Molecular vibrations and structure of high polymers. II. Helical parameters of infinite polymer chains as functions of bond lengths, bond angles, and internal rotation angles

Abstract Helical conformations of infinite polymer chains may be described by the helical parameters including ρ i (the distance of the i th atom from the helix axis), d ij (the translation along the axis), and θ ij (the angle of rotation about the axis on passing from the i th atom to the j th). For the polymer main chain (M) ∞ , (M 1 M 2 ) ∞ , (M 1 M 2 M 3 ) ∞ , (M 1 M 2 M 3 M 4 ) ∞ , (M 1 M 2 M 3 M 4 M 5 ) ∞ , (M 1 M 2 M 3 M 4 M 5 M 6 ) ∞ concise mathematical equations for the helical parameters are given in terms of the internal coordinates, such as the bond lengths, the bond angles, and the internal rotation angles. These equations are useful in calculating the internal coordinates and in selecting likely structure models from the helical parameters experimentally determined. The internal coordinates and helical parameters of polyethylene, polytetrafluoroethylene, sulfur, selenium, tellurium, isotactic polypropylene, poly‐4‐methyl‐1‐pentene, poly‐ m ‐methylstyrene, poly‐o‐methylstyrene, polyoxymethylene, polyisobutylene, polypeptides (α helix, parallel‐chain, or antiparallel‐chain extended form), polyglycine II, polyethylene glycol, and syndiotactic polypropylene were calculated and were used for discussing the structure of these helical polymers.