11942
J. Phys. Chem. 1994, 98, 11942-11947
Evaluation of Ion-Annihilation Reaction Kinetics Using High-Frequency Generation of Electrochemiluminescence Maryanne M. Collinson and R. Mark Wightman* Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290
Paolo Pastore Universita di Padova, Dipartimento di Chimica Inorganica, Metallorganica e Analitica, Via Marzolo I , 35131 Padova Italy Received: June 4, 1994; In Final Form: August 31, 1994@
The bimolecular rate constants for the annihilation reactions of the radical ions of 9,lO-diphenylanthracene (DPA), 9,lO-dimethylanthracene (DMA), and ruthenium(I1) tris(bipyridine) (Ru(bpy)3*+)in acetonitrile and DPA in propylene carbonate have been measured using electrogenerated chemiluminescence (ECL). In this work, a high-frequency multicycle square wave was applied to a microelectrode and the resulting luminescence curves were fit to an appropriate computer simulation. The analysis was complicated by the direct interaction of the emission with the metallic electrode due to the close proximity of the ECL reaction layer to a reflecting surface. Significant deviations between theory and experiment were apparent during the rising portion of the ECL curve and when high frequencies (short step times) were used. Under these conditions, the ECL reaction layer is within a distance of 200 nm from the electrode surface. These effects were least apparent with carbon-fiber microelectrodes consistent with their lower electrode reflectivity and density-of-states. Diffusioncontrolled ion-annihilation rates of ( 2 f 1) x 1O’O M-’ s-l were measured for DPA, DMA, and Ru(bpy)3*+ in acetonitrile and (4 f 1) x lo9 M-’ s-’ for DPA in propylene carbonate, a more viscous solvent. The unimolecular rate constant for singlet formation for DPA in acetonitrile and propylene carbonate was calculated to be ca. 3 x lo9 and 5 x lo8 s-l, respectively. The ca. 6-fold smaller unimolecular rate for DPA in propylene carbonate can be attributed to the longer solvent relaxation time for propylene carbonate compared to acetonitrile. The rate to form the triplet state proceeds at the diffusion-controlled limit for DMA, DPA, and Ru(bpy)3*+ consistent with the predictions based on electron-transfer theory.
Introduction Electrochemiluminescence (ECL) is a process in which electrogenerated products react to form a population of excited states via electron-transfer reactions.’-3 Modem electrontransfer theories predict that the highly exothermic production of the ground states proceeds in the inverted r e g i ~ n . This ~ allows the formation of the excited state to be kinetically competitive with other nonradiative pathways which are predicted to occur near the diffusion-controlledlimit. The relative rates of formation of the excited states can be obtained from experimental measurements of the ECL efficiency (eq 8 below) if all the reaction pathways are The direct measurement of the rates of electron transfer associated with ECL, however, has not been reported. In the complementary reaction scheme which involves photoinduced electron transfer, timeresolved fluorescence quenching has been used to measure the rates to form the separated radical ions and ground state donor and acceptor The “back” electron-transfer rate to reform the emitting excited state, however, is not readily accessible from such experiments. This value can be obtained from the ECL providing the ECL efficiency and total rate of ion annihilation ( k d ) are known. Thus, the direct measurement of the ion-annihilation rate constant should render insight into the highly energetic electron-transfer reactions involved in both ECL and photoinduced electron-transfer processes. In this work, we use high-speed electrochemical techniques to monitor the real time rate of ECL generation. A simplified
* To whom correspondence should be addressed. @Abstractpublished in Advance ACS Abstracts, October 15, 1994. 0022-3654/94/2098-11942$04.50/0
reaction sequence for ECL from DPA, the principal compound used in this work, is shown below. The energy supplied by the ion-annihilation reaction, 3.1 eV, is sufficient to directly populate the emitting singlet state (3.0 eV) although the nonemitting triplet (1.8 eV) is also energetically accessible, and hence populated.*
DPA
+ e- - DPA’-
DPA - e-
-
+
(1)
DPA’+
(2)
+
DPA*+ DPA*- k,‘~DPA* DPA
+ DPA’- 3DPA* + DPA DPA” + DPA’2DPA ‘DPA* - DPA + hv kmnh = k,’ + k,‘ + kgs’
DPA”
+EcL =
where
+ex
= kS’@,’
+ k,‘ + kgs’)
(3) (4) (5)
(6)
(7) (8)
In these experiments, a microelectrode is continuously stepped between the oxidation and reduction potentials of the precursor molecule, i.e., DPA, to alternately generate the radical ions.’* The cation and anion radicals react in a thin plane at a point where the inward and outward fluxes meet and subsequently produce light. When the dimensionless kinetic parameter, A = 0 1994 American Chemical Society
Evaluation of Ion-Annihilation Reaction Kinetics km&fC, approaches infinity, the reaction layer is an infinitely thin parallel plane which moves nearly linearly away from the electrode surface with time.13-15 This plane of light broadens and becomes Gaussian-like as A decreases. When A drops below 1000, i.e., when tf and C are significantly reduced, the transfer from diffusion to kinetic control begins and distinct changes in the shapes of the ECL curves become apparent.16-17 The ionannihilation rate constant can be theoretically evaluated from the characteristic shapes of ECL curves obtained in dilute solutions and at reduced step times.17 This interpretation is complicated, however, by the interaction of the emission with the metal electrode surfaces. As will be shown, these effects were least apparent with carbon electrodes. Rate constants at the diffusion-controlled limit were measured for DPA, dimethylanthracene, and ruthenium(II) tris(bipyridine)in acetonitrile (ACN) and for DPA in propylene carbonate (PC) using carbonfiber microelectrodes.
Experimental Section Electrode Preparation and Procedures. Platinum or gold microdisk electrodes were prepared by heat sealing the microscopic wires (Goodfellow) with nominal radii of 1-5 p m in 4 mm 0.d. soft glass tubing.18 Carbon-fiber microelectrodes (T300, nominal radii of 3.5 pm) were prepared by sealing the fibers in glass tubing with epoxy (EPON 828 with 14% metaphenylenediamine, Miller Stephenson) and curing at 75 "C for 2 h and 150 "C for at least 2 h. A piece of silver foil (0.3 mm thick, Johnson Matthey) was placed concentrically around the glass tubing, and this assembly was then encased in epoxy. The epoxy-encased electrode assembly was polished with fine sandpaper until the working and reference electrodes were completely exposed. This assembly was then polished with 6and 1-pm diamond paste on Nylon cloths (all, Buehler). The microelectrodes were polished with 1-pm diamond paste and thoroughly rinsed with ACN before use. The carbon-fiber microelectrodes used in the kinetic measurements were further polished with 0.05-pm alumina on a napless cloth and rinsed with water and ACN. The experimental apparatus and procedures have been described elsewhere.'* Briefly, the experimental setup is a flowinjection system (FIA) incorporating single-photon counting detection. A Wavetek Model 143 function generator applied a continuous symmetric square wave to the cell and also triggered the photon counter. The microelectrode was either connected to ground or to a current amplifier. The electrode potentials were optimized at each frequency as previously described and monitored with a digital oscilloscope (LeCroy 9450). In all cases, the ECL curves represent the sum of data acquired from either 100 or 1000 cycles which have been triggered when the electrode potential is stepped negative. FIA dilution factors of 0.80 f 0.05 (ACN) and 0.88 f 0.05 (PC) were determined from a comparison of the ECL intensity obtained with the ca. 100-pL injector loop used to introduce the sample in this work to the steady-state response acquired with a 1-mL loop. Reagents. Acetonitrile (ACN, UV, Burdick & Jackson) and toluene (TOL, Burdick & Jackson) were used as received. Propylene carbonate (PC, Burdick & Jackson) was passed through a column of activated alumina in a glovebox under a nitrogen atmosphere. 9,lO-diphenylanthracene (DPA, Aldrich) and 9,lO-dimethylanthracene (DMA, Aldrich) were recrystallized twice from absolute ethanol. Tris(2,2'-bipyridyl)ruthenium hexafluorophosphate, Ru(bpy)pFs was prepared by metathesis of tris(2,2'-bipyridyl)ruthenium chloride hexahydrate (Aldrich) and ammonium hexafluorophosphate in water. The filtered product was recrystallized twice in an ethanol/ACN mixture.
J. Phys. Chem., Vol. 98, No. 46, 1994 11943 1 .o
8
0.5
-;
1 '.
0.0
H
0.5
-E 1 '.
0.0 0.0
0.5 t/t,
0.0
0.5
1 .o
ut,
Figure 1. Normalized ECL from 0.38 mM DPA in ACN containing 0.1 M TBAH at a Pt disk ( r = 1 ym) (-) and corresponding simulated curves (- - -) as a function of frequency. Simulations for kmnih = 2 x 1OloM-' s-l and RCdl = 0.10 ys.
