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A Monte Carlo (MC) simulation method based on the Gillespie algorithm isdeveloped for the polymerization of branched polyetherimides from two back-bonemonomers [4,4'-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], achain terminator [phthalic anhydride (PA)], and a branching agent[tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. This polymerization involves 4reactions that all can be reduced to a condensation reaction between an aminegroup and a carboxylic anhydride group. By comparing the MC simulation resultsto the predictions of the Flory-Stockmayer theory on the molecular weightdistribution, we show that the rates of the 4 reactions in the MC simulationsshould be set based on the concentrations of the functional groups on themonomers involved in each reaction. Using the MC simulations, we show that theFlory-Stockmayer theory predicts the molecular weight distribution well forsystems below the gel point that is set by the functionality of the branchingagent but starts to fail for systems around or above the gel point. However,for all the systems the MC simulations can be used to reliably predict themolecular weight distribution. Even for a macroscopic system, a convergingdistribution can be quickly obtained through the MC simulations on a system ofonly a few hundred to a few thousand monomers but with the same molar ratios ofmonomers as in the macroscopic system.

Polymerization of Branched Polyetherimides: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory