NUCLEATION THEORY APPLIED TO POLYMER CRYSTALS WITH CURVED EDGES

The nucleation-based theory of polymer crystal growth has been extended to apply to the growth rate and morphology of polyethylene (PE) single crystals with curved edges. The treatment is employed to analyse in detail the data of Organ and Keller on PE crystals formed from n-hexadecane and n-tetradecanol, which possess both {1 1 0} and {2 0 0} sectors; the subordinate {2 0 0} sectors exhibit the curved edge. The theory (1) introduces the concept of lattice strain in the {2 0 0} sectors through a parameter sigma-s (which has an independent justification), (2) takes a {2 0 0} growth front to have the energetics associated with its being 'serrated' on a molecular level in addition to being strained, and (3) treats the dominant {1 1 0} growth front in terms of the energetics of the customary Lauritzen-Hoffman 'flat-surface' nucleation model. For the correct-sigma-s, the theory accurately predicts the aspect ratio and curvature as a function of crystallization temperature for each solvent. The treatment provides insights relating to (1) the different melting points, fold surface energies, angles of tilt and fold surface regularities of the {1 1 0} and {2 0 0} sectors, (2) the prediction of an upper limit T(max) above which such crystals will not form, (3) the occurrence of a regime I --> II transition on the {1 1 0} growth front and its absence on the {2 0 0} front, and (4) the reason that both melt- and solution-crystallized PE exhibit a preference for b axis growth. The proposed treatment removes an objection to nucleation theory and, with appropriate modifications, is potentially useful in treating morphological problems in other systems.