Tetrabutylammonium hexafluorophosphate (TBAH, Aldrich) was recrystallized twice from 95% ethanol. All chemicals were dried under vacuum at 60 "C and stored in a desiccator. Solutions were prepared fresh each day and were deoxygenated with solvent saturated nitrogen. The PC solutions were prepared in a glovebox under a nitrogen atmosphere. Simulation. The program was written in Pascal using a Hopscotch algorithm. Simulations were performed on an 80486 computer. The background current was calculated using the equation, i, = CddE/dt, where Cd is the double-layer capacitance and dE/dt represents the potential step. The faradaic current (if) was determined by a conventional finite difference approximation of diffusion to a plane. The true multicycle potential wave form was calculated from the difference between the applied potential and the (if -I-i,)R drop through an iterative procedure. The simulation program contained a number of parameters: rz (number of squarewave cycles) = 5 (the ECL is approximately pseudo-steady-state at this point in the simulation); tf, tr (forward and reverse step times); R (solution resistance, calculated from values of the electrode radius (determined from steady-state voltammetry) and the specific resistivity of the ele~trolyte'~); c d l (double-layer capacitance, determined from the charging current measured by cyclic voltammetry); D (diffusion coefficient, determined from steadystate v ~ l t a m m e t r y ~=1.3 ~ ~ ~x) (DPA, ACN), 8.3 x (DPA, 5050 ACNTTOL), 1.6 x (DPA, PC), 9 x cm2/s (Ru(bpy)32+,ACN); C (DPA concentration, experimental value incorporating FIA dilution factor); A = electrode area (calculated from electrode radius); E'R, E O 0 (applied potentials); k-h (ion-annihilation rate constant, eq 7); a (electron-transfer coefficient) = 0.5; ,@ (heterogeneous electron-transfer rate constant) = 1 cm/s. Additional details regarding the simulation will be published elsewhere.
Results ECL from DPA. ECL curves for 0.38 mM DPA at an r = 1 pm Pt electrode in ACN as a function of the applied square wave frequency are shown in Figure 1. The radical anion produced during the first step reacts with the radical cation
Collinson et al.
11944 J. Phys. Chem., Vol. 98, No. 46, 1994
R
0.38 m M /
1 .o
0.5
t, 1 s
t, P
Figure 2. ECL from 5.8 mM DPA in 5050 ACN/TOL containing 0.1 M TBAH and 0.38 mM DPA in ACN containing 0.1 M TBAH at 5.3 kHz at a Pt disk ( r = 1 pm) (-). Corresponding simulated curves (- - -) for k m i h = 2 X 10'' M-' S-' and RCdl = 0.22 PS (50:50)and 0.10 ps (ACN). The first curve corresponds to the reduction of DPA.
generated on the previous step to produce ECL. The luminescence increases sharply as the radical ions meet and then decays as the reactants are depleted. The transfer from diffusion to kinetic control is evidenced from the decrease in amplitude, the increase in width, and the shift in the peak maximum of the curves as the step time, and hence A, decreases.16J7 Figure 1 also shows a comparison of the simulated curves to the experimental data with a k d of 2 x 1O'O M-l s-l. The simulation predicts certain features in the data such as the delay time in the initial ECL and the diminished amplitude and increased breadth of the ECL curve with decreasing step time. The delay time is due to the electrochemical time constant (the product of the double-layer capacitance and the uncompensated solution resistance) whereas the diminished amplitude and increased breadth are due to the finite ECL kinetics. The simulation, however, does not predict the slow rise in emission or the substantially lower amplitude evident in Figure 1 as the step time is decreased from 48 to 5 ps. Similar results were obtained with r = 3-10 pm Au or Pt disk electrodes, with different compounds and solvents, with half the electrolyte concentration, and when the ECL pulse from the second half of the cycle was examined.21 Electrode Reflectivity. Figure 2 shows a direct comparison of experimental and simulated ECL curves obtained with 0.38 and 5.8 mM DPA at an r = 1 p m Pt electrode. In both cases, the ECL is lower in intensity and takes longer to rise than predicted. However, at high concentrations of DPA, distinct oscillations in the ECL intensity can be observed on the decaying emission. We have previously attributed these features to the direct interaction of the emission with the metal electrode due to the close proximity of the light-emitting species to the metal electrode surface.22 At an applied frequency of 2 kHz (tf = 200 ps), the ECL reaction layer is located within 1000 nm from the metallic surface throughout one potential step. At 200 kHz (rf = 2.5 p s ) , the reaction layer travels only 100 nm. The oscillations are not observed at low concentrations because the ECL reaction layer is significantly broader (vide infra). At all concentrations and especially at high frequencies, however, both the ECL intensity and the area under the experimental ECL curves are significantly less than the simulated curves. This has been attributed to nonradiative energy transfer and electron transfer to the metal ~ u r f a c e . ~ ~ - ~ ' A comparison of the ECL curve shapes obtained with different electrode materials is shown in Figure 3 for 0.2 mM DPA. The normalized ECL curves obtained with a carbonfiber microelectrode rise faster than those observed with Au or Pt electrodes. This result is consistent with carbon's lower reflectivity and density-of-states compared to the metallic
0.0
5
0.0
1 .o
0.5
0.0
0.5
t/t,
I a,
0.0
11
0.5 t/t,
0.0
21 KHz
0.5
1 .o
t/t,
Figure 4. Normalized ECL from 0.17 mM DPA in ACN containing 0.1 M TBAH at a carbon-fiber microelectrode ( r = 3.5 pm) (-) and corresponding simulated curves (- - -) as a function of frequency. The experimental data have been corrected for signal losses due to fouling of the electrode. Simulations for km,h = 2 x 10''' M-' s-l and RCdl = 0.89 PS.
When the electrodes are polished with a finer polish (0.05-pm Alumina), the ECL curves provide a better agreement to theory due to the lowered scatteringheflectivity. Since the ECL is less affected by reflectivity/quenching, ionannihilation rate constants were determined from the emission obtained with finely polished carbon-fiber microelectrodes. Measurement of k d . A comparison of experimental ECL curves obtained with an r = 4 p m carbon-fiber electrode and simulated curves with k d = 2 x 1Olo M-' s-' is shown in Figure 4 for 0.2 mM DPA.29 The overall fit is significantly better than fits obtained with either platinum or gold microe l e c t r o d e ~ .The ~ ~ experimental ECL curves decrease in amplitude and increase in breadth as the applied frequency is increased consistent with theory. Under these conditions (A < 250), the ECL signal is quite sensitive to variations in the ion-annihilation rate constant. If k d is increased to 5 x 1OO ' M-' s-l, the full-width at half-height is ca. 33% narrower than the experimental data. Alternatively, if k d is decreased to 1 x 1O'O M-' s-', the full-width at half-height is ca. 25% broader than the experimental data. Figure 5 shows the comparison of simulated and experimental curves for 0.23 mM DPA in PC at a carbon-fiber microelectrode with k d = 5 x lo9 M-' s-'. The shapes of the ECL pulses for DPA are considerably different in PC compared to ACN in accord with the near order-ofmagnitude smaller rate constant. The larger delay time in the initial ECL when compared to ACN is consistent with the ca. 6-fold increase in the electrochemical time constant due to the
Evaluation of Ion-Annihilation Reaction Kinetics
J. Phys. Chem., Vol. 98, No. 46, 1994 11945
largest differences between theory and experiment occurred when t/tf was small and/or at high applied frequencies (small tf). As previously described, the presence of the oscillations in the ECL intensity at high concentrations provides unique experimental evidence of the movement of the ECL reaction layer through the course of reactant generation.22 Under these conditions, the ECL reaction layer is a very narrow plane which 0.0 0.5 0.0 0.5 1.00.0 0.5 1.0 1.5 moves nearly linearly away from the electrode surface with time. t/t, t/t, t/t, This effect is greatly diminished at low concentrations because Figure 5. Normalized ECL from 0.23 mM DPA in PC containing 0.1 the second-order rates are slowed and the ECL reaction layer M TBAH at a carbon-fiber microelectrode ( r = 3.5 pm) (-) and is sufficiently broadened.13 corresponding simulated curves (- - -) as a function of frequency. The effect of a metal reflecting surface on the lifetime of an Simulations for kmlh = 5 x lo9 M-' s-' and RCdl = 6.1 p s . emitting species has been investigated by a number of research ca. 6-fold decrease in the ionic conductivity of the e l e ~ t r o l y t e . ~ ~ groups including those of Drexhage, Kuhn, and C h a n ~ e . ~ ~ - ~ ~ In their experiments, a fluorescent molecule is tethered at various Since PC is more viscous than ACN and has a considerably distances from a metal surface using fatty acid spacers deposited larger delay time, reaction of the radial ions with impurities is with the Langmuir-Blodgett technique. At small distances, the more problematical in this solvent even at high frequencies. excited molecules are strongly quenched via nonradiative energy Therefore, the PC solutions were prepared under a nitrogen transfer to the metallic surface while at long distances oscillaatmosphere as described in the Experimental Section to minitions in the lifetime of the emitting species are observed. mize the presence of these impurities. Quenching of the ECL intensity via nonradiative energy and Other Compounds. ECL from DMA and R ~ ( b p y ) 3 ~in+ electron transfer pathways with the electrode surface has also ACN at high frequencies was also examined with carbon-fiber been observed by Bard and co-workers using Langmuir microelectrodes. The normalized ECL pulse shapes for DMA deposited and adsorbed monolayers of ruthenium complexes.27 are nearly identical to those obtained with DPA when the same Significantly higher ECL intensities from the organized monoconcentrations are used (data not shown). The ECL intensity layer were observed when tin oxide electrodes were used relative from DMA is ca. 50% smaller than that obtained for DPA as to metal electrodes in agreement with this quenching previously described