J. Phys. Chem. 1985,89, 3675-3679
3675
Kinetic Parameters for the Electron-Transfer Quenching of the Luminescent Excited State of Ruthenium( II)-Polypyridine Complexes by Aromatic Amines in Acetonitrile Solution D. Sandrini,'" M. Maestri,'" P. Belser,lb A. von Zelewsky,lb and V. Balzani*'*~c Istituto Chimico "G. Ciamician" dell'Universita' and Istituto FRAE- CNR, Bologna, Italy, and Institute of Inorganic Chemistry, University of Fribourg, Fribourg, Switzerland (Received: September 5, 1984; In Final Form: January 31, 1985)
Rate constants are reported for the reductive electron-transfer quenching of the luminescent excited state of four Ru(11)-polypyridine complexes by seven aromatic amines in acetonitrile solution. The log k, vs. AG plots obtained have been analyzed on the basis of the current theories for electron-transfer processes. The quenching constants for Ru(bpy)32+, Ru(bpy)z(biq)2+,and Ru(bpy)z(DMCH)Z+,where bpy is 2,2'-bipyridine, biq is 2,2'-biquinoline, and DMCH is a 2,2'-biquinoline derivative, lie on the same log k, vs. AG curve whose best-fitting analysis yields the following values for the intrinsic barrier and electronic transmission coefficient of the *RuL?+/RuL3+ self-exchangeelectron-transfer reactions: AG*(O) = 3.1 kcal/mol, ti = 1 X 1O-z. The quenching constants concerning R U ( D T B - ~ ~ ~where ) , ~ + DTB-bpy , is 4,4'-di-tert-butyl-2,2'-bipyridine, are rather scattered and lie clearly below the curve which fits the quenching constants of the other complexes, showing that substitution of the hydrogen atoms in the 4 and 4' positions of the bpy ring by bulky tert-butyl groups lowers the electronic The kinetic parameters obtained for self-exchange electron transfer transmission coefficient ti to values of the order of of the Ru complexes are compared with those previously obtained for self-exchange energy transfer.
amines were of the highest purity commercially available and were used as received. Acetonitrile (AN) was Merck Uvasol and was used without further purification. The apparatus for luminescence intensity measurements and emission lifetime measurements was described e1~ewhere.l~ The quenching of the luminescence emission and luminescence lifetime was measured with at least four different quencher concentrations. All experiments were carried out at room temperature (-22 "C). The ionic strength of the solution was controlled by the concentration of the Ru complex (k = 2 X M).
Introduction Electronically excited states which are sufficiently long lived to be in thermal equilibrium with their surroundings are distinct entities having characteristic chemical and physical properties of their own.2 The extraordinary redox properties of such entities3" are currently drawing the attention of many research workers for at least two reasons: (i) they can be used for the conversion of light energy (including solar energy) into chemical and (ii) they allow us to check the validity of outer-sphere electrontransfer theories over a broad range of free-energy change and to obtain reliable kinetic parameters.'*13 This paper deals with a systematic study of the electron-transfer quenching of excited ruthenium-polypyridine complexes by aromatic amines and it is thus relevant to point (ii) above. The complexes used as excited-state electron acceptors are R ~ ( b p y ) , ~ + , Ru(bpy)2(biq)2+,Ru(bpy)z(DMCH)2+,and Ru(DTB-bpy)32+, where the bpy, biq, DMCH, and DTB-bpy ligands are shown in Figure 1. The aromatic amines used as ground-state electron donors are listed in Table I.
Results The absorption spectra of the complexquencher solutions were equal to the sum of the two component spectra and the maxima and shapes of the emission bands of the complexes were qualitatively unaffected by the quenchers. The quenching of emission intensity coincided, within the experimental uncertainty, with the quenching of emission lifetime and in all cases linear Stem-Volmer plots were obtained. The values of the bimolecular quenching constants, calculated from the Stern-Volmer constants and the lifetimes of the excited states, are shown in Table I. The spectroscopic energies, reduction potentials, and excited-state lifetimes of the Ru complexes are reported in footnotes of Table I.
