Determination of Heterogeneous Electron Transfer Kinetics in the

These systems were ferrocene/ferrocenium (Fc/Fc+ in acetonitrile, 0.1 mol .... redox system, supporting electrolyte, D/1 × 10-6 cm2 s-1, gradient/mV,...
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Anal. Chem. 1997, 69, 2055-2062

Determination of Heterogeneous Electron Transfer Kinetics in the Presence of Ultrasound at Microelectrodes Employing Sampled Voltammetry Peter R. Birkin* and Susana Silva-Martinez

Department of Chemistry, University of Southampton, Southampton, SO17 1BJ, U.K.

The technique of sampled voltammetry at microelectrodes irradiated with ultrasound is demonstrated for the first time. This technique is used to determine the heterogeneous electron transfer rate constants for the redox couples ferrocene/ferrocenium, Ru(NH3)63+/2+, and IrCl63-/IrCl62-. Determination of the heterogeneous rate constants is also achieved for comparison purposes by analysis of fast sweep rate voltammetry of the redox systems studied at microelectrodes and comparison of the results obtained to the theory developed by Nicholson and Shain. The heterogeneous rate constants determined using sampled voltammetry were 1.0, 0.6, 1.23, and 0.18 cm s-1 for the ferrocene/ferrocenium (0.1 mol dm-3 TEATFB, CH3CN), Ru(NH3)63+/2+ (0.1 mol dm-3 KCl), IrCl63- (1 mol dm-3 KCl), and IrCl63-/IrCl62- (1 mol dm-3 NaCl), respectively, in agreement with those obtained in the absence of ultrasound. The effects of ultrasound on many electrochemical processes can be found in the literature. These effects include altered product distribution of an electrosynthetic reaction, the depassivation of an electrode surface, the erosion of electrode surfaces, and increased electrochemiluminescence.1-3 The effects of ultrasound on an EC reaction have also been reported.4 Recently, Compton et al. employed steady-state voltammetry to determinate the rate of heterogeneous electron transfer in the presence of ultrasound.5 They observed that there was no direct effect of intense ultrasound on the rate of simple heterogeneous electron transfer processes for any of the systems they studied. Alternatively, Coury and Madigan showed that the electrode kinetics of the system could be altered by the presence of ultrasound.6 Apparent increases in the rate of electron transfer were reported, and the authors inferred from this that the temperature of the solution at the electrode surface had been raised from 298 to 410 K by the impact of alumina particles added to the solution and thrown onto the electrode by the cavitation process. Huck has also investigated the effect of ultrasound on electrode kinetics. He reported that ultrasound slowed the rate of electron transfer for the Fe(CN)63+/4+ redox system and attributed this to surface (1) Zhang, H.; Coury, L. A. Anal. Chem. 1993, 65, 1552-1558. (2) Compton, R. G.; Eklund, J. C.; Page, S. D.; Sanders, G. H. W.; Booth, J. J. Phys. Chem. 1994, 98, 12410-12414. (3) Walton, D. J.; Phull, S. S.; Bates, D. M.; Lorimer, J. T.; Mason, T. J. Electrochim. Acta 1993, 38, 307-310. (4) Compton, R. G.; Eklund, J. C.; Page, S. D.; Rebbitt, T. O. J. Chem. Soc., Dalton Trans. 1995, 389-393. (5) Marken, F.; Eklund, J. C.; Compton, R. G. J. Electroanal. Chem. 1995, 395, 335-339. (6) Madigan, N. A.; Coury, L. A. Anal. Chem. 1997, 69, 5-15. S0003-2700(96)01128-6 CCC: $14.00

