Equilibrium Degrees of Crystallization Predicted for ``Single Pass'' and Folded Chain Crystallite Models

Abstract

The free energy change for the crystallization of a bulk polymer consists of two parts: the ``single crystal'' term exhibited by low molecular weight compounds, and that arising from the deformation produced in the intervening amorphous chains as crystallization proceeds. The latter term limits the degree of crystallinity which can be achieved in a polymeric material at a given temperature. Beginning with an initially unstretched, isotropic sample, the entropy change associated with the deformation of the amorphous chains is calculated for two models, in which the chain either passes through a crystallite once and departs, or folds back and forth within the crystallite several times before re-entering the amorphous region. The folded chain morphology imposes less strain upon the amorphous chains, and hence results in the development of higher degrees of crystallinity from the original isotropic melt. The folded chain model, in which the amorphous portions are represented by flexibly linked chains, gives good agreement with the observed equilibrium degrees of crystallinity, for high molecular weight fractions of polyethylene, over a considerable temperature range. An approximate treatment is also given for the molecular weight dependence of crystallinity at a fixed temperature.