Experimental Section The preparation (as PF6- salts), purification, and characterization of R ~ ( b p y ) , ~ +Ru(bpy)z(biq)2+, , Ru(bpy)z(DMCH)2+,and Ru(DTB-bpy)?+ have been reported e1~ewhere.l~The aromatic
Discussion Quenching Mechanism. As discussed in more detail elsein fluid solution the deactivation of an excited state by a quencher may take place by several distinct mechanisms. For excited states of transition-metal complexes, when the bimolecular quenching constants are as large as those reported in Table I, only energy- and electron-transfer quenching processes have to be considered. For triphenylamine and phenothiazine, the energy of the lowest excited state is known (3.04l' and 2.65 eV,I8 re-
( I ) (a) Istituto 'G. Ciamician" dell'Universita', Bologna. (b) Institute of Inorganic Chemistry, University of Fribourg. (c) Istituto FRAE-CNR, Bologna. (2) Adamson, A. W., Fleischauer, P. D., Eds. "Concepts of Inorganic Photochemistry"; Wiley-Interscience: New York, 1975. (3) Balzani, V.; Bolletta, F.; Gandolfi, M. T.; Maestri, M. Top. Curr. Chem. 1978, 75, 1 . (4) Sutin, N . ; Creutz, C.Pure Appl. Chem. 1980, 52, 2717. (5) Whitten, D. G. Acc. Chem. Res. 1980, 13, 83. (6) Meyer, T. J. Prog. Inorg. Chem. 1983, 11, 94. (7) Connolly, J. S., Ed. 'Photochemical Conversion and Storage of Solar Energy"; Academic Press: New York, 1981. (8) Rabani, J., Ed. "Photochemical Conversion and Storage of Solar Energy"; Weizmann Science Press of Israel: Jerusalem, 1982. (9) Graetzel, M., Ed. "Energy Resources by Photochemistry and Catalysis"; Academic Press: London, 1983. (10) Sutin, N. Acc. Chem. Res. 1982, 15, 275. (11) Sutin, N. Prog. Inorg. Chem. 1983,30, 441. (12) Endicott, J. F.; Kumar, K.; Ramasani, T.; Rotzinger, F. P. Prog. Znorg. Chem. 1983, 30, 141. (13) Balzani, V.; Scandola, F. In "Energy Resources by Photochemistry and Catalysis", Graetzel, M., Ed.; Academic Press: London, 1983; p 1 .
0022-3654/85/2089-3675$01.50/0 , , I
(14) Juris, A,; Balzani, v.;Belser, p.; von Zelewsky, A. Helu. Chim. Acra 1981, 64, 2175. Juris, A,; Barigelletti, F.; Balzani, V.; Belser, P.; von Zelewsky, A . Zsr. J . Chem. 1982, 22, 87. ( 1 5) Ballardini, R.; Mulazzani, Q. G.; Venturi, M.; Bolletta, F.; Balzani, V. Znorg. Chem. 1984, 23, 300. (1 6 ) Balzani, V.; Moggi, L.; Manfrin, M. F.; Bolletta, F.; Laurence, G. S. Coord. Chem. Reu. 1975, 15, 321. (1 7) Parker, C. A . "Photoluminescence of Solutions"; Elsevier: Amster-
dam, 1968. (18) Alkaitis, S. A.; Graetzel, M.; Henglein, A. Ber. Bunsenges. Phys. Chem. 1975, 79. 541.
0 1985 American Chemical Societv -
3676 The Journal of Physical Chemistry, Vol. 89, No. 17, 1985
Sandrini et al.
TABLE I: Bimolecular Quenching Constants *Ru(bpy),Z+ wenchers ( E , (1) (2) (3) (4) (5) (6) (7)
kcal/mol
1.3 X 10" 9.2~109 7.3 X lo9 5.5 x 109 1.3 X lo9 9.8 X lo7 1.1 X lo7
-13.9 -11.3 -9.5 -5.3 -2.5 +0.9 +2.3
M- s
kcal/mol
N,N,N',N'-tetramethyl-p-phenylenediamine(0.16)* 4-aminodiphenylamine (0.27)'
N,N-diphenyl-p-phenylediamine(0.35)' phenothiazine (0.53)'
N,N-dimethyl-p-toluidine (0.65)' N,N-dimethylaniline (0.78pk triphenylamine ( 0 . 8 6 ) ' ~ ~
-13.6 -11.1 -9.2 -5.1 -2.3 +0.7 +2.6
ksf M-I s-I
AG,.
kBf- I
AG,e
,,, V)
*Ru(bpy)2(biq)2+b
*Ru (bpy)2(DMCH)*+'
*Ru(DTB-bpy)32+d
AGge
k f
kcal/mol
M-?'s-I
1.4 X 10" -12.2 8 . 2 ~ 1 0 9 -9.7 8.0 X lo9 -7.9 7.1 x 109 -3.7 2.1 X lo9 -0.9 2.4 X lo8 +2.1 1 X lo7 +3.9
1.3 X 10" 7.1~109 6.6 X lo9 4.2 x 109 8.8 X lo8 4.1 X lo7 4.8 X lo6
AG,. kcal/mol -12.2 -9.7 -7.9 -3.7 -0.9 +2.1 +3.9
k g M-ys-l 5.9 X lo9 3.0~109 1.9 X lo9 1.1 x 109 4.0 X lo7 1 X lo5 1
"ET= 2.13 eV, Erd = +0.78 V vs. S C E ( A N solution, ref 14); T = 160 ns, aerated A N solution, room temperature. bET = 1.70 eV, E,, = +0.79 V vs. S C E ( A N solution, ref 14); T = 235 ns, aerated A N solution, room temperature. ' E T = 1.72 eV, Erd = +0.72 V vs. S C E (AN solution, ref 14); T = 200 ns, aerated A N solution, room temperature. d E T = 2.16 eV, Erd = +0.72 V vs. S C E (AN solution, ref 14); T = 105 ns, aerated A N solution, room temperature. CFree-energychange for reaction 1, corrected for work term wp 0.03 eV (see Appendix). /Error limits are &lo%. gError limits are &20%. *Reference 22. 'Mann, C. K.; Barnes, K. K. "Electrochemical Reactions in Non-aqueous Systems"; Marcel Dekker: New York, 1970; see also ref 35. 'Hino, T.; Akazawa, H.; Masuhara, H.; Mataga, N. J. Phys. Chem. 1976, 80, 33. 'This couple is electrochemically irreversible. Bock et aL2' have tried to evaluate a corrected potential. In view of the uncertainty of the kinetic data used in the correction, we prefer to use the experimental irreversible value. 'Not measured because of the low solubility of triphenylamine.
-
biq
D++A-
Products
k-d
Figure 2. Kinetic scheme for the electron-transfer quenching.
-
DTB bpy
DMCH
Figure 1. Structural formulas of 2,2'-bipyridine (bpy), 2,2'-biquinoline (biq), a 2,2'-biquinoline derivative (DMCH), and 4,4'-di-tert-butyl2,2'-bipyridine (DTB-bpy).
spectively) and energy transfer can thus be excluded since it would be strongly endergonic. By contrast, reductive electron transfer (eq 1, where Ru2+ and
k,
*Ru2+ + Am Ru+ + Am+ (1) Am indicate generically the ruthenium complexes and the aromatic amines studied in this work) is exergonic in most cases (Table I). Strong support in favor of a reductive electron-transfer reaction is given by the formation of Ru(bpy),+ and of the radical cations Clear evidence for of amines observed in flash a common, reductive electron-transfer quenching mechanism for all the system studied in this work comes from the smooth variation of kq with the free-energy change of the electron-transfer process, as is shown in Table I and in Figure 3 which will be discussed later. Approach to Electron- Transfer Kinetics. An electron-transfer ~ .the ~ ~basis ~ ~ of the kinetic quenching process can be d i s c u s ~ e d 'on scheme shown in Figure 2. The bimolecular quenching constant k, of reaction 1 can be written as
k, =
kd
k-d k-d k-e l+-+y--ke k-ci ke
(19) Maestri, M.; Graetzel, M. Ber. Bunsenges. Phys. Chem. 1977, 81, 504. ....
(20) Anderson, C. P.; Salomon, D. J.; Young, R. C.; Meyer, T. J. J . Am. Chem. SOC.1977, 99, 1980. (21) Bock, C. K.; Conner, J. A,; Gutierrez, A. Jr.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. J. Am. Chem. SOC.1979, 101, 4815. (22) Permanent products are also observed in continuous irradiation experiment~.*~ (23) Unpublished results from this laboratory. (24) Rehm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259. (25) Balzani, V.; Scandola, F.; Orlandi, G.; Sabbatini, N.; Indelli, M. T. J. Am. Chem. SOC.1981, 103, 3370. ( 2 6 ) Creutz, C.; Keller, A. D.; Sutin, N.; Zipp, A. P. J. Am. Chem. SOC. 1982, 104, 3618.
where kd is the diffusion rate constant, k4 and k14 are the rate constants for dissociation of the precursor and successor complex, and k , and k , are unimolecular rate constants for electron transfer.27 From a classical a p p r ~ a c h , ' ~ J 'k,/k, J ~ is given by exp(AG/RT), where AG is the free-energy change of the electron-transfer step, and the rate constant of the electron transfer step is given by
k, = ko, exp(-AG*/RT) =
KV,
exp(-AG*/RT)
(3)
where ko, is the frequency factor, K is the electronic transmission coefficient, v, is an effective frequency for nuclear motion, and AG* is the free activation energy. In the current terminology, a reaction is said to be adiabatic when the electronic interaction is sufficiently strong so as to make the electronic transmission coefficient equal to unity, and nonadiabatic when the electronic interaction is small and the electronic transmission coefficient is lower than unity. The term A c t of eq 3 can be expressed by the following free-energy relationship:28 AG* = AG
+In 2
In this equation, AG is the previously Seen free-energy change and AG*(O) is the so-called intrinsic barrier, a parameter related to the amount of distortion of both the inner coordination spheres and the outer solvation shells accompanying electron transfer. As far as AG*(O) and K are concerned, it is convenient to split these parameters of the cross reaction (eq 1) into intrinsic parameters of the two exchange reactions:
+ Ru+ Am + Am+
*Ruz+
-
+ *Ru2+ Am+ + Am Ru+
-.
