9660
J . Phys. Chem. 1991. 95, 9660-9666
flexible molecules. However, the resolution obtained from a single measurement can be modest (see xR2surfaces for single files) and estimated values of the recovered parameters can be questionable. Beechem and H a d have recently discussed this problem for time-domain measurements and suggested simultaneous analysis of the donor and acceptor decay kinetics. This type of global analysis is potentially valuable and intuitively obvious, but is very difficult to realize in practice. Usually, acceptors are excited simultaneously during the excitation of the donor, and the amount of excited acceptor molecules due to energy transfer can be small compared with the whole population of excited-state acceptors. That is, the population or^excited acceptors can be predominately the result of acceptors which are directly excited. The time-dependent decays of these acceptors do not contain any information on the distance distributions or dynamics, and this component can only result in decreased information content and/or resolution from the data. One must also separate donor and acceptor absorption and emission spectra and introduce additional parameters into the analysis to account for direct acceptor excitation and/or spectral overlap. I n contrast, the global analysis obtained by varying the donor lifetime does not introduce any additional parameters, gives an acceptable increase of the resolution for each fitted parameter, and can be used for any donor-acceptor system including nonfluorescent acceptors.
The recovered initial distance distribution (Figure 9, insert, solid line) is in very good agreement with that found previously for TU2D in viscous solution32(Figure 9, insert, dashed line). The cm2/s (I26 A2/ns), is in diffusion coefficient, D = I .26 X the range of expected values for small molecules in low-viscosity solutions. I t is interesting to compare the end-to-end diffusion coefficient with that obtained for a nonlinked system. Indoleto-dansyl intermolecular energy transfer has been investigated previously in propylene glycol and methanol.33 The data were fitted well to a Gosele et al. model” yielding a diffusion coefficient cm2/s. The end-to-end in methanol at 20 “C, D = 2.64 X diffusion coefficient obtained for TU2D in methanol is only twice smaller than that recovered from the mixture of indole and dansyl, where the polyethylene linker was not present. The data obtained for the TU2D donor-acceptor system and indole-dansyl mixture show that the polyethylene linker containing 22 carbons is highly flexible and has a moderate influence on end-to-end diffusion.
Acknowledgment. This work was supported by Grants G M 39617 and GM-35154 from the National Institutes of Health, with support for instrumentation from DMB-8710401 and DMB-8502835 from the National Science Foundation. J.R.L. and W.W. express appreciation for support from the Medical Biotechnology Center at the University of Maryland.
Contribution of Long-Range Coulomb Interactions to Bimolecular Luminescence Quenching Reactions Mark D. Newsham, Robert I. Cukier,* and Daniel G . Nocera*.+ Department of Chemistry and the Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824 (Receiued: May 6, 1991: In Final Form: July 22, 1991)
The luminescence quenching of the hexanuclear cluster ions Mo,CI,,~- and W6II4’- by pyridinium and bipyridinium ions in nonaqueous solution has been investigated. Stern-Volmer (SV) plots of the emission intensity and lifetime quenching data for the reaction of M6X142-*with pyridinium acceptors are linear, and slopes of -0.48 for plots of R T In kobsvs the free energy driving force for electron transfer are in accordance with the prediction of Marcus’ theory. At driving forces greater than -0.1 V, the diffusion limit is obtained as indicated by the independence of rate with increasing driving force. In contrast to the pyridinium acceptors, the SV plots for the reaction of W6114*-with bipyridinium quenchers exhibit positive deviations from linear SV behavior. The anomalous SV behavior for the quenching of W61,42-*by I , I ’-deuterio-2,2’-bipyridinium and I -methyL2,2’-bipyridinium was investigated in dichloromethane, acetone, and acetonitrile over a range of ionic strengths. In a given solvent, the nonlinearity increases with decreasing ionic strength and, at a given ionic strength, deviation from linear behavior is observed to be greatest for quenching reactions performed in acetone. Our observations of nonlinear behavior for the quenching reaction between the oppositely charged hexanuclear cluster dianion and bypyridinium dications are qualitatively in accordance with theoretical predictions for diffusion-controlled electron-transfer reactions that are governed by long-range Coulomb interactions.
Introduction The rates of electron-transfer reactions between ions or molecules in inert solvents are characterized by three distinct regimes. Figure 1 illustrates these three regimes, which follow directly from Marcus’ classical theory of electron transfer.’ The relation between the free energy driving force AGO (which is negative for exothermic reactions) and the energy X required to reorganize the inner and outer coordination environments is
Here, kac,(0)% which is always greater than k,,,, is the electrontransfer rate in the so-called activationless regime where (AGO( X. The rate for activated electron transfer can be extremely
-
‘Alfred P. Sloan Fellow and NSF Presidential Young Investigator.
0022-365419 1/2095-9660$02.50/0
-
fast when IAGOI X for the case of bimolecular reactions exhibiting sufficient electronic coupling, and hence the observed rate, kobr = k,,,kD/(k,,, + k ~ )can , be diffusion controlled (kob = kp). When AGO is considerably greater or less than A, eq 1 gives rise to activation-controlled rates (kob = kat,). T o date, experimental investigations have emphasized the factors governing the activated electron-transfer regimes. The majority of these studies have centered on photoinduced electron transfer because a large range in driving forces can be spanned by molecules in electronic excited states2” Ample data support an increase of the electron-transfer ( 1 ) Marcus, R. A. J . Chem. Phys. 1956, 24, 966, 979.
(2) Photoinduced Electron Transfer; Fox, M. A,, Chanon, M., Eds.; Elsevier: Amsterdam, 1988; Part D. ( 3 ) Meyer, T. J. Acc. Chem. Res. 1989, 22, 163. (4) Kavarnos, G. J.; Turro, N. J. Chem. Reo. 1986, 86, 401. ( 5 ) Balzani, V.; Sabbatini, N.; Scandola, F. Chem. Rec. 1986, 86, 319.
