Topological analysis of long-chain branching patterns in polyolefins

Patterns in molecular topology and complexity for long-chain branching are quantitatively described. The Wiener number, the topological complexity index, and a new index of 3-starness are used to quantify polymer structure. General formulas for these indices were derived for the cases of 3-arm star, H-shaped, and B-arm comb polymers. The factors affecting complexity in monodisperse polymer systems are ranked as follows: number of arms >> arm length > arm central position approximately equal to arm clustering > total molecular weight approximately equal to backbone molecular weight. Topological indices change rapidly and then plateau as the molecular weight of branches on a polyolefin backbone increases from 0 to 5 kD. Complexity calculations relate 2-arm or 3-arm comb structures to the corresponding 3-arm stars of equivalent complexity but much higher molecular weight. In a subsequent paper, we report the application of topological analysis for developing structure/property relationships for monodisperse polymers. While the focus of the present work is on the description of monodisperse, well-defined architectures, the methods may be extended to the description of polydisperse systems.