(5)
(6)
(27) In eq 2, k'+ should actually be replaced by k, = kL + k+). When dissociation of the successor complex takes place and leads to permanent products as in our case, k, can be taken as k'4 without affecting the analysis of the data. (28) Agmon, N.; Levine, R. D. Chem. Phys. Lett. 1977.52, 197. Equation 4 is preferred to the classical Marcus equation, because it can better account for the behavior of highly exoergonic reactions.29 In the case of slightly endoergonic or slightly exoergonic reactions like those dealt with in this paper, the two equations give practically equivalent results.29
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985 3611
Quenching of Ru-Polypyridine Excited States This can be done30by eq 7 and 8, where AGtR,(0) and KR,, are the intrinsic barrier and the electronic transmission coefficient for reaction 5, and AG*Am(0)and K,~,. are the corresponding quantities for reaction 6:j'
I
6 K
= (KR,,KA,,,)'/'
(8)
If we consider a series of homogeneous electron-transfer rea c t i o n ~such ' ~ ~as~ those ~ between a group of oxidants having the same size, shape, electronic structure, and electric charge, and a group of reductants also having the same size, shape, electronic structure, and electric charge, we may assume that throughout the series the reaction parameters kd, k4, k L in eq 2, K in eq 3, and AG*(O) in eq 4 are constant. (Procedures are also available to account for a small degree of nonh~mogeneity).~~ Under these assumptions, kq in eq 2 is only a function of the free-energy change, which is given by AG = -[E(*Ru2+/Ru+) - E(Am+/Am)]
+ wp - WR
4 I
-20
-10
.,
1
0 A G (kcal mo1-l)
.--A
10
Figure 3. Diagram showing the variation of log k, as a function of AG for eq 1: 0,R ~ ( b p y ) , ~ + ; Ru(bpy),biqZ+; 0, Ru(bpy),DMCHZ+. The amines are labeled by numbers as in Table I.
(9)
where wp and wR are the work terms (see Appendix). For such a homogeneous series of reactions, eq 2-4 predict that a plot of log k, vs. AG consists of (i) a plateau region for sufficiently exergonic reactions, (ii) an Arrhenius type linear region (slope 1/(2.3RT))for sufficiently endergonic reactions, and (iii) an intermediate region (centered at AG = 0) in which k, increases in a complex but monotonous way as AG decreases. The plateau value is given by
4
i I
I
I
-20
-10
0
I 10
A G (kcal mol'l) Figure 4. Best-fitting curves in the frame of the adiabatic hypothesis. For details see text.
and it is equal to kd or koe(kd/k4)depending on whether koe is much larger or much smaller than k4. It follows that a very low value of the frequency factor (Le., K < k4/vn) is reflected in a lower than diffusion value of kPq. On the other hand, the value of the intrinsic barrier AG*(O) does not affect kp, but strongly influences the values of the rate constant in the intermediate nonlinear region. This type of approach, which in favorable cases allows the disentanglement of the effects of nonadiabaticity and intrinsic barrier on the rate constant, has been applied to interpret the results of several electron26~34*35 and e n e r g ~ ~transfer ~ . ~ ' processes. Kinetic Parameters. To a first approximation, the Ru(I1) complexes used as excited-state electron acceptors and the aromatic amines used as ground-state electron donors constitute homogeneous families in the sense discussed before. Thus, we will try to use the above-described kinetic approach in an attempt to get some pieces of information on the role played by electronic and nuclear factors in determining the reaction rate.38 To do
(29) Scandola, F.; Balzani, V. J. Am. Chem. SOC.1979,101,6140; 1980, 102, 3663. (30) Sutin, N. In "Bioinorganic Chemistry", Eichhorn, G. L., Ed.; American Elsevier: New York, 1973; Vol. 2, Chapter 19, p 611. (31) It should be noted that eq 8 might not be a good approximation especially when orbitals of a different nature are involved in the cross and self-exchange (32) Macartney, D. H.; Sutin, N. Inorg. Chem. 1983, 22, 3530. (33) Endicott, J. F.; Ramasani, T.; Gaswick, D. C.;Tamilasaran, R.; Heeg, M. J.; Brubaker, G. R.; Pyke, S. C. J. Am. Chem. SOC.1983, 105, 5301. (34) For a review see ref 13. (35) Sandrini, D.; Gandolfi, M. T.; Maestri, M.; Bolletta, F.; Balzani, V. Inorg. Chem. 1984, 23, 3017. (36) For a review see Scandola, F.; Balzani, V. J. Chem. Educ. 1983, 60, 814. (37) Gandolfi, M. T.; Maestri, M.; Sandrini, D.; Balzani, V. Inorg. Chem. 1983, 22, 3435. (38) To keep the system as homogeneous as possible, we will not include in our discussion the literature data concerning the quenching of *Ru(bpy)?+ by other amines and/or at different ionic ~trength.*l*'~