© 1997 American Chemical Society

cleaning of the electrode.7 Clearly, from these alternative findings, different observations have been reported, depending on the experimental conditions employed. In this article, we demonstrate a new technique for determining the heterogeneous electron transfer rate constant for redox couples with a standard rate of heterogeneous electron transfer up to ∼1 cm s-1 in the presence of ultrasound. It should also be noted that the technique reported here for the first time, sampled sonovoltammetry, focuses on the electrochemical phenomena under investigation as close as possible to the point of impact of the ultrasonic event produced by asymmetric cavitation bubble collapse near the electrode surface. This technique has many advantages over the previously reported time and spatially averaged sonoelectrochemistry. First, the employment of microelectrodes (sometimes referred to as ultramicroelectrodes) in conjunction with ultrasound enables high mass transfer rates to be achieved.8,9 Second, any effects of ultrasound should, in theory, be concentrated at the moment of impact with the electrode surface. The phenomenon of cavitation has been investigated in a multidisciplined research effort.10,11 Cavitation of a liquid can be achieved by a variety of techniques and, in general, can be defined as the activation of preexisting nuclei to form stable or transient bubbles or voids in the liquid structure. The easiest and most widespread technique employed to generate transient cavitation is the application of power ultrasound to a solution. The attraction of power ultrasound is the ability to create localized transient high temperatures and pressures, as a result of cavitation, in solutions with relatively low bulk temperature. These transient high-energy regions have been inferred from experimental observations, and, for short periods of time, temperatures12 of ∼5000 K and pressures13 of 500 atm have been proposed to exist in the interior of the cavitation void. These “hot spots” comprising approximately 500 molecules and the associated liquid sphere (∼200 nm thick at 1900 K) are thought to be responsible for the beneficial effects of ultrasound on chemical reactions.14,15 In this article, we show the results of a study on the electron transfer kinetics of ferrocene/ferrocenium in acetonitrile (CH3(7) Huck. H. Ber. Bunsenges. Phys. Chem. 1987, 91, 648-654. (8) Birkin, P. R.; Silva-Martinez, S. J. Chem. Soc., Chem. Commun. 1995, 18071808. (9) Birkin, P. R.; Silva-Martinez, S. J. Electroanal. Chem. 1996, 416, 127-138. (10) Leighton, T. G. The Acoustic Bubble; Academic Press: London, 1994 and references therein. (11) Young, F. R. Cavitation; McGraw-Hill: London,1989. (12) Flint, E. B.; Suslick, K. S. Science 1991, 253, 1397-1399. (13) Suslick, K. S. Science 1990, 247, 1439-1445. (14) Suslick, K. S.; Hammerton, D. A.; Cline, R. E. J. Am. Chem. Soc. 1986, 108, 5641-5642. (15) Flint, E. B.; Suslick, K. S. J. Am. Chem. Soc. 1989, 111, 6987-6992.

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CN), hexaammineruthenium(III/II), and hexachloroiridium(IV/ III) couples in aqueous solutions. This study was performed at platinum or gold 25 µm diameter microelectrodes irradiated with ultrasound. In a previous paper,9 we have shown that power ultrasound enhances mass transport of material to a microelectrode. We attributed this increase in mass transport to two transient processes: first, bubble collapse at or near the solidliquid interface with the consequent formation of a high speed liquid microjet directed at the electrode surface, and second, bubble motion near or within the diffusion layer of the electrode. These situations were shown to produce transient high rates of mass transfer. There are several advantages of employing microelectrodes. First, microelectrodes are relatively small compared to cavitation events.13,15 This enables us to record individual impacts of the imploding cavitation bubble by monitoring the current produced by the oxidation or reduction of an electroactive species at the microelectrode. Second, the current can be measured under mass transport limiting conditions and compared with the wall tube electrode (WTE).16,17 In the experimental procedure reported here, the maximum current-time transient is recorded and assumed to be caused by a cavitation event occurring in the solution directly above the electrode surface. This can be compared to the WTE at the point at which the event impacts onto the electrode surface. Under these conditions, it is assumed that our experimental technique approach operates under uniform accessibility. The largest events are assumed to be caused by similar cavitation events over the center of the electrode. This assumption is supported by experiments performed previously in the mass transfer limiting region (see later).9 To obtain evidence of the effect of ultrasound on the electrode kinetic behavior of the redox systems specified, we have employed ultrasound as a mass transport enhancement tool. These particular redox systems were chosen because of the preexisting knowledge of their heterogeneous electron transfer rates in the literature.18-28 This enables us to make a direct comparison of our results with those obtained in experiments by other workers. Investigations of three redox systems are reported here. These systems were ferrocene/ferrocenium (Fc/Fc+ in acetonitrile, 0.1 mol dm-3 tetraethylammonium tetrafluoroborate, TEATFB), hexaammineruthenium(III/II) chloride ([Ru(NH3)6]Cl3, in aqueous 0.1 mol dm-3 potassium chloride solutions), and hexachloroiridate(III/IV) (K3[IrCl6]/Na2[IrCl6] in 1.0 mol dm-3 NaCl and K3[IrCl6] in 1 mol dm-3 KCl). The kinetic parameters for these couples were compared with those obtained from fast scan (16) Chin, D. T.; Tsang, C.-H. J. Electrochem. Soc.: Electrochem. Sci. Technol. 1978, 125 (9), 1461-1470. (17) Macpherson, J. V.; Beeston, M. A.; Unwin, P. J. Chem. Soc., Faraday Trans. 1995, 91 (5), 899. (18) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1993, 361, 93-101. (19) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1994, 375, 213-218. (20) Beriet, C. Ph.D. Thesis, Southampton University, 1993. (21) Mirkin, M. V.; Richards, T. C.; Bard, A. J. J. Phys. Chem. 1993, 97, 76727677. (22) Saji, T.; Maruyama, Y.; Aoyagui, S. J. Electroanal. Chem. 1978, 86, 219222. (23) Bond, A. M.; Henderson, T. L. E.; Mann, D. R.; Thormann, W.; Zoski, C. G. Anal. Chem. 1988, 60, 1878-1882. (24) Montenegro, M. I.; Pletcher, D. J. Electroanal. Chem. 1986, 200, 371-374. (25) Bard, A. J.; Mirkin, M. V.; Unwin, P. R.; Wipf, D. O. J. Phys. Chem. 1992, 96, 1861-1868. (26) Wipf, D. O.; Kristienson, E. W.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1988, 60, 306-310. (27) Gennett, T.; Weaver, M. J. Anal. Chem. 1984, 56, 1444-1448. (28) Oyama, N.; Ohsaka, T.; Yamamoto, N.; Matsui, J.; Hatozaki, O. J. Electroanal. Chem. 1989, 265, 297-304.

