On the statistics of Gaussian two and three-dimensional networks: Fluctuations of junctions and collapse driven by structure.

We investigate ideal Gaussian networks both analytically and with computer simulations using the Bond Fluctuation model with and without excluded volume interactions. The focus of this study is on fluctuations and the collapse of networks with different connectivity and dimensionality. We show that the size of a perfect square 2D network made from $n^2$ Gaussian chains with $N$ monomers each is $R_{g} \sim N^{1/2}log(n)$. Thus fluctuations in two-dimensional networks diverge logarithmically with the size of these films while fluctuations of three-dimensional networks $\sim N^{1/2}$ and do not increase with their size. We study the cross-over between two and three-dimensional networks by following the dependence of junction fluctuations on the thickness of films. The results of model systems are compared with more realistic networks in order to understand the effect of disorder on the properties of the network and fluctuations of network junctions.