Polymer crystallization: The bundle model

Polymer crystallization is assumed to be controlled by an equilibrium distribution of intramolecular clusters (“bundles”), insofar as it consists of their aggregation to the side surface of the crystallites. The average contour length of the loops within the bundles dictates the lamellar thickness. Each bundle contains at least three packed stems; unlike previous assumptions their length is considered to be variable and it is shown that their statistical weight *** like ((exp(-E/kBT)-exp(-E/kBT°)), where E is the (negative) packing energy and T° is the melting or dissolution temperature. Adopting two different models having opposite limitations in terms of the configurational enumeration of the bundles, the calculated thickness of polyethylene crystals at different temperatures is in reasonable agreement with observation. The average number of stems per bundle is of order 10 at moderate undercoolings, in rough agreement with neutron diffraction experiments on solution-grown crystals. The same model applied to finite chains permits a semiquantitative interpretation of chain segregation from the crystal phase, in terms of kinetic arguments.