The kinetic crystallization model of Avrami is generally accepted as a starting point for the analysis of isothermal polymer crystallization. It is shown in this paper that, in the case of non‐isothermal crystallization kinetics with constant heating or cooling rates, an apparent m‐order reaction model is approximately equivalent to the nucleation and growth model of Avrami in the vicinity of the inflection points of the corresponding crystallization curves. Since the apparent m‐order reaction model is defined for every real, positive apparent reaction‐order m, a distinct Avrami index n, which is valid for the characterization of isothermal and non‐isothermal crystallization experiments with constant heating or cooling rates, can always be related to any apparent reaction‐order m. Therefore, two types of Avrami master curves, which are dependent merely on the Avrami index n and which describe the isothermal polymer crystallization thoroughly, can be obtained by performing non‐isothermal experiments with constant heating or cooling rates.

The kinetic crystallization model of Avrami is generally accepted as a starting point for the analysis of isothermal polymer crystallization. However, in most cases, the experimental situation is complicated by a n incubation time prior to isothermal crystallization, so that the Avrami equation must be modified. Moreover, the experimental data are often limited in number and restricted to a n intermediate crystallinity range. Furthermore, data of isothermal crystallization experiments performed at different temperatures, cannot be evaluated together by using a n evaluation procedure being based on the Avrami equation. An iterative procedure and a crystallization-temperature independent Avrami master curve, which overcome these problems if the Avrami index n is bigger than one, are displayed in this work.

The kinetic crystallization model of A vrami is the generally accepted starting point for the analysis of isothermal nucleation and crystallization of polymers.1 -3 It will be shown in this communication that, in the case of non-isothermal crystallization experiments performed with constant heating or cooling rates and analyzed by using differential scanning calorimetry (DSC), even an apparent m-order reaction model, being defined for every real, positive reaction-order m, is appropriate to describe the corresponding crystallization curves in the vicinity of the inflexion points. The latter approach will be shown to be approximately equivalent to the isokinetic nucleation and growth model of Nakamura 4 as well as to the non-isothermal crystallization kinetics theory applied to DSC-curves of Ozawa. 5 The apparent m-order reaction model is given by the following equation, 6 if constant heating or cooling rates are maintained during the DSC-experiments:whereby a(T) represents the conversion factor at the absolute temperature T (varying from O to 1), K 0 the frequency factor, R the gas constant, ER the activation energy, q the heating or cooling rate, k,(T) the temperature-dependent rate constant and m the apparent reaction-order. The inflexion point of the function a(T) is denoted by a(Tin). It is found by solving the equa-This has already been done in a previous publication. 6 The following result has been obtained:In deriving eq 5 some approaches have been made assuming that the investigated chemical reactions, curing reactions, phase transformations or crystallization processes occur over a relatively narrow temperature range around Tin in comparison with the absolute 262 temperature T. This assumption is justified in most practical cases. Thus, a( Tin) has been found to be approximately independent of the temperature, the temperature-dependent rate constant and the heating (or cooling) rate q. a(Tin) is only dependent on the apparent reaction-order m. Because m is approximately independent of q, if an inflexion point exists, eq 5 is valid for a wide range of q-values, although not for q = 0. 6 On the other side, the isothermal crystallization model of A vrami, being based on the nucleation and growth characteristics of crystalline phases, also shows an inflexion point for n > 1 as well as for the formal cases with n < 0. The three-parameter Avrami equation function, 7 • 8 being the result of the isothermal nucleation and growth theory, is given bywhereby 8(t) is the relative crystallinity at time t, k the crystallization rate constant containing the nucleation and growth rates, r the induction period and n the Avrami index. Moreover, the value of B(tin) at the inflexion point is given by 7If a(Tin) is formally set equal to 8(tin), the following relation between the Avrami index n and the apparent reaction-order m is found 6 :Equation 8 implies that, with the exception of the singularity at m = 1, every real, positive value of an apparent reaction-order m corresponds exactly to one real value of n, being larger ...

The kinetic crystallization model of Avrami is generally accepted as a starting point for the analysis of isothermal polymer crystallization. In a previous communication, the author has shown that data of isothermal crystallization experiments can be evaluated together with the help of Avrami master curves, if the Avrami index n is larger than one. These Avrami master curves have been obtained by scaling the three‐parameter Avrami equation functions θ(t) with the time‐values of its inflection points. In this work, alternative Avrami master curves will be displayed; they are obtained by scaling θ(t) with the mean‐time t̄ = ∫ 01 t dθ. These alternative Avrami master curves can be constructed for every Avrami index n > 0.

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