Three statistical mechanical arguments that favour chain folding in polymer systems of lamellar morphology

Abstract

Three arguments are given that imply substantial chain folding in crystalline-amorphous polymer systems of lamellar morphology. These arguments assume random coil behaviour in the amorphous region. (1) The random walk character of the polymer chain portions comprizing the amorphous regions topologically constrains the number of crystalline stems that connect covalently with the amorphous regions to be small. Quantitative estimates are made and lower bounds on the amount of chain folding are given. Estimates of (2) the tightness of loops and (3) the average spatial separation between consecutive crystal stems (along a given chain) are made. The results favour substantial amounts of adjacent and near-adjacent re-entry. Existing experimental measurements on diblock copolymers consisting of crystallizable and non-crystallizable blocks provide a measure of the random walk character of the chains in the amorphous region. It is argued that such systems form lamellar structures with large amounts of chain folding in the crystalline regions as a condition of thermodynamic equilibrium.