Comments on “Diffusion of Free Radicals in Solution. TEMPO, Diphenylpicrylhydrazyl, and Nitrosodisulfonate”

Donkers and Leaist reported the diffusion constants of some stable free radicals (Drad) by the Tayler dispersion (TD) method.1 At the same time, D of carbonyl, quinones, and azaromatic compounds were measured and compared with our data determined from the transient grating (TG) method.2-5 They found that Drad is similar to the nonradical molecules, and D of several stable (parent) molecules (Dpar) in some solvents seriously differ from those determined by the TG method. Although they have stated that “Direct comparison of the two sets of results may not be entirely appropriate”, the authors appear to question the slow diffusion of transient free radicals in their paper. In this comment, we point out that D of many stable free radicals have already been published, which showed that D of the radicals are close to D of the analogous closedshell molecules, and discussed in terms of the chemical stability.6 We also examine sources of the discrepancy between D determined by the TG and TD methods and emphasize that the transient (unstable) radicals actually diffuse slower than the stable molecules of similar sizes and shapes. To begin with, sources of the discrepancy between the two methods are examined. Compared with the rather simple and stable setup of the TD method, D from the TG method have to be determined by taking account of several factors, and the accuracy is not generally as good as that from the TD method, although the TG method has a unique potential for transient species. There are two possible sources of the error in the TG measurement. First, we admit that the fitting of the doubleexponential function leads to some uncertainties. In particular, since the time profile due to the parent molecule is superimposed on the decay of the radical signal, the error in Dpar is more serious than Drad. In Figure 1, we plot previously reported Dpar and Drad together with Dpar determined by the TD method against r-1 (r ) radius of the molecule) with statistical error bars. Considering the different method and experimental conditions for TG and TD, we think that most of Dpar from the TG method agree reasonably with those from the TD method within the error range of Dpar. Some serious disagreements are found in pyrazine (52%), xanthone (32%), and quinoline (38%). In these cases, we think that relatively small contribution of the parent molecules in the TG signal produces larger errors. In spite of these errors in Dpar, Drad are more accurate because the signals due to the radicals are longer-lived without any contribution from the parent molecules. Indeed, even if we fix Dpar to the values reported by Donkers and Leaist in the double-exponential fitting process (adjustable parameters are the relative intensity and Drad), the differences in Drad are not so large (Table 1). Second, Dpar of benzophenone (BP) in nonpolar solvents3 were not accurate enough for comparison with other data in pure solvents because the samples contained hydrogen donors, such as dimethylaniline, triethylamine, and 1,4-cyclohexadiene. Recently, we noticed that these donors produced additional TG signals, and Dpar were less accurate. We also found that, instead of adding the hydrogen donors, the species grating signal can be observed by a slight increase of the excitation laser power and sensitivity even in some nonpolar solvents. We carried out D measurement of BP in various solvents, and Dpar and Drad are plotted against η-1 (η ) viscosity) in Figure 2. Dpar agree with the values calculated from an equation proposed by Evans Figure 1. Molecular size dependence of Dpar (open circles) and Drad (squares) in 2-propanol with statistical error bars. Dpar determined from the TD method are presented by closed circles. The broken line is D calculated from the equation proposed by Evans et al.7 The solid line is D calculated from the Stokes-Einstein equation.