Combination of Scanning Electron Microscopy in the Characterization

Aug 16, 2010 - To what extent the effective radius of a nanometer-sized electrode matches its geometric radius is a concern because it is believed tha...
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Combination of Scanning Electron Microscopy in the Characterization of a Nanometer-Sized Electrode and Current Fluctuation Observed at a Nanometer-Sized Electrode Isaac Agyekum, Christopher Nimley, Chenxi Yang, and Peng Sun* Department of Chemistry, Box 70695, East Tennessee State UniVersity, Johnson City, Tennessee 37614 ReceiVed: May 13, 2010; ReVised Manuscript ReceiVed: July 19, 2010

To what extent the effective radius of a nanometer-sized electrode matches its geometric radius is a concern because it is believed that the continuum assumptions of the Nernst-Planck equation do not work when the diameter of the electrode is less than 100 nm. In our research, high-resolution scanning electron microscopy images have been employed to characterize the electrodes whose effective radii have been obtained from electrochemical methods. Thus, electrode geometric and effective dimensions could be compared. Our results show that the geometric radius matches the effective radius very well when the effective radius is larger than 20 nm. There is a significant difference between the effective and the geometric electrode radii when the effective electrode radius is smaller than 20 nm. Current fluctuation can be observed on a 1.6 nm radius electrode at slow scan rates. Possible reasons for the current fluctuation on the electrode are discussed. 1. Introduction Compared with a microelectrode or submicroelectrode, an electrode whose diameter is less than 100 nm has important applications. One of the important applications is that the mass transfer rate at a nanometer-sized electrode is so high that the kinetics of very fast electron transfer reactions could be studied.1-6 Also, a nanometer-sized electrode can be used to detect single molecules and to study single-electron-transfer events.7-11 Another important application is the study of the effect of the electric double layer (EDL) on electrochemical reactions because it is believed that the electrochemical behavior starts to deviate from that at larger electrodes when the electrode’s critical dimension is decreased to the same order as the thickness of the EDL or the molecular size.12-19 Considering nonequilibrium and nonelectroneutrality effects on the EDL and on the basis of the Nernst-Planck equation, equations that can predict the voltammetric response on a nanometer-sized electrode whose radius is comparable to the thickness of the EDL have been given.15 However, it has been pointed out that the continuum assumptions of the Nernst-Planck equation can lead to erroneous results, and Brownian dynamics provides a better way to describe the reaction in small dimensions, particularly when the size of interest is comparable to a Debye length.20 White et al. have studied the effect of Brownian motion on the kinetics of an electrochemical reaction on a nanometer-sized electrode.5 Meanwhile, the effective radius of a nanometer-sized electrode that is used for an electrochemical measurement is usually obtained from its diffusion-limiting steady-state current by using eq 121

Iss ) 4nFDCr

(1)

where Iss is the limiting current, F is Faraday’s constant, and D is the diffusion coefficient, C is the concentration of the electroactive mediator, and r is the effective electrode radius. * To whom correspondence should be addressed. E-mail: [email protected].

In some cases, especially where a nanometer-sized electrode has been used to detect the kinetic parameters of a reaction, the effective electrode radius is used as its geometric radius. Because eq 1 is derived on the basis of a pure diffusion-based theory, which is a special case of the Nernst-Planck equation, one concern is to what extent the effective electrode radius matches its geometric electrode radius, especially when the effective electrode radius is less than 50 nm. Because the geometric radius of a nanometer-sized electrode can only be obtained from scanning electron microscopy (SEM), the solution to this concern is to characterize the electrode by both electrochemical methods and SEM. White’s study showed that there is very good agreement between the effective and geometric radii when the effective electrode radius is larger than 90 nm.22 To our knowledge, no studies have been reported when the effective electrode radius is less than 50 nm. In this paper, a well-polished nanometer-sized electrode has been characterized by both electrochemical methods and SEM (except for electrodes having radii less than 5 nm, which is beyond the resolution of the scanning electron microscope) to determine the extent to which the effective electrode radius calculated from the limiting diffusion current by using eq 1 matches the geometric radius obtained from SEM. Generally, we find that the effective electrode radius is smaller than its geometric radius. The difference is small when the electrode radius is larger than 20 nm, but the difference becomes larger when the radius of the electrode becomes smaller. There is an apparent current fluctuation on the electrode whose radius is less than 2 nm; the current fluctuation has been attributed to the potential fluctuation at the nanometer-sized electrode/solution interface and the fluctuation of the charging current at the EDL. 2. Experimental Section 2.1. Chemicals. KNO3 (99+%, Fisher Chemical) was used as a supporting electrolyte. Ru(NH3)6Cl3 was purchased from Strem Chemicals (Newburyport, MA). Solutions were prepared with deionized water (Milli-Q, Millipore Co.).

