Topological analysis and intramolecular cyclic feature evaluation of polymers derived from A_m + B_n step-growth polymerization

In this contribution, we investigated the evaluation strategy for intramolecular cyclic features of polymers derived from A_m + B_n (m ≥ 2 and n ≥ 2) step-growth polymerization from a topological analysis perspective. The general quantitative relationship between the structural units and the cyclic structures was presented regardless of the terminal groups of polymers. Further, two strategies for evaluating cyclic features were developed. First, the general expression of the average number of cyclic structures per macromolecule (ANC) for polymers derived from the A_m + B_n route was obtained, which could be easily determined by NMR and SEC analytics. The contents of cyclic structures of polymers from step-growth polymerization of monomer pairs were measured, especially for the polymers with different terminal groups. Second, a new parameter of the cyclic index (CI) was defined as the ratio of the number of terminal units to the number of dendritic units in order to determine the extent of intramolecular cyclization in polymers derived from the representative A₂ + B₃ route. CI < 1 refers to the intramolecular cyclic structures existing in polymers, and a lower CI value indicates a higher degree of intramolecular cyclization. The CI value can be determined using quantitative NMR spectra of polymers, thereby allowing the easy evaluation of their cyclic features. With the validation of the model polymer of polycarbosilanes from the A₂ + B₃ route, the ANC and CI were verified to effectively evaluate their intramolecular cyclic features.