Kinetics of Electron-Transfer Reactions at Nanoelectrodes

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Anal. Chem. 2006, 78, 6526-6534

Kinetics of Electron-Transfer Reactions at Nanoelectrodes Peng Sun and Michael V. Mirkin*

Department of Chemistry and Biochemistry, Queens CollegesCUNY, Flushing, New York 11367

The kinetics of several fast heterogeneous electrontransfer reactions were investigated by steady-state voltammetry at nanoelectrodes and scanning electrochemical microscopy (SECM). The disk-type, polished Pt nanoelectrodes (3.7-400-nm radius) were characterized by a combination of voltammetry, scanning electron microscopy, and SECM. A number of experimental curves were obtained at the same nanoelectrode to attain the accuracy and reproducibility similar to those reported previously for micrometer-sized probes. A new analytical approximation was developed and used for analysis of steady-state tip voltammograms. The self-consistent kinetic parameter values with the uncertainty margin of ∼10% were obtained for electrodes of different radii and for a wide range of the SECM tip/substrate separation distances. The determined standard rate constants are compared to those previously measured at the electrodes of different dimensions, and the correlation between the heterogeneous and self-exchange rate constants is discussed. Measuring the rates of rapid outer-sphere, electron-transfer (ET) reactions is of special interest because these mechanistically simple processes are used to check the ET theory.1 The question about the upper limit for the standard rate constant of a heterogeneous ET reaction (k°) has been haunting electrochemists since 1950s when Marcus formulated his ET theory,2 and the first experimental approaches to fast kinetic measurements were proposed.3 From the Marcus formula relating k° to the selfexchange rate constant (kex) for the same redox couple

k° ) Zhetxkex/Zbi

(1)

where Zhet ∼ 104 cm/s and Zbi ∼ 1011 M-1 s-1 are the heteroge* To whom correspondence should be addressed. E-mail: mmirkin@ qc.cuny.edu. (1) (a) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (b) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148. (c) Adams, D. M.; Brus, L.; Chidsey, C. E. D.; Creager, S.; Creutz, C.; Kagan, C. R.; Kamat, P. V.; Lieberman, M.; Lindsay, S.; Marcus, R. A.; Metzger, R. M.; Michel-Beyerle, M. E.; Miller, J. R.; Newton, M. D.; Rolison, D. R.; Sankey, O.; Schanze, K. S.; Yardley, J.; Zhu, X. J. Phys. Chem. B 2003, 107, 6668. (2) (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (b) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (3) (a) Delahay, P. New Instrumental Methods in Electrochemistry; WileyInterscience: New York, 1954. (b) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley & Sons: New York, 2001.

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neous and bimolecular collision frequencies, respectively;2b with the highest measured kex values exciding 109 M-1 s-1,4 one can expect the upper limit for k° to be g103 cm/s. The standard rate constants experimentally determined for many rapid outer-sphere heterogeneous reactions have been several orders of magnitude lower. Although various reasons for the measured heterogeneous ET rate constants to be lower than the values predicted by eq 1 have been discussed,5,6 the question of whether higher k° values could be determined using faster electrochemical techniques remains open. The early measurements of fast electrode kinetics were severely affected by uncompensated resistive potential drop in solution (IR drop) and adsorption of reactants or products.3b The use of micrometer-sized ultramicroelectrodes7 allowed the experimentalists to minimize the IR drop effect, increase the masstransfer rate, and measure the heterogeneous rate constants up to ∼5 cm/s.8-13 In scanning electrochemical microscopy (SECM),14a a high value of the mass-transfer coefficient (m) can be achieved under steady-state conditions by decreasing the tip-substrate separation distance (d). When the tip is brought within about one tip radius (a) of a conductive substrate, the mass-transfer rate increases and becomes inversely proportional to d. Thus, the ET rates, which are too fast to be measured when the tip is far from the substrate, can be determined at sufficiently small d. In this way, several fast rate constants (k° > 1 cm/s) were measured with micrometer-sized SECM tips.14b,c,15 (4) (a) Sutin, N. Acc. Chem. Res. 1982, 15, 275. (b) Nelsen, S. F.; Pladziewicz, J. R. Acc. Chem. Res. 2002, 35, 247. (5) Hupp, J. T.; Weaver, M. J. J. Phys. Chem. 1985, 89, 2795. (6) White, R. J.; White, H. S. Anal. Chem. 2005, 77, 214A. (7) (a) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 15, p 267. (b) Amatore, C. In Physical Electrochemistry: Principles, Methods, and Applications; Rubinstein, I., Ed.; Marcel Dekker: New York, 1995; p 131. (8) Wipf, D. O.; Kristensen, E. W.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1988, 60, 306. (9) Bond, A. M.; Henderson, T. L. E.; Mann, D. R.; Mann, T. F.; Thormann, W.; Zoski, C. G. Anal. Chem. 1988, 60, 1878. (10) Baranski, A. S.; Winkler, K.; Fawcett, W. R. J. Electroanal. Chem. 1991, 313, 367. (11) (a) Montenegro, M. I.; Pletcher, D. J. Electroanal. Chem. 1986, 200, 371. (b) Beriet, C.; Pletcher, D. J. Electroanal. Chem. 1994, 375, 213. (12) Birkin, P. R.; Silva-Martinez, S. Anal. Chem. 1997, 69, 2055. (13) Rees, N. V.; Klymenko, O. V.; Maisonhaute, E.; Coles, B. A.; Compton, R. G. J. Electroanal. Chem. 2003, 542, 23. (14) (a) Scanning Electrochemical Microscopy; Bard, A. J., Mirkin, M. V., Eds.; Marcel Dekker: New York, 2001. (b) Mirkin, M. V.; Richards, T. C.; Bard, A. J. J. Phys. Chem. 1993, 97, 7672. (c) Mirkin, M. V.; Bulho ˜es, L. O. S.; Bard, A. J. J. Am. Chem. Soc. 1993, 115, 201. (15) Miao, W. J., Ding, Z. F.; Bard, A. J. J. Phys. Chem. B 2002, 106, 1392. 10.1021/ac060924q CCC: $33.50