10.1021/jp105812r  2010 American Chemical Society Published on Web 08/16/2010

Characterization of a Nanometer-Sized Electrode 2.2. Fabrication of Electrodes with a Radius Larger than 10 nm. A 25 µm in diameter Pt wire is first sealed in a borosilicate glass capillary; then a laser puller (Sutter instrument Co, Novato, CA) is used to break the glass capillary.6 Different pulling programs for the laser puller are used to produce electrodes whose radii vary from around 10 to 80 nm. The laser puller-made electrode is then polished on the rotating disk of a micropipet beveler, which is monitored by a long working distance video microscope. The disk is covered with a layer of lapping tape on which a layer of tiny Al2O3 particles are attached. After polishing, the electrode is sonicated in deionized water for 1 min. The electrode is then annealed in 200 °C for about 3 h. 2.3. Fabrication of Electrodes with a Radius of Less than 10 nm. The pulling program used to get an electrode whose radius is around 10 nm is used to break the glass capillary (the parameters for the puling program are the following: heat, 450; filament, 3; velocity, 22; delay, 185; pull, 200). Under the monitor of a long working distance microscope, the pulled electrode is then moved by a micromanipulator toward a straight red-hot nichrome wire so as to locally melt the glass at the very end of the pulled electrode (see Figure s1 in the Supporting Information). The local heating makes certain that the Pt wire is totally sealed in the glass. The potential on the electrode is then continually scanned in the range where Ru3+ could be reduced in solution containing 10 mM Ru(NH3)6Cl3 and 0.02 HF/water (V/V) until evidence shows that the electrode will be exposed soon (see Figure s2 in the Supporting Information). After the electrode is completely washed with deionied water, the very end of the electrode is locally heated for 2 s. The last two steps are repeated if the electrode is not exposed. 2.4. Scanning Electron Microscopy. The effective electrode radius is calculated from the sigmoid-shaped cyclic votammograms obtained on the electrode in 1 mM Ru(NH3)6Cl3 and 0.2 M KNO3 aqueous solution. If the curve of the limiting current or the baseline of the voltammogram is not flat, the method introduced in chapter 7 of ref 23 is used to find the diffusioncontrolled limiting current. The electrode is then kept in a clean box under ambient humidity and temperature for 2 or 3 days. The radius of the electrode is then checked once again. If the radius of the electrode did not change, the electrode is further characterized with SEM; otherwise, the electrode is discarded. To avoid overcoating, the electrode is not coated with conductive materials before SEM characterization, but the electrode is conductively connected to the sample holder of the scanning electron microscope. The geometric electrode radius is obtained by comparing the pixels of the SEM images (white spot in the pictures) to the pixels of its scale bar. The uncertainty of the geometric or the effective radius is computed from a set of measurements at a 95% confidence level. 2.5. Instrument and Procedure. A Tescan Vega scanning electron microscope is used to observe the surface of a nanometer-sized electrode. Voltammetries were performed in a two-electrode mode using an Epsilon potentiostat with a low current module (BSAi, West Lafayette, IN). A 0.25 mm in diameter Ag/AgCl wire is inserted into a glass pipet containing 100 mM NaCl to serve as a reference electrode. 3. Results and Discussion 3.1. Fabrication of Nanometer-Sized Electrodes. 3.1.1. Effect of Annealing on a Nanometer-Sized Electrode with a Radius from 10 to 50 nm. A nanometer-sized electrode with a radius bigger than 10 nm could be easily fabricated using our previous method.6 We found annealing to be a very important step. Curves 1 and 2 in Figure 1A are obtained using the same

