Combinatorial calculations of topological defects in tetrafunctional polymer networks

The structure of real polymer networks admits many kinds of topological defects related to the way in which polymer chains are connected to crosslinks. The fractions of crosslink types have been derived from combinatorial considerations concerning the probabilities of various combinations of structural elements of crosslinks. 34 fractions of different crosslinks, possible in tetrafunctional systems, have been obtained as explicit functions of concentrations of seven structural elements — free-end chains, single-, double-, triple-, and quadruple-connected chains, loops, and unsaturated (void) functionalities. It was shown that different distributions (and different properties) result from end-to-end linking of precursor chains vs. vulcanization of long chains by bridging along their contours.