The kth radius of gyration for a polycondensation reaction with identical structural units AaBb

For a polycondensation reaction with identical structural units A_aB_b (i.e. each unit has a functional groups of type A and b of type B) the kth radius of gyration $ begin{array}{*{20}c} {leftlangle {R^2 } rightrangle _k = sumlimits_n {n^k cdot leftlangle {R_n^2 } rightrangle P_n } } & {({rm sum over all }n{rm - mers; see Eqs}{rm . (11) and (17))}{rm }} end{array} $ is investigated. By means of a differential method, a recursion formula that holds true for both the pre-gel and the post-gel state is obtained for the evaluation of the kth radius.