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Figure 1. (A) Cyclic voltammograms obtained before (curve 1) and after (curve 2) annealing in 1 mM Ru(NH3)6Cl3 and 0.2 M KNO3 aqueous solution. The effective electrode radius calculated from eq 1 is 13.6 ( 0.5 nm. Scan rate ) 100 mV/s. (B) Scanning electron microscopy images of the electrode used to obtain (A). The geometric radius is 18.5 ( 1.7 nm. The inset shows a low-magnification image of the same electrode. The scale bars in the picture and the inset are 200 nm and 1 µm, respectively.

electrode before and after annealing. The effective radii calculated from the limiting diffusion current by using eq 1 are 5.8 ( 0.4 and 13.6 ( 0.5 nm (for Ru(NH3)63+ in 0.2 M KNO3). (D is 6.02 × 10-6 cm2 s-1, which was obtained by steady-state voltammetry at a micrometer-sized electrode. Ru(NH3)63+ is used as the electroactive species because evidence showed that the reduction of the species is almost reversible.6) In principle, eq 1 is applicable only when the disk electrode is embedded in an infinite insulating plane; otherwise, deviation from eq 1 would be expected due to the mediator diffusion from the back of the electrode. Although typically the radius of the insulation layer in our electrodes is about 10 times larger than the radii of the electrodes (it can be verified from SEM images), eq 1 can still be used to evaluate the effective radius because results of both Shoup and Szabo24 and Mirkin25 showed that the deviation from eq 1 is negligible if the radius of the insulation layer is 5 times larger than the radius of the electrode. The geometric radius of the electrode measured from its SEM image in Figure 1B is around 18.5 ( 1.7 nm. This means that the effective radius is under-evaluated before annealing. The decrease in the diffusioncontrolled limiting current before annealing may result from surface blocking by the following contaminations: (1) organic impurities located in tiny grooves formed on the Pt surface in polishing when the electrode scratches the rotating disk and (2) tiny Al2O3 particles that are inlayed into the Pt surface in

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Figure 2. Cyclic voltammograms obtained on a 12 nm electrode before (black curve) and after (red curve) annealing. The electrochemical cell is Ag/AgCl/100 mM NaCl/0.5 M H2SO4/Pt. In the red curve, two groups of peaks can be observed around -0.4 and -0.28 V. Scan rate ) 100 mV/s.

Figure 3. Scanning electron microscopy image of the very end of a puller-made Pt wire. The glass layer around the Pt wire has been removed in HF solution. The scale bar in the picture is 200 nm.

polishing. Both contaminations are hard to be removed by sonication. Annealing can make the Pt surface smoother so that the aforementioned contaminations can be removed. Thus, an increase in the diffusion-controlled limiting current corresponding to an increase in the effective electrode radius is observed after annealing. The improvement in the quality of the surface by annealing could also be demonstrated from the CVs in Figure 2. Two groups of characteristic peaks corresponding to reductive adsorption and oxidative desorption of hydrogen could be observed after annealing, which is very similar to the case of a well-polished polycrystal Pt macroelectrode.26,27 Although the peak area of the curve before annealing is larger than that after annealing, it does not mean that the area of the electrode before annealing is definitely larger than the area after annealing because the size of the peaks for adsorption or desorption of hydrogen also depends on the crystal faces of platinum exposed and pretreatment of the electrode.23 3.1.2. Nanometer-Sized Electrodes with a Radius of Less than 10 nm. The pulling of the heated glass resulted in a narrowing of both the glass and the wire within. In a pulling program, four parameters (heat, velocity, filament, delay; these parameters do not have units, but the instrument can recognize them) can be adjusted. Velocity and delay are two important parameters affecting the shape and size of the Pt wire. Generally, the higher the velocity, the thinner is the Pt wire. Delay is

