On the theory of polymer crystallization

Abstract

The systematic pleating of polymer molecules in their crystallization, in segments of a length of the order of 100 A, which depends on the crystallization temperature, is interpreted in terms of the kinetics of crystal growth. The theory begins with but departs from a theory proposed by Lauritzen & Hoffman, in which the statistical probability of a bend occurring somewhere gives a factor disfavouring long segments, and the probability of a deposited chain coming off again gives a factor disfavouring short segments, the two defining an optimum segment length. A basic analysis of ‘nucleation theory’ is included in this paper (and in an appendix) to clarify the points of departure. Whereas the Lauritzen-Hoffman theory postulates that successive fold segments are of the same length as the first on a crystal face, this paper shows that there must be considerable fluctuation in length from segment to segment. An approximate calculation of these fluctuations indicates that (within a specific range of supercoolings) there is a characteristic segment length l * such that after shorter segments than l * the next fluctuation is more likely to be to a longer one, and after longer segments than l * the next fluctuation is likely to be to a shorter one: so that l * defines a stable mean strip - width into which the chain molecule folds. The next strip of crystal deposited on this one has a narrow er corresponding stable width. With successive strips depositing on each other, within a certain specific range of supercooling, the strip widths converge to a stable value l **, which depends on temperature in the observed manner. For smaller supercoolings the strip width converges to a value too narrow for any further growth to occur. At larger supercoolings multiple nucleation of crystals within the same molecular chain is considered to change the mode of crystallization— dendrites rather than tabular crystals are in fact observed at these lower temperatures. Though the theory is approximate, acceptable parameters give satisfactory agreement with observation.