Neighbor Interactions and Internal Rotations in Polymer Molecules. I. Stereospecific Structure and Average Dimensions

Abstract

The skeletal bonds of vinylic polymer molecules are classified as (+) bonds and (—) bonds according to the arrangement of the side groups relative to the bonds. The detailed structure of isotactic and syndiotactic polymers is characterized by the different regularities of arrangement of these two bond types along the molecular chain. Symmetry properties of (+) and (—) bonds, and of (+) (+), (—) (—), and (—) (+) bond pairs, are discussed. These lead to relations between the average values of functions of the internal-rotation angles of the various bond-pairs. The end-to-end distance of isotactic and syndiotactic molecules is expressed in terms of bond lengths, bond angles, and internal rotation angles of the skeletal bonds, using methods of matrix algebra. The mean-square end-to-end distance 〈h2〉 of these molecules is determined by certain averages of trigonometric functions of the internal rotation angles enclosed between neighboring skeletal bond pairs. The averages depend on the energy of interaction of neighboring side groups as well as on the internal interactions within the skeletal bonds, and are different in the isotactic and syndiotactic molecules.