Peroxide modification of polyethylene. Prediction of molecular weight distributions by probability generating functions

We present a mathematical model able to describe the complete molecular weight distributions of polyethylene during reactive modification by organic peroxides. The method is applicable to batch processes, such as modification in a press or a plug-flow extruder, and in its present form is valid up to the gel point. We apply probability generating function definitions to the mass balances of radical and polymer species in the reacting medium. Three different probability generating functions are applied, each one directly applicable either to the number, weight or chromatographic distributions. These generating functions are numerically inverted to obtain the corresponding calculated molecular weight distribution. Two different inversion methods are used, and their relative performances analyzed. Predictions are compared with qualitative experimental data obtained in a press. Model predictions on molecular weight distributions are in agreement with experimental trends.