A comprehensive model for the calculation of molecular weight–long-chain branching distribution in free-radical polymerizations

Abstract

A new method for the calculation of the joint molecular weight–long-chain branching distribution in free-radical highly branched polymerizations is developed. The method is based on the numerical fractionation of the total polymer population into a series of ‘classes’, each one representing a population of polymer chains with the same long chain branching content (e.g., linear chains, chains with one long–chain branch, etc.). Accordingly, dynamic molar balance equations are derived for the leading moments of the molecular weight distribution (MWD) of each polymer class as well as for the moments of the overall ‘live’ and ‘dead’ polymer chain distributions. A two-parameter Wesslau distribution is employed to reconstruct the MWD of each class in terms of its leading moments. The overall distribution is then calculated by the weighted sum of all class distributions. Simulation results are presented for a high-pressure ethylene continuous stirred tank reactor (CSTR) and a series of two CSTRs with or without a recycle stream. The effect of process parameters (e.g. temperature, chain transfer agent concentration and reactor residence time) on the MWD of low-density polyethylene (LDPE) is analyzed. It is shown that under typical operating conditions the calculated MWD exhibits a bimodal character in agreement with experimental measurements on MWD of LDPE produced in industrial autoclaves.