that, we have first to choose appropriate values for the quantities kd, k4, k L , v,, and AG which intervene in eq 2-4. This is done in the Appendix, using available experimental data and current expressions for the evaluation of diffusion parameters. Then, we use a best-fitting procedure to obtain estimates of the intrinsic barrier AG'(0) or of the electronic transmission coefficient k after having chosen a value for one of these two quantities. It should be noted that while the treatment leads to fairly well-defined solutions for AG*(O) or K because of the great number of kinetic data which are available (Table I and Figure 3), the best-fitting values so obtained depend on the values chosen for the other parameters. The reliability of the values for AGIR,(0) or KR,, obtained from eq 7 and 8 also depend, of course, on the reliability of the data or assumptions used to evaluate AGtAm(0)and KA,,,. Adiabaticity is considered the rule for electron-transfer reactions in homogeneous solutions$0 even if indications of nonadiabatic behavior begin to emerge for several Thus, we shall make first the assumption that reaction 1 is adiabatic for all the systems examined in this work. In other words, we assume that in eq 3 K = 1; from eq 8, it follows that KR,, and KA,,, are also equal to unity. Under this assumption, the value of the intrinsic barrier AG'(0) can be obtained from the log k, vs. AG plot by using a best-fitting procedure. As one can see from Figure 4, the data concerning R ~ ( b p y ) ~ ' +R, ~ ( b p y ) ~ ( b i q ) and ~ + , Ru( ~ P ~ ) ~ ( D M C fit H )well ~ + a curve which corresponds to AG*(O) = 5.7 f 0.5 kcal mol-', whereas the data concerning Ru(DTBbpy)32+are considerably scattered and would (poorly) fit a curve corresponding a higher intrinsic barrier ( - 8 kcal mol-'). With (39) Ballardini, R.; Varani, G.; Indelli, M. T.; Scandola, F.; Balzani, V. J. Am. Chem. SOC.1978, 100, 7219. (40) For reviews, see: Bennett, L. E. Prog. Inorg. Chem. 1973, 18, 1. Cannon, R. D. "Electron Transfer Reactions"; Butterworths: London, 1980. (41,) Sutin, N.; Brunschwig, B. S. In 'Mechanistic Aspects of Inorganic Reactions", Rorabacher, D. B.; Endicott, J. F., Eds.; American Chemical Society: Washington, DC, 1982; ACS Symp. Ser., p 105.
3678 The Journal of Physical Chemistry, Vol. 89, No. 17. 1985
1 -20
I
-10
10
0
A G ( k c a l molm11 Figure 5. Best-fitting curves in the frame of the nonadiabatic hypothesis. For details see text.
AGtAm(O)= 4 kcal mol-I (see Appendix), eq 7 yields a value of 7.4 f 1.0 kcal mol-' for AG*Ru(0) in the case of R ~ ( b p y ) , ~ + , R~(bpy),(biq)~+, and R U ( ~ ~ ~ ) ~ ( D M Cwhereas H ) ~ + the , corresponding value for R U ( D T B - ~ ~would ~ ) ~ be ~ + 12 kcal mol-'. As is w e l l - k n ~ w n , ' ~the ~ ' ~intrinsic ~'~ barrier receives contributions from changes in the inner nuclear coordinates of the molecule ("inner-sphere" reorganizational energy, AG*(0)i), and from changes in the solvent arrangement around the molecule ("outer-sphere" reorganizational energy, AG*(O)J:
Sandrini et al. nonadiabatic for all our systems and that the K estimates reported above are substantially correct. Within a nonadiabatic model, the smaller rate constants, exhibited by R u ( D T B - ~ ~ ~ )can ,~+, easily be accounted for on the basis of the bulky DTB substituents which reduce the overlap between the donor amine orbital and the a(ta) acceptor metal orbitals which are partly delocalized over the T * ligand orbitals.44 The scattering of the data concerning R u ( D T B - ~ ~is~ also ) ~ ~expected + because a family of quenchers will appear less and less homogeneous as the electronic transmission coefficient of the reaction partner decreases.', A nonadiabatic behavior is also in agreement with other results which will be discussed in the next section. Self Exchange Reactions of Ru-Polypyridine Complexes. On the basis of the results obtained in this paper and of other literature data, we can make some speculations on the rates of self-exchange reactions of Ru-polypyridine complexes. As discussed in detail by several author^,^-^ the quenching of *Ru2+can take place by reductive electron transfer (eq 12), oxidative electron transfer (eq 13), and energy transfer (eq 14). Other reactions relevant to our
+ *Ruz+ + Q *Ru2++ Q
*Ru2+ Q
-
AG'(0) = AG*(O)i + AG*(O),
-
-
+ Q' Ru3+ + QRu2+ + *Q Ru+
(12) (13) (14)
discussion are those involving reduction of Ru3+ (eq 15) or oxidation of Ru' (eq 16). From the point of view of the electronic
+Q +Q
Ru3+
(1 1)
-
+ Q' Ru2+ + QRu2+
(15)
