Theory of Molecular Size Distribution and Gel Formation in Branched-Chain Polymers

The most probable distributions of molecular sizes are calculated for certain types of branched-chain polymers. The results represent an extension of the previous work of Flory, who showed that very large polymeric molecules appear suddenly at a critical extent of reaction, which is predicted to occur very nearly at the experimentally observed gel point. This transition from liquid to gel is shown to be analagous to the condensation of a saturated vapor. It is believed that the size distributions obtained herein will aid in a study of viscosity-molecular weight relationships in branched-chain polymers.