Agyekum et al. proportional to the time lapse between heating and pulling. The effect of delay on the size of Pt wire is complicated. Less delay means the glass is softer so that it can be extended very easily, but, Pt wire may be broken because the speed of the extension of the Pt wire may not catch up with the speed of the extension of glass. Thus, the value of the delay should be neither too big nor too small to yield a very small Pt wire. Also, variation in the purity of the Pt wire can definitely affect the thickness of the Pt wire from a pulling. Thus, the fabrication of nanometersized electrodes with radii less than 10 nm is severely dependent upon chance. Without polishing, the electrode fabricated from the program used for a 10 nm electrode is a recessed electrode. This is because the narrowing of Pt is not proportional to the narrowing of the glass, and Pt wire will be broken first. The cyclic voltammograms on such a recessed electrode show no difference from that of an inlaid disk nanometer-sized electrode; its limiting current can easily fall into sub-pA range. Enormous results can be obtained on such a recessed electrode.28,29 After local heating, the local glass can soften and will shrink upon cooling. Thus, the gap between Pt wire and glass can be sealed (see Figure 3s in the Supporting Information). Finally, a very small and wellsealed electrode can be fabricated because the shape of the stretched Pt wire is conical (see Figure 3). 3.2. Ratio of the Geometric to the Effective Radius of a Nanometer-Sized Electrode. The cyclic voltammograms and SEM images shown in Figure 4 are obtained on the same electrode. The radius of the white spot in the inset in Figure 4A is around 20 nm, which is apparently larger than the 10.0 ( 2.8 nm calculated from a higher-magnification SEM image (Figure 4A). We think that the surface reflection may play a role because only the top of the conical-shaped electrode is flat and the size of the flat area is comparable to the size of the electrode. Figure 5 shows cyclic voltammograms and SEM images on a nanometer-sized electrode whose effective radius is 5.4 ( 0.7 nm. Its geometric radius obtained from Figure 5A is 12.5 ( 2.1 nm. The ratios of the geometric to the effective radius for the two electrodes used in Figures 4 and 5 are 2.5 ( 0.7 and 2.3 ( 0.5, respectively. The ratio becomes closer to 1 as the geometric electrode radius becomes larger. For example, the ratios for the 18.5 ( 1.7 nm (used in Figure 1), 32.9 ( 1.9 nm (figures not shown), 66.7 ( 0.7 nm (see Figure 4s in the Supporting Information), and 87.2 ( 0.5 nm (figures not shown) in geometric radius electrodes are 1.4 ( 0.2, 1.2 ( 0.1, 1.06 ( 0.03, 1.01 ( 0.09, respectively. Thus, there is a trend that the ratio of the geometric to the effective electrode radius of a nanometer-sized electrode becomes larger as the electrode becomes smaller (see Figure 6). The relatively large ratio of geometric to effective radius for a very small electrode may result from overevaluation of the geometric radius or underevaluation of the effective electrode radius. Overevaluation of the geometric radius is possible because the SEM images for very small electrodes are blurry. The charging effect and the resolution of the instrument (>3 nm) play roles in the blurring of the SEM images. Although it is generally accepted that the effective electrode radius may deviate from that calculated from eq 1, it is hard to determine if the effective electrode radius is overevaluated or not because a contradictory component can be found in the literature. For instance, Feldberg’s recent paper pointed out that the limiting current at an extremely small electrode predicted by the Marcus-Hush formalism could be smaller than that calculated from eq 1,30 indicating that the effective electrode radius is underevaluated. However, a reverse conclusion could be ob-

Characterization of a Nanometer-Sized Electrode

Figure 4. (A) Scanning electron microscopy images of a nanometersized electrode. Its geometric radius is 10.0 ( 2.8 nm. The inset shows a low-magnification image of the same electrode. The scale bars in the picture and the inset are 200 nm and 1 µm, respectively. (B) Cyclic voltammograms obtained on the electrode used to obtain (A) in 1 mM Ru(NH3)6Cl3 and 0.2 M KNO3 aqueous solution. Its effective electrode radius calculated from eq 1 is 4.0 ( 0.2 nm. Scan rate ) 100 mV/s.

tained from Chen’s research. Considering the extended electron transfer effect and the EDL effect, Chen et al. found that the current of the reduction of Ru(NH3)63+ at a nanometer-sized electrode can be enhanced.15-17 This means that the value of the effective electrode radius should be smaller than the one calculated from eq 1. The common conclusion in Chen and Feldberg’s papers is that the deviation of the effective radius from eq 1 is not great if the effective electrode radius is larger than 5 nm. Considering these factors, it would be reasonable to say that the effective electrode radius calculated from eq 1 almost equals its geometric electrode radius when the electrode radius is larger than 20 nm. SEM images show that the electrode is not recessed and is well-sealed. There is some hysteresis between the back and forth segments of cyclic voltammograms in Figures 1A, 4B, 5B, and 7. The typical amplitude of the gap is around 1 pA. The gap arises from leaking current at electronic components, such as the operational amplifier, etc. 3.3. Current Fluctuation Observed at a Nanometer-Sized Electrode. The effective radius of the electrode used to obtain Figure 7 is less than 1.6 nm. Although the scanning electron microscope cannot find any white spot on the electrode at the SEM limit of resolution, the geometric radius of the electrode should be less than 4 nm because the aforementioned discussions show that the electrochemically calculated radius is smaller than its geometric radius calculated from SEM images, the difference being normally less than a factor of 2-3.

