Characterization of Polymer Structures on Helical Point Nets

Abstract

The extension of a polymer chain through many contiguous unit cells in a crystallite requires a discrete relationship between the crystallographic translation identity period and the structural identity period within the chain. This relationship can be uniquely expressed by describing the chain structure in terms of a helical point net. Helical point nets can be defined in terms of standard screw axis nomenclature, using the translation-rotation operators pq. Integral values of the p's and q's produce all possible nets and their enantiomorphs. The net points thus defined have the property of identity through the operators pq. The chain structures of polymers in the crystalline state can thus be defined simply in terms of the structure about one net point. Introduction of the restrictions of bond distances and angles limits the number of possible nets for a given translation identity period. One-atom and two-atom structures are considered in detail, and the extension to multiatom structures is indicated.