Polymer crystallization kinetics can be quantitatively described by a two-range equation, based on a simple nucleation model which is in agreement with experimental observations; it accounts in a unitary form for various possible nucleation mechanisms.
The agreement of the new equation with experimental data is shown ; the differences with regard to the usual Avrami equation are discussed.
CRYSTALLIZATION kinetics of polymers are usually described in terms of the Avrami equation :
where v,, vo and v~ are the specific volume values respectively at time t, initially, and at infinite time; K is a constant at constant temperature, depending upon the nucleation and growth rates; n is an integer which may assume the values 1, 2, 3 or 4 depending both on the number of dimensions in which ~owth occurs and on the nature of the nucleation process (instantaneous or sporadic, i.e. heterogeneous or homogeneous).
Several authors have discussed the validity of the Avrami equation (t), since experimental results of crystallization kinetics very often yield non-integral values of the exponent n, which have no definite physical meaning. Some modified equations have been also proposed by various assumptions such as a simultaneous occurrence of homogeneous and heterogeneous nucleation ~3) and a nonconstant density of the growing crystalline bodies/3-5~
We now propose an improved formulation, based on a simple model, in which the nucleation process is unitary and accounts for a wider range of physical possibilities. Some experimental observations of nucleation in polymers lead to the conclusion that the homogeneous nucleation is generally scarcely relevant ~6~ and that the heterogeneous nucleation is not necessarily instantaneous.
A typical behaviour of heterogeneous nucleation can be simply postulated as follows, according to experimental observations: ~-9) initially the number of nuclei increases linearly with time, until a limiting number is reached, which remains constant throughout the subsequent crystallization.
A somewhat similar, but more complex, nucleation model was assumed by Avramff ~) in his original theory of crystallization kinetics and from this theory (I) has been derived for the particular cases of homogeneous or instantaneous heterogeneous