Bivariate chain length and long chain branching distribution for copolymerization of olefins and polyolefin chains containing terminal double-bonds

Polyolefins containing long chain branches can be synthesized using certain metallocene catalysts such as Dow Chemical's constrained geometry catalyst. These polyolefins combine the excellent mechanical properties of polymers with narrow molecular weight distribution with the easy processability of polymers containing long chain branches. A mathematical model for the chain length distribution for these novel polyolefins was derived from basic principles and an analytical solution for the chain length distributions of the populations containing different number of long chain branches per polymer molecule was obtained. The analytical solution agrees with the direct solution of the population balances and with a Monte-Carlo simulation model. It is also shown that this solution applies for copolymers using pseudo-kinetic rate constants and Stockmayer's bivariate distribution.