Tetrafunctional chain coupling of polymers is an important process for introducing long-chain branching to modify flow behavior and for forming cross-linked networks. Reactor modeling for polymers branched beyond the gel point is a difficult problem because of the divergence of the moments of the MWD to infinity. A newly developed technique, numerical fractionation, based on the method of moments is applied to modeling chain coupling (cross-linking) kinetics in continuous flow stirred tank (CFST) and batch reactors. The resulting model is applicable from 0 to 100% gelation and predicts the amount of sol fraction and its molecular weight and MWD as a function of operating conditions. This technique is easier to apply to reactor simulation than others for calculating properties of polymers in the post-gel region. An examination of CFSR dynamics during reactor startup indicates a wide range of behavior depending on the critical residence time for gel formation. At residence times close to the critical, long times are needed to reach steady state, but at residence times much greater than the critical, the reactor can reach steady state in less than three turnovers. For both the batch and CFST reactors, polymer properties are determined by only two parameters: initial polymer MWD and reduced reaction time or reduced residence time. Consequently, at a given sol fraction, the molecular weight and MWD of the sol polymer are fixed. Narrowing the initial polymer MWD increases the amount of gel present at a given reaction time. Considerable differences are shown in the rate of the chain coupling reaction and properties of the sol phase between the two reactor types.
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