Avrami-Evans-Nakamura equation

Pantani et al. [11] gave an extensive review on available models to predict and characterize the morphology of injection-molded parts. The authors themselves proposed a model to predict the morphology of injection-molded iPP, in which flow kinematics are computed using a lubrication approximation. Polymorphism was accounted for, using the Avrami-Evans-Nakamura equation to describe the crystallization kinetics of the mesomorphic phase, while the evolution of the a phase was modeled using Kolmogorov s model [122]. 

Under the aforementioned hypotheses, as two different crystalline phases are formed (a and mesomorphic), at least two kinetic processes take place simultaneously. The simplest model is a parallel of two kinetic processes non-interacting and competing for the available molten material. The kinetic equation adopted here for both processes is the non-isothermal formulation by Nakamura et al. (Nakamura et al., 1973, Nakamura et al., 1972) of the Kolmogoroff Avrami and Evans model (Avrami, 1939,1940,1941, Evans, 1945). 

It has to be emphasized that the classic Avrami and Evans equations, and consequently the Nakamura approach, were derived by assuming random positions of nuclei in a material therefore, they do not apply strictly when there is a correlation between positions of nucleation sites. Such nucleation of spherulites is accounted for in the model developed originally for fiber-reinforced polymers [53], described in Chapter 13. 

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