Extension of theory of growth of chain-folded polymer crystals to large undercoolings

Abstract

The kinetic theory of the rate of growth G and the initial lamellar thickness lg* of chain-folded crystals is extended so that it is applicable at high undercoolings. Attention is centered on the details of how the first step element and the first fold are put down on the substrate. A parameter φ that varies between zero and unity, which apportions the free energy of attachment of the step element between the forward and backward reactions, is used to denote variations in this process. Expressions for G are derived from flux equations for two limiting cases: regime I, single surface nucleation act with rapid substrate completion and regime II, numerous surface nucleation acts with very slow substrate completion. Data from the literature on G for isotactic polystyrene (regime II) and polyethylene single crystals (regime I) are analyzed to obtain surface free energies, and these are used with the revised theory for lg* to predict the lamellar thickness of these polymers. Good agreement between lg* and published data is found for 1 > φ > 0. Values of φ below unity imply that the molecules are physically adsorbed onto the substrate prior to actual crystallographic attachment. A discussion is given of the segmental transport effects that dominate the behavior of G at high undercoolings in bulk polymers.