Modeling of bulk copolymerization reactor using chain-length-dependent rate constants

A mathematical model is developed for a batch reactor in which binary free radical copolymerization occurs. The diffusion-controlled features of the propagation and termination reactions are taken into account by applying the free volume theory, whereas the chain-length-dependent termination rate constant is formulated by using the continuous probability function. Application of the pseudokinetic rate constant method, as well as the terminal model, reduces the complex rate expressions for the copolymerization system to those for the corresponding homopolymerization system. In addition, the moment equations of the living and dead polymer concentrations, as well as the equation for copolymer composition, are derived to compute the average molecular weight and the copolymer composition. The model is proven adequate when applied to the copolymerization system of styrene and acrylonitrile with AIBN(2,2′-azobisisobutyronitrile) initiator. The results of model prediction clearly show that even the propagation reaction is limited by the diffusion of monomers at higher conversion and that the azeotropic fraction of styrene is about 0.6. It is noticed that as the monomer conversion increases, the molecular weight distribution tends to become broader because the weight-average molecular weight increases at a faster rate than the number-average molecular weight.