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Figure 5. (A) Scanning electron microscopy images of a nanometersized electrode. Its geometric radius is 12.5 ( 2.1 nm. The inset shows a low-magnification image of the same electrode. The scale bars in the picture and the inset are 200 nm and 1 µm, respectively. (B) Cyclic voltammograms obtained on the electrode used to obtain (A) in 1 mM Ru(NH3)6Cl3 and 0.2 M KNO3 aqueous solution. Its effective electrode radius calculated from eq 1 is 5.4 ( 0.7 nm. Scan rate ) 100 mV/s.

Figure 6. Plot of the ratio of geometric to effective radius over the geometric radius of nanometer-sized electrodes. The uncertainty of the ratio (along the Y axis) and the geometric radius (along the X axis) has been shown at each point.

The cyclic voltammograms on the electrode are shown in Figure 7. One can find apparent current fluctuations in the green curve, but the amplitude of the current fluctuations decreases as the scan rate increases. The current fluctuation almost disappeared at a scan rate higher than 50 mV/s. Most current

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Agyekum et al. calculated from eq 1 is almost equal to its geometric radius. A relatively big difference between the effective and the geometric electrode radii can be observed when the effective electrode radius is smaller than 20 nm. Cyclic voltammograms show that there is an apparent current fluctuation on a 1.6 nm radius electrode at slow scan rates. The current fluctuation may result from the potential fluctuation at the electrode/solution interface or the EDL effect.

Figure 7. Cyclic voltammograms obtained on a nanometer-sized electrode in 1 mM Ru(NH3)6Cl3 and 0.2 M KNO3 aqueous solution (purple, green, and blue curves) or in 0.2 M KNO3 aqueous solution (red curve). The effective radius of the electrode calculated from eq 1 is 1.6 nm. The scan rate is 10 mV/s for the red and the green curves, 20 mV/s for the blue curve, and 50 mV/s for the purple curve.

fluctuation in the green and blue curves in Figure 7 is in the limiting current region. The current fluctuation is not from electronic noise because a blank experiment shows little current fluctuation (see the red curve in Figure 7) and the green curve is obtained right after the blank experiment was done. Furthermore, it should not come from the discrete and stochastic behavior of electron-transfer events because the concentration is high and the time scale in our scan is too slow.8,9 Although applications of nanometer-sized electrodes of effective radii of less than 2 nm have been made for some time, we believe that this is the first report of a relatively large amplitude current fluctuation at a nanometer-sized electrode at a slow scan rate. Quantitative explanation of the current fluctuation may be difficult because there are still lots of unknowns for small electrodes, but theories developed for small amplitude current fluctuation of an electrochemical reaction31-33 may give us some hints. Gabrielli et al. studied current fluctuation on diffusion-limited electrochemical reactions.32,33 According to their theories, the current fluctuation may come from the following sources: (1) the fluctuation of flux of the electroactive species to the electrode surface, ∆In, (2) fluctuation of the potential drop at the electrode/solution interface, ∆E, and (3) the fluctuation of the charging current at the EDL, ∆C. Because there is not much current fluctuation at high scan rates and the flux of electroactive species at a small electrode should be independent of the scan rate, the amplitude of ∆In should be very small or rather ∆In is just noise. Thus, the scan rate dependent current fluctuation could be attributed to ∆E or ∆C. A recent paper also pointed out that the fluctuation of electrode potential (∆E) is not negligible when the area of the electrode is small enough.34 This means that some factors, such as electrode potential fluctuation and the EDL effect, etc., should be considered when we treat the data obtained at a small electrode, particularly when the scan rate is slow. 4. Conclusion Annealing is a very important step in preparing a wellpolished puller-made nanometer-sized electrode with a radius larger than 10 nm. The fabrication of a puller-made nanometersized electrode whose radius is less than 10 nm is chancedependent. For a well-polished nanometer-sized electrode with an effective radius larger than 20 nm, the effective radius

