The quenched instationary polymerization system, 1. Derivation of the radical and polymer chain length distributions for the case of δ-pulse like initiation

Abstract

Full Paper: A new instationary polymerization system is presented including, as an essential element, the complete deactivation of all active radicals by reaction with an inhibitor at a certain time after chain initiation. The complete kinetic scheme, the set of differential equations, as well as the analytical solutions are presented. A proof is presented that the reaction with the inhibitor during the quench period dominates any other possible reaction such as propagation and bimolecular termination. As a result, the radical spectrum present at the beginning of the quench period is converted (almost) completely unchanged and instantaneously into a polymer chain length distribution. The quenched radical spectrum appears as a single additional peak in the experimentally observable total chain length distribution. In the case of δ-pulse initiation the analytical solutions of the differential equations reduce to a simple poisson distribution for the radical concentrations as a function of time. Theoretical expressions for the maximum and the points of inflections (low and high molecular weight side) were derived and their applicability for the direct determination of k p was tested. All of them turned out to be equally well suited for this purpose.