Contraction effects in ideal networks of flexible chains

The mean-square distances between various points of regular Gaussian networks are calculated using a new electrical analog and solving exactly a set of difference equations both in two and in three variables through an appropriate Fourier lattice transformation. The results show that the mean-square radius of gyration of the network is of the same order of magnitude as that of a single chain for networks having a three-dimensional connectivity, while it increases logarithmically with the total number of chains for networks having a two-dimensional connectivity.