Polyradical distribution in free radical crosslinking of polymer chains

The full molecular weight distribution of the polymer molecules containing i radical center are derived for the random crosslinking reaction of the primary polymer molecules that conform to the Schulz-Zimm distribution. This equation provides straightforward understanding concerning the significance of the polyradicals. The amount of polyradicals in the pregelation period become significant only when the weight-average degree of polymerization of the whole system reaches the comparable size to 1/φ. This indicator is valid also for the free-radical crosslinking polymerization, although the definition of 1/φ must be changed from that for polymerization. The Flory-Stockmayer type theory is valid for the whole polymer distribution.