Evaluation of data on the kinetics of isothermal polymer crystallization

Abstract

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.

Non-Isothermal Crystallization Kinetics of Poly(ethylene terephthalate) from the Point of View of Isokinetic Models

“…melt-crystallization with respect to the temperature-mark at about l 70°C. 6 Moreover, the results for k(Tin) and x(Tin) are in qualitative agreement with data reported elsewhere for isothermal and non-isothermal melt-crystallization of PET. 12 • 13 It is concluded that the kinetics of polymer crystallizations, being characterized by a single A vrami index n, can be described in the vicinity of the inflexion point as well with a nucleation and crystal-growth model as, formally, with an apparent m-order reaction model.…”

“…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 by…”

“…6 Thus, Avrami's microscopic, isothermal crystallization model of nucleation and growth is on the macroscopic scale, with respect to the crystallization process in the vicinity of the inflexion point, nearly equivalent to an apparent, non-isothermal m-order reaction model; however, the formal reaction-order m must be defined for every positive, real value. 6 Thus, the reaction-order m can also be considered as an atomic parameter, which determines the dimensionality of the growing solid phase-domains of any chemical reaction during the time-period characterized by the maximum reaction rate. Besides, the inflexion point region of the Avramic curve denotes the period of maximum reaction rate.…”

“…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:…”

Evaluation of data on the kinetics of isothermal polymer crystallization: Part II

“…The three-parameter Avrami equation functions @(t) show a n inflection point for n > 1. The time-values of the inflection points ti, and the values of O(t,,) have been calculated by the author in a previous work (8). They are given by…”