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voltammetry.19 It is believed that all three systems have relatively rapid electrode kinetics under the conditions employed. In this work, an alternative approach is presented to characterize fast electron transfer kinetics in the presence of ultrasound. EXPERIMENTAL SECTION Apparatus. To reduce electrical noise, all experiments were performed inside a Faraday cage employing an in-house-built potentiostat, a triangle wave generator, and a potential step source. In the experiments performed at high sweep rates, a Gould 200 MHz 465 (DSO) linked to a 486 sx33 personal computer through serial port RS432 was used to record the data. A HI-TEK PP R1 wave form generator was employed to generate the voltage ramps for high sweep rates (above 500 mV s-1). Voltammetry of the redox systems (below 500 mV s-1) was also recorded on a PC interfaced through an ADC card (Talisman Electronics, Computer Boards CIO-DAS08-PGL) to the potentiostat. A “virtual oscilloscope” was also used in the experiments performed in the presence of ultrasound with the aforementioned PC and interface card. This was achieved by using software written in-house. This system has the ability to measure at a sampling rate of 33 kHz and record ∼3 s of real-time data (90 000 data points). A Heat Systems ultrasonic processor (Model Microson Ms-50), 50 W, titanium P1 horn (tip area 0.08 cm2), operating at 23 kHz was employed to produce cavitation. The tip of the ultrasonic source was electrically insulated from the solution with a thin layer of Teflon tape placed between the detachable tip and the main body of the probe. This ensured good mechanical connection through the probe and electrical insulation. The electrical resistance between the tip and the body of the horn was typically >20 MΩ. The electrochemical experiments were performed in a threeelectrode arrangement, with and without ultrasound. Platinum and gold microelectrodes (25 µm diameter) were fabricated as described in the literature.29 The auxiliary electrode was Pt gauze. A saturated calomel electrode (SCE) was employed as a reference electrode, and all potentials are quoted with respect to SCE. The microelectrodes were initially polished on “wet and dry” silica paper, followed by 1, 0.3, and 0.05 µm alumina (Buehler) powder/ water slurry on velvet polishing pads (Buehler, Microcloth). Once the electrodes had been exposed, subsequent polishing was performed on 0.3 and 0.05 µm alumina. After polishing, the electrodes were rinsed with water, buffed on a clean polishing cloth, and finally rinsed again with the relevant solvent used in the particular experiment. To test the microelectrodes, a cyclic voltammogram was recorded in the relevant redox system employed in the subsequent ultrasound experiment. If classic voltammetry of the redox probe was not observed, the polishing process was repeated until the expected voltammetry was obtained. The temperature was controlled by a recirculating water bath (Grant Instruments W14). The temperature was measured using a mercury thermometer and reported in the appropriate figure legend. The working microelectrodes were placed directly underneath the ultrasonic probe tip at a distance of 2 mm. The electrode/ultrasonic horn separation was kept constant throughout the experiment. The experimental setup has been reported previously.9 The state of the microelectrodes was tested after ultrasound was applied by recording a cyclic voltammogram in the particular redox probe employed in the experiment. Each experiment exposed the microelectrode to ∼10 s of ultrasound, (29) Caruana, D. J. Ph.D. Thesis, Southampton University, 1994.

