Dimension of heterogeneous network architecture formed in emulsion cross-linking copolymerization

The mean-square radius of gyration Rg(2) and the graph diameter D of highly heterogeneous network polymers formed in emulsion vinyl/divinyl copolymerization are investigated to find a linear relationship, Rg(2) = a D. The proportionality coefficient, a, is dominated by the cycle (circuit) rank, k(c), or the number of intramolecular cross-links. The magnitude of a is slightly larger than that for the random cross-linked network polymers, but the functional form of a (k(c)) is simply proportional to that for the random networks proposed earlier. This relationship makes it possible to determine Rg(2) based on D and k(c), enabling quick estimation of Rg(2) for large network polymers. It is found that the contraction factor g of the present heterogeneous network polymer is larger than that for the homogeneous networks formed through random cross-linking of polymer chains. The ratio of these two contraction factors is kept constant, irrespective of the magnitude of k(c).