, in a second part, the interplay of stress evolution and stress relaxation and its effect on nucleation and growth are analyzed. It is shown then in a third part, in which directions classical nucleation theory has to be extended possibly in the future development in order to arrive at a satisfactory description of experimental data in the whole range of temperature and/or pressure. Particular attention is directed here, in this respect, to deviations of the properties of critical clusters as compared to the properties of the evolving macroscopic phases and different aspects of the interplay of glass transition and crystallization. These general considerations are supplemented by an analysis of some specific features of polymer crystallization completing the present chapter. Keywords Glass · Crystal nucleation · Crystal growth · Diffusion · Viscosity · Decoupling · Fragility
J. W. P. Schmelzer (B) · C. Schick Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany e-mail: [email protected] C. Schick e-mail: [email protected] C. Schick Kazan Federal University, Kremlyovskaya str. 18, Kazan 420008, Russian Federation © Springer Nature Switzerland AG 2020 T. A. Ezquerra and A. Nogales (eds.), Crystallization as Studied by Broadband Dielectric Spectroscopy, Advances in Dielectrics, https://doi.org/10.1007/978-3-030-56186-4_1
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J. W. P. Schmelzer and C. Schick
Abbreviations kB g(T, p) μi v D (ε) αp κT τR sm , hm xi η c nc , V c ε, ε0 J0 p, pm R, A, V d0 cp J σ T, T m t τ ns δ Wc
Boltzmann constant Change of the Gibbs free energy in crystallization per unit volume of the newly evolving crystalline phase Chemical potential of the i = 1, 2, …, k components Differences of the volumes between liquid and crystal phases per unit volume of the crystal phase Diffusion coefficient Energy of elastic deformation caused by the formation of a crystallite of volume V in a liquid Isobaric thermal expansion coefficient Isothermal compressibility Maxwell’s relaxation time Melting entropy and melting enthalpy per unit volume of the crystal phase Molar fraction of the i = 1, 2, …, k components Newtonian viscosity Number of nucleation centers per unit volume of the liquid Number of particles and volume of a critical crystal cluster Parameters determining the elastic effects caused by crystal evolution in the liquid (ε) and in a Hookean solid (ε0 ) Pre-factor in the expression for the steady-steady-state nucleation rate determined by the kinetic
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