which one point on the I vs E plot could be obtained. Over an entire set of experiments, the microelectrode was exposed to ∼3 min of irradiation with ultrasound, from which a complete I vs E plot could be obtained. Over this period of time, the microelectrodes were found to be stable and free from leakage. Calibration of the ultrasonic horn was performed as previously described in the literature.30 It should be noted that this technique only gives the energy flow through the surface of the acoustic horn and does not predict the acoustic pressure at a point within the media under investigation. Chemicals. [Ru(NH3)6]Cl3 (Strem Chemicals, 99%), K3[IrCl6] (Aldrich, 99%), Na2[IrCl6] (Aldrich, 99.9%), KCl (Anal R BDH, 99%), NaCl (Anal R BDH, 99%), (C2H5)4NBF4 (Fluka, >99%), and ferrocene (BDH) were used as received. All solutions were prepared with water from a Whatman RO 50 reverse osmosis followed by a Whatman Stillplus water purification system. Water purified in this manner had a conductivity of less than 0.1 µS cm-1. Aqueous solutions were degassed with argon gas for ∼15 min to remove oxygen when required. After this period, argon gas was passed over the surface of the solution to prevent diffusion of oxygen back into the solution during the experiment. Acetoniltrile (Aldrich HPLC grade, 99.9%) was distilled over calcium hydride (Aldrich) under a dry argon atmosphere and used immediately. RESULTS AND DISCUSSION In the absence of ultrasound, a cyclic voltammogram of the redox probe under investigation was recorded. Figure 1 shows the three cyclic voltamograms of the respective redox systems recorded at a 25 µm diameter Pt or Au microelectrode. The data obtained from these cyclic voltamograms in conjunction were used to determine the reversibility of each redox system under the conditions employed.31 The reversibility of each system was determined by plotting E vs log[(i - icl )/ (ial - i)]. The terms E, E0, R, T, n, F, i, icl , and ial are the electrode potential, the formal potential of the couple, the molar gas constant, the temperature, the number of electrons involved in the redox reaction, the Faraday constant, the current, the limiting cathodic current, and the limiting anodic current, respectively. The gradient of such a plot for a reversible redox couple should be 59 mV and can be used as a reversibility test, while the intercept indicates the formal potential of the particular couple under investigation. Table 1 shows a collection of the results obtained from this analysis and the diffusion coefficient of the respective redox couple. The diffusion coefficient was obtained from the steady-state current and the relationship, iss ) 4nFaDC, where iss, n, C, F and a represent the steady-state current, the number of electrons, the concentration of redox probe, the Faraday constant, and the radius of the microdisc electrode, respectively. It is important to note that the high value obtained for ferrocene/ferrocenium, as compared to those of the water-soluble redox systems employed here, is the consequence of the solvent employed, in this case acetonitrile, although the value of D for ferrocene from this analysis is in good agreement with the literature.32 However, this high value of D is advantageous as this enhances the transient mass transfer coefficients obtained for this system, in this case ∼1.4 cm s-1, in the presence of ultrasound. (30) Mason, T. J.; Lorimer, J. T. Ultrasonics 1992, 30, 40-42. (31) Electrochemical Methods; Bard, A. J., Faulkner, L. R., Eds.; John Wiley & Sons: New York, 1980. (32) Kuwana, T.; Bulitz, D. E.; Hoh, G. J. Am. Chem. Soc. 1960, 82, 5811-5817.

Figure 1. Plots showing cyclic voltammograms obtained at a 25 µm diameter Pt or Au microelectrode. Trace A corresponds to the response of the electrode placed in a solution containing ∼2.3 mmol dm-3 Fc/Fc+ (acetonitrile) in 0.1 mol dm-3 TEATFB supporting electrolyte. Trace B corresponds to the response of the electrode placed in a solution containing ∼5 mmol dm-3 Na2[Ir(Cl)6] and ∼5 mmol dm-3 K3[Ir(Cl)6] in 1.0 mol dm-3 NaCl supporting electrolyte. Trace C corresponds to the response of the electrode placed in a solution containing ∼11 mmol dm-3 [Ru(NH3)6]Cl3 in 1.0 mol dm-3 KCl supporting electrolyte. The cyclic voltammograms were recorded at 25 °C at a sweep rate of 5 mV s-1, except for Fc/Fc+, which was recorded at 20 mV s-1. In the experiments performed on the [Ru(NH3)6]Cl3, the cyclic voltammogram was recorded under anaerobic conditions. The cyclic voltammetry of the Fc/Fc+ and [Ir(Cl)6]3-/[Ir(Cl)6]2- systems was recorded under aerobic conditions.

To determine the electron transfer kinetics of each system, we employed two techniques. The first involves the ultrasonic irradiation of a microelectrode in the presence of the redox species under investigation. The second technique employed was fast sweep rate voltammetry at microelectrodes, from which the value of k0 was calculated by comparison of the results to the theory developed by Nicholson and Shain.33,34 It has been reported by many authors that ultrasound can provide an impressive enhancement in mass transfer rates at electrode surfaces. In a previous paper, we demonstrated the ability of microelectrode to resolve individual cavitation events.9 However, it should be noted that the potential of the electrode was held in the mass transport limiting region of the particular redox probe employed. To determine the electrode kinetics of the systems studied in the presence of ultrasound, the potential of the electrode was varied and the technique of sampled voltammetry employed. Sampled voltammetry relies on the acquisition of data over a sufficiently long time window, in which it is assumed that the microelectrode detects a direct hit from a transient cavitation event. In essence, the microelectrode acts as a target for the transient bubble events produced by the ultrasonic field. Events close to or directly above the electrode surface will produce the largest mass transfer enhancements. It is assumed that the potential of the electrode does not affect the (33) Nicholson, R. S. Anal. Chem. 1965, 37, 1351-1355. (34) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706-723.

