Avrami equation parameters

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 above set of equations can be solved numerically given input parameters, including surface tension a, temperature, solubility relation, D and p as a function of total H2O content (and pressure and temperature), initial bubble radius ao, initial outer shell radius Sq, initial total H2O content in the melt, and ambient pressure Pf. For example. Figure 4-14 shows the calculated bubble radius versus time, recast in terms of P versus t/tc to compare with the Avrami equation (Equation 4-70). 

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. 12.12. Avrami plots for (a) two P(S—6—ODMA) block copolymers (Lam-9 nm,Cyl-ll nm) and a PODMA homopolymer and (b) block copolymers containing PODMA cylinders with different diameters (Cyl-11 nm,Cyl-16 nm,Cyl-24 nm) constructed based on master curves as shown in Fig. 12.11. Fits to the Avrami equation are indicated by solid lines. The fit parameters are given in Table 12.2...

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 ... 

When the molecular system is a solid or cross-linked fluid subject to constant deformation, the orientation of the molecule is independent of time and the rate parameters are constants dependent only on the deformation. However, if the orientation changes with time, then the rate constants, and possibly the mechanism, will also change and this time dependence will alter the basic form of the Avrami equation, i.e. to... 

The analysis of these calorimetric isotherms in terms of the Avrami equation (Fig, 11) shows that the kinetics of the mesophase formation is described by the Avrami parameter n = 1.75 0.05. Such a value of the morphological parameter was interpreted as two-dimensional growth of lamellar structures on heterogeneous nuclei. 

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... 

Thus, with the help of Avrami equations or their modified analogs we can determine the optimal duration of the process to obtain the required result. It opens up the possibility of defining other parameters of the process and characteristics of nanostmctures obtained (by shape and sizes). 

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. 

The Kolmogorov-Avrami equation for the case when the crystallisation parameter is the stress in a uniaxially stretched sample can be presented as follows [39] ... 

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