Polymer crystallization sporadic nucleation

Table 8.1 shows the dependence of K and n on the mechanism of nucleation and growth. Measurements of n have shown that it decreases as crystallization proceeds. Mandelkem [28)] has considered the case of sporadic nucleation on predetermined nuclei that cause a decrease in as crystallization proceeds. However, n may also decrease when A cs is not constant but varies with time. A comparison of degree of crystallinity measurements with spherulitic growth rate measurements on the same polymer [29] shows this. The polymer continues to crystallize after the volume fills with spherulites. The value of n for this secondary crystallization is usually less than for the primary crystallization process. This difference gives rise to a change of n with time. Reference 30 treats this problem theoretically as do Hilliar [31] and Price [32]. 

The problem now resides on the evaluation of T,. There are two cases to be considered (a) the nuclei are predetermined— that is, they all develop at once on cooling the polymer to the temperature of crystallization—and (b) there is sporadic nucleation of the spheres. 

The kinetics of crystallization from melts was studied by Avrami and was adapted later on to the case of polymers. Due to the economic repercussions of the crystallization phenomenon and of its kinetics, many smdies were conducted to simplify or refine Avrami s treatment. With respect to nucleation and to its kinetics, the temperature is obviously a parameter of paramount importance. For a sporadic nucleation, it was established that the rate N, which corresponds to the number of nuclei generated per unit time and volume, is given by... 

Carefully conducted experiments have shown that it is possible for spherulites to develop sporadically in both time and space in thin polymer films.(22,23,101,102) Repetitive experiments have indicated that spheruhtes do not necessarily form in identical positions if complete melting of the sample is ensured. However, a study of poly(decamethylene terephthalate) has shown that although spherulites are formed sporadically in time, they appear in identical positions within the sample.(103) Experimental evidence showed that for this sample the spheruUtic centers are initiated from a fixed number of heterogeneities. There is a strong tendency for spherulites to appear in the same position in the field of view after successive crystallizations.(73,74,104-106) In some cases this observation is solely a result of incomplete melting.(33,36,102) In others, it can also be due to the presence of a finite number of nucleation catalysts in the polymer melt. 

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