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Table 1. Results Obtained from the Analysis of Microelectrode Cyclic Voltammograms of the Three Redox Couples Studied redox system

supporting electrolyte

D/1 × 10-6 cm2 s-1

gradient/mV

E0/ mV vs SCE

Fc/Fc+ [Ru(NH3)6]3+ [IrCl6]2[IrCl6]3-

0.1 mol dm-3 TEATFB, CH3CN 0.1 mol dm-3 KCl, H2O 1.0 mol dm-3 NaCl, H2O 1.0 mol dm-3 NaCl, H2O

26.1 ( 0.15 8.94 ( 0.16 7.44 ( 0.08 7.45 ( 0.12

59.0 59.4 58.5 58.5

407.8 -186.0 719.0 719.0

Figure 3. Histogram obtained from the analysis of a set of events recorded as described in the text and sorted with respect to frequency and current. The data used to create the histogram were recorded under the conditions reported in Figure 6 at +835 mV vs SCE.

Figure 2. Plots showing samples of the current-time transients obtained from the experimental procedure described in the text for the oxidation of ferrocene to ferrocenium (0.1 mol dm-3 TEATFB in acetonitrile) at a 25 µm diameter Au microelectrode in the presence of ultrasound (6.87 W cm-2). Three current-time responses are shown, corresponding to three different regions in the potential window employed. The data were obtained with a 2 mm separation between the ultrasonic probe and the microelectrode. The experiment was performed under aerobic conditions at 25 °C.

dynamics of the ultrasonic field. To collect the data required, it is necessary to employ a virtual oscilloscope as outlined in the Experimental Section. Sampled voltammetry data are collected over a constant time period and then sorted to determine the magnitude or height of the largest transient event at a particular potential. The process is then repeated at different potentials and the highest recorded event in each data set plotted as a function of the applied potential. Figure 2 shows a set of current-time transients recorded using the virtual oscilloscope described here and in the Experimental Section. The three sampled potentials correspond to a potential in the mass transport limited condition, a potential where no oxidation of the redox couple occurs, and a potential in between these two extremes, as indicated in the figure. The current-time transients recorded in this manner are then sorted in order to determine the current maximum at each potential chosen. In this way, a sampled voltammogram of the redox couple under investigation was constructed at the highest and assumed constant rate of mass transfer. To show how the microelectrode behaves under the conditions employed in these experiments, Figure 3 shows a histogram of events determined from the sort routine of one experiment. If we consider the microelectrode as a target for the cavitation events, we would 2058

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expect that a direct hit onto the electrode will be the least most likely event and will occur with the lowest frequency. However, a direct hit onto the microelectrode is likely to produce the highest mass transfer rate. The farther away from the electrode, the more likely that an event will be (as the target increases), but the smaller the effect of the event on the diffusion layer of the electrode will be. Consequently, the most frequent events occur at lower currents, as shown in Figure 3. The analysis produces a histogram that falls off at lower currents to zero; this can be explained as a resolution problem, as the smallest perturbations of the diffusion layer may be masked by larger events occurring in a close period of time. However, the overall shape of the distribution of events is as expected from the physical description of the model. Further analysis of these distributions and their potential dependence is beyond the scope of this paper and will be reported elsewhere.35 The high rates of mass transfer obtained in the presence of ultrasound (up to ∼1.5 cm s-1) result in the redox system investigated no longer being reversible. If we consider the situation where both an oxidized species, O, and a reduced species, R, are present in solution, it is possible to describe the reactions at the electrode interface as kf

O + ne \ {k } R b

where kf and kb represent the rate of the forward (reduction) process, and backward (oxidation) process, respectively. It is possible to convert equations generated for voltammetry of quasireversible systems at rotating disk electrodes to an equation which depicts voltammetry at a wall tube electrode, a system (35) Birkin, P. R.; Silva-Martinez, S. In preparation.

analogous to the point of impact of a microjet onto a microelectrode, as both RDE and WTE are known to be uniformly accessable.17,18,32 The condition of uniform accessibility can be verified from comparison to the WTE literature. Chin and Tsang have shown that WTE theory will be obeyed under laminar flow conditions for

