Ivan S. Gutzow

Reconciling Gibbs and van der Waals: A new approach to nucleation theory

A new approach for the determination of the work of critical cluster formation in the description of nucleation processes is developed. For an illustration, the method is applied here to phase formation processes in solid and liquid solutions. However, it is applicable quite generally and not restricted to this particular important case. The present approach represents a generalization of the classical Gibbs’ method. It is—like the classical method—conceptionally simple and directly applicable to real systems, but avoids its shortcomings. Central to our method is the formulation and application of a new well-founded principle we denote as generalized Ostwald’s rule in nucleation. The method allows the determination of the work of critical cluster formation provided the bulk properties and the macroscopic values of the surface tension (at planar interfaces) for the possible different states of the system under consideration are known. Similarly to the van der Waals–Cahn–Hilliard and density functional calc...

The Prigogine-Defay ratio revisited

One of the basic characteristics of the glass transition, the Prigogine-Defay ratio, connecting jumps of the thermal expansion coefficient, isothermal compressibility, and isobaric specific heat capacity in vitrification is rederived in the framework of the thermodynamics of irreversible processes employing the order-parameter concept introduced by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)]. In our analysis, glass-forming liquids and glasses are described by only one structural order parameter. However, in contrast to previous approaches to the derivation of this ratio, the process of vitrification is treated not in terms of Simons simplified model [Z. Anorg. Allg. Chem. 203, 219 (1931)] as a freezing-in process proceeding at some sharp temperature, the glass transition temperature T(g), but in some finite temperature interval accounting appropriately for the nonequilibrium character of vitrifying systems in this temperature range. As the result of the theoretical analysis, we find, in particular, that the Prigogine-Defay ratio generally has to have values larger than 1 for vitrification in cooling processes. Quantitative estimates of the Prigogine-Defay ratio are given utilizing a mean-field lattice-hole model of glass-forming melts. Some further consequences are derived concerning the behavior of thermodynamic coefficients, in particular, of Youngs modulus in vitrification. The theoretical results are found to be in good agreement with experimental data.

Thermodynamics and kinetics of the glass transition: A generic geometric approach

A generic phenomenological theory of the glass transition is developed in the framework of a quasilinear formulation of the thermodynamics of irreversible processes. Starting from one of the basic principles of this science in its approximate form given by de Donder’s equation, after a change of variables the temperature dependence of the structural parameter ξ(T), the thermodynamic potentials ΔG(T), the thermodynamic functions and the time of molecular relaxation τ of vitrifying systems is constructed. In doing so, a new effect in the ΔG(T) course is observed. The analysis of the higher derivatives of the thermodynamic potential, and especially the nullification of the second derivative of the configurational specific heats ΔCp(T) of the vitrifying liquid defines glass transition temperature Tg and leads directly to the basic dependence of glass transition kinetics: the Frenkel–Kobeko–Reiner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of t...

Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts

Abstract Glassforming melts behave, in the vicinity of the temperature of vitrification T g , as viscoelastic bodies. A general theory of nucleation in a viscoelastic body developed elsewhere is applicable to the description of phase formation processes in such systems. The present contribution is directed to the demonstration of the relevance of this proposed general theory to describing phase transformation processes in glassforming melts. The application of the theory is shown to explain a number of experimental results on crystallization of glassforming melts, which have not found a satisfactory interpretation so far.

On the theoretical determination of the Prigogine-Defay ratio in glass transition

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.

Elastic stress effects on critical cluster shapes

Crystallization of solids at planar solid–air surfaces was analyzed. Shape and size of clusters of the newly evolving phase are determined which correspond to the minimal work of cluster formation in nucleation. Both elastic field and surface energy terms are taken into consideration. This work is not restricted to the consideration of spherical interfaces cluster–ambient solid phase but allows, more general arbitrary shapes of the new phase. Application to crystallization of glassforming melts, gives additional support to the idea that differences in the degree of evolution of elastic strains in crystallization in the bulk and near external or internal surfaces of highly viscous glassforming melts in the vicinity of the temperature of vitrification Tg may be the origin for the preferential surface crystallization of glasses.

Thermodynamic functions of both simple (monomeric) and polymeric melts : MFA approach and Monte Carlo simulation

Abstract The influence of equilibrium polymerization on the thermodynamic properties of model systems consisting of building units with well-defined characteristics and interactions is investigated. The systems under study are thought to resemble more or less accurately undercooled melts, and the calculations performed give the configurational part of the thermodynamic functions of these melts. The whole investigation is performed by using two approaches. In the first one, the temperature courses of the entropies and the specific heat of the systems as well as the average flexibility and the mean chain length of the polymer molecules are obtained in the framework of a mean field approximation (MFA). In the second approach, the bulk characteristics and the configurational properties of the model systems are obtained by using Monte Carlo simulations (MCS). The correspondence and the differences between the thermodynamic properties for the same systems in the two approaches are analyzed and discussed. The mo...

Catalyzed Crystallization of Glass—Forming Melts

Present day theory of nucleation predicts a number of possibilities for increasing the rate of nucleation in processes of phase formation. In science and technology, such possibilities are applied as various methods of induced or catalyzed nucleation. Possible approaches in nucleation catalysis are discussed in the literature beginning with the classical monographs on nucleation theory. Here a summary of methods of nucleation catalysis is given in application to crystallization of undercooled melts.

Liquid Phase Separation in Glass—Forming Melts

Up to now in considering in our derivations possible phase transformations in undercooled glass-forming melts mainly segregation and crystallization processes were considered proceeding via nucleation and growth and independently from each other. However, in most multi-component systems crystallization may be accompanied by processes of liquid phase separation and vice versa. In addition, another mechanism of phase separation may be also of importance denoted commonly as spinodal decomposition. In the present chapter, a brief overview on this circle of problems is given.

Kinetics of Overall Crystallization: Kinetic Criteria for Glass-Formation

This division of the phase formation process into nucleation and growth gives the possibility to investigate separately various specific features of these two particular stages of the process of phase transformation. However, such a division is in some respect artificial since it separates into different parts one process which in fact involves both nucleation and growth of clusters generally taking place simultaneously in the same volume of the melt. Thus we have to solve the problem of how the knowledge obtained in exploring separately nucleation and growth can be interconnected in a subsequent step to give a satisfactory description of the process of overall crystallization or of the overall course of phase transformations, in general. The solution of this problem is addressed in the present chapter by an outline of the Kolmogorov-Avrami theory of overall crystallization. Based on these concepts, kinetic criteria of glass-formation are developed and their relation to different historically established criteria of glass-formation is discussed in detail.