Problems with Applying the Ozawa–Avrami Crystallization Model to Non-Isothermal Crosslinking Polymerization

Abstract

Ozawa has modified the Avrami model to treat non-isothermal crystallization kinetics. The resulting Ozawa–Avrami model yields the Avrami index (n) and heating/cooling function (χ(T)). There has been a number of recent applications of the Ozawa–Avrami model to non-isothermal crosslinking polymerization (curing) kinetics that have determined n and have used χ(T) in place of the rate constant (k(T)) in the Arrhenius equation to evaluate the activation energy (E) and the preexponential factor (A). We analyze this approach mathematically as well as by using simulated and experimental data, highlighting the following problems. First, the approach is limited to the processes that obey the Avrami model. In cases of autocatalytic or decelerating kinetics, commonly encountered in crosslinking polymerizations, n reveals a systematic dependence on temperature. Second, χ(T) has a more complex temperature dependence than k(T) and thus cannot produce exact values of E and A via the Arrhenius equation. The respective deviations can reach tens or even hundreds of percent but are diminished dramatically using the heating/cooling function in the form [χ(T)]1/n. Third, without this transformation, the Arrhenius plots may demonstrate breakpoints that leads to questionable interpretations. Overall, the application of the Ozawa–Avrami model to crosslinking polymerizations appears too problematic to be justified, especially considering the existence of well-known alternative kinetic techniques that are flexible, accurate, and computationally simple.