© 2006 American Chemical Society Published on Web 07/28/2006

Nanometer-sized electrodes (e.g., disks, bands, cones, and other types of nanoelectrodes produced by several research groups16-28) may be suitable for measuring faster heterogeneous ET kinetics. Steady-state voltammetry at nanoelectrodes offers high mass-transfer rates in combination with practically negligible effects of the resistive potential drop in solution, double layer charging current, and low levels of reactant adsorption. To use a nanoelectrode for kinetic measurements, one has to determine its size and shape. While the electrode radius can be roughly evaluated from the steady-state diffusion-limiting current, this method does not provide information about electrode geometry. The current state of the art in nanoelectrode characterization is represented by the recent work of Watkins et al.,28 where fastscan voltammetry of adsorbed species was used to determine the geometric surface area of the electrode. The combination of the area value with the radius value obtained from steady-state voltammetry of dissolved redox species allowed more complete characterization of the nanoelectrode geometry. However, it was difficult to use the same electrode for area measurements and kinetic experiments. The smallest electrode that could be characterized was ∼60-nm radius,28 though it was suggested that smaller electrodes may be investigated by this method in the future. Here, we evaluate the size and shape of nanoelectrodes by using them as SECM tips. (This approach has previously been developed for nanoelectrodes19a,20 and pipet-based amperometric probes.29) In SECM, a redox species is either reduced or oxidized at the tip electrode. The product of this reaction diffuses to the substrate, where it may be reoxidized or rereduced. This process produces an enhancement in the faradic current at the tip electrode depending on the tip shape and the normalized separation distance, L ) d/a. An SECM current versus distance (iT d) curve is obtained by measuring the diffusion current to the tip while moving it slowly toward the substrate surface. From a highquality current-distance curve, one can determine a, the RG value (i.e., the ratio of the insulating sheath radius to a), and also check whether the electrode surface is flat and not recessed into the insulator. If the tip is convex or recessed, the feedback response is significantly lower than that for a planar tip whose entire flat surface can be brought close to the substrate.19a,20 (16) (a) Morris, R. B.; Franta, D. J.; White, H. S. J. Phys. Chem. 1987, 91, 3559. (b) Conyers, J. L.; White, H. S. Anal. Chem. 2000, 72, 4441. (c) Zhang, B.; Zhang, Y.; White, H. S. Anal. Chem. 2004, 76, 6229. (17) Pendley, B. P.; Abrun ˜a, H. D. Anal. Chem. 1990, 62, 782. (18) Penner, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118. (19) (a) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. J. Electroanal. Chem. 1992, 328, 47. (b) Mirkin, M. V.; Fan, F.-R. F.; Bard, A. J. Science 1992, 257, 364. (c) Fan, F.-R. F.; Bard, A. J. Science 1995, 267, 871. (20) Shao, Y.; Mirkin, M. V.; Fish, G.; Kokotov, S.; Palanker, D.; Lewis, A. Anal. Chem. 1997, 69, 1627. (21) Slevin, C. J.; Gray, N. J.; MacPherson, J. V.; Webb, M. A.; Unwin, P. R. Electrochem. Commun. 1999, 1, 282. (22) Campbell, J. K.; Sun, L.; Crooks, R. M. J. Am. Chem. Soc. 1999, 121, 3779. (23) Kranz, C.; Friedbacher, G.; Mizaikoff, B.; Lugstein, A.; Smoliner, J.; Bertagnolli E. Anal. Chem. 2001, 732, 2491. (24) Sun, P.; Zhang, Z.; Guo, J.; Shao, Y. Anal. Chem. 2001, 73, 5346. (25) (a) Chen, S.; Kucernak, A. Electrochem. Commun. 2002, 4, 80. (b) Chen, S.; Kucernak, A. J. Phys. Chem. B 2002, 106, 9396. (26) Katemann, B. B.; Schuhmann, W. Electroanalysis 2002, 14, 22. (27) Chen, J.; Aoki, K. Electrochem. Commun. 2002, 4, 24. (28) Watkins, J. J.; Chen, J.; White, H. S.; Abrun ˜a, H. D.; Maisonhaute, E.; Amatore, C. Anal. Chem. 2003, 75, 3962.

In this article, we address an intriguing question about possible differences between ET dynamics observed at macroscopic and nanometer-sized interfaces. It was predicted that significant deviations from conventional electrochemical theory should be observed at electrodes smaller than ∼10 nm.30a More recent calculations showed that the magnitude of those deviations should be smaller.30b Other authors suggested that the heterogeneous rate constants measured at larger (g20 nm) nanoelectrodes may also differ significantly from those determined at macroscopic electrodes because of mass transport27 and diffuse double layer25b effects specific for nanointerfaces. In contrast, the results in ref 28 indicate that the rate constants determined using nanoelectrodes may be similar to those measured at larger interfaces. From steady-state voltammetry at very small nanoelectrodes (the effective radius, a g 1 nm), Penner et al.18 obtained standard rate constant values significantly larger than those reported by other groups. For example, k° ) 220 ( 120 cm/s was found for the well-studied oxidation of ferrocene in acetonitrile, in contrast to the values between 1 and 6 cm/s reported elsewhere.8-12,14b,31 The validity of those results was questioned by several authors because of the lack adequate characterization of the electrode geometry.32 It was suggested that the overestimation of the rate constants in ref 18 resulted from the recession of the electrode into a small chamber of surrounding insulator (“lagooned geometry”).32a,b This criticism was not supported by experimental data because there was no technique at the time for characterization of nanoelectrode geometry. Below, we present the kinetic data obtained at well-characterized nanoelectrodes for two of the faster ET reactions studied in ref 18. EXPERIMENTAL SECTION Chemicals. 7,7,8,8-tetracyanoquinodimethane (TCNQ, 98%) and ferrocenemethanol (FcCH2OH, 97%) from Aldrich (Milwaukee, WI) were recrystallized twice from acetone. Ferrocene (Fc, 98%, Aldrich) was sublimed twice before use. Hexaammineruthenium(III) chloride (99%) was obtained form Strem Chemicals (Newburyport, MA). Tetrabutylammonium perchlorate (TBAP, Fluka), sodium chloride, and potassium chloride (99+%, Aldrich) were used as supporting electrolytes. Aqueous and organic solutions were prepared from deionized water (Milli-Q, Millipore Co.) and 99.95% acetonitrile (Aldrich), respectively. Electrodes and Electrochemical Cells. Polished Pt working electrodes (3-400-nm radius) were prepared and characterized as described below. A two-electrode configuration was employed with a 0.25-mm-diameter Ag wire coated with AgCl serving as a reference electrode. The 100-nm-thick evaporated Au films on glass prepared with the aminosilane coupler and annealed33 were obtained as a gift from Alexander Vaskevich (Weizmann Institute of Science) and used as a conductive SECM substrate. The cell (29) (a) Shao, Y.; Mirkin, M. V. J. Phys. Chem. B 1998, 102, 9915. (b) Amemiya, S.; Bard, A. J. Anal. Chem. 2000, 72, 4940. (30) (a) Smith, C. P.; White, H. S. Anal. Chem. 1993, 65, 3343. (b) He, R.; Chen, S.; Yang, F.; Wu B. J. Phys. Chem. B 2006, 110, 3262. (31) Clegg, A. D.; Rees, N. V.; Klymenko, O. V.; Coles, B. A.; Compton, R. G. J. Electroanal. Chem. 2005, 580, 78. (32) (a) Baranski, A. S. J. Electroanal. Chem. 1991, 307, 287. (b) Oldham, K. B. Anal. Chem. 1992, 64, 646. (c) Weaver, M. J. In Electrified Interfaces in Physics, Chemistry and Biology; Guidelli, R., Ed.; NATO ASI Series; Kluwer: Dordrecht, The Netherlands, 1992; p 427. (33) Wanunu, M.; Vaskevich, A.; Rubinstein, I. J. Am. Chem. Soc. 2004, 126, 5569.

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was made by attaching a 7-mm glass tube to the Au-coated slide, which was mounted on a vibration-isolated horizontal stage. In the negative feedback mode, a bare glass slide was used as an insulating substrate to check the tip geometry. SECM Instrumentation and Procedures. SECM experiments were carried out using a home-built instrument, which was similar to those described previously20,34 except that a PI-841 piezoactuator (Physik Instrumente) was used for z-axis scanning. The piezoactuator was controlled by a E-500 position controller (Physik Instrumente), which provided the 0.1-nm resolution in a closed-loop mode. The input signal for the position controller was produced by a home-built ramp generator with a 16-bit resolution. All experiments were carried out at room temperature (23 ( 2 °C) inside a Faraday cage. The solution containing Ru(NH3)63+ was purged with high-purity nitrogen for at least 30 min before voltammetric measurements. The initial approach of the nanotip to the substrate surface was monitored by a video microscope. The tip was moved toward the substrate at a relatively slow speed (e.g., 200 nm/s) using a z-axis Inchworm motor. The motion was stopped instantly when the change in tip current was detected. At this point, the tip/ substrate separation distance was equivalent to several tip radii. Before obtaining an approach curve, the tip was moved a few micrometers away from the substrate. Then, the PI-841 piezoactuator was used to move the tip toward the substrate at a very low speed (5-30 nm/s), and the tip current was recorded as a function of separation distance. In this way, several current versus distance curves could be obtained by moving the tip up and down without any apparent damage to it. To obtain an approach curve, the tip was biased at a potential where the oxidation (or reduction) of the mediator species occurred at a diffusion-controlled rate. The cyclic voltammograms were obtained by positioning the nanotip at a suitable distance from the substrate and scanning its potential. The Au substrate was always unbiased. Fabrication of Working Electrodes. The nanoelectrodes were fabricated by pulling 25-µm annealed Pt wires into borosilicate glass capillaries (1.0-mm o.d., 0.58-mm i.d.) under vacuum with the help of a P-2000 laser pipet puller (Sutter Instrument Co., Novato, CA). Several parameters of the pulling program were varied in order to control the shape and the size of the nanoelectrode.20 After pulling, the metal surface was exposed by micropolishing. A manipulator was used to move the pipet vertically toward the slowly rotating disk of the micropipet beveller (model BV-10, Sutter Instrument Co.). Polishing was performed under video microscopic control (maximum on-screen magnification g1000×) on a 50-nm lapping tape (Precision Surfaces International, Houston, TX). To obtain a tip that can be brought close to the substrate surface, one has to ensure that its axis is strictly perpendicular to the polishing surface. This was done by using a plumb bob to check that the electrode axis is vertical and using a two-axis bubble level to make sure that the polishing disk plane is horizontal. The same approach was used to check the tip/substrate alignment before SECM experiments. Polished electrodes were washed by distilled water and annealed in oven at 150 °C to further smooth the surface. The (34) (a) Wipf, D. O.; Bard, A. J. J. Electrochem. Soc. 1991, 138, L4. (b) Wipf, D. O.; Bard, A. J. J. Electrochem. Soc. 1991, 138, 469.