due to its lower fluorescence efficiency mechanism.27a (0.49).32 ECL from Ru(bp~)3~+ is not as stable as that obtained ECL is less affected by reflectivity/quenching when carbonwith DPA or DMA. A smaller ECL pulse is observed when fiber microelectrodes are used consistent with carbon's lower the electrode potential is stepped negative indicating the Rureflectivity coefficient and a lower density-of-states than Au or ( b ~ y ) 3 ~is+not completely stable on these time scales. When Pt.28 Indeed, the luminescence curve for DPA in ACN obtained normalized, the shape of the ECL corresponding to the more with a carbon-fiber microelectrode consistently rose more stable form of R~(bpy)3~+ is nearly identical to the shape sharply than those obtained with either Au or Pt, Figure 3. obtained with DPA at a carbon-fiber microelectrode (data not Typical light intensities obtained with carbon were also about shown). half that obtained with a Au electrode consistent with lower Discussion reflectivity. When this data was fit to the simulation, k d was determined to be (2 & 1) x 1Olo M-l s-l for DPA in A C G 9 ECL from DPA. High-frequency generation of ECL has and (4 & 1) x lo9 M-' s-l for DPA in PC. These rates are in many significant advantages including improved reactant stabilagreement with the diffusion-controlled values of 2.1 x 1Olo ity and the capability to measure the ECL reaction kinetics.12 and 2.3 x lo9 M-I s-l, respectively, calculated via the Eigen In previous work, we evaluated a lower limit of k d for DPA equation.33 The direct measurement of diffusion-controlled in ACN by analyzing high-frequency ECL curves in terms of reaction rates for DPA in two different solvents experimentally Feldberg's theoretical model13 and showed it was near the verifies the theoretical prediction that k( is at the diffusiondiffusion-controlled limit.12 In the present work, we obtained controlled limit.7 This is also in agreement with previous work a more accurate measurement of km& by simulating the time which places the radical-ion recombination reaction between distribution of the emitted photons and matching it to the pyrene and diethylaniline to form the excited state triplet at the experimental data. This experiment is similar to that proposed diffusion-controlled limit in ACN.' Id by Van Duyne and Drake17 in the 1970s which had limited The experimental measurement of k d coupled with the success due to the greater time constant of the larger electrode previous measurements of ECL efficiency7 for DPA enables employed. In the present work, the use of microelectrodes the unambiguous determination of the rate constant for light enabled the time scale of the experiment to be significantly emission for the first time for ECL reactions. Since the reduced in order to access the reaction kinetics without denominator of eq 8 and k d (eq 7) are synonymous and significantly distorting the results.18 However, as evident in represent the sum of all rates which lead to the emitting and Figures 1 and 2, there are still some obvious discrepancies nonemitting states, the bimolecular rate constant for singlet between the model and the experiment. These differences can formation, k,', can be readily obtained without any simplifying be directly attributed to direct interaction of the emission with assumptions. When the spin statistics (1/4 singlet; 3/4 triplet) the metallic electrode surface. While the reduced time scale are taken into account, k,' is calculated to be 5 x lo9 M-' s-l enables the reaction kinetics to be accessed, it also places the with k-h = 2 x 1Olo M-' s-l, = 6.1%,7 and 4fl = ECL reaction plane within a wavelength of light from a metallic A similar analysis for DPA in PC ( k d = 4 x lo9 M-' s-l, surface. As a result, significant deviations in the rate of light &CL = 3.5%7)gives a k,' of 6 x lo8 M-' s-l. emission occur due to nonradiative energy transfer and electrode r e f l e ~ t i v i t y . ~ The ~ - ~ magnitude ~ of reflectivity/quenching will In prior steady-state measurement^^^ of ECL, we have shown be strongly dependent on the position of the light-emitting layer that &CL increases with decreasing ionic strength, a result which with the largest effect occurring when the ECL reaction layer suggests that the ECL efficiency is a function of the rate of is closest to the metal surface (small tltf, tf). In agreement, the encounter of the radical ions.7 Having established that k d is
Collinson et al.
