CYCLES FRUSTRATING FRACTAL FORMATION IN AN AB(2) STEP-GROWTH POLYMERIZATION

The step growth of a flexible AB(2) monomer, normally considered to pr oduce dendrimers or fractal molecules, as they are themselves self-sim ilar to their branches, is frustrated by the formation of one cycle wi thin each molecule, according to a Monte Carlo lattice study of the ev olution of the topological trees that are embedded in three-dimensiona l space; the number of cycles of m residues is well fitted by the rela tionship R-m = K(0)p(a)(m) m(-e), p(a) being the extent of reaction of the A groups; at the end of a polymerization of N-0 monomers the tota l number of cycles, and of molecules, is given by the product of K-0 a nd the Euler-Riemann function xi(e) so there is a simple relationship between these quantities and the mean number average degree of polymer ization at infinite time: N-0 = K-0 < x >(n,infinity) xi(e).