Kinetics of phase transitions

Raghavan, V., and Cohen, M. (1975). "Solid-State Phase Transformations," Chapter 2, in N. B. Hannay, Ed., Treatise on Solid State Chemistry Changes in State, Vol. 5. Plenum Press, New York. A mathematical treatment of the subject including a good treatment of the kinetics of phase transitions. 

The problems of phase transition always deeply interested Ya.B. The first work carried out by him consisted in experimentally determining the nature of memory in nitroglycerin crystallization [8]. In the course of this work, questions of the sharpness of phase transition, the possibility of existence of monocrystals in a fluid at temperatures above the melting point, and the kinetics of phase transition were discussed. It is no accident, therefore, that 10 years later a fundamental theoretical study was published by Ya.B. (10) which played an enormous role in the development of physical and chemical kinetics. The paper is devoted to calculation of the rate of formation of embryos—vapor bubbles—in a fluid which is in a metastable (superheated or even stretched, p < 0) state. Ya.B. assumed the fluid to be far from the boundary of absolute instability, so that only embryos of sufficiently large (macroscopic) size were thermodynamically efficient, and calculated the probability of their formation. The paper generated extensive literature even though the problem to this day cannot be considered solved with accuracy satisfying the needs of experimentalists. Particular difficulties arise when one attempts to calculate the preexponential coefficient. 

This paper by Ya.B. helped lay the foundation for the study of the kinetics of phase transitions of the first kind. It considers the fluctuational formation and subsequent growth of vapor bubbles in a fluid at negative pressures. It is assumed that the fluid state is far from the boundary of metastability and that the volume of the bubbles formed is still small in comparison with the overall volume of the fluid. The first assumption ensures slowness of the process the time of transition to another phase is large compared to the relaxation times of the fluid per se. This allows the application of the Fokker-Planck equation in the space of embryo dimensions to describe the growth of the embryos. 

The course of the process at a later stage, where the second assumption is not satisfied, was studied by I. M. Lifshitz and V. V. Slezov.1 The kinetics of phase transitions of the first kind near absolute zero, where fluctuations have a quantum character, were described by I. M. Lifshitz and Yu. M. Kagan2 and by S. V. Iordanskii and A. M. Finkelshtein.3 In these works the ideas of Ya.B. s paper also play an important role. 

The kinetics of the mesophase transitions can be discussed by comparison with the crystallization-melting and the vitrification-devitrification transitions of the three limiting phases of Fig. 2. Except for the crystallization kinetics, the literature on the kinetics of phase transitions is limited. For the mesophases, information is scarce. 

Starch pastes obtained by heating in a recording viscometer are seldom completely dispersed, but are a mixture of granular fractions and dispersed molecules. The kinetics of phase transition of native and modified starches are analyzed by DSC.55... 

Mossbauer spectroscopy provides phase identification, determination of oxidation states, and incidentally structure information and particle size. A little used application is to follow in real time the kinetics of phase transitions (carburization, reduction) in catalysts by monitoring the intensities of a few selected peaks in a single velocity experiment. Examples of applications on catalysts have recently been reviewed [43]. 

A. Gatlin, Kinetics of phase transition in frozen solution. Dev. Biol. Stand. 74 93-104,(1991). 

Kinetics of Phase Transitions in the Systems Involving Rigid-Chain... 

The rapid growth of the number of publications concerning polymeric liquid crystals indicates that we should expect the appearance of new fundamental studies on the transition of rigid- and semirigid-chain polymers into this state. The range of moderately concentrated solutions for these polymers is studied sufficiently well, while the development of the methods of establishing the liquid. crystalline state in superconcentrated systems and in pure polymers with semirigid chains, as well as the analysis of kinetics of phase transitions, are the subject for further theoretical and experimental works. 

The p-T phase diagram of sulfur is about the most complicated amongst the chemicd elements, and many open questions still exist with respect to phase boundaries, structures in detail, and kinetics of phase transitions in the solid as well as in the hquid state. Not only the molecular and crystalline variety of sulfur contributes to this complexity but also the metastabihty of high-pressure phases which is related to the application of different experi-mentd procedures. For example, early structural studies on the p-T phase diagram of sulfur could not be performed in-situ. Therefore, in these experiments the sulfur samples were quenched from a selected temperature-pressure point to STP conditions. The results obtained by such a procedure depend strongly on the variables AT and Ap as well as on their time derivatives (gradients), dT/dt and dp/dt, respectively. Especially, dynamic compression (shock wave) methods may introduce further complications since melting of... 

Reiss, H. (1950). The kinetics of phase transitions in binary systems. J. Chem. Phys. 18, 840-848. 

Thomas Russell is Silvio O. Conte Distinguished Professor, Polymer Science and Engineering Department Director, Energy Frontier Research Center (EFRC), Polymer-Based Materials for Harvesting Solar Energy. His research interests are polymer-based nanoscopic structures, polymer-based nanoparticle assemblies, electrohydrodynamic instabilities in thin polymer films, surface and interfacial properties of polymers, polymer morphology kinetics of phase transitions, and supercritical fluid/polymer interactions. 

Tanaka, T. Kinetics of phase-transition in polymer gels. Phys. A 140(1-2), 261-268 (1986)... 

Modern materials science is mainly based on three sections of physical chemistry, namely, the thermodynamics of multicomponent multiphase systems, the kinetics of phase transitions, and morphology. I he location of the configurative point on the state diagram, the trajectory ajid velocity of its transfer determine the type of phase separation and the mechanism of kinetics, which, in turn, determines the morphology of the system, and, finally, the performance of materials and articles. 

In conclusion, the Landau theory provides a welcome quantitative description of the thermodynamics and kinetics of phase transitions in minerals, including ferroelectric ceramics, by using macroscopic order parameters and their relationship to physical properhes and symmetry, as shown below. For an excellent review of the apphcation of Landau theory to displacive phase transitions in minerals, see Dove (1997). 

Tanaka, T. (1986) Kinetics of Phase Transition in Polymer Gels. Physica A Stat. Mech., 140, 261-268. 

Now w e consider one of the simplest models for the kinetics of phase transitions. 

It is possible by using pressure-jump (p-jump), temperature-jump (T-jump), and stopped-flow setups (see Chapter 2) to induce a phase transition from one t3rpe of structure to another. This has permitted the study of the kinetics of phase transitions in surfactant (including amphiphilic block copolymer) and lipid systems (see Chapter 7). In these studies, the relaxation of the system is monitored using time-resolved intensity of light (or turbidity), of neutrons, and more particularly of x-rays. Indeed, the powerful x-ray sources from S5m-chrotron radiation now available permit the recording of full diffraction spectra in only a few milliseconds. 

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