11946 J. Phys. Chem., Vol. 98, No. 46, 1994
for it are not available for DPA in ACN or PC. However, since
I is significantly larger than AGO, (-0.1 eV (ACN); -0.024
0 ’
0
I
I
4
8
k-,
x lo-’
I 12
s-’
obtained from steady-state Figure 6. Double reciprocal plot of measurements of DPA in ACN as a function of ionic strength3’ and k-d calculated via the Eigen equation.33The solid line represents the linear regression fit of the experimental data (slope = 1.5 x s, y-intercept = 1.7, R2 = 0.996).38
eV (PC)), the differences in the exponential term in eq 11 in the two solvents are at most a few percent. Thus, the ratio of the unimolecular rate constants determined in this work yields the ratio of Y , K ~ ~for DPA in ACN relative to PC. Assuming an adiabatic electron-transfer reaction ( ~ = ~ l), 1 then (vn)ACN/ (Yn)pc is ca. 6. The smaller value of v, for DPA in PC is consistent with the longer longitudinal dielectric relaxation time for PC compared to ACN.6c,41 Other Compounds. A comparison of the normalized shapes of the ECL pulses for DMA and Ru(bp~)3~+ in ACN to DPA reveal that these reactions also proceed at the diffusioncontrolled rate of ca. 2 x 1O1O M-’ s - ~ ! ~ When the lower fluorescence of DMA is accounted for, the values of +ex for producing the excited state are similar for the two compounds.12 Since the energy available for formation of the singlet is nearly the same as for DPA, this similarity is an anticipated result. ECL from Ru(bp~)3~+ results from the formation of the excited triplet state as described by the following reacti01-1.~~
+
R ~ ( b p y ) , ~ + Ru(bpy),’+
+
3(Ru(bpy)32+)*
Ru(bpy);+
diffusion controlled and assuming that triplet formation is the only competitive reaction, then eq 8 can be rewritten7 as
where k, is the unimolecular rate for electron transfer after formation of the encounter complex and k-d is the rate of dissociation of the encounter complex back into the radical ions. An independent estimate of the rate of singlet formation can be determined from the slope of a plot of ~/&cLvs k-d as previously d e ~ c r i b e d . ~Data3’ ~ - ~ ~ for DPA obtained in ACN, but at different electrolyte concentrations to alter k-d, are analyzed in this way in Figure 6. As expected, a linear dependance of l/(beclvs k-d (calculated via the Eigen equation33) and an y-intercept near the expected value of 4 are obtained.38 A unimolecular rate constant of 2 x lo9 s-l was calculated from the slope. This value is in good agreement with the unimolecular rate of 3 x lo9 s-l (u = 0.1 M) calculated from the following e q ~ a t i o n ~ ~with - ~ Ok,’ = 5 x lo9 M-’ s-l (above) where Ka = kd/k-d and kd is the diffusion-controlled rate constant.33
-
( 12)
The energy supplied by the ion-annihilation reaction (2.6 eV) is sufficient to directly populate the triplet state (2.1 eV), and ECL proceeds through the energy sufficient “S-route” reaction mechanism similar to DPA!3 In distinct contrast to DPA, the efficiency for the production of the excited state in the ionannihilation reaction approaches 100%at low temperatures. This has been regarded as evidence for the presence of an inverted region according to Marcus theory, i.e., kgi strongly it1hibited.4~~ Consistent with the near 100%production of the emitting triplet state, the ECL efficiency does not show an ionic strength dependence as observed for DPA.’I~~ The direct measurement of a diffusion-controlled reaction rate ( k d = k,‘ kgl) further validates this result and confirms that k,‘ is at the diffusioncontrolled limit for R~(bpy)3~+.
+
Conclusion
High-frequency generation of ECL can be used to acquire fundamental information about highly energetic electron-transfer reactions. The individual rates of reaction for the formation of the emitting and nonemitting excited states can be directly measured through the comparison of the experimental ECL data A unimolecular rate for DPA in PC of 5 x lo8 s-l (u = 0.1 M) with a theoretical model. The electrochemical time constant was similarly calculated via eq 10 from the bimolecular rate needs to be incorporated into the theoretical model since its constant of 6 x lo8 M-’ s-l determined from km& and &CL value dictates the delay in the luminescence curve. Careful consideration should also be given to electrode reflectivity/ above. The solvent dependence of the unimolecular rate constants quenching effects. While the reduced time scales enable the reaction kinetics to be measured, it also places the ECL reaction apparent for DPA in ACN and PC can be accounted for in the following way. According to modem electron-transfer the0ry,3~-~~ layer within a wavelength of light from a metallic surface. With the unimolecular rate constant for electron transfer is expressed the exception of Van Duyne and co-workers, previous work in the following form where AGO, is the driving force for the involved the second and millisecond time scales where these reaction, 2 is the sum of the inner- (vibrational) and outereffects would not be apparent. The use of finely polished (solvational) sphere reorganizational energy (&), ~~1 is the carbon-fiber microelectrodes enables k m , and hence k,‘ and electronic transmission coefficient, and v, is the electron-transfer k:, to be determined since reflectivity/quenching is less due to frequency, kB is the Boltzmann constant, and Tis the temperature carbon’s lower reflectivity and density-of-states. These values (298 K).39-40 in conjunction with electron-transfer theory enable nuclear and electronic factors to be determined. In agreement with previous k, = Y,K,’ exp[-(AGO, L)2/4AkBT] work and electron-transfer theory, the rate to form the triplet (1 1) state proceeds at the diffusion-controlled limit for DPA, DMA, While modem estimates for aromatic molecules in ACN similar and R~(bpy)3~+. The direct measurement of the rate constant to DPA place 2 at values greater than 1 eV,l0 accurate values for light emission should provide useful information in the
+
Evaluation of Ion-Annihilation Reaction Kinetics investigation of the complementary reaction sequence involved in photoinduced electron transfer.
