Avrami equation parameters, crystallization

The crystallization of poly(ethylene terephthalate) at different temperatures after prior fusion at 294 C has been observed to follow the Avrami equation with the following parameters applying at the indicated temperatures ... 

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

The primary crystallization process is characterized by three parameters. These are the rate of radial growth of the spherulite, G, the time constant for nucleation, t , and the time constant for the primary crystallization process, Tc, which is determined from the Avrami equation. All three parameters seem to depend on the stereoregularity of the polymer, but the nucleation rate seems to depend most strongly. 

Fig. 1 shows the crystallization isotherms for the samples crystallized at 392 K. Table 1 compiles the crystallynity grades achieved at this temperature for all the samples and the kinetic parameters inferred from the graphic representation of the Avrami equation. 

The overall kinetic parameters of polymers crystallized isothermally from the melt can be measured by DSC. The overall crystallization kinetics follow the Avrami equation ... 

It was proposed to use the thermodynamics of small systems and Avrami equations to describe the formation processes of carbon nanostmctures during recrystallization (graphitization) [6, 7]. These equatiorrs are successfully applied [8] to forecast permolecular stmctures and prognosticate the conditions on the level of parameters resulting in the obtaining of nanostmctures of definite size and shape. The equation was also used to forecast the formation of fibers [9]. The application of Avrami equations in the processes of nanostmcture formation a) embryo formation and crystal growth in polymers [8... 

The general Avrami equation is applicable to any type of crystallization. It is not restricted to polymers. It describes the time evolution of the overall crystallinity. The pioneer work was conducted during the 1930s and 1940s by Evans, Kolmogoroff, Johnson and Mehl, and Avrami. Wunderlich (1978) concludes that without the parallel knowledge of the microscopic, independently proven mechanism, the macroscopic, experimentally derived Avrami equation and the Avrami parameters are only a convenient means to represent empirical data of crystallization. However, interest in the Avrami equation has been... 

To study kinetic parameters of nonisothermal crystallization processes, several methods have been developed and the majority of the proposed formulations are based on the Avrami equation, which was developed for isothermal crystallization conditions. 

Plotting the left part of this equation against logt should result in a straight line, from which both Avrami parameters, n (slope) and k (intercept), can be obtained. In Table 3.7 some literature data on the Avrami constants and the half time of crystallization are presented. 

Isothermal crystallization of polymers is normally performed by cooling the sample at the fastest cooling rate possible from an (assumed) isotropic melt to a predetermined temperature where the crystallization process is monitored as a function of time. Coefficients similar to the reaction rate kinetic parameters have been developed to describe the isothermal crystallization of polymers based on Avrami s equation ... 

Equation 3.21 is valid for a < [, and Eq. 3.22 for a > C- InstEad of two Avrami parameters, five parameters are required to describe the process. They have the following physical meaning k and n (the primary crystallization parameters) depend on crystallization temperature, nature of primary nucleation, and the fast growth the secondary crystallization parameters, k and n, depend on the conditions under which the slow crystallization of the remaining amorphous regions takes place and a fifth parameter, i, indicates the weight fractiOTi of material crystallized up to the moment the primary crystallization ends, t is the moment at which the third region starts (e.g., pure secondary crystallization). 

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