For the self-exchange reaction involving the Ru complexes (eq Ru' (16) 5), AG*Ru(0),is calculated to be 3.1 kcal mol-' for R ~ ( b p y ) , ~ + , transmission coefficient (orbital overlap requirement), reaction R~(bpy),(biq)~+, and Ru(bpy)z(DMCH)2+,and 2.4 kcal mol-' 12 is equivalent to reaction 15 (transfer of an electron from the for R U ( D T B - ~ P ~ )(see , ~ +Appendix). The inner-sphere contriH O M O orbital of Q to a r(t2J metal orbital) and reaction 13 bution AG*Ru(0)iis negligible because the only difference between is equivalent to reaction 16 (transfer of an electron from a T * *RuL,~+and RuL3+is the presence of 5 or, respectively, 6 electrons ligand orbital to the LUMO orbital of Q). Reaction 14, which in the n(t2J metal orbitals.42 It follows that AG*Ru(0) = AGtRU(O),, Le., 3.1 kcal mol-' for R ~ ( b p y ) , ~ R + ,~ ( b p y ) ~ ( b i q ) ~ + , takes place via an exchange interaction, can be described36as the occurrence of both the electron-transfer processes and R U ( ~ ~ ~ ) ~ ( D M Cand H )2.4 ~ +kcal , mol-] for R u ( D T B - ~ ~ ~ ) ~ ~simultaneous +. described above. Since it is obviously impossible to study reactions Comparison with the values obtained above on the basis of the 12-16 with the same partner Q, for the sake of discussion of the adiabatic assumption (7.4 f 1.0 and -12 kcal mol-', respectively) kinetic parameters of the Ru complexes it is convenient to compare leads to the conclusion that such an assumption is clearly wrong the corresponding self-exchange reactions: for R u ( D T B - ~ ~ ~because ) , ~ + (i) it would require an unreasonably high value for the intrinsic barrier and (ii) it would imply that *Ru2+ Ru+ Ru+ *Ru2+ (17) the intrinsic barrier for R U ( D T B - ~ ~ ~is) much , ~ + higher than that for R ~ ( b p y ) , ~ +R, ~ ( b p y ) ~ ( b i q ) ~and +, R U ( ~ ~ ~ ) , ( D M C H ) ~ + , (18) *Ru2+ Ru3+ Ru3+ *Ru2+ whereas it must be smaller. For the other Ru complexes the *Ru2+ Ru2+ Ru2+ *Ru2+ (19) adiabatic assumption seems also unreasonable because of the large discrepancy between the best-fitting (7.4 kcal mol-') and calculated (20) Ru3+ Ru2+ Ru2+ Ru" (3.1 kcal mol-') values for the intrinsic barrier.43 As discussed elsewhere,13the kinetic approach described above Ru' Ru2+ Ru2+ Ru+ (21) can also be used to evaluate the electronic transmission coefficient of nonadiabatic processes. Taking the calculated values 3.1 kcal From the point of view of the electronic transmission coefficient, mol-' for the intrinsic barrier of R ~ ( b p y ) , ~ +R~(bpy),(biq)~+, , reactions 17 and 20 are equivalent because they involve a r(t2J and R u ( ~ ~ ~ ) ~ ( D M Cand H )2.4 ~ +kcal mol-' for the intrinsic a(tzg)electron transfer between the central metals, reactions barrier R u ( D T B - ~ ~yields ~ ) ~ from ~ + a best-fitting procedure (see 18 and 21 are also equivalent because they involve a x*-T* Appendix) K = 1 X 10-1*0.5for the quenching reactions involving electron transfer between the ligands of the two complexes, and the first three complexes and K E 5 X lo-, for the last one. If reaction 19 can be described as the simultaneous occurrence of for KR,, of the we assume K ~ , , , = 1, eq 8 yields a value of 1 X both the metal-metal and ligand-ligand electron transfer. Simple f o r Ru(DTB-bpy),*+. A comfirst three complexes and considerations based on the localization of the orbitals involved parison of the x 2 values shows that the fitting of the experimental suggest that the T*--?T*overlap should be more effective than the data to the solid curves of Figure 5 is better than that to the solid r(tZg)7(tZg) overlap.& In the latter case, the electronic interaction curves of Figure 4. Since there is no reason to believe that the can be small enough to make the process nonadiabatic in nature. calculated AG*Ru(0)values are wrong, we conclude that, if the When this happens, considering that reaction 19 requires siother parameters used are (as we believe) reliable, reaction 1 is multaneous and favorable p * ~ and * r(t2J--7r(t2J orbital overlap,
+ + + + +
-
+ + + + +
-
-
(42) The electron exchange reaction between *Ru(bpy)32+and Ru(bpy),+ (eq 5 ) is identical, from the point of view of the change in electronic config-
uration, to the electron exchange reaction between R ~ ( b p y ) ~ and l + Ru(bpy!12+. The inner-sphere contribution to the intrinsic barrier for the latter reaction is generally assumed to be negligible.4~'0~26~3*~41 (43) Note that the disagreement between the calculated and best-fitting values of AGtRu(0)would increase if k T / h were used instead of v, in eq 3 (see Appendix).
