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

The mean-square radius of gyration Rg² and the graph diameter D of highly heterogeneous network polymers formed in emulsion vinyl/divinyl copolymerization are investigated to find a linear relationship, Rg² = 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 Rg² based on D and k_c, enabling quick estimation of Rg² 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.