Published: June 02, 2011
r 2011 American Chemical Society 7858 dx.doi.org/10.1021/jp111064q | J. Phys. Chem. A 2011, 115, 7858–7860
COMMENT
pubs.acs.org/JPCA
Comment on “Exothermic Rate Restrictions in Long-RangePhotoinduced Charge Separations”Gonzalo Angulo,† Arnulf Rosspeintner,‡ and Eric Vauthey*,‡
†Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland, and ‡Physical Chemistry Department,Sciences II University of Geneva, Geneva 1211, Switzerland
Gomes et al. have recently reported in this journal on theirexperimental observation of exothermic rate restrictions
(i.e., Marcus inverted region behavior) in long-range photo-induced charge separation in rigid matrices.1,2 Although theMarcus inverted region has been well established in chargerecombination reactions,3,4 its observation for photoinducedbimolecular charge separation in solution (rigid or not) hasso far not been reported unambiguously.5�15
The authors performed fluorescence quenching experimentsbetween immobile reactants in glycerol:methanol (9:1) mixturesat 255 K. This medium is supposed to be flexible enough to allowfor charge separation and accommodate the reaction productsthereof, whereas it efficiently hinders the mutual translationaldiffusion of the reactants. By doing so, the problem of diffusionlimited reactions is notably simplified, because only “static quench-ing” will be observed. The experimental methods used in thesestudies were steady-state and nanosecond time-resolved (bymeans of time correlated single photon counting) fluorescencespectroscopy. The experimental results comprise the change offluorescence quantum yields and fluorescence time traces atdifferent quencher concentrations spanning a reasonable rangeof free energy for electron transfer with 8 fluorophore/quencherpairs. These data are analyzed using a model for remote electrontransfer with an exponential distance dependence (eq 3 in ref 1),which eventually leads to a fluorescence intensity decay (eq 4 in ref 1)depending on only three parameters: r, the contact distance of thereactants, which the authors estimate usingConnolly surfaces; kET
0 ,the rate constant of electron transfer; and β, its distance decayfactor (kET
0 and β being obtained from the fits to the experiments).The data analysis consists basically of rescaling the experimentaltime traces with the fluorescence quantum yields (obtained fromthe steady-state experiment) and fitting the model to them.Eventually one identical β is obtained for all systems studied andthus the free energy dependence of electron transfer is completelycontained in the kET
0 values. The so observed “existence ofexothermic rate restrictions in photoinduced charge separationsin rigid media” is then extensively discussed by the authors.
Unfortunately, however, the authors omitted a self-consis-tency test on their results. If the time traces, I(t), and thus thekinetics, are well accounted for by the applied model and theobtained parameters, the steady-state quenching experiments(i.e., the change of the fluorescence quantum yield, φ, withquencher concentration, c) also ought to be well reproduced bythe time integrals of the model. We may briefly explain thisobvious and necessary self-consistency.
φ ¼Z ¥
0
Z ¥
0Iðλ;tÞ dλ dt ¼ C
Z ¥
0Iðλ¼λem;tÞ dt ð1Þ
Iðt¼0Þ ¼ 1 "c ð2Þ
φðc¼0ÞφðcÞ ¼
Z ¥
0Iðc¼0;tÞ dt
Z ¥
0Iðc;tÞ dt
¼ τZ ¥
0Iðc;tÞ dt
ð3Þ
The first equation merely states that the full kinetics is containedin the steady-state spectrum and that the quantum yield is, exceptfor some scaling factor, C, when only one specific emissionwavelength, λem, is observed instead of the entire emissionspectrum, given by the time integral of the fluorescence decay(as long as the effect of the dynamic Stokes shift is negligible).The second equation states that the initial population just afterexcitation is independent of the quencher concentration. This istrue if there is no ground-state complex formation or changes inthe properties of the medium that could affect the radiativeproperties of the fluorophore upon addition of the quencher.Finally, the third equation states that the ratio of steady-statefluorescence intensities at increasing quencher concentration, c,is equal to the ratio of the time integrals of the fluorescencedecays at the same concentrations. It can be easily seen that thelast equation is simply the outcome of the consequent applicationof the former two equations.
We tested the self-consistence of the used model and of theobtained parameters by simulating the steady-state results, givenin the Supporting Information of ref 2, with the electron transferparameters given in Table 1 of ref 2. To this end, the samereactivity model (eq 4 from ref 1) was applied to evaluate I(c,t)and eventually integrated numerically to give φ(c). The results ofthis attempt are shown in Figure 1. It can clearly be seen thatthere is a significant discrepancy between the experimental andsimulated data. Irrespective of the inherent reasons for thisdiscrepancy (inappropriateness of the scaling procedure, wrongmodel, wrong parameters), we are convinced that the appropri-ateness of the model and the adjoint parameter set ought to betested on, and should equally well describe, both data sets.16�19
As a consequence, the obtained parameters in general and theelectron transfer rate constant, kET
0 , in particular cannot becorrect. We thus conclude that the inverted region for this kindof reactions still remains unobserved.
Additionally, we make some further comments:• It should be noted that the Perrin equation is not correctlywritten in ref 1 and if used as such will lead to erroneous
Received: November 19, 2010Revised: April 5, 2011
7859 dx.doi.org/10.1021/jp111064q |J. Phys. Chem. A 2011, 115, 7858–7860
The Journal of Physical Chemistry A COMMENT
results. The proper equation is given as follows:20
φðc¼0ÞφðcÞ ¼ exp
43πRc
3c
� �ð4Þ
where Rc is the critical radius (in Å) and c is the quencherconcentration (in Å�3).
• The critical radii, which, incidentally, are different in the twomanuscripts do not reproduce the experimental Perrin plots.In addition, the way they have been extracted is unclear,especially considering that they do not reproduce thePerrin plots.
• In the Correction not only the time-resolved data but also allsteady-state data are not the same as the original ones. Thisfact was neither explained nor pointed out in the Correction.
’AUTHOR INFORMATION
Corresponding Author*E-mail: [email protected]. Phone: þ41 22 379 65 37. Fax:þ41 22 379 65 18.
’REFERENCES
(1) Gomes, P. J. S.; Serpa, C.; Nunes, R. M. D.; Arnaut, L. G.;Formosinho, S. J. Exothermic Rate Restrictions in Long-Range Photo-induced Charge Separations in Rigid Media. J. Phys. Chem. A 2010, 114,2778–2787.
(2) Gomes, P. J. S.; Serpa, C.; Nunes, R. M. D.; Arnaut, L. G.;Formosinho, S. J. Exothermic Rate Restrictions in Long-Range Photo-induced Charge Separations. J. Phys. Chem. A 2010, 114, 10759–10760(Addition/Correction).
Figure 1. Comparison between experimental (gray line and circles) and simulated (black lines) Perrin plots. The experimental data are calculated on thebasis of the linear fits to the Perrin plots shown in the Supporting Information of ref 2 while the simulated data have been calculated using eq 4 and itsnumeric integral with the parameters given in ref 2.
7860 dx.doi.org/10.1021/jp111064q |J. Phys. Chem. A 2011, 115, 7858–7860
The Journal of Physical Chemistry A COMMENT
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