Site-Bond Correlated-Percolation Problem: A Statistical Mechanical Model of Polymer Gelation

Abstract

A new model for polymer gelation is presented that predicts new effects that can not be derived from the conventional theory of Flory and Stockmayer. An exact solution is obtained for the Bethe lattice, and is related to recent experimental results of Tanaka. Under certain conditions, the gelation curve terminates at the consolute point; at this point, both connectivity and concentration fluctuations are critical, just as in the random magnet at the percolation threshold.