0.1 < R/d < 0.5 where R and d represent the radius of the disk electrode and the diameter of the tube, respectively.16 Considering the dimensions of the microelectrode employed in this study (R ) 12.5 µm) and the relationship between bubble size and microjet size (∼0.1 × the maximum bubble radius, observed photographically), the maximum bubble radius would have to be greater than 125 µm.10,11 Numerical solution of nonlinear bubble motion in a sound field enables us to predict the lower pressure level for which uniform accessibility can be assumed.11 Acoustic pressures of greater than ∼1.8-2 atm are required. Considering the pressure at the surface of the sound source estimated from calorific values (6.7 W cm-2), at ∼5 atm the assumption that bubble size will be large enough to attain uniform accessibility is reasonable, even considering the fall in acoustic pressure expected as a function of distance from the sound source. Additional supporting evidence for the assumption of uniformly accessibility can be obtained from the variation of current maximum as a function of electrode size.9 Under identical experimental conditions, it was shown that the current maximum scaled directly as a function of electrode radius. This is in agreement with WTE theory and experiment.16,17 Consequently, it is evident that uniform accessibility can be assumed under the experimental conditions reported here. Equation 1 shows the result of this combination and the assumption that the mass transfer coefficient of the reduced and oxidized species are equal, where n, F, A, CO, CR, kf, kb, and km(WTE)

[

]

kf + kb 1 1 ) 1+ i nFA(kfC0* - kbCR*) km(WTE)

(1)

represent the number of electrons, the Faraday constant, the area of the electrode, the bulk concentration of the oxidized species, the bulk concentration of the reduced species, the rate of the forward reaction, the rate of the backward reaction, and the mass transfer coefficient relevant to the wall tube electrode, respectively. Expressions describing the mass transfer coefficient from wall tube electrode theory are described elsewhere.17 In sampled voltammetry, the mass transfer coefficient is related to the maximum of the current-time transient by a similar expression shown in eq 2, where kM(SV), D, a, and IN represent the mass

kM(SV) )

I (4D πa )

N

Figure 4. Plots showing a sampled voltammogram (b) for the oxidation of Fc/Fc+ (0.1 mol dm-3 TEATFB in acetonitrile) at a 25 µm diameter Au microelectrode in the presence of ultrasound (6.87 W cm-2). The solid line (s) corresponds to a plot obtained from the nonlinear least mean square analysis of the experimental data employing eq 1. The data were obtained with a 2 mm separation between the ultrasonic probe and the microelectrode. The experiment was performed under aerobic conditions at 25 °C.

Figure 5. Plot showing a sampled voltammogram (b) for the electroreduction of [Ru(NH3)6]3+ (∼4 mmol dm-3, 0.1 mol dm-3 KCl supporting electrolyte) at a 25 µm diameter Pt microelectrode in the presence of ultrasound (6.87 W cm-2). The solid line (s) corresponds to a plot obtained from the nonlinear least mean square analysis of the experimental data employing eq 1. The data were obtained with 2 mm separation between the ultrasonic probe and the microelectrode surface. The experiment was performed under anaerobic conditions at 25 °C.

(2)

transfer coefficient for sampled voltammetry, the diffusion coefficient of the species under investigation, the radius of the microelectrode, and the maximum transient current normalized to the steady-state current obtained at the microelectrode at the mass transfer limiting condition and in the absence of forced convection, respectively. This mass transfer coefficient is then used in eq 1.

Figures 4-6 show the experimental data obtained from the sampled voltammogram experiments, plotted as a function of potential. The solid lines on these plots indicate nonlinear least mean square analysis of the data from eq 1 shown above, with Butler-Volmer kinetic expressions employed to describe the potential dependence of the heterogeneous rate constants.31 This method of analysis relies on a two-parameter fit (k0 and R as the two variables). This analysis leads to the determination of the standard rate constant for electron transfer (k0) and the exchange Analytical Chemistry, Vol. 69, No. 11, June 1, 1997

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Figure 6. Plot showing a sampled voltammogram (9) for the electrochemical reduction/oxidation of [IrCl6]3-/[IrCl6]2- (∼5 mmol dm-3, 1 mol dm-3 NaCl supporting electrolyte) at a 25 µm diameter Pt microelectrode in the presence of ultrasound (6.87 W cm-2). The solid line (s) corresponds to a plot obtained from the nonlinear least mean square analysis of the experimental data employing eq 1. The data were obtained with 2 mm separation between the ultrasonic probe and the microelectrode surface. The experiment was performed under aerobic conditions at 25 °C. Table 2. Results Obtained from the Analysis of the Sampled Voltammograms Shown in Figures 4-6 redox system

