Multiradicals

Discovery of the hydrated electron and pulse-radiolytic measurement of specific rates (giving generally different values for different reactions) necessitated consideration of multiradical diffusion models, for which the pioneering efforts were made by Kuppermann (1967) and by Schwarz (1969). In Kuppermann s model, there are seven reactive species. The four primary radicals are eh, H, H30+, and OH. Two secondary species, OH- and H202, are products of primary reactions while these themselves undergo various secondary reactions. The seventh species, the O atom was included for material balance as suggested by Allen (1964). However, since its initial yield is taken to be only 4% of the ionization yield, its involvement is not evident in the calculation. 

Schwarz s model is a multiradical extension of the Ganguly-Magee model with some additional improvements, to be described later. Schwarz assumes that initially—that is, 10 11 s after the act of energy deposition in water—there appear five species, namely eh, H, OH, H30+, and H2. Their initial yields, indicated by superscript zero, are related by charge conservation and material balance. Thus, there are three independent initial yields, taken to be those of eh, H, and Hr The initial yield of H2 is identified with the unscavengable molecular hydrogen yield. No mechanism of its production is speculated, except that it is not formed by radical recombination. For the gaussian distribution of the radicals, two initial... 

The master equation methodology can be readily generalized to multiradical spurs, but it is not easy to include the reactions of reactive products (Green et al, 1989 Pimblott and Green, 1995). This approach is therefore limited to spur reactions where the reaction scheme is relatively simple. 

Bushby, R.J. and Gooding, D. (1998). Higher-spin pi multiradical sites in doped po-lyarylamine polymers. J. Chem. Soc. Perkin 2, 1069-1075... 

The greater thermal stability (and lower solubility) of these multiradicals (compared with monoradicals) has allowed several derivatives to be isolated in the solid state, e.g., 863-, 8T2, and 892-. However, of these only 872 has been fully characterized by an X-ray crystal structure determination. Its structure (Fig. 26) is unique and shows a regular polymeric array of radicals held together in a head-to-tail fashion through spin-paired out-of-plane S. . . S interactions, and these are accompanied by other inplane S. . . N interactions [91JCS(D)1099]. 

Zhu and Hamielec [94] studied the FRC of vinyl monomers with chain transfer to polymer and the copolymerization of vinyl/divinyl monomers using a multiradical approach. They used the method of moments and focused on the pre-gelation period. They concluded that... 

Tab. 9.7. Reaction equations for radical polymerization of ethylene 2D chain length-multiradical approach.

We conclude, however, that the classes approach in this case produces useful information on the multiradical issue, even when employing a limited number of classes. 

Fig. 9.7. Radical polymerization with transfer to polymer multiradical problem. CLDs of chains with 0... 4 radical sites per chain. Comparison of two- and five-classes model. Accounting for multiradicals leads to lower...

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