(44) The effect of bulky substituents in slowing down the rate of electron-transfer reactions between ruthenium and cobalt complexes has recently been observed and tentatively attributed to nonadiabati~ity.~~ (45) Koval, C. A,; Pravata, R. L. A,; Reidsema, C. M . Znorg. Chem. 1984, 23. 545. (46) As discussed in ref 41 the direct s ( t & r ( t 2 , ) overlap would yield a K value < IO". However, the actual ~ ( t ~ ~ j - )xinteraction (t~ may be much larger because of mixing with the T * orbitals ob the ligands.
The Journal of Physical Chemistry, Vol. 89, No. 17, 1985
Quenching of Ru-Polypyridine Excited States the electronic transmission coefficients of reactions 17-21 are expected to decrease in the series K18
K21
> K17
K20
> K19
3619
values of KA which are very similar to those given by the classical Eigen-Fuoss equation
(22)
Some estimates concerning the electronic transmission coefwhen u (which is the sum of the radii al and a2 of the reactants) ficients of eq 17-21 begin to be available and seem qualitatively is equal to r and 6r is assumed to be equal to u/3. This assumption obey the expected trend (eq 22). For Q = bipyridinium cations, is considered to be a good approximation for adiabatic reactions 1 ) both in reaction 13 for Ru2+ = R ~ ( b p y ) , ~is+adiabatic ( K and has been used in this paper to obtain k4 in the framework water and in AN.2',26 From the relationship among the electronic of the adiabatic assumption. For the aromatic amines, the mean transmission coefficients of cross- and self-exchange reactions (see eq 8 ) , it follows that K~~ N 1 . Reaction 16 has not yet been studied ~+, radius was taken as 4.0 A. For R ~ ( b p y ) , ~ +R,~ ( b p y ) ~ ( b i q )and systematically, so no experimental estimate is available for K ~ I . Ru(bpy)z(DMCH)2+, the mean radius was taken as 7.0 h;, For reaction 12 with Q = Am and Ru2+ = R ~ ( b p y ) , ~ +Ru, whereas the value 9 h; was used for Ru(DTB-bpy)?+. Using such values resulted in k , , = 5.4 X lo9 s-' for the quenching of Ru( b ~ y ) ~ ( b i q )or ~ +R, U ( ~ ~ ~ ) ~ ( D M CK~~Hhas ) ~ been + , estimated to (bpy)j2+,R ~ ( b p y ) ~ ( b i q )and ~ + ,R u ( ~ ~ ~ ) ~ ( D M C Hand ) * 3.3 +, X be 1 X 10;' in this paper. If we assume, as it seems reasonable, lo9 s-I for the quenching of R U ( D T B - ~ ~ ~ )As , ~far + . as kL,, is that the electronic transmission coefficient for the self-exchange concerned, the values obtained by using eq A5 of ref 35 are 9.6 reaction of aromatic amines is unity, it follows that ~ 1 =7 1 X From the data obtained in this paper it also results that K17 N X lo9 and 5.3 X lo9 s-l, respectively. when Ru2+ = R U ( D T B - ~ ~ ~ )Reactions , ~ + . 20 with Ru2+ = So that the experimental data could be discussed within the nonadiabatic hypothesis, eq A2 was used with 6r = 0.8 R ~ ( b p y ) , ~has + been studied in A N by Chan and Wah147who The k4 and k'-,, values resulted to be 1.9 X 1 O ' O and 4.4 X 1OIos-' reported a rate constant 8 . 3 X lo6 M-' s-' . Using v, = 1 x I O L 2 s-' and the calculated value for the intrinsic barrier ( 3 . 1 kcal for Ru(bpy)?+, R~(bpy),(biq)~+, and Ru(bpy)2(DMCH)2+,and 1.4 X 1OIo and 2.9 X 1OIo s-] for R u ( D T B - ~ ~ ~ ) , ~ + . mol-'), one gets K 2 0 N 8 X lo-,. An estimate of K~~ can also be Work Terms. The free-energy change for the electron-transfer obtained from the value k = 5 X 1Olo s-I for the unimolecular step within the encounter reported in Table I has been obtained electron-transfer step of reaction 15 with Ru3+ = Ru(bpy),)+ and Q = MV+.2',26This reaction is very exergonic so that one can from assume AG*(O)= 0, which yields ~ 1 =5 5 X if one takes v, AG = -[E(*Ru2+/Ru+) - E(Am+/Am) + w p ( r )- w R ( r ) ] = 1 X 10l2 s-I. If we assume that the self-exchange reaction of (A41 bipyridinium cations is adiabatic,26from eq 8 K20 results to be 3 X IO-,. It seems fair to conclude that reactions 17 and 20 carry where the work terms is given by2j a nonnegligible degree of nonadiabaticity. Wp,R(r)= ZAZBe2N/[tr(1 A r y l / * ) ] (A5) Finally, reaction 19 has recently been reported to have rate Ru(bpy)constant k I gN 5 X lo7 M-'s-' for R~(bpy),(biq)~+, where z A and zBare the electric charges of the reactants, e is the (biq)22+, Ru(bpy)2(DMCH)2+, and R U ( ~ ~ ~ ) ( D M C in H ) ~ ~ +electron charge, the dielectric constant, and A is ( 8 r N e 2 / acetonitrile solution.48 For this reaction the outer-sphere re1000kT)'12. In our case, wR(r)= 0 because one of the reactants organizational energy should be negligible and an upper limit value is uncharged, and w p ( r )is -0.03 eV. for the inner-sphere reorganization energy is calculated to be 1.2 Nuclear Frequency. The effective frequency for nuclear motion kcal mol-' from the Stokes shift value Q0.2 eV.4349 Using a (v,, eq 3 ) was taken to be 1.0 X 10l2 s-' because the main conconservative estimate of 1.5 kcal mol-' for the overall intrinsic tribution to the intrinsic barrier comes from solvent reorganizaIn barrier and taking v, = 1 X 10l2 s-' results in K~~ E tion. conclusion, the available results suggest that the expected trend Intrinsic Barrier for the Amines. Bard et al.52have reported for the electronic transmission coefficients (eq 22) is observed. self-exchange rates for several aromatic amines in A N solution. From these data an average value AGtAm(O)= 4.0 kcal/mol has Appendix been obtained by using v, = 1.0 X l o t 2s-' and in the assumption Diffusion and Dissociation Rate Constants. According to of an adiabatic behavior. D e b ~ e , when ~ ' at least one of the reaction partners is uncharged, Intrinsic Barrier for the *Ru2+/Ru+Couple. As discussed in the diffusion rate constant kd is given by the text, the inner-sphere contribution AC*R,(O)i to the intrinsic barrier of reaction 5 is negligible. The outer-sphere contribution kd = 8RT/30007 (AI) has been calculated by using where 17 is the viscosity of the solvent. For acetonitrile solutions at 20 O C , eq A1 gives kd = 1.8 X 1O'O M-' s-I. Following Sutin," the equilibrium constant KA for the formation of reactant pairs separated by a distance between r and r f dr, is given by where Ae is the change in the charge of each reactant, al and a2 are the radii of the two reactants, d is taken as ( a l + a2),n is the refractive index of the solvent, and 6 is the static dielectric constant." where w ( r ) is the work required to bring the reactants to the Acknowledgment. This work was supported by the Consiglio separation distance r. Sutin" has pointed out that eq A2 gives Nazionale delle Ricerche (Italy), Minister0 della Pubblica Istruzione (Italy), and Schweizerischer National Fonds zur For(47) Chan, M. S.; Wahl, A. C. J . Phys. Chem. 1978, 82, 2542. derung der Wissenschaftlichen Forschung (Switzerland). (48) Maestri, M.; Sandrini, D.; Balzani, V.; Belser, P.; von Zelewsky, A.
+
Chem. Phys. Lett. 1984, 110, 611. (49) Crosby, G. A.; Perkins, W. G.; Klassen, D. M. J . Chem. Phys. 1965, 43, 1498. (50) Assuming that the effective nuclear frequency is that corresponding to metal-ligand vibration." (51) Debye, P. Trans. Electrochem. Soc. 1942,82, 265.
Registry No. Ru(bpy),Z+,15158-62-0; Ru(bpy),(biq)*+. 75777-90-1; Ru(bpy)z(DMCH)2+, 75778-00-6; Ru(DTB-bpy),*+, 75777-86-5. (52) Kowert, B. A,; Marcoux, L.; Bard, A. J. J . Am. Chem. Soc. 1972,94, 5538.
