7912
J. Phys. Chem. A 2010, 114, 7912–7917
Photoinduced Electron-Transfer Reactions: A Study of the Diffusion-Controlled and Activation-Diffusion-Controlled Processes I. Villa, F. Sanchez, T. Lopes, P. Lopez-Cornejo, and P. Perez-Tejeda* Department of Physical Chemistry, Faculty of Chemistry, UniVersity of SeVille. c/Profesor Garcı´a Gonza´lez, s/n, 41012. SeVille, Spain ReceiVed: May 21, 2010; ReVised Manuscript ReceiVed: June 24, 2010
The diffusion-controlled electron transfer rate constants (kd) of several quenching reactions of ruthenium complexes [Ru(L)3]2+* (L ) bpy, phen, and 4,7-(CH3)2phen) with [Fe(CN)6]3- were experimentally determined at different concentrations of NaNO3. From these rate constants, the effective values of viscosity coefficients for NaNO3 solutions were calculated using EMSA (exponential mean spherical approximation) and EF (EigenFuoss) approaches in order to take into account the mean force potential between reactants. The reliability of the effective parameters were checked through calculations of the rate constants of the reaction [IrCl6]2-+ [Ru(bpy)3]2+* in these NaNO3 solutions. The rate constants of this reaction were also obtained by fluorescence quenching measurements. The agreement between the two sets of data (experimental and predicted) is excellent. The trends of association (kd) and dissociation (k-d) rate constants for 2+/3-, 2+/2-, and 2+/2+ reactions in NaNO3 solutions are discussed. The use of effective diffusion coefficients for estimating kd and k-d allowed us to obtain the intrinsic electron transfer rate constant (ket) for the activation-diffusion-controlled process between [Ru(bpy)3]2+* and [Co(NH3)5Cl]2+ complexes from the observed (quenching) rate constant. The trend of electron-transfer rate constant in NaNO3 for this reaction was rationalized by using the Marcus electrontransfer treatment. Introduction The kinetics of fast photoinduced outer-sphere electron transfer (ET) reactions in solution has been a subject of interest for many years.1,2 For this type of processes the observed second order rate constant (kobs) is given by:
kobs )
kdket k-d + ket
(1)
where kd is the bimolecular diffusion-controlled rate constant for the association of reactants to give the encounter-complex, k-d is its dissociation rate constant, and ket the intrinsic ET rate constant within the encounter-complex. Taking into account eq 1 two cases can be differentiated: (i) If k-d , ket, eq 1 reduces to kobs ) kd. In this case, the chemical reaction step is fast, and a diffusion-controlled reaction (DCR) takes place. (ii) If k-d ≈ ket, a simplification of eq 1 cannot be used, and an activationdiffusion controlled reaction (ADCR) takes place. Quite frequently, photochemical ET processes are of DCR and ADCR types.3 In the first class of reactions, of course, the Marcus-Hush formulation is not applicable, but in the second one, the application of this treatment will require the separation of ket from kobs, which in turn requires having kd and k-d. Obviously, the separation of ket from the experimental rate constant is of essential importance in order to apply ET treatments to the activation-diffusion controlled processes. In this work, the diffusion-controlled rate constants of the quenching reactions of three ruthenium complexes in their excited states [Ru(L)3]2+* (L ) bpy, phen and 4,7-(CH3)2phen) * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +34954557175. Fax: +34954557174.
with [Fe(CN)6]3- were experimentally determined at several concentrations of NaNO3. The ruthenium complexes were selected in order to have chromophores with different redox potentials,4 which allows the assurance that these reactions are DCR type (see Discussion section). Once kd is obtained, the effective viscosity (ηeff) coefficients of NaNO3 solutions were calculated using the Simonin-Hendrawan treatment,5 and employing the EMSA (exponential mean spherical approximation) and EF (Eigen-Fuoss)6 approaches in order to take into account the mean force potential between reactants. The values thus obtained (ηeff) are checked by comparing experimental and calculated rate constants for another diffusion-controlled reaction, [IrCl6]2- + [Ru(bpy)3]2+*, in NaNO3 solutions. That is, one of the purposes of this work is to have a procedure to estimate kd and k-d from the values of effective viscosities. In fact, the use of effective parameters (viscosities and relative dielectric constants) is intended to correct the deviations of reality, implied by EF and EMSA approaches in the calculation of the diffusion rate constant. These deviations, mainly, are to consider the solvent as a dielectric continuum, the ions as hard spheres and the absence of specific effects. These specific effects (for the interaction of supporting electrolyte with solvent) would be incorporated in the effective values of the parameters. This question is important because, in concentrated electrolyte solutions, these interactions play a major role in the determination of solvent viscosity7 and solvent relative dielectric constant.8 On the other hand, estimation of diffusion rate constants (kd and k-d) opens the possibility of obtaining the intrinsic electron transfer rate constant from observed (experimental) rate constants for activation-diffusion-controlled processes. This possibility has been used in the study of a photoinduced ET reaction, [Ru(bpy)3]2+* + [Co(NH3)5Cl]2+, which is in the activation-diffusion-controlled regime.
10.1021/jp104681n 2010 American Chemical Society Published on Web 07/12/2010
Photoinduced Electron-Transfer Reactions
J. Phys. Chem. A, Vol. 114, No. 30, 2010 7913
Experimental Methods Materials. Tris (2,2′-bipyridine) ruthenium(II) chloride ([Ru(bpy)3]Cl2), potassium hexacyanoferrate(III) (K3[Fe(CN)6]), and ammonium hexachloro iridium(IV) ((NH4)2[IrCl6]) from Fluka; NaNO3 from Merck; potassium hexacyanoruthenate (II) (K4[Ru(CN)6]) from Johnson Matthey Company; and pentaammine chloride ruthenium(III) chloride ([Ru(NH3)5Cl]Cl2) from Alfa were used as received. The complexes tris (1,10-phenanthroline) ruthenium(II) chloride ([Ru(phen)3]Cl2) and tris (4,7dimethyl-1,10-phenanthroline) ruthenium(II) chloride ([Ru(4,7(CH3)2phen)3]Cl2) were prepared and purified according to published procedures.4 Also, the cobalt compound, pentaammine chloride cobalt(III) chloride ([Co(NH3)5Cl]Cl2), was prepared and purified following the method described in ref 9. All the solutions were prepared with deionized water from a Millipore Milli-Q system, having a conductivity