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Figure 1. SEM of a 70-nm-radius polished Pt ultramicroelectrode.

effective radius of an electrode was evaluated from steady-state voltammetry, and only electrodes producing well-shaped sigmoidal voltammograms of 2 mM Ru(NH3)63+ at a scan rate v ) 10 V/s were used for SECM experiments. Cyclic voltammograms (CVs) were obtained using a BAS 100B electrochemical workstation (Bioanalytical Systems, West Lafayette, IN). A representative SEM micrograph of a 70-nm-radius Pt electrode (Figure 1) shows the disk-type, flat geometry of the conductive surface surrounded by well-polished insulating glass (RG = 10). The RG value can vary from 3 and typically close to 10 (Figures 1 and 5). Also, the IT was essentially independent of RG value in our kinetic experiments because the mediator regeneration at the substrate occurred at the diffusion-controlled rate.29a ET Kinetics at Nanoelectrodes. Steady-state tip voltammetry was employed to determine kinetic parameters of ferrocenemetha(37) (a) Cai, C.; Tong, Y.; Mirkin, M. V. J. Phys. Chem. B 2004, 108, 17872. (b) Cai, C.; Mirkin, M. V. J. Am. Chem. Soc. 2006, 128, 171.

Table 1. Kinetic Parameters of FcCH2OH Oxidation at Pt Nanoelectrodes in 0.2 M NaCl

Figure 5. Experimental (symbols) and theoretical (solid curve) SECM current vs distance curves obtained with an 83-nm-radius polished Pt tip approaching an insulating substrate. The approach speed was 10 nm/s. For other parameters, see Figure 3.

Figure 6. Experimental (symbols) and theoretical (sold lines) steady-state voltammograms of 1 mM ferrocenemethanol obtained at different separation distances between the 36-nm Pt tip and Au substrate. d ) ∞ (1), 54 (2), 29 (3), and 18 nm (4). v ) 50 mV/s. For other parameters, see Figure 3. Theoretical curves were calculated from eq 3.

nol oxidation and check the validity of kinetic measurements at nanoelectrodes. In a feedback-mode SECM experiment, FcCH2OH was oxidized at the tip nanoelectrode, and the product of this reaction was rereduced at the Au substrate surface. The potential of an unbiased substrate was sufficiently positive for the substrate ET reaction to be diffusion-controlled, while the tip potential was swept slowly to record a steady-state voltammogram. Figure 6 shows such voltammograms obtained at different distances between the 36-nm-radius Pt tip and the Au film substrate. The kinetic parameters (k°, R) and the formal potential of the ET reaction were extracted by fitting the experimental voltammograms (symbols) to the theoretical curves (solid lines) calculated from eq 3.38 Using this approach, the mass-transfer rate can be changed in two different ways: by changing either the tip radius or the tip/substrate separation distance. Table 1 contains the data obtained for FcCH2OH oxidation at nanoelectrodes of different radii (from 25 to 290 nm) positioned at various distances from the substrate surface. It was shown previously, that the steadystate tip voltammogram is essentially Nernstian if the dimensionless kinetic parameter, λ′ ) k°d/D ) Lk°a/D is J10.14b,39 (When the tip is far from the substrate, the condition of reversibility is λ (38) TableCurve 2D program (Jandel Scientific) was used for curve fitting. (39) Mirkin, M. V.; Bard, A. J. Anal. Chem. 1992, 64, 2293.

a, nma

L

k°, cm/s

290 290 290 290 290 257 257 257 257 257 183 183 183 183 183 167 167 167 167 167 147 147 147 147 147 73 73 73 73 67 67 67 67 36 36 36 36 25 25 25

∞ 0.95 0.44 0.26 0.13 ∞ 0.84 0.42 0.24 0.15 ∞ 0.79 0.42 0.26 0.19 ∞ 0.83 0.34 0.24 0.17 ∞ 0.83 0.34 0.24 0.17 ∞ 1.30 0.75 0.49 ∞ 0.95 0.65 0.47 ∞ 1.50 0.80 0.50 ∞ 1.80 1.16

reversible reversible reversible 4.4 4.3 reversible reversible 7.1 7.4 7.8 reversible reversible 6.3 6.1 5.9 reversible reversible 6.4 8.9 8.9 reversible 6.6 6.4 8.9 8.9 5.3 4.1 3.9 4.0 4.9 4.9 5.2 6.4 6.9 8.9 9.5 10.0 9.6 9.3 7.0

R

E°′

0.40 0.41

205 205

0.44 0.49 0.47

129 127 125

0.41 0.41 0.40

160 155 157

0.49 0.49 0.49

117 116 115

0.47 0.49 0.49 0.49 0.42 0.34 0.33 0.34 0.32 0.33 0.33 0.34 0.42 0.46 0.44 0.58 0.45 0.37 0.34

