Avrami-Evans theory

Isothermal crystallization of a polymer is frequently characterized by the induction time and the crystallization half-time. The crystallization induction time is the time that elapses from the moment when the desired crystallization temperature is reached to the onset of crystallization, characterized by the formation of the first nuclei. The crystallization half-time is the time when relative crystallinity reaches 0.5. More detailed analyses of the isothermal crystallization are usually based on the Avrami-Evans theory. Equation (7.10) yields ... 

It was also demonstrated that in polymer composites, volume inhabited by embedded fibers inaccessible for crystallization and additional nucleation on internal interfaces [53,62,63], can markedly influence the overall crystallization kinetics, as described in Chapter 13. Similar problems might be encountered during crystallization in other polymer systems such as composites with particulate fillers and immiscible polymer blends. Under such conditions, the simplified Avrami equation (Eq. 7.10) does not apply and, as a consequence, the classic Avrami analysis may yield nonlinear plots and/ or noninteger n values. It must be emphasized that the problem cannot be solved by application of other, incorrect models, like that of Tobin, which are essentially based on the same assumptions as the Avrami-Evans theory but yield different equations due to incorrect reasoning. 

It is obvious that the presence of fibers and nucleation on fibers affects the overall crystallization kinetics. The nucleation on fibers accelerates the crystallization. Moreover, the overall crystallization kinetics in fiber-reinforced polymers frequently deviates from predictions by the Avrami-Evans theory because the basic assumption of random positions of nuclei is not fulfilled. For instance, the Avrami exponent, calculated regardless of inapplicability of the theory, is lower (or decreases... 

It is rather clear that the classic Avrami-Evans theory, outlined in Chapter 7, does not permit description of the conversion of polymer melt into spherulites in polymer composites with fibers, even in the simplest case of isothermal crystallization. Therefore, the coefficients calculated based on the Avrami plots are only adjustable parameters and do not have clear meanings in such cases. 

Evans, U.R. (1945) The laws of expanding circles and spheres in relation to the lateral growth of surface films and the grain-size of metals. Transactions of the Faraday Society, 41, 365. (a)Avrami, M. (1939) Kinetics of phase change I general theory. Journal of Chemical Physics, 7, 1103 (b)Avrami, M. (1940) Kinetics of Phase Change II transformation-time relations for random distribution of nuclei. Journal of Chemical Physics, 8, 212. 

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