Population balance modeling of polymer branching and hyperbranching

Branched polymers have rheological and morphological properties that make them important subjects for investigation. We propose a chain polymerization model for branching kinetics that is not restricted to primary branching on the chain backbone, but incorporates branches on branches (hyperbranching). The proposed method involves multivariate distributions, a subject of considerable interest and activity in population balance modeling. For unsteady-state continuous-flow stirred reactors, the mathematical description is based on population balance equations for branch formation and growth by addition of chains of distributed molecular weight (MW). Computer algebra software facilitates the complex mathematical manipulations for the continuous MW and the discrete branch number. Key properties of branched macromolecules are presented, such as MW moments for various levels of branching, number of branches, and average MW of branches. A major conclusion is that hyperbranching presents distinctly different properties for unsteady batch and steady-state stirred flow reactors, whereas for primary branching, the results are similar.