Derivation of the distributions of long chain branching, molecular weight, seniority, and priority for polyolefins made with two metallocene catalysts

We obtained the molecular weight and long chain branching distribution for polyolefins made with a combination of two single-site metallocene catalysts in a CSTR. Long chain branches are assumed to be formed by the incorporation of chains formed with a double bond end (macromers) at the catalyst sites. In the case where one of the catalysts produces only linear chains, we obtain explicit expressions for both the bivariate molecular weight and branching distribution, and the overall molecular weight distribution. In the general case where both catalysts incorporate branches, we are unable to obtain an explicit expression, but we can define a recusive algorithm which rapidly gives exact results for these two distributions. We compare the distributions with results from a more conventional population balance on the same system. We also obtain recursive algorithms for the statistical distribution of the topological variables seniority and priority for this general case, illustrating how they change with the reactor variables.