Crystallization kinetic description

In the absence of a full kinetic description of the crystallization process, the assumption that the solidification of chocolate can be modeled using effective heat capacity data as a function of temperature and cooling rate is an acceptable engi-... 

Rousset and Rappaz (3) have attempted to provide a kinetic description of the crystallization of triacylglycerols using an Avrami-type expression (Eq. 4) ... 

The formalism introduced in the previous subsections is able to incorporate the effect of these influences in the crystallization kinetics, thus providing a more realistic modeling of the process, which is mandatoiy for practical and industrial purposes. Due to the strong foundations of our mesoscopic formalism in the roots of standard non-equilibrium thermodynamics, it is easy to incorporate the influence of other transport processes (like heat conduction or diffusion) into the description of crystallization. In addition, our framework naturally accounts for the couplings between all these different influences. 

Besides the universally accepted kinetic description of a process based on a proper analysis of the shape of vaporization curves (see Sect. 2.4), the Arrhenius approach has been widely used to probe the mechanism of decomposition at the level of elementary processes in solids, which are associated with rearrangement of the crystal lattice. These studies rest on two fundamental branches of the physical chemistry of solids, namely, the theory of disorder and the theory of transport, whose foundations had been laid in the 1920s-1930s by the outstanding Russian physicist, FYenkel, and the well-known German physical chemists, Wagner and Schottky. 

There have been many attempts to develop theories to explain the important aspects of crystaUizatirMi [3,4]. The most widely accepted approach to the analysis of the linear crystal growth rates is the kinetic description due to Laur-itzen and Hoffman [3]. There are alternative approaches which will not be considered here since this is not meant to be a comprehensive review chapter of theoretical approaches. 

In the modelling of industrial processing of flexible chain polymer melts we often need physically sensible description of the crystallization kinetics. Usually, the melt is subjected to time-dependent deformation rates (fibre spinning,... 

This chapter presents the most recent advances in this domain, divided into two parts. First microscopic models are presented. These use the theory of crystallization kinetics at the crystal level. Second, macroscopic models are detailed. These treat crystallization more globally through its description at the macroscopic scale. 

The locus of points sharing this property is a branch of a hyperboloid or a plane, the latter being the case when Ti = t2. After impingement on neighboring spherulites, the volume of each individual spherulite evolves in a complex way that depends on the nucleation (positions and times) of spherulites involved. All growing entities contribute to the conversion degree. The two best known approaches to the description of overaU crystallization kinetics in infinite samples are those of Avrami and Evans, both based on the isovolume assumptions, which enabled to assimilate volume and volume fraction terms. 

The present discussion will focus on the physical principles of the measurement and how to interpret the recorded data under nonisothermal conditions. This technique is also useful to study the polymer crystallization kinetics however, this topic is beyond the scope of this discussion. Fully detailed description and... 

An important achievement of the theory of the mean separation works is the detailed kinetic description of the equilibrium between a small crystal and the ambient phase. In that case the equilibrium state is attained only at a supersaturation Ap > Q and is expressed through the equality of the probabilities of attachment P+ t/ and detachment of atoms to and Irom the different crystallographic faces. 

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

The contribution of different crystal planes to the overall surface area of the particle can thus be calculated and is shown in Fig. 8.12(b). The results have been included in a dynamical micro-kinetic model of the methanol synthesis, yielding a better description of kinetic measurements on working catalysts [C.V. Ovesen, B.S. Clausen, J. Schiotz, P. Stoltze, H. Topsoe and J.K. Norskov, J. Catal. 168 (1997) 133]. 

The kinetics of electrocrystallization conforms to the above description only under precisely defined conditions. The deposition of metals on polycrystalline materials again yields products with polycrystalline structure, consisting of crystallites. These are microscopic formations with the structure of a single crystal. 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

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