On the (im)possibility of evaluating correct individual rate constants of chain propagationkp and chain terminationkt by combiningkp2/kt andkp/kt data for chain-length dependent termination

Abstract

On the basis of simulated data two ways of evaluating individual rate constants by combining kp2/kt and kp /kt (kp , kt = rate constants of chain propagation and termination, respectively) were checked considering the chain-length dependence of kt. The first way tried to make use of the fact that pseudostationary polymerization yields data for kp2/kt as well as for kp /kt referring to the very same experiment, in the second way kp2/kt (from steady state experiments) and kp/kt data referring to the same mean length of the terminating radical chains were compared. In the first case no meaningful data at all could be obtained because different averages of kt are operative in the expressions for kp /kt and kp2/kt. In spite of the comparatively small difference between these two averages (≈15% only) this makes the method collapse. The second way, which can be regarded as an intelligent modification of the “classical” method of determining individual rate constants, at least succeeded in reproducing the correct order of magnitude of the individual rate constants. However, although stationary and pseudostationary experiments independently could be shown to return the same kt for the same average chain-length of terminating radicals within extremely narrow limits no reasonable chain-length dependence of kt could be derived in this way. The reason is an extreme sensitivity of the pair of equations for kp/kt and kp2/kt towards small errors and inconsistencies which renders the method unsuccessful even for the high quality simulation data and most probably makes it even collapse for real data. This casts a characteristic light on the unsatisfactory situation with respect to individual rate constants determined in the classical way, regardless of a chain-length dependence of termination. As a consequence, all efforts of establishing the chain-length dependence of kt are recommended to avoid this way and should rather resort to methods based on inserting a directly determined kp into the equations characteristic of kp2/kt or kp/kt, properly considering the chain-length dependent character of kt.