A priori prediction of propagation rate coefficients in free-radical polymerizations: Propagation of ethylene

A method is derived for calculating Arrhenius parameters for propagation reactions in free-radical polymerizations from first principles. Ab initio molecular orbital calculations are carried out initially to determine the geometries, vibrational frequencies, and energies of the reactants and the transition state. Transition state theory then yields the Arrhenius parameters. The lowest frequencies are replaced by appropriate (hindered or unhindered) internal rotors, to better model these modes in the calculation of frequency factors. It is found that a high level of molecular orbital theory (e.g., QCISD-(T)6-311G**) is required to produce reasonable activation energies, whereas satisfactory frequency factors can be obtained at a relatively simple level of theory (e.g., HF/3-21G), because the frequency factor is largely determined by molecular geometries which can be reliably predicted at such a level. Obtaining reliable frequency factors for quite large systems is thus possible. The overall procedure is illustrated by calculations on the propagation of ethylene, and the results are in accord with literature experimental data. Means are also derived for extending the results from propagation of monomeric radicals to propagation of polymeric radicals, without additional computational requirements. The method is expected to be generally applicable to those propagation reactions that-are not significantly influenced by the presence of solvent (i.e., relatively nonpolar monomers in nonpolar solvents). The calculations show that the magnitude of the frequency factor is largely governed by the degree to which the internal rotations of the transition state are hindered. They also suggest that there can be a significant penultimate unit effect in free-radical copolymerization. Furthermore, the calculations explain the rate-enhancing effect found upon deuteration of the monomers and explain why the rate coefficient for the first propagation step is larger than that for the long-chain propagation step.