147 147 148 146 117 132 128 123 170 168 170 170 161 160 164 158 120 120 123

λ′ or λb 25.3 24.0 11.1 4.3 2.1 22.4 18.8 9.8 5.9 3.9 16.0 12.6 6.2 3.7 2.6 14.6 12.1 4.7 4.6 3.2 12.8 10.3 4.1 4.0 2.9 5.0 5.0 2.7 1.8 4.2 4.0 2.9 2.6 3.2 6.2 3.5 2.8 3.1 5.4 2.6

a Calculated from eq 5 with D ) 7.8 × 10-6 cm2/s, which was obtained by steady-state voltammetry at micrometer-size electrodes. b For reversible curves, λ was calculated using the mean value, k° ) 6.8 cm/s.

) k°a/D J 10.) Accordingly, the voltammograms obtained at larger electrodes and large tip/substrate distances (e.g., a ) 290 nm, L ) ∞) were found to be essentially reversible. From Table 1, one can see that the parameter values extracted from the CVs obtained at the same electrode were reproducible within the limits of the experimental error. The formal potential value was constant within (5 mV. The variations between E°′ values obtained with different tip electrodes are not surprising: these measurements were taken during a several-week period using different coated-wire references. The potential of each reference was stable on the experimental time scale, but slightly different from those of other Ag/AgCl reference electrodes. The mean values of the kinetic parameters from Table 1 are k° ) 6.8 ( 0.7 cm/s and R ) 0.42 ( 0.03. The uncertainties of both values (i.e., 95% confidence intervals) are very low, and there is no strong correlation between the kinetic parameters and either the tip radius or separation distance. These results suggest that polished nanoelectrodes with a g 25 nm used either alone or as SECM tips (d g 18 nm) are suitable for ET kinetic measurements. Analytical Chemistry, Vol. 78, No. 18, September 15, 2006

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Table 3. Kinetic Parameters of Ru(NH3)63+ Reduction at Pt Nanoelectrodesa

Table 2. Kinetic Parameters of Fc Oxidation in Acetonitrile at Pt Nanoelectrodesa a, nmb

L

k°, cm/s

R

E°′

λ′ or λ

a, nmb

L

k°, cm/s

142 142 142 142 142 142 96 96 96 96 96 84 84 84 84 46 46 46 46 12 3.7

∞ 0.97 0.49 0.34 0.26 0.14 ∞ 0.73 0.33 0.26 0.17 ∞ 0.82 0.45 0.25 ∞ 1.2 0.75 0.59 ∞ ∞

7.7 8.2 8.3 8.1 7.7 7.8 8.6 8.8 8.6 8.9 8.5 9.0 8.6 8.9 8.2 8.4 8.6 8.0 8.2 9.1 11.6

0.43 0.48 0.49 0.42 0.42 0.40 0.40 0.43 0.51 0.52 0.47 0.49 0.51 0.47 0.47 0.51 0.49 0.49 0.49 0.47 0.53

461 461 461 457 458 460 460 461 456 456 456 462 462 465 468 481 477 472 467 486 462

5.3 5.5 2.8 1.9 1.4 0.8 4.0 3.0 1.3 1.1 0.7 3.7 2.9 1.6 0.8 1.9 2.3 1.3 1.1 0.5 0.2

282 282 282 282 282 282 127 127 127 127 127 73 73 73 73 73 56 56 56 56 43 43 43 43 43 29 29 29 14.7 14.7

∞ 0.38 0.24 0.21 0.16 0.13 ∞ 0.6 0.41 0.3 0.24 ∞ 1.1 0.49 0.32 0.17 ∞ 0.87 0.43 0.32 ∞ 1.1 0.69 0.46 0.36 ∞ 1.7 0.91 ∞ 1.05

reversible reversible reversible reversible 14.1 14.0 reversible reversible reversible 15.5 15.5 reversible reversible 16.5 16.7 16.3 reversible reversible 17.4 18.6 reversible reversible 18.8 19.1 19.6 18.1 reversible 15.1 19.2 18.1

a Solution contained 2 mM Fc and 0.3 M TBAP. b Calculated from eq 5 with D ) 2.05 × 10-5 cm2/s, which was obtained by steady-state voltammetry at micrometer-size electrodes.

