Estimation of critical points of branched polymers

The authors' theory of the gel point is applied to the gelation experiments in nonstoichiometric systems of Gordon and Scantlebury. Agreement between the theory and the observations is found to be excellent in every region examined, confirming the mathematical soundness of the theory. The theory is transposed to the site-bond problem. With the aid of a high dimension expansion of the ring distribution function, we derive an analytic expression for the bond percolation threshold. The resultant equation is in good conformity with the site-bond percolation simulation of Stauffer. The present theory is scrutinized over a wide range of dimensions for pure bond percolation; the result shows that the theoretical line abruptly merges with the observed points at d=8, consistent with the Lubensky-Isaacson excluded volume theory which predicts the critical dimension d(c)=8 for sol clusters on lattices.