1991 American Chemical Society
Bimolecular Luminescence Quenching Reactions
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9661
2 is applied to the quenching of luminescence of electronically excited species at dilute concentrations, the classical Stern-Volmer (SV) result is obtained20
I/
\I
I I I I
C h
=h -AGet I V
>h
Figure I . Plot of the general dependence of R T In k,, vs the free energy driving force for electron transfer as expressed by eq 1. The three distinct electron-transfer regimes are depicted for lAG,,l < A (activated normal), ~AG,,I = A diffusion controlled and lAG,J > A (activated inverted). The diffusion limit is signified by the horizontal dashed line.
rate with driving and recent investigations of acceptor/donor complexes have verified the existence of the inverted region (see Figure l),’b’5 where rates decrease as the driving force is increased further to more exothermic values. Conversely, investigations of electron-transfer reactions confined to the diffusional regime have been overlooked for the most part, due to the perception that little mechanistic information is embodied in the diffusional process. Yet, because the overall rate can depend on both the diffusional and electron-transfer rates, study of the role of the diffusional contribution to the overall rate constant kobscan be useful in elucidating the mechanism of bimolecular reactions.i6-i8 In the diffusion-controlled regime, the bimolecular steady-state rate is given by Smoluchowski’s result’9
kD = 4 ~ D i i
(2)
+
with D = DD DA the sum of donor and acceptor diffusion coefficients and ii their effective encounter distance. When eq (6) Energy Resources through Phoiochemisiry and Caialysis; Gritzel, M., Ed.; Academic Press: New York, 1983. (7) (a) Nocera, D. G.; Gray, H. B. J. Am. Chem. Soc. 1981, 103,7349. (b) Marshall, J. L.;Stobart, S.R.; Gray, H. B. J . Am. Chem. Soc. 1984,106, 3027. (8) Scandola, F.; Balzani, V.;Schuster, G.B. J . Am. Chem. Soc. 1981, 103, 2519. (9) Heuer, W. B.; Totten, M. D.; Rodman, G.S.;Hebert, E. J.; Tracy, H. J.; Nagle, J. K. J . Am. Chem. SOC.1984, 106, 1163.
(IO) (a) Closs, G.L.; Johnson, M. D.; Miller, J. R.; Piotrowiak, P. J. Am. Chem. Soc. 1989, 111, 3751. (b) Closs, G.L.; Miller, J. R. Science 1988, 240,440. (c) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J . Phys. Chem. 1986, 90, 3673. (d) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J . Am. Chem. Soc. 1984, 106, 5057. ( I 1) (a) Gould, 1. R.; Ege, D.; Mattes, S.L.; Farid, S.J . Am. Chem. Soc. 1987, 109, 3794. (b) Gould, I. R.; Moser, J. E.; Armitage, B.; Farid, S.; Goodman, J. L.; Herman, M. S.J . Am. Chem. Soc. 1989, 111, 1917. (c) Gould, 1. R.; Ege, D.; Moser, J. E.; Farid, S.J . Am. Chem. SOC.1990, 112, 4290. (12) Ohno, T.; Yoshimura, A.; Mataga, N. J . Phys. Chem. 1990, 94,4871
and references therein. (13) Wasielewski, M. R.; Niemczyk, M. P.; Svec, W. A,; Pewitt, E. B. J . Am. Chem. Soc. 1985, 107, 1080. (14) (a) Irvine, M. P.; Harrison, R. J.; Beddard, G. S.;Leighton, P.; Sanders, J. K. M. Chem. Phys. 1986, 104,315. (b) Harrison, R. J.; Pearce, B.; Beddard, G. S.; Cowan, J. A.; Sanders, J. K. M. Chem. Phys. 1987, 116, 429. (15) Chen, P.; Duesing, R.; Tapolsky, G.; Meyer, T. J. J . Am. Chem. Soc. 1989, 1 1 1 , 8305. (16) Stevens, B.; Marsh, K. L.; Sylvia, M. A. J . Phys. Chem. 1984, 88, 669. (17) (a) Joshi, G.C.; Bhatnagar, R.; Doraiswamy, S.; Periasamy, N. J . Phys. Chem. 1990, 94, 2908. (b) Periasamy, N.; Doraiswamy, S.; Venkataraman, B.; Fleming, G. R. J . Chem. Phys. 1988,89, 4799. (c) Periasamy, N.; Doraiswamy, S.; Maiya, G. B.; Venkataraman, B. J . Chem. Phys. 1988, 88, 1638. ( I 8) Ware, W.; Andre, J. C. In Time-Resolved Fluorescence Spcrmscopy
in Biochemistry and Biology;Cundall, R. B., Dale, R. E., Eds.; NATO AS1 Ser. A; Plenum: New York, 1980; Vol. 69. (19) Smoluchowski, M. V. Z . Phys. Chem. 1917, 92, 129.
