Unperturbed Chain Dimensions of Polymeric Chains

Methods are given for the calculation of polymer chain dimensions unperturbed by excluded volume effects but dependent on restricted rotation around the chain bonds as a result of interactions between substituents on neighboring chain atoms. The matrix methods used by most previous investigators are valid only for cases where the rotations, or pairs of neighboring rotations, are noninteracting. The methods recently developed by Lifson to account for interactions between any two consecutive rotations in chains of the type (CR2)i are extended to chains of the type (CH2–CR2)i and isotactic chains of the type (CH2–CHR)i.As an illustration the chain dimensions of polyisobutylene are calculated by using parameters from x‐ray data in the crystalline state and results from stress‐temperature measurements on amorphous networks. Reasonable agreement is obtained with experimental data on dilute solutions of polyisobutylene.