No “nonclassical” effects discussed in refs 25b, 27, and 30 have been observed for this range of a and d values (smaller a and d are discussed below). The determined kinetic parameters are similar to those obtained for the oxidation ferrocenylmethyltrimethylammonium in 0.2 M KCl at quasi-hemispherical Pt nanoelectrodes, i.e., k° ) 4.8 ( 3.2 cm/s and R ) 0.64 ( 0.15.28 It is interesting to compare our kinetic data to those obtained for the same ET reaction at larger (i.e., micrometer-sized) electrodes. In ref 15, a significantly lower rate constant (k° ) 2.06 cm/s) and a smaller transfer coefficient (R ) 0.2) were measured for the oxidation of FcCH2OH in the 50.0 mM (CH3)4NClO4 aqueous solution by SECM with a ) 5.06 µm and L ) 0.204. The reason for this difference becomes apparent if one calculates the dimensionless kinetic parameter, λ′ ) Lk°a/D ) 0.204 × 2.06 cm/s × 5.06 × 10-4 cm/7.8 × 10-6 cm2/s ) 27.3. This value corresponds to a completely reversible voltammogram and suggests that the kinetic parameters in ref 15 were underestimated. One should notice that the three-parameter fit of an experimental CV to the theory somewhat depends on the initial guess and on the best-fit criteria. Thus, the kinetic parameters obtained from a single voltammogram may not be completely reliable, especially if the measured rate constant is close to the masstransfer limit. However, fitting a number of curves obtained at different electrodes and for different L values yields reliable results with a very low margin of uncertainty. Kinetic parameters measured for the ferrocene oxidation in acetonitrile (Table 2) were even more reproducible (k° ) 8.4 ( 0.2 cm/s; R ) 0.47 ( 0.02). The average k° is somewhat higher than the values obtained at micrometer-sized electrodes8-11,14b,31 and close to an estimate found from steady-state voltammetry at 0.3-0.5-µm-radius electrodes in ref 9 (k° ∼ 10 cm/s). An SECM study with a 1-µm-radius Pt tip yielded k° ) 3.7 cm/s.14b The origin of this difference is probably in the use of somewhat less accurate approximations,14b which should have produced underestimated 6532 Analytical Chemistry, Vol. 78, No. 18, September 15, 2006

R

E°′

0.42 0.40

-158 -159

0.42 0.42

-220 -220

0.46 0.52 0.62

-205 -199 -193

0.40 0.42

-213 -205

0.41 0.43 0.47 0.53

-210 -210 -201 -208

0.46 0.41 0.43

-198 -205 -205

λ′ or λc 71.6 27.2 17.2 15.0 9.5 7.7 32.2 19.3 13.2 8.8 7.1 18.5 20.4 8.8 5.8 3.0 14.2 12.4 6.3 5.0 10.9 12.0 8.3 5.6 4.5 7.8 12.5 5.9 4.2 4.2

a Solution contained 2 mM Ru(NH ) 3+and 0.5 M KCl. b Calculated 3 6 from eq 5 with D ) 6.7 × 10-6 cm2/s, which was obtained from steadystate voltammetry at micrometer-size electrodes. c For reversible curves, λ was calculated using the mean value, k° ) 17.0 cm/s.

k° (see Supporting Information). On the other hand, k° ) 8.4 cm/s is close to the upper limit for the rate constant measurable under the experimental conditions of ref 14b. In ref 18, the rate constant of Fc oxidation was measured at a nanoelectrode with the effective radius of ∼1 nm. To facilitate the comparison of our results to those in ref 18, we carried out experiments at two smaller electrodes (a ) 12 and 3.7 nm). Since it is difficult to evaluate the shape of such tips and to polish them effectively, the determined kinetic parameters are less reliable than those obtained at larger (i.e., a > 15 nm) electrodes. Nevertheless, for a 12-nm electrode, both the standard rate constant and the transfer coefficient are very similar to the values obtained from other voltammograms. Both k° and R values obtained at the 3.7nm electrode were slightly higher than those measured at larger tips, but the difference is probably within the range of experimental error for this measurement (these data were not used in calculating the average parameter values). Overall, the rate constants of Fc oxidation measured at our nanoelectrodes were somewhat larger than the values obtained at micrometer-sized interfaces, but incomparably smaller than that reported in ref 18. Another fast reaction in ref 18 was the reduction of Ru(NH3)63+ in 0.5 M KCl (k° ) 79 ( 44 cm/s18). Our experiments (Table 3) yielded the average values of k° ) 17.0 ( 0.9 cm/s and R ) 0.45 ( 0.03 for this system. As in two previous cases, the extracted kinetic parameters are essentially independent of the tip radius, which was varied from 14.7 to 282 nm, and separation distance. This reaction is faster than oxidations of Fc and FcCH2OH

