Step-growth polymerizing systems of general type “AfiBgi”:calculating the radius of gyration and the g-curve using generating functions and recurrences

Step-growth polymerized systems of general type “AfiBgi” are considered. One or more of the monomer species carries at least three reactive groups and thus can act as a branching point in a polymeric molecule. An algorithmic method is presented to calculate the topology-averaged square radius of gyration, R 2[s], of the molecules in the class of s-mers. The degree of polymerization, s, may run through its full range. In addition to R 2[s], the shrinking factor, g[s], is calculated. The method uses integer arithmetic, generating functions, and computer algebra. (Figure presented.).