Modeling of RAFT Polymerization using Probability Generating Functions. Detailed Prediction of Full Molecular Weight Distributions and Sensitivity Analysis

A mathematical model of RAFT polymerization processes is presented capable of predicting the full molecular weight distribution (MWD) through the use of probability generating functions (pgf). The bivariate distribution of the intermediate RAFT species is calculated. The model is able to work with the three kinetic mechanisms currently under discussion for explaining the observed behavior of this type of polymerization. For comparison purposes, the population balances are also solved by direct integration of the resulting equations. The results show that the pgf technique allows obtaining accurate solutions with very small computational times for systems of any average molecular weight. Spurious oscillations observed in the high molecular weight tail of the MWD can be easily disregarded. A sensitivity analysis over several of the kinetic constants is also performed, showing the effects of changing their values over several orders of magnitude. This analysis aims to showcase the enormous potential of the pgf technique for modeling and optimization of complex polymerization kinetics.