Theory of Polymer-Chain Folding

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Abstract
A molecular theory is proposed to account for the regular folding of polymer chains during crystallization. It predicts that an isolated polymer chain greater than some critical length can lower its energy by crystallizing into a regular folded-chain conformation. Similarly, a single molecular chain crystallizing upon an infinitely large substrate will also lower its free energy by regular folding. In a crystal composed of polymer molecules all having the same length the lowest free energy occurs when all chains are completely extended, however, there also exists a whole series of metastable states corresponding to one, two, three, etc., folds per molecule. When the crystal is composed of a distribution of molecular lengths, the lowest free energy corresponds to a folded-chain crystal whose thickness is a sensitive function of the distribution. If the low end of the molecular-length distribution is assumed to be truncated at the observed length of extended-chain crystals, the theory satisfactorily predicts the observed thicknesses of folded-chain crystals obtained by melt crystallization of both fractions and whole polymer.