A-PRIORI PREDICTION OF PROPAGATION RATE COEFFICIENTS IN FREE-RADICAL POLYMERIZATIONS - PROPAGATION OF ETHYLENE

A method is derived for calculating Arrhenius parameters for propagati on reactions in free-radical polymerizations from first principles. Ab initio molecular orbital calculations are carried out initially to de termine the geometries, vibrational frequencies, and energies of the r eactants and the transition state. Transition state theory then yields the Arrhenius parameters. The lowest frequencies are replaced by appr opriate (hindered or unhindered) internal rotors, to better model thes e modes in the calculation of frequency factors. It is found that a hi gh level of molecular orbital theory (e.g., QCISD-(T)6-311G*) is requ ired to produce reasonable activation energies, whereas satisfactory f requency factors can be obtained at a relatively simple level of theor y (e.g., HF/3-21G), because the frequency factor is largely determined by molecular geometries which can be reliably predicted at such a lev el. Obtaining reliable frequency factors for quite large systems is th us possible. The overall procedure is illustrated by calculations on t he propagation of ethylene, and the results are in accord with literat ure experimental data. Means are also derived for extending the result s from propagation of monomeric radicals to propagation of polymeric r adicals, without additional computational requirements. The method is expected to be generally applicable to those propagation reactions tha t-are not significantly influenced by the presence of solvent (i.e., r elatively nonpolar monomers in nonpolar solvents). The calculations sh ow that the magnitude of the frequency factor is largely governed by t he degree to which the internal rotations of the transition state are hindered. They also suggest that there can be a significant penultimat e unit effect in free-radical copolymerization. Furthermore, the calcu lations explain the rate-enhancing effect found upon deuteration of th e monomers and explain why the rate coefficient for the first propagat ion step is larger than that for the long-chain propagation step.