Acknowledgment. Support of this work by a New Faculty Start Up Grant from East Tennessee State University and an ACS Petroleum Research Fund Grant for Undergraduate New Investigator is gratefully acknowledged. The authors thank Dave Calvert from Eastman Co. for obtaining the SEM images and Dr. John A. Hyatt for proofing the manuscript. Also, we appreciate professor M. V. Mirkin from Queens College for helpful discussions. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Penner, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118. (2) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. J. Electroanal. Chem. 1992, 328, 47. (3) Chen, S.; Kucernak, A. J. Phys. Chem. B 2002, 106, 9396–9404. (4) Watkins, J. J.; Chen, J.; White, H. S.; Abrun˜a, H. D.; Maisonhaute, E.; Amatore, C. Anal. Chem. 2003, 75, 3962–3971. (5) White, R. J.; White, H. S. Anal. Chem. 2005, 77, 215A. (6) Sun, P.; Mirkin, M. V. Anal. Chem. 2006, 78, 6526–6534. (7) Fan, F.-R. F.; Bard, A. J. Science 1995, 267, 871. (8) Fan, F. F.; Kwak, J.; Bard, A. J. J. Am. Chem. Soc. 1996, 118, 9669–9675. (9) Fan, F.-R. F.; Bard, A. J. Science 1997, 277, 1791. (10) Sun, P.; Mirkin, M. V. J. Am. Chem. Soc. 2008, 130, 8241–8250. (11) Hoeben, F. J. M.; Meijer, F. S.; Dekker, C.; Albracht, S. P. J.; Heering, H. A.; Lemay, S. G. ACS Nano 2008, 2, 2497–2504. (12) Smith, C. P.; White, H. S. Anal. Chem. 1993, 65, 3343–3353. (13) Oldham, K. B.; Bond, A. M. J. Electroanal. Chem. 2001, 508, 28– 40. (14) Watkins, J. J.; White, H. S. Langmuir 2004, 20, 5474–5483. (15) He, R.; Chen, S.; Yang, F.; Wu, B. J. Phys. Chem. B 2006, 110, 3262. (16) Sun, Y.; Liu, Y.; Liang, Z.; Lu, X.; Wang, A.; Chen, S. J. Phys. Chem. C 2009, 113, 9878. (17) Liu, Y.; He, R.; Zhang, Q.; Chen, S. J. Phys. Chem. C [Online early access], 2010. (18) Krapf, D.; Quinn, B. M.; Wu, M.; Zandbergen, H.; Dekker, C.; Lemay, S. Nano Lett. 2006, 6, 2531. (19) Dickinson, E.; Compton, R. J. Phys. Chem. C 2009, 113, 17585. (20) Corry, B.; Kuyucak, S.; Chung, S. H. Biophys. J. 2000, 78, 2364– 2381. (21) Saito, Y. ReV. Polarogr. 1968, 15, 177. (22) Zhang, B.; Zhang, Y.; White, H. S. Anal. Chem. 2004, 76, 6229– 6238. (23) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications. ed., 2nd ed.; John Wiley & Sons, Inc.: New York, 2001. (24) Shoup, D.; Szabo, A. J. Electroanal. Chem. 1984, 160, 27. (25) Shao, Y.; Mirkin, M. V. J. Phys. Chem. B 1998, 102, 9915. (26) Zhan, D.; Velmurugan, J.; Mirkin, M. V. J. Am. Chem. Soc. 2009, 131, 14756–14760. (27) Rodrı´guez-Lo´pez, J.; Bard, A. J. J. Am. Chem. Soc. 2010, 132, 5121–5129. (28) Baranski, A. S. J. Electroanal. Chem. 1991, 307, 287. (29) Oldham, K. B. Anal. Chem. 1992, 64, 646. (30) Feldberg, S. W. Anal. Chem. [Online early access], 2010. (31) Gabrielli, C.; Huet, F.; Keddam, M. Electrochim. Acta 1986, 31, 1025. (32) Gabrielli, C.; Huet, F.; Keddam, M. J. Chem. Phys. 1993, 99, 7232. (33) Gabrielli, C.; Huet, F.; Keddam, M. J. Chem. Phys. 1993, 99, 7240. (34) Garcia-Morales, V.; Krischer, K. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 4528–4532.

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