Nonlinear Polymerization in an HCSTR, the Age Distribution and the Inhomogeneous Distribution of Branch Points

ABSTRACT The effect of the broadening of the molecular weight distribution (MWD) in a continuous operation in an HCSTR accompanied by an increased tendency to form gel caused by branching and crosslinking reactions is well known. A more detailed understanding of this phenomenon can be gained from the age distribution. This new concept, introduced here, is a generalization of the residence time distribution and describes the age of individual monomeric units of a polymer chain, which is the time elapsed since the unit entered the reactor as a monomer. It is shown that in living and step growth polymerization the branching density depends on the length of the polymer chain. In living polymerization, it is a linear function of chain length whereas in step growth polymerization it follows a square root function. This leads to high molecular weight tailing and the formation of very inhomogeneous polymer molecules or networks. The onset of gelation is much earlier than in case of an uniform distribution of branch points. The concept of the age distribution is very general and applies to general reaction systems. In a reactor with recycles, the time a chemical species spends in the reactor depends on the reaction path.