Diffusion and gelation in polyadditions. III. Statistical‐kinetic theory of the trommsdorf rate acceleration

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Abstract
In a polyfunctional polyaddition system, such as methyl methacrylate/ethylene dimethacrylate (MMA/EDMA), the first elementary reaction step to become affected by diffusion control is the termination step. This is true also in absence of EDMA (pure MMA polymerization), but in the presence of EDMA this diffusion control occurs at much lower conversions. It becomes manifest as the usual Trommsdorf effect (over‐all rate acceleration), and begins after the gel point. A general statistical kinetic theory is developed for the Trommsdorf effect. Surprisingly, the theory is more readily applied to crosslinked systems such as MMA/EDMA than to linear systems such as MMA alone. This happens because crosslinking causes useful discontinuities both in the viscosity/time curve and in the size distribution curve of the radicals, whose diffusion behavior determines the Trommsdorf effect. The theory divides these radicals by a size barrier into small radicals which freely diffuse and large radicals which are immobilized. A successful termination step is taken to require at least one mobile radical. To assume that all the radicals are mobile, or that all are immobile, is neither sound in theory nor successful in practice. Theory leads to the conclusion that uncrosslinked radicals should be mobile, while those bearing crosslinks are immobilized beyond the gel point. This conclusion determines the rate curve, and no reasonable amendment will make any difference to the theoretical curve. The curve lends itself to reduction to dimensionless form. Experimental plots are successfully brought to mutual coincidence by this reduction, but not into quantitative coincidence with the theoretical curve. This is attributed to incomplete efficacy of the size barrier, in that even pairs of nominally frozen radicals will occasionally succeed in mutual termination. The theoretical rate curve lies closer to experimental results if radical combination rather than disproportionation is the assumed termination mechanism. The rate theory furnishes an improved explanation of kinks, previously observed in rate curves going through a gel point. The success of the treatment confirms the classical network theory of gelation, and the diffusion control theory of the Trommsdorf effect.