supporting electrolyte

k0/cm s-1

R or β

Fc/Fc+ [Ru(NH3)6]3+ [IrCl6]3[IrCl6]3-/[IrCl6]2-

0.1 mol dm-3 TEATFB 0.1 mol dm-3 KCl 1.0 mol dm-3 KCl 1.0 mol dm-3 NaCl

1.02 ( 0.09 0.6 ( 0.16 1.23 ( 0.18 0.18 ( 0.03

0.40 ( 0.05 0.3 ( 0.06 0.58 ( 0.01 0.57 ( 0.03

coefficient (R or β) for the respective redox probes employed in the experiments. Table 2 shows a collection of the results obtained for the three systems we have investigated. The 95% confidence intervals are also shown in Table 2, calculated from the standard error valve given by the curve fit routine. These low values indicate that the fit between the experimental data and the equation is reasonable. It should also be noted that the technique is reproducible. This may be shown by looking at the plateau region of Figure 6 (∼+300-500 mV vs SCE), where under mass transfer limiting conditions only a small variation of the current can be seen over five experiments. This supports the assumption that, over the time period chosen, a cavitation event in the same position over the electrode and of the same magnitude will occur. Figure 7 shows the result of averaging the current-time transients recorded by the virtual oscilloscope at each potential and plotting the current average as a function of potential. This averaged voltammogram shows reversible behavior for this redox couple, specifically ferrocene, as indicated by the inset in the figure (a plot of E vs log(i/(ilimav - i)) with a gradient of 64 mV, a value close to reversibility). However, the sampled voltammogram shown in Figure 4 showed quasireversible behavior, indicating the advantage of employing the microelectrode sampled voltammetry over the more conventional time-averaged signal obtained for a macroelectrode employed with low time resolution equip2060

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Figure 7. Plot showing the time-averaged current (b) obtained from the analysis of the current-time transients obtained for the Fc/Fc+ system (0.1 mol dm-3 TEATFB in acetonitrile) at a 25 µm diameter Au microelectrode in the presence of ultrasound (6.87 W cm-2). The inset shows a plot of E vs log(i/(ilimav - i)) for the data obtained in this way.

ment. The kinetics of the ferrocene system can only be determined under these ultrasound conditions if sampled voltammetry is employed, indicating its superiority over other time-averaged techniques. To compare and verify the results obtained from the analysis of the sampled voltammetry, a second technique, specifically fast scan rate cyclic voltammetry, was employed on the same set of redox systems under identical experimental conditions. However, these experiments were performed in the absence of ultrasound. The theory behind the technique of fast scan rate cyclic voltammetry was first reported by Nicholson and Shain. The technique involves recording cyclic voltamograms at high sweep rates, where the kinetics of the redox couple are no longer considered to be reversible.33,34 Microelectrodes are ideally suited to fast sweep rate voltammetry because of their inherently low capacitive current and low iR drop. Equation 3 shows the relationship between Ψ and the standard rate of electron transfer, where DO, DR, n, F, R,

Ψ)

( ) DO DR

R/2

k0

[DOπν(nF/RT)]1/2

(3)

T, R, and k0 have their meanings described earlier in the text and ν is the sweep rate. Peak-to-peak separations are then used to calculate the rate of electron transfer for a set of fast scan rate voltammograms.36 Figure 8 shows a collection of some fast scan rate cyclic voltamograms recorded at a 25 µm diameter Pt (36) Ahlberg, E.; Parker, V. D. Acta Chem. Scand. 1980, B43, 71-72.

Table 3. Results Obtained from the Analysis of the Fast Sweep Rate Voltammetry of the Respective Redox Couples Along with the Concentrations Employed in the Experiments and the Literature Values of the Redox Couplesa k0/ cm s-1 a redox system/mmol Fc/Fc+ [Ru(NH3)6]3+ 6.72 9.95 [IrCl6]35.06 10.05 a

dm-3

supporting electrolyte dm-3

0.1 mol TEATFB 0.1 mol dm-3 KCl

exptl

lit. 0.6,21 0.7,22

>6.0,23 1.124

1.02 ( 0.06

3.7 (

0.38 ( 0.11 0.62 ( 0.10

0.076.25 0.8,19,20 0.45,26 0.3527

1.07 ( 0.21 1.03 ( 0.11

0.5,22 0.74 ( 0.12,19,20 0.11 ( 0.0428

1.0 mol dm-3 KCl

The table also shows the 95% confidence interval obtained from the analysis of the experimental data or from the literature where available.

