Chain folding and polymer crystallization: A statistical–mechanical approach

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Abstract
The essential factor controlling the formation of chain folded polymer crystals is attributed to the statistical distribution of many subcritical nuclei pre‐existing within the chains. Each nucleus should consist of at least three parallel segments belonging to the same chain; its statistical probability is higher, the shorter are the chain loops connecting the segments. It is shown that the average fold‐to‐fold thickness both of the critical nuclei and of the actual crystals may reasonably be expected as equal to the average countour length of the loops within the subcritical nuclei. Under proper simplifying assumptions, statistical–mechanical calculations are carried out for polyethylene crystals precipitated from dilute solutions, showing a reasonable agreement with experimental observations. The present theory readily explains the tendency towards lamellar crystallization even in bulk polymer samples. It also suggests that at sufficiently low temperatures amorphous polymers may contain crystallinelike associations where segments relatively contiguous along the chain sequence are present with a higher probability. The present theory is somehow related with the classical kinetic viewpoint insofar as crystal size is not dictated by its own free energy requirements, and its growth is accompanied by a free energy decrease.