Simultaneous main-chain scission and crosslinking

The mathematical theory developed by Charlesby [2] only concerns polymers with initial random distribution. Degradation and crosslinking are considered to occur consecutively rather than simultaneously. 

After absorption of a dose, r, if degradation only occurs, the mean degrees of polymerisation u and u2 are 

Crosslinking of the degraded polymer of degree of polymerization u and u2 is then considered to occur. A new crosslinking coefficient 5, is defined as 

The relation between 5 and 5 can be easily obtained from eqns. (20) and (21) as 

The experimental gel point, rge, is obtained from eqn. (23) when u2 tends to infinity, giving 

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The soluble fraction (s) of a polymer, with an initial random molecular mass distribution (Pw)o/(F )o, undergoing simultaneous main chain scission and crosslinking, is related to the intensity of radiation absorbed (/J by the equation [336, 431, 1769] ... 

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