7/70 = 1 ~D.O[Q] (3) where ro(lo)and r(l) refer to the excited-state lifetime (emission intensity) in the absence and presence of quencher at concentration [Q],respectively. Thus a linear dependence of r0/7 (lo/l)vs [Q] is predicted by eq 3. Deviations from linear behavior, however, are typically observed when the controlling quenching m e c h a n i ~ m ~ Iinvolves - ~ ~ ion-pair formation between the lumophore and quencher to yield a complex that does not luminesce (static quenching). More intriguing is the observation of nonlinear SV behavior for reactions in the diffusion-controlled regime that cannot be attributed to ion-pair Baird and co-workers,” K e i ~ e r ?and ~ Cukier and c o - ~ o r k e r s following ,~~ the work of Deutch and Felderh~f,~’ have derived models, based on the Smoluchowski theory of diffusioncontrolled reactions, that predict the quenching rate constant to deviate positively from linear SV behavior a t high quencher concentrations. More recently, one of us has shown3*that when the intermolecular interaction potential is of long range (e.g., is a Coulomb interaction), the above concentration effects can still be in evidence. And, for ions of opposite charge, these concentration effects are much more dramatic than those predicted for quenching when one or both species are neutral. In effect, it is as if the reaction between oppositely charged lumophores and quenchers can occur over distances much greater than their contact encounter separations. This long-range potential effect is manifested in significant deviations from linear behavior in S V plots for charged reactants a t low concentrations. Because bimolecular electron-transfer reactions of many inorganic,3eq20 r g a n i c , 4 ~and *~ p r ~ t e i n ~systems ~ - ~ ~ are characterized by intrinsically large
(20) Balzani. V.; Moggi, L.; Manfrin, M. F.; Bolletta, F. C w r d . Chem. Reu. 1975, 15, 321. (21) (a) Ballardini, R.; Gandolfi, M. T.; Balzani, V. J . Phys. Chem. 1988, 92, 56. (b) Ballardini, R.; Gandolfi, M. T.; Balzani, V. Inorg. Chem. 1987, 26, 862. (22) Rybak, W.; Haim, A.; Netzel, T. L.; Sutin, N. J. Phys. Chem. 1981, 85, 2856. (23) Frank. R.: Rau. H. J . Phvs. Chem. 1983. 87. 5181. (24) Jami&on,’M. A.; Langfoid, C. H.; SerGne, N.; Hersey, M. W. J . Phys. Chem. 1983, 87, 1004. (25) White, H. S.;Becker, W. G.;Bard, A. J. J . Phys. Chem. 1984, 88, 1840. (26) Sabbatini, N.; Bonazzi, A.; Ciano, M.; Balzani, V. J. Am. Chem. Soc. 1984, 106,4055. (27) Prasad, D. R.; Mandal, K.; Hoffman, M. 2.Coord. Chem. Reu. 1985, 64, 175. (28) Peak, D.; Werner, T. C.; Dennin, R. M.; Baird, J. K. J. Chem. fhys. 1983, 79, 3328. (29) Chattopadhyay, S . K.; Das, P. K.; Hug, G. L. J. Am. Chem. Soc. 1982, 104, 4507. (30) Nemzek, T. L.; Ware, W. R. J . Chem. Phys. 1975, 62, 477. (31) Lakowicz, J. R.; Weber, G.Biochemistry 1973, 12, 4161. (32) (a) Keizer, J. Chem. Reu. 1987,87, 167. (b) Keizer, J. Acc. Chem. Res. 1985, 18, 235. (33) Rau, H.; Frank, R. J . Phys. Chem. 1983,87, 5181. (34) Baird, J. K.; Escott, S. P. J . Chem. Phys. 1981, 74, 6993. (35) Keizer, J. J . Am. Chem. Soc. 1983, 105, 1494. (36) (a) Muthukumar, M.; Cukier, R. I. J. Siai. Phys. 1981,26,453. (b) Tokuyama, M.; Cukier, R. 1. J . Chem. Phys. 1982,76,6202. (c) Cukier, R. 1.; Freed, K. F. J. Chem. Phys. 1983, 78, 2573. (37) Felderhof, B. U.; Deutch, J. M. J. Chem. Phys. 1976, 64, 4551. (38) (a) Yang, D. Y.; Cukier, R. I. J. Chem. Phys. 1987,86, 2833. (b) Cukier, R. 1. J . Chem. Phys. 1985,82, 5457. (c) Cukier, R. 1. J . Am. Chem. Soc. 1985, 107,4115. (39) Zuckerman, J. J. Inorganic Reaciions and Methods; VCH: Darfield Beach, FL, 1986; Vol. 15, Chapter 12. (40) (a) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984,35,437. (b) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441. (41) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acra 1985, 811, 265. (42) Anderson, K. A.; Wherland, S. Inorg. Chem. 1991, 30, 624 and
references therein. (43) Gould, I. R.; Young, R. H.; Moody, R. E.; Farid, S.J . Phys. Chem. 1991. 95. 2068. (44) Kellett, M. A.; Whitten, D. G.; Gould, I. R.; Bergmark, W. R. J . Am. Chem. Soc. 1991. 113. 358. (45) Magner, E.; McLendon, G.J . Phys. Chem. 1989, 93, 7130. (46) Brunschwig, B. S.; DeLaive, P. J.; English, A. M.; Goldberg, M.: Gray, H. B.; Mayo, S.L.; Sutin, N. Inorg. Chem. 1985, 24, 3743.