Acknowledgment. We wish to thank Christian Amatore and Edward L. Ciolkowski for helpful discussions concerning digital simulations and Karolyn M. Maness for preparation of the propylene carbonate solutions and helpful discussions regarding Marcus theory. We gratefully acknowledge support of this work by the National Science Foundation and the Italian National Council of Research, CNR (P.P.). References and Notes (1) Hercules, D. M. Acc. Chem. Res. 1969, 2, 301-307. (2) Faulkner, L. R.; Bard, A. J. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel1 Dekker: New York, 1977; Vol. 10, pp 1-95. (3) Park, S.-M.; Tryk, D. A. Rev. Chem. Intenned. 1981, 41, 43-79. (4) Marcus, R. A. J. Chem. Phys. 1965, 43, 2654-2657. (5) (a) Mussell, R. D.; Nocera, D. G. J. Am. Chem. SOC. 1988, 110, 2764-2772. (b) Mussell, R. D.; Nocera, D. G. Inorg. Chem. 1990, 29, 3711-3717. (c) Mussell, R. D.; Nocera, D. G. J. Phys. Chem. 1991, 95, 69 16-6924. (6) (a) Kapturkiewicz, A. Chem. Phys. 1992, 166, 259-273. (b) Kapturkiewicz, A. J. Electroanal. Chem. 1991, 302, 131-144. (c) Kapturkiewicz, A. Z. Phys. Chem. 1991, 170, 87-105. (7) Maness, K. M.; Bartelt, J. E.; Wightman, R. M. J. Phys. Chem. 1994, 98, 3993-3998. ( 8 ) Kavamos, G. J. In Topics in Current Chemistry; Mattay, J., Ed.; Springer-Verlag: New York, 1990; Vol. 156, pp 21-58. (9) Peters, K. S.;Lee, J. J. Phys. Chem. 1992, 96, 8941-8945. (10) (a) Gould, I. R.; Ege, D.; Moser, J. E.; Farid, S. J. Am. Chem. SOC. 1990, 112,4290-4301. (b) Gould, I. R.; Farid, S. J. Am. Chem. SOC. 1993, 115, 4814-4822. (c) Gould, I. E.; Farid, S. J. Phys. Chem. 1993, 97, 13067- 13072. (11) (a) Rehm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259-271. (b) Weller, A. Z Phys. Chem. 1982,130, 129-138. (c) Schomburg, H.; Staerk, H.; Weller, A. Chem. Phys. Lett. 1973,22, 1-4. (d) Schomburg, H.; Staerk, H.; Weller, A. Chem. Phys. Lett. 1973, 21, 433-436. (12) Collinson, M. M.; Wightman, R. M. Anal. Chem. 1993,65,25762582. (13) Feldberg, S. W. J. Am. Chem. SOC. 1966, 88, 390-393. (14) Faukner, L. R. J. Electrochem. SOC. 1977, 124, 1724-1728. (15) Cruser, S. A.; Bard, A. J. J. Am. Chem. SOC., 1969,91, 267-275. (16) Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183-197. (17) Drake, K. F. Ph.D. Thesis, Northwestem University, Evanston, 1979. (18) Wightman, R. M.; Wipf, D. 0.In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel1 Dekker: New York, 1988; Vol. 15, pp 267-353. (19) Kadish, K. M.; Ding, J. Q.;Malinski, T. Anal. Chem. 1984, 56, 1741-1744. (20) Bartelt, J. E. Ph.D. Thesis, Indiana University, Bloomington, 1990. (21) In some cases, larger differences between the experimental ECL curve obtained when the potential is stepped positive (second pulse) and theory can be observed. These differences are not large and may be due to the potential dependence of reflectivity. (22) Collinson, M. M.; Pastore, P.; Maness, K. M.; Wightman, R. M. J. Am. Chem. SOC. 1994, 116, 4095-4096. (23) Drexhage, K. H. J. Lumin. 1970, 12, 693-701. (24) Kuhn, H. J. Chem. Phys. 1970, 53, 101-108. (25) Waldeck, D. H.; Alivisatos, A. P.; Harris, C. B. SUI$ Sci. 1985, 158, 103-125.
