Study on the Propagation Step in Radical Polymerization by the Restricted-type Frontier MO Theory

Abstract

As for the activation energy, E_p^≠, of the propagation step in radical polymerization, Eq.1 was deduced,
where, A and B are constant, andE_SOMO and E_LUMO are eigenvalues of SOMO (radical) and LUMO (monomer), respectively. The reason can be explained from Figs.1, 2 and 3 (Text). In order to derive Eq.1 theoretically, the following discussion was progressed.
According to Nagase et al. the perturbation formura for the addition reaction of a radical Ciwith a monomer CH2=CH-R is expressed by Fig.4 (Text). The first perturbation occurs between SOMO and HOMO (the perturbation energy is ΔE₁). And the second perturbation occurs between the newly generated SOMO and LUMO (the perturba tion energy is ΔE₂). The authors pointed out that in the first perturbation the electron flows from the monomer to the radical, but in the second perturbation the electron flows inversely from the radical to the monomer.
It is considered that the electro n transfer is one of the necessary conditions for the reaction. And the electron transfer is estimated to be proportional to the largeness of (ΔE₁-ΔE₂).
Thus, Eq.10 was proposed.
E_p^≠=C-γ(ΔE₁-ΔE₂) (10)
In this equation, C and γ are constant and ΔE₁ and ΔE₂ can be calculated by Eqs.6and 7 in the text.ΔE₁ is almost constant at 1.9±0.4 eV. Accordingly, Eq.10 can be converted to Eq.3 through Eq.11, in which ΔE₁ was neglected by its small value compaired with Esomo.