Proposed solution for the Flory-Charlesby equation for crosslinked polymers and application for 1,2-polybutadiene crosslinked with AIBN and aryl diazide

The derivation and properties of a tractable function that approximates well the solution of the Flory-Charlesby equation for crosslinked polymers with logarithmic normal primary molecular size distribution is presented. This function gives the possibility to determine the crosslinking density, ρ, from measurements of insoluble fraction, what is the only quantitative method that can be applied for postsynthesis crosslinked polymers. Applications to 1,2-polybutadiene crosslinked with AIBN and 2,6-bis(4-azidobenzylidene)-4-methylcyclohexanone by heating allowed to obtain information about the gel point as well as about the crosslinking yield and mechanism. In addition, it was found that the temperature where the damping factor in DMA curves is maximum increases with ρ following a second order dependence.