we now compare the values obtained from the sampled voltammetry in the presence of ultrasound with the fast scan rate voltammetry, it is apparent that, for the ferrocene/ferrocenium and IrCl63-, IrCl63-/2- systems that essentially the electrode kinetics have been unaffected by ultrasound. The sampled voltammetry for Ru(NH3)63+/2+ does show some deviation from the line of best fit; however, the heterogeneous rate constant obtained from these results is in reasonable agreement with that obtained from the fast scan rate experiments and the literature. Presumably, the poor fit indicates that the electrode kinetics of this complex may be more complex. This is being investigated at this time. Temperature effects have been proposed to explain an apparent increase in the rate of electron transfer observed by Madigan and Coury in experiments where alumina particles were added to the solution.6 However, if the temperature of the solution is raised by the impact of the alumina particles on the surface of the electrode, then, because of the thermodynamics of the system, the E0 of the redox couple should also be affected using eq 4, Figure 8. Plot showing a series of fast sweep rate voltammograms recorded at a 25 µm diameter Pt microelectrode placed in a solution containing ∼5 mmol dm-3 K3[IrCl6] and 1.0 mol dm-3 KCl supporting electrolyte. The voltammograms were recorded at 100, 300, 500, 750, and 1000 V s-1. The experiment was performed under aerobic conditions at 25 °C.

microelectrode placed in a solution containing ∼5 mmol dm-3 [IrCl6]3+. It should be noted that the analysis of the data assumes a value of the exchange coefficient, R, to be 0.5, and this value is independent of peak-to-peak separation. The ratio of DO/DR is also assumed to be 1, an assumption partly supported by the values of the diffusion coefficients for the [IrCl6]3-and the [IrCl6]2systems reported in Table 1. In any case, if one considers the power dependence of the DO/DR term, it is clear that the dependence on this variable is small. Table 3 shows a collection of the results obtained for the three redox systems in comparison with literature values. It is clear that the value obtained for the rate of heterogeneous electron transfer depends strongly on the technique used and the solution conditions. This is demonstrated markedly for the [IrCl6]2-/3- system, where the rate of heterogeneous electron transfer changes by one order of magnitude if one changes the cation present in the background electrolyte from K+ to Na+. The literature values18-28 highlighted in Table 3 in italics, are taken from papers where the conditions used resemble those employed here. Clearly, the agreement is reasonable between the literature values and the values reported here. If

0

∂E0 Sreact ) ∂T nF

(4)

0 where n, F, Sreact and E0 represent the number of electrons, Faraday’s constant, the entropy change of the reaction, and the standard potential of the redox couple, respectively.31 Equation 4 demonstrates that the redox potential of the probe should vary with temperature. The change in the redox potential of the couple can be calculated from tables; however, some have been calculated under thermal conditions and reported by de Bethune et al.37 If the temperature at the electrode surface increased from 298 to 410 K, then we would also expect a corresponding change in the E0 of Fe2+/Fe3+ of -230 mV. However, such a shift in E0 was not observed in the paper by Madigan and Coury. This leads us to believe that increased temperature cannot be responsible for the experimental results shown by Madigan and Coury. The results reported here, even though obtained under different experimental conditions, also imply that ultrasound does not affect the kinetics of electron transfer for the redox systems chosen. This is, perhaps, not surprising, as the hot spot theory inferred from experimental observations proposes that only a relatively small amount of the liquid is heated. Considering the response

(37) de Bethune, A. J.; Light, T. S.; Swendeman, N. J. Electrochem. Soc. 1959, 106, 616-625.

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time of electrochemical systems as well as the small volume of hot liquid produced by the cavitation event, it is not surprising that temperature effects have not been observed here. CONCLUSIONS In this article, we have shown that it is possible to characterize fast electron transfer kinetics in the presence of ultrasound employing the technique of sampled voltammetry. The presence of ultrasound did not influence measurably the rate of the electron transfer processes for the ferrocene/ferrocenium, IrCl63-/IrCl62-, IrCl63-, and Ru(NH3)63+/2+ systems. The advantages of employing sampled voltammetry at microelectrodes are twofold. First, the high rates of mass transfer obtainable (up to ∼1.5 cm s-1) using this technique enable fast electron transfer processes to be (38) Birkin, P. R.; Silva-Martinez, S. Ultrason. Sonochem. In press.

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Analytical Chemistry, Vol. 69, No. 11, June 1, 1997

determined as demonstrated above. Second, the influence of ultrasound on chemical reaction will be concentrated at the point of impact of the microjet onto the electrode.38 Clearly, this technique, which employed such a strategy, will be more sensitive to coupled chemical reactions as the result of the effects of ultrasound. Such reactions are currently under investigation. ACKNOWLEDGMENT We thank Prof. D. Pletcher and Prof. P. N. Bartlett for “loans” of equipment and useful discussions. We also thank the Nuffield Foundation for an equipment grant (SCI/180/94/356/G). Received for review November 7, 1996. Accepted March 26, 1997.X AC961128V X

Abstract published in Advance ACS Abstracts, May 1, 1997.