9662
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
Coulomb potentials, the design of experimental schemes probing long-range potential interactions will provide insight into the dynamical processes governing fast electron exchange of a wide variety of reaction types. To this cnd, the luminescence quenching of hexanuclear molybdenum( 11) and tungsten(l1) halide cluster dianions by pyridinium and bipyridinium ions is described herein. The M6X142( M = Mo, W; X = CI, Br. I ) ions are ideal systems for the investigation of long-range potential interactions because the free energy driving force of excited-state electron transfer can be systematically varied over a wide range by simply tuning the cluster redox Thus. the activated and diffusional electrontransfer rcgions may be experimentally established for these lumophores. Moreover, the long excited-state lifetimes and high emission quantum yields that characterize this class of cluster ions49 permit quenching reactions to be investigated over extensive ranges of quencher concentration, thereby enabling the encounter distance between the lumophore and quencher to be adjusted with facility. We now report the observation of quenching reactions that are governed by long-range Coulomb interactions. Analysis of the concentration-dependent quenching rates of the M6X,42-ions with selected bipyridinium ion quenchers allows us to assess experimentally the influence of factors such as ionic strength and solvent dielectric constant that bear directly on the long-range potential interaction. Experimental Section Materials. The tetrabutylammonium salts of M6X,42-cluster ions were prepared by previously described methods.49a The chloro- and iodopyridinium salts were synthesized by addition of either excess methyl iodide or benzyl chloride to a 1:l acetone:ethanol solution of the appropriately substituted pyridine, which were used 3s received (Aldrich Chemical Co.). Addition of 1 equiv of methyl iodide to the appropriate bipyridine yielded monosubstituted 1 -methyl-2,2’-bipyridinium. Pyridinium and bipyridinium hexafluorophosphate salts were isolated upon the addition of ammonium hexafluorophosphate to acidified solutions of the chloro and iodo salts; for the 1 .I’-deuterio-2.2’-bipyridinium compound. the metathesis reaction was carried out in 6 M DCI. The isolated salts of the pyridinium and bipyridinium quenchers were twice recrystallized from acetone-water mixtures, and the purified solids were characterized electroanalytically and by ‘ H N M R spectroscopy (Bruker WM-250). Tetrabutylammonium hexafluorophosphate (Southwestern Analytical Chemicals), prior to use in electrochemical and quenching studies, was dissolved in ethyl acetate, dried over M g S 0 4 , and recrystallized from pentane-ethyl acetate solution and dried in vacuo for 12 h at 60 OC. All solvents were subject to seven freezepumpthaw (fpt) cycles and vacuum distilled into flasks containing high-vacuum Teflon valves. Acetone and dichloromethane, obtained from Burdick and Jackson, were distilled under a high-vacuum manifold onto 4-A molecular sieves. Acetone was removed from 4-A sieve by distillation into a high-vacuum flask to prevent sieve-catalyzed decomposition of acetone to mesityl oxide over long storage periods. Acetonitrile was dried over 3-A sieves by using similar methods. Methods and Instrumentation. Quenching experiments were performed by using the Stern-Volmer quenching method of luminescence intensities and lifetimes. Intensity (A,,, = 436 nm) and lifetime (X, = 355 nm from a Nd:YAG with fwhm = 8 ns) measurements were determined on equipment designed and constructed at Michigan State U n i v e r ~ i t y . ~ *Stern-Volmer .~~ ~
(47) Wherland, S.; Gray, H. 9 . In Biological Aspects of Inorganic Chemistry; Addison, A. W., Cullen, W. R.: Dolphin, D., James, 9 . R., Eds.: Wiley: New York, 1977; Chapter IO. (48) Mussell, R . D.; Nocera. D. G. J . Am. Chem. SOC.1988, 110, 2764. (49) (a) Jackson, J. A.: Turro, C.; Fiewsham. M. D.; Nocera, D. G . J . Phys. Chem. 1990, 94. 4500. (b) Zietlow. T . C.; Nocera, D. G.: Gray, H. B. Inorg. Chem. 1986, 25, 1351. (50) Newsham, M . D.; Giannelis, E. P.; Pinnavaia, T. J.: Nocera. D. C . J . A m . Chem. Sot. 1988, 110. 3885.
Newsham et al. experiments were performed on solutions containing 3 m M MO,CI,,~- cluster ion over a quencher concentration range of 10-6-10-2 M. For the W61142-quenching experiments, it was necessary to use much lower concentrations of cluster and quencher; in these experiments, the ionic strength was held constant between IO-! and IO-’ M by using tetrabutylammonium hexafluorophosphate as the supporting electrolyte. A specially constructed, high-vacuum cell, consisting of a 1-cm quartz cuvette attached to a side arm terminating with a 10-mL round-bottom flask, allowed all manipulations to be performed under highvacuum conditions. Solutions of the cluster ion were subject to 7 fpt cycles after the pure solvent was distilled from the solvent pot into the sample cell and 1, and I, measurements were performed. The solution was isolated in the I-cm cuvette with a Kontes quick-release Teflon valve. Aliquots of a standard quencher solution (-2 mM) were added to the round-bottom flask of the sample cell with a 100” Hamilton syringe and the excess solvent was distilled off. After the flask pressure was -5 X 10” Torr, the cell was removed from the vacuum line and the cluster solution isolated in the I-cm quartz cuvette was mixed with the quencher. Formal reduction potentials of the quenchers and hexanuclear clusters were determined by cyclic voltammetry using standard methods and i n s t r u m e n t a t i ~ n .Diffusion ~~ coefficients were experimentally determined for W,I,,2- and the bipyridinium quenchers by potential step chronoamperometry. A plot of i vs I / t l / ? (i, current in amperes; t , time in seconds) yields D (cm2/s) for a species of concentration Co* (mol/cm3), as described by the CottreII equation“ i(t) =
nFADIIZCo* ,I/Ztl
I2
(4)
where n is the number of equivalents, F is Faraday’s constant (9.648 X I O 4 C/equiv), and A (=0.0314 cm2) is the area of the electrode, which was purchased from Bioanalytical Systems. Diffusion coefficients were measured on W61,42-,1 ,I/-deuterio2,2’-bipyridinium, and 1-methyl-2,2’-bipyridinium solutions at concentrations of 4.44 X lo-’. 31.0 X IO-’, and 7.29 X IO-’ mol/cm3, respectively, and the supporting electrolyte was tetrabutylammonium hexafluorophosphate (0.01 M). Variable-temperature luminescence and lifetime measurements were recorded on samples cooled with an Air Products closed-cycle cryogenic system by methods described e 1 s e ~ h e t - e . ~ ~ energies were estimated from emission spectra corrected for the instrument response. The spectral responses of the monochromator and PMT were calibrated with a standard of spectral irradiance Model 245C 45- W tungsten halogen lamp from Optronics Laboratories (Serial Number L-374). The lamp spectrum was recorded using a constant current source of 6.500 f 0.002 A at 6.7 V designed and constructed by Martin Rabb (Electronics Design Engineer, Department of Chemistry, Michigan State University), and corrections in 1-A intervals from 450 to 1050 nm were made using the spectral irradiance profile of the lamp provided by Optronics. Correction files were calculated by normalizing the corrected lamp spectrum with the standard response curve of the Optronics lamp. Results Cluster ions dissolved in acetone at room temperature exhibit one-electron oxidation processes that are reversible, as evidenced by linear plots of anodic and cathodic peak currents vs (scan rate)lI2 and iJiC ratios between 0.95 and 1.05.5’ Anodic to cathodic peak separations of the reversible cluster systems were comparable to that measured for ferrocene (125 mV), thereby establishing that deviations of AE from the theoretical value of 59 mV are due primarily to uncompensated cell resistance. The reduction potentials for the Mo,CI,,-/~- and W,I,42- couples in acetone were measured to be 1.46 and 0.69 V vs SCE, respectively. ( 5 1 ) Bard, A . J.; Faulkner, L. R.Electrorhemicol Methods: Wiley: New York, 1980: p 143. ( 5 2 ) Shin, Y:g. K.; Miskowski, V . M.: Nocera, D. G.Inorg. Chem. 1990, 29. 2308.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9663
Bimolecular Luminescence Quenching Reactions TABLE I: Rate Constants for the Oxidative Quenching of MJ,:-* Pyridinium Acceptors sysAGc/ tem lumophore/pyridinium quenchePb eV 1 M0~C1~42-/4-amino-N-methylpyridinium +0.75 (AMP) 2 M0~CI~~~-/4-amino-N-benzylpyridinium (ABP) +0.70 3 M0~C1~~~/4-carbethoxy-N-ben~ylpyrid~n~um +OS4 (CBP) 4 Mo6C11~-/4-cyano-N-methylpyridinium (CMP) +0.48 5 W61,42-/1-methyl-4,4’-bipyridinium (MP) -0.19 6 W61142-/4-amino-N-methylpyridinium -0.22 7 W611~-/4-carbethoxy-N-benzylpyridinium -0.43 8 W6II4’-/4-cyano-N-methy~pyridinium -0.49 9 W61,~-/1.1’-deuterio-2,2’-bipyridinium (DBP) -0.81 IO W611~-/I-methyl-2,2’-bipyridinium (MBP) -0.89
TABLE 11: Calculated Diffusion CoeMcients and Effective
by
Quenching Distances for the Reaction of W6114*-*with Bipyridinium
khd/ M-I 5-I 1.6 X IO’ 1.3 X IO’ I .4 X IO6 3.5 X 2.9 X 3.9 x 4.1 X 3.1 X
IO7 1Olo
10’0 IO’O
Acceators
lumophore/bipyridinium quencher
LP* cm2 s-I
W61i2-/1,1’-deuterio-2,2’-bipyridinium 9 W61i2-/ l-methyl-2,2’-bipyridinium 1
X X
F,//A FDHc/A
IO-’ IOd
136
I57
38 38
“Determined from fit of data in Figure 2 to eq 12. dDiffusion coefficients experimentally determined from potential step chronoamperometry are given in ref 59. ‘Calculated from the Debye-Huckel formalism described by eq 13.
1Olo
50
e
Hexafluorophosphate salts of the yridinium (Pyt) and bipyridinium (BPy2+) acceptors. bPy+/oand BPyt/ reduction potentials measured in acetone containing 0.1 M tetrabutylammonium hexafluorophosphate at 23 i1 OC. Pyt or BPy2+, EI~,(PytI0or BPyZt/+)/V vs SCE: CMP, -0.78; CBP, -0.84; ABP, -1.00; AMP, -1.05; MP, -1.08; MBP, -0.38; DBP, -0.46. CFreeenergy driving force for oxidative quenching of MgX142-*by acceptors (ref 56). dQuenching rate constants (eq 6) determined from time-resolved luminescence measurements. ‘Nonlinear Stern-Volmer plots (see text).
I
P
e
P’
From these ground-state oxidation-reduction potentials, the redox potential of the electronically excited M6X142-can be estimated with knowledge of its spectroscopic energy according to the thermodynamic relation
Eo (M6X14-/M6X142-*) = E o (M6x14-/ M6X142-) - E0.0(M6X I?-*)
(5)
Because the free energy content of the excited state is primarily enthalpic and possesses only a small entropic the excited-state free energies of the hexanuclear cluster ions are approximated by the 0-0 energies of the luminescent excited state, which were determined directly from the high-energy tail of the low-temperature luminescence bands of the respective cluster ions by Adamson’s methodss4 The spectroscopically determined Eo,o values of 1.9 and 2.1 eV yield M6X1 I ) , eq 8 reduces to = 1
T ~ / T
(10)
and positive deviations from SV behavior will result. For larger & r O / r and [ Q ] are related by the quadratic expression
t
o.2 0.0 I ' ' -1.0
+ k D r o [ Q ] [+l (3$)''*]
70/7 "
'
' '. ' '
-0.5
I '
0.0
' .-'
"
0.5
"' '
10
' I .
''
'
1.5
' ' '
1
2.0
- AGet i V Figure 3. Plot of RT In kobs vs the free energy driving force for electron Ace,for the quenching of Mo6Cll4*-*and W61,:-* by aromatic pyridinium acceptors in acetone at 23 f I O C . The quencher numbering scheme is givcn in Table I. The solid line is a calculated fit of the data to eq I with h = 1.04 V.
transfer
vestigated with pyridinium-based quenchers of relatively low redox potential. The dependence of the activated rate on driving force for reactions above the diffusion-controlled limit can be determined by evaluating eq I . Substitution into eq I of our previous determination of X = l .04 V (Xi = 0.25,55Xo = 0.79 V in acetone) for the oxidative quenching of M6X142-ions by organic acceptors yields activated electron-transfer rates summarized by the solid line of Figure 3 . Inspection of these data reveals that the calculated (Le., the solid line) electron-transfer rates for systems 5-8 are 10'-103 greater than the diffusion-controlled rate ( R T In kobs = (0.62-3.6) X IO'O M-' s-'). This result suggests that reactions with driving forces more negative than systems 5-8 will possess sufficiently fast activated processes to ensure that the observed electron-transfer rate will reflect electron-exchange processes governed solely by diffusion (Le., k,,, >> kD). The bipyridinium ion quenchers satisfy this criterion. Activated electron-transfer rates for these systems are calculated to be I X I O i 3 M-I SKI, which is 3 orders of magnitude greater than the diffusion rate. Moreover, the increased charge of the bipyridinium will enhance the contribution of long-range Coulomb interactions to the overall diffusional process. Indeed, the combination of activationless electron exchange coupled with the encounter between a dianion and dication appears to result in deviations from conventional SV behavior for the W61,42-*/bipyridinium systems, as reflected in the data displayed in Figure 2. As one of us has previously shown,3s positive deviations from linear SV behavior are predicted from effective medium theory upon the introduction of an effective volume fraction (b),which is dependent on the quencher concentration [ Q J
-
4= 4TN~P~[Q]/3000
(7)
where 7 is an effective encounter distance between the lumophore and quencher. This effective volume fraction, which can be much larger than the material volume fraction, arises from electrostatic interactions of charged reactants. For example, for ions of opposite charge, zA and zQ, i: approaches Onsager's length5' rc = -zAZQe2/crcokBTfor rc/R large compared to unity. Here, R is the contact distance, to is the permitivity of free space, and t , is the dieleztric constant of the solvent. Since the effective volume fraction 6 replaces the material volume fraction 4 in the theoretical expressions governicg deviations from linearity in the S V expression, the small @ nonlinear SV relation is described by the following equation
= 1 -t k ~ r o [ Q 1 ( 3 b )
(1 1)
Experimentally, the quencher concentrations required to obtain large 4 are difficult to achieve, and eq I O describes most quenching reactions certainly including the M,X,42-/bipyridinium systems, which exhibit positive deviations at quenching concentrations as low as 10" M. Substitution of eqs 7 and 9 into eq 10 yields
where the S V subscript represents parameters ascertained from Stern-Volmer analysis. Therefore, a fit of eq 12 with the experimentally determined r o / r vs [ Q ] data will yield Dsv and the length of the Coulomb interaction is". T o this end, the data in Figure 2 were analyzed within the context of eq 12. The results of the best fit as determined by Kinfit analysis5*of eq 12 occur for a value of Dsv = 1 X IOd cm*/s to yield the FSv values listed in Table 11; the fits for the three systems are indicated by the solid curves in Figure 2. These values qualitatively agree well with the experimental diffusion coeffic i e n t ~and ~ ~ an independent determination of 7 for the W61,;-/bipyridinium systems calculated within a Debye-Huckel framework,6" PDH
(13)
= -zAzQrce-xrc
I n eq 13, rc = 560.6 A/tr and
K~
is defined by
2e2N~p(31 ,$ = 1 OOO€f$,
(14)
where p is the solution density, (3 = l / k B T ,and I is the solution ionic strength. Evaluation of eq 14 for the W611d2-/bi yridinium systems in acetone of I = 0.001 M gives PDH = 38 . The quenching model encompassed by eq 12 not only leads to a qualitative assessment of the long-range encounter distance but also accounts for the role that solution properties play in mediating the dependence of ro/r on [Q]; namely, deviation from the linearity expected from S V kinetics is predicted to depend markedly on solution ionic strength and dielectric constant. The effect of the solution ionic strength on quenching is exemplified by the reaction between W61142-*and l-methyl-2,2'-bipyridinium in acetone. Because PDH decreases with increasing ionic strength (eq 14), a plot of r O / 7 vs [ Q ] is predicted to approach linearity with increasing I . The data in Figure 4 confirm this prediction. The deviation from linearity clearly diminishes as the ionic strength is increased. As previously observed, Kinfit analysis of eq 12 generates experimentally determined values of FSv (Table 11) that are larger than those calculated from simple Debye-Huckel theory. Nevertheless, the expected trend of a monotonic decrease in FSv with increasing ionic strength is strictly followed. Unlike the ionic strength effect, the perturbation of the solvent's dielectric constant on the long-range quenching interaction is not
w
(58) Dye, J . L.; Nicely, V. A . J . Chem. Educ. 1971, 48, 443. (59) As predicted by eq 4, plots of i ( r ) vs l / t l / 2 for W6II4*-, 1.1'-
where ro is the usual lifetime in the absence of quencher and = k , , / k D with k D defined as (57) Onsager, L. Phys. Rec. 1938, 54, 554.
Y
deuterio-2,2'-bipyridinium, and 1 -methyL2,2'-bipyridinium are linear with respectively, and intercepts to 0.00 h slopes of 2.81, 25.4, and 6.58 mA 0.7 mA. The calculated diffusion coefficients for W6112-. 1,l'-deuterio2.3 X IO-'. 2,2'-bipyridinium. and I-methyl-2,2'-bipyridinium were 1.5 X and 2.8 X cm2/s, respectively, in acetone. (60) Weston, R. E.; Schwartz, H. A. Chemical Kinefics; Prentice-Hall: Englewood Cliffs. YJ, 1972; Section 6 . 5 .
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9665
Bimolecular Luminescence Quenching Reactions
m
40
"
20
0
60
40
it is known that diffusion coefficients decrease with decreasing ionic strength.6' However, this ionic strength effect cannot account for the magnitude of the discrepancy we find. The quantitative differences between 7. as determined from the SV analysis and Debye-Huckel theory is also difficult to rationalize. The calculation of 7,H involved integration over all distances ( x ) of a electrostatic potential interaction (V(x)) between the charged reactants,
80
[Q]/106M Figure 4. Stern-Volmer plots of the quenching reaction between W611p* and I-methyl-2,2'-bipyridinium in acetone at ionic strengths of 0.001 (0), 0.01 I (A),and 0.102 (0) M. Symbols represent experimental data and
solid curves are best fits to eq 12.
In the present analysis, V(x) was chosen to be a Debye-Huckel potential. More generally, V(x) may include a Debye-Huckel term, Vl(x), as well as other potential interactions, V(X) = V1(x) V,(x) ... (16)
+
+
The importance of ion-dipole interactions in transition-metal excited-state nonradiative decay processes have been considered for polypyridyl complexes of ruthenium and osmium.62 The ion-dipole i n t e r a ~ t i o n ~ ~
30
20 P
V2(x) = rID4/x4
2 .
0
(17)
P
10
0
0
20
40
60
80
100
[Q]/106M
Figure 5. Stern-Volmer plots of the quenching reaction between W611~-* and 1 -mcthyl-2,2'-bipyridinium in acetone (0),acetonitrile (A),and dichloromethane (0) at an ionic strengths of 0.001 M. Symbols represent experimental data and solid curves are best fits to eq 12. quite as straightforward. Cursory examination suggests that the encounter distance may decrease as the solvent's dielectric constant increases. But inspection of eqs 13 and 14 reveals that increases in i D H derived from the argument of the exponential will be accompanied by a concurrent decrease in the preexponential factor (the Onsager length decreases) as e, monotonically increases. The value of t, yielding the maximum FDH, and hence the largest predicted deviation from linear SV behavior, is determined by differentiating eq 13 with respect to t,. Solving eq 13 for diDH/ac, = 0 yields t, = 28 (for Z,ZQ = -4) and therefore quenching reactions in solvents with es; nearest 28 should exhibit the largest deviations from linear behavior. Figure 5 displays the SV plots and their Kinfits to eq 12 for the quenching reaction between W61142-and 1-methyl-2,2'-bipyridinium in dichloromethane (6, = 8.93), acetone (,e, = 20.7), and acetonitrile (e, = 38.8) a t I = 0.001 M. Clearly the anticipated behavior predicted by eqs 12-14 is corroborated.
Conclusions
In this work, the predicted positive deviations from SV behavior resulting from electrostatic interactions in the dynamical quenching regime have been verified by the W61142-/bipyridinium electron-transfer chemistry. Deviations from linear SV behavior were found to arise only when the electron-transfer rate became so large that the rate-determining step was the relative diffusion of the reactants in their mutual Coulomb field. The predicted trends for the influence of the solution dielectric constant and ionic strength on the magnitude of the deviations from linearity were experimentally verified. In particular, the initial increase and subsequent decrease in the positive deviations from SV behavior, as the dielectric constant is increased, are nicely illustrated by the quenching data. The important parameters, the effective capture distance 7 and the diffusion constant D,are qualitatively predicted. However, there are quantitative discrepancies. With regard to the diffusion coefficient, the electrochhical and luminescence quenching measurements were carried out at, respectively, high and low ionic strengths. That the D obtained from eq 12 is smaller than the one determined electrochemically is not surprising inasmuch as
where r l D = [ e p / 4 ~ e ~ e k , T ] with ~ / ~ p the dipole moment can be included in V ( x ) and the resulting integral in eq 15 carried out. Unless the ion-dipole length is comparable to rc, an unlikely circumstance, the effect of this term only produces a small (about 10%)increase of 7. compared with that calculated considering only the Debye-Huckel potential. Additionally, dielectric saturation, whereby the dielectric constant appears smaller near the ion than in the bulk of the solvent, may contribute to V(x) in ionic envir o n m e n t ~ . ~Unless ~ the dielectrically saturated region extends to an unrealistically large extent, approaching rc, this effect was also found to be minimal a t best. The fact that short-range interactions, such as ion-dipole interactions and dielectric saturation, or the inclusion of a contribution from the finite distance over which an electron-transfer reaction can occur, provide a negligible increase to the magnitude of 7. is not surprising on the basis of the fact that the Debye-Huckel interactions are relatively large and dominate a t long distances. Another possible correction to the theory employed here comes from the accounting for the possibility that the fluorophore concentration decays via the intrinsic lifetime 7o mechanism in addition to quenching. This effect was pointed out by Weller65 and further discussed by Szabo.66 For the ionic case, it leads / ~ could lead to the replacement of (34)II2 by (34 ? / D T ~ ) Iand to an increase in the apparent value of P. However, even for the lowest quencher concentration used here, this correction is much too small to be of significance. A final possibility which may influence the theoretical result is the violation of the condition that the ionic atmosphere has had time to develop warranting a steady-state approach to the quenching process. The characteristic time for the development . lowest of the ionic atmosphere is given by 7atm ~ / D KAt~ the ionic strength used here, K = 0.02 A-I and 7atm 4.5 ns. This time is comparable to the time it takes to diffuse a distance 7.. The manifestation of such a possibility would be a lack of exponential decay in the time course of the fluorescence intensity. Thus, while this mechanism would lead to an enhanced quenching rate, and an apparent increase in 7. (since the initial rate would be larger than that obtained after the steady-state concentration gradient is established), it would have to be accompanied by deviation from exponential decay in the fluorescence intensity.
+
- -
(61) Kolthoff, I. M.; Lingane, J. J. Polarography, 2nd ed.; Wiley Interscience: N e w York, 1952; Chapter 4. (62) Vining, W.J.; Caspar, J. V.;Meyer, T. J. J . Phys. Chem. 1985,89, I 1-195
(63) Bakale, G.; Gregg, E. C.; McCreary, R. D. J. Chem. Phys. 1977,67, 5788. (64) Kober, E. M.; Sullivan, B. P.; Meyer, T. J. fnorg. Chem. 1984, 23, 2098. (65) Weller, A. Z . Phys. Chem. 1957, 13, 335. (66) Szabo, A. J. Phys. Chem. 1989, 93, 6929.
J . Phys. Chem. 1991, 95, 9666-9612
9666
In summary, the results of electron-transfer reactions in a dynamical quenching regime can be qualitatively rationalized. Nevertheless, quantitative aspects relating theory and experiment presently remain unresolved. To this end, a comparison of theory and experiment which focuses on the combined effects of shorttime dynamics and concentration effects on the transient behavior of the fluorescence lifetime would be welcome.
Acknowledgment. We thank Claudia Turro for computational assistance. Financial support from the National Science Foundation (D.G.N., CHE-8705871; R.I.C., CHE-8318101) and the Center for Fundamental Material Research. D.G.N. also gratefully acknowledges a Presidential Young Investigator Award administered by the National Science Foundation and the financial assistance provided b) Dow Chemical Co.
Conformation-Dependent Intramolecular Electronic Energy Transfer in a Molecular Beam Mita Chattoraj, Balakrishna Bal, G. L. Gloss,* and Donald H. Levy* The Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (Received: May 28, 1991)
The electronic spectrum of a molecule consisting of two chromophores separated by a spacer was observed in a supersonic molecular beam. The chromophores were anisole and dimethylaniline (DMA), the spacer was cyclohexane, and the chromophores were attached to the I - and 4-positions of the spacer. Each chromophore could be attached axial ( a ) or equatorial (e) with respect to the cyclohexane and the conformers ae, ea, and ee were observed. The aa conformer is not energetically allowed and was not observed. Following excitation of the SI state of the anisole moiety, emission was observed from both the anisole and DMA parts of the molecule. Since there was no direct absorption by the DMA, the emission from the DMA was produced by intramolecular electronic energy transfer. Measurement of the relative intensities of the anisole-like and DMA-like emissions provided a measure of the relative electronic energy transfer rates of the various conformers. It was found that energy transfer was considerably slower in the two trans (ee) conformers than in the four cis (ae and ea) conformers. This observation is not consistent with either simple Forster energy transfer theory, which predicts that the electronic energy transfer rate of all six conformers should be nearly the same, or the Dexter formalism, predicting that the trans isomers should be faster.
Introduction In addition to being of intrinsic scientific interest, electronic energy transfer has important implications in various fields such as biological systems, dye lasers, and wavelength shifters.' Recently much work has been done on intramolecular systems of the type A-Sp-D, where A using bichromophoric is an acceptor chromophore, D is a donor chromophore, and S p is a spacer. If the intervening spacer is rigid and the distance between and the relative orientation of the acceptor and donor is known, it is possible to probe the effects of geometrical factors on energy transfer. Several theoretical models have been formulated to account for the energy transfer observed. On the most fundamental level, radiationless transition theory explains the phenomena completely. Often the systems studied are too unwieldy to do a b initio calculations and a simpler formulation for the process becomes essential. ForsterIo modeled the interaction between the donor and acceptor as a simple Coulombic one and came up with one of the more widely accepted and easy to apply theories. When the chromophores are close enough to one another that the overlap of wave functions cannot be ignored, the Forster model becomes inapplicable and the Dexter model," using the Speiser, S. J . Pholochem. 1983. 22, 195. (2) Getz. D.; Ron, A.; Rubin, M. B.: Speiser. S. J . Phys. Chem. 1980, 84. 768. ( 3 ) Zimmerman, H. E.; Goldman, T. D.; Hirzel. T. H.; Schmidt, S. J . Org. Chem. 1980. ~ 45. .3935. ~ , (4) Hassoon, S.; Lustig (Richter), H.; Rubin, M. B.; Speiser, S Chem. Phys. Lerl. 1983, 98, 345. ( 5 ) Hassoon, S.:Lustig. H.: Rubin. M. B.; Speiser. S . J . Phys. Chem. 1984. (1)
~
88. 6367 ...
(6) Mugnier, J.; Valeur. B.; Gratton. E. Chem. Phys. Lett. 1985, 119, 217. (7) Ernsting, N. P.; Kaschke, M.; Kleinschmidt, J.; Drexhage. K. H.; Huth. V . Chem. Phys. Left. 1988, 122, 431. (8) Gryczynski, 1.; Wiczk, W.; Johnson, M. L.: Lakowicz. J. R . Chem. Phys. Lelf. 1988. 145, 439. (9) Closs. G.L.; Piotrowiak. P.;Maclnnis, J . M., Fleming, G R . J . Am. Chem. Soc. 1988, /IO,2652. (IO) Forster. Th. Discuss. Faraday SOC.1959, 27, 7.
0022-365419 112095-9666$02.50/0
exchange interaction between two charge clouds, has been used to model the phenomenon. Most of the work on energy transfer has been done in condensed phases where the solvent plays an active role and it is not possible to observe solely the intramolecular electronic relaxation process. Only very limited gas-phase studies have been performed.'* In the present work we have observed intramolecular electronic energy transfer in the rigid bichromophoric molecule 1-(4anisyl)-4-(N,N-dimethyl-4-anilinyl)cyclohexane (AC6D) under the isolated conditions of a supersonic jet expansion. The interpretation of the spectra was facilitated by studying the monochromophoric systems 4,N,N-trimethylaniline (TMA) and 4-anisylcyclohexane (AC,) shown in Figure 1. The electronic absorption spectrum of the bichromophore is practically a superposition of the spectra of anisole and N,N-dimethylaniline (DMA), indicating that the electronic interaction between them is weak. As a result, we have been able to exclusively excite the donor and probe the energy transfer process by dispersing the fluorescence emission. In the ultracold environment of a molecular beam it has been possible to isolate individual conformers and examine the dependence of the rate of energy transfer on the conformer excited. We find that the cis isomer in its various conformations transfers energy much more rapidly than the trans isomer. These observations are examined in the light of previous theorq. Experimental Section The model compounds were synthesized by standard methods.I3 The spectra presented here were recorded using resonantly enhanced two-photon ionization, fluorescence excitation, and dispersed fluorescence techniques. Detailed descriptions of the ex( I I ) Dexter. D. L. J . Chem. Phys. 1952, 2 1 , 836. ( 1 2 ) (a) Ebata, T.: Suzuki, Y.; Mikami, N.; Miyashi, T.; Ito, M. Chem. Phys. Left 1984. 110, 597. (b) Felker, P. M.; Syage, J. A.; Lambert. W. R.; Zewail, A. H. Chem. Phys. Lert. 1982, 92, I . i 13) Sigman, M. E.; Closs, G L . J . Chem. Phys., to be published.
0 199 1 American Chemical Society
