The final elucidation of the NMP mechanism was obtained by the groups of Fischer [15] and Fukuda [250], who theoretically explained the minimization of the irreversible terminations by the persistent radical effect (PRE, see below for details). Previously, Johnson et al. highlighted this phenomenon using theoretical modelings but without performing a full rationalization [251].
The PRE can be qualitatively explained as follows (Fig. 26). We consider a compound (RY) that decomposes into a transient (Rradical dot) and a persistent radical (Yradical dot), with the initial concentration of radicals equals zero. At the beginning of the reaction, the concentrations of both radical species increase linearly with time, as governed by the decomposition rate coefficient kd. This period (the pre-equilibrium regime) lasts until the total radical concentration becomes large enough so that the radical species could react by bimolecular reaction (either self-termination of Rradical dot or recombination between Rradical dot and Yradical dot). The irreversible self-termination leads to a decrease of the concentration of Rradical dot and consequently to a slow accumulation of the persistent species Yradical dot (which cannot self-terminate). Therefore, the recombination of transient and persistent radicals becomes more and more favored compared to the self-reaction, which inhibits itself as it proceeds, although it never completely ceases. This is the intermediate regime. Then, after a long reaction time, the concentration of transient radicals drops to zero and the persistent radical reaches its highest concentration, which corresponds to the initial RY concentration.