Calculation of molecular weight distributions in free-radical polymerization with chain branching

The molecular weight distribution (MWD) of a branched polymer has been calculated by using approximate techniques based on the partition of the overall polymer chain population into classes according to molecular dimension or the number of branches. These techniques are especially useful in segregated systems, such as emulsion polymerization, where rigorous methods are too onerous. A comparison with the correct MWD obtained through a detailed solution method has shown that, of these techniques, 'numerical fractionation' predicts in some cases a marked shoulder at the high molecular weights that does not exist in the true MWD. On the other hand, besides offering an intelligent description of gel formation, 'numerical fractionation' permits to calculate quickly the correct average molecular weights and constitutes a significant improvement compared to the classical method of moments when a complete MWD is required. In the latter case, however, the most accurate approximate technique has been found to be based on the subdivision of the polymer chains according to the number of branches. This technique, though more time-consuming than 'numerical fractionation', provides also the branching distribution along with the MWD. A quick method is suggested to estimate the minimum number of branches required by this technique to calculate the correct complete MWD.