Branching in polymers. I. Network defects

The problem of inactive chains in a polymer network is considered in this paper. It is shown that the previous treatment is only approximate. More rigorous treatments are derived here for random crosslinking of polymers which are initially either geometrically distributed in molecular weight or are monodisperse. The new treatments give values for active chain concentrations which are lower than those calculated by the approximate method. At high crosslink densities and for chains of molecular high weight initial, all methods yield approximately identical values.