J. Phys. Chem., Vol. 98, No. 46, 1994 11947 (26) Chance, R. R.; Prock, A,; Silbey, R. Adv. Chem. Phys. 1978, 37, 1-65. (27) (a) Zhang, X.; Bard, A. J. J. Phys. Chem. 1988, 92, 5566-5569. (b) Obeng, Y. S.; Bard, A. J. Langmuir 1991, 7, 195-201. (c) Miller, C. J.; McCord, P.; Bard, A. J. Langmuir 1991, 7, 2781-2787. (28) Kneten, K. R.; McCreery, R. L. Anal. Chem. 1992, 64, 25182524. (29) An identical rate constant for DPA in ACN was obtained by fitting the tail of the luminescence curves obtained with Au and Pt electrodes via a Feldberg plot.13 Since the reaction layer is furthest from the electrode surface at large tltf, reflectivity effects are minimal during this time. This region, however, is very sensitive to interfering reactions of the radical ions with impurities. This instability is reflected in the Feldberg plot as an increased negative slope and curvature compared to theory. At frequencies above ca. 10 W z , both ion radicals are stable and an excellent fit was obtained for a k-h of 2 x loLoM-' s-l. (30) Adsorption of DPA on carbon-fiber microelectrodes is more problematical than with either Au or Pt microdisks. This does not, however, affect the shape of the ECL curves but effectively decreases the electrode area and hence the overall ECL intensity. (31) Sawyer, D. T.; Roberts, J. L. Experimental Electrochemistry for Chemists; John Wiley and Sons: New York, 1974. (32) Berlman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd ed.; Academic Press: New York, 1974. (33) (a) Chiorboli, C.; Indelli, M.; Scandola, M.; Scandola, F. J. Phys. Chem. 1988,92, 156-163. (b) In this calculation, the distance between the reactants and the radius of the reactant plus ionic sphere were taken to be 0.7 and 0.55 nm, respectively. E = 37.5 (ACN) and 64.4 (PC), D = 1.3 x (ACN) and 1.6 x loe6 (PC) cm2/s?,20and p = 0.1 M. (34) Bartelt, J. E.; Drew, S. M.; Wightman, R. M. J. Electrochem. SOC. 1992, 139, 70-74. (35) Equation 17 and subsequently Figure 6 are not correct in ref 7. Figure 6 should show a plot of l / & c ~vs k-d as described by eq 16 in ref 7. When the data reported in Table 2 (DPA in 5050 ACNRoluene) are plotted in this form, a y-intercept of 3.8 and a slope of 3.2 x s are obtained. The bimolecular rate for singlet emission of 4 x lo9 M-' s-l at p = 0.1 M was then obtained using eq 7 in ref 7. (36) Since the driving force for the reaction is dependent on ionic strength (AGO = AG,, AG,, - wr),the unimolecular rate constant could be affected. However, only minor variations are expected because wr only changes ca. 2-fold with a 1000-fold decrease in ionic strength and the reorganizational energy is large. (37) Bartelt, J. E. M. S. Thesis, Indiana University, Bloomington, 1989. (38) The values for k-d and thus the y-intercept are very sensitive to the distance between reactants. For solvent-separated ion pairs in ACN the average distance is typically taken as 0.7 nmg-10which was used to construct Figure 6. If the distance between reactants is taken to be 0.5 nm,a y-intercept of 3.5 is obtained. (39) (a) Sutin, N. Acc. Chem. Res. 1982, 15, 275-282. (b) Marcus, R. A,; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265-322. (40) Meyer, T. J. In Progress in Inorganic Chemistry; Lippard, S. J., Ed.; John Wiley & Sons: New York, 1983; Vol. 30, pp 389-441. (41) Maroncelli, M.; MacInnis, J.; Fleming, G. R. Science 1989, 243, 1674- 1681. (42) The small differences in the diffusion coefficients, and hence the diffusion-controlledrates of DMA and Ru(bpy)s2+compared to DPA, would not be distinguishable in this analysis. The diffusion coefficient of DMA was ca. (1.7 k 0.4) times larger than DPA (Bartelt, J. E. Unpublished results). (43) (a) Wallace, W. L.; Bard, A. J. J. Phys. Chem. 1979, 83, 13501357. (b) Tokel-Takvoryan, N. E.; Hemingway, R. E.; Bard, A. J. J. Am. Chem. SOC. 1973, 95, 6582-6589.
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