Figure 7. Cyclic voltammograms of 1 mM Ru(bpy)32+ in 0.2 M KCl at (A) 2-µm and (B) 39-nm-radius Pt electrode. The curves in (B) are the first, fifth, and tenth scans, respectively; the corresponding curves in (A) are indistinguishable.

discussed above. Although the measured k° is much slower than the one reported in ref 18, it is significantly higher than the values previously obtained for this process at larger electrodes (e.g., 0.8 cm/s from fast-scan voltammetry at the 25-µm Pt disk in 1 M KCl11b and 0.6 cm/s from sampled voltammetry at the 25-µm Pt electrode in 0.1 M KCl12). The rate of this reaction may actually be too fast to measure at micrometer-sized electrodes. The upper limit for the rate constant measurable at SECM nanotips can be evaluated from the reversibility condition discussed above. Taking λ′ ) k°d/D < 10 with d ) 5 nm (which is close to the smallest separation distance achievable in our experiments) and D ) 10-5 cm2/s, one obtains k° < 200 cm/s. The self-exchange ET rate constants of both Ru(NH3)63/2+ (800-4300 M-1 s-1)5,40 and ferrocene (9 × 106 M-1 s-1)41b are smaller than those measured for many other redox couples.41 Therefore, we wanted to check whether a redox couple with a large kex would yield a very fast heterogeneous rate constant expected from eq 1. Some of those species (e.g., cobaltocene and anthracene) with high negative standard potentials are less suitable for SECM experiments in which the complete oxygen removal is difficult to achieve. In contrast, the reversible Ru(bpy)33+/2+ couple (kex ) 4 × 108 M-1 s-1)4a is not air-sensitive. In agreement with previous studies, well-shaped steady-state voltammograms of Ru(bpy)32+ were obtained at micrometer-sized Pt and Au electrodes both in aqueous (Figure 7A) and organic (not shown) solutions. Surprisingly, the diffusion-limiting current measured at nanoelectrodes decreased with time (Figure 7B) and did not completely stabilize even after 30 min of continuous scanning. This behavior was observed for a number of nanoelectrodes (a j 0.5 µm) in both aqueous and acetonitrile solutions with different supporting electrolytes. All attempts to eliminate this effect by purifying the chemicals, changing concentrations of redox species and electrolyte, and polishing the electrodes were unsuccessful. This behavior, which was not observed for any other ET reaction we have studied (including the reduction of triple-charged Ru(NH3)63+), suggests additional (40) (a) Wherland, S.; Gray, H. B. In Biological Aspects of Inorganic Chemistry; Addison, A. W., Cullen, W., James, B. R., Dolphin, D., Eds.; Wiley: New York, 1977; p 289. (b) Brunschwig, B. S.; Creutz, C.; Macartney, D. H.; Sham, T. K.; Sutin, N. S. Faraday Discuss. Chem. Soc. 1982, 74, 113. (41) (a) Weaver, M. J. Chem. Rev. 1992, 92, 463. (b) Gennett, T.; Milner, D. F.; Weaver, M. J. J. Phys. Chem. 1985, 89, 2187. (c) Fawcett, W. R.; Opallo, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 2131.

Table 4. Kinetic Parameters of TCNQ Reduction in Acetonitrile at Pt Nanoelectrodea a, nmb

L

k°, cm/s

R

E°′, mV

λ′ or λ

386 386 386 386 127 127 127 127 127 76 76 76 76

∞ 0.56 0.34 0.26 ∞ 0.97 0.72 0.46 0.35 ∞ 0.93 0.5 0.39

1.1 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.1 1.0 1.0 1.0

0.32 0.39 0.45 0.47 0.38 0.43 0.43 0.40 0.42 0.43 0.43 0.51 0.45

-160 -152 -145 -147 -172 -169 -168 -165 -166 -177 -170 -165 -165

2.1 1.1 0.7 0.6 0.7 0.7 0.5 0.4 0.3 0.4 0.4 0.2 0.1

a Solution contained 2 mM TCNQ and 0.1 M TBAP. b Calculated from eq 5 with D ) 1.98 × 10-5 cm2/s, which was obtained from steadystate voltammetry of TCNQ at micrometer-size electrodes.

complexity of Ru(bpy)32+ oxidation that may not be apparent from voltammetry at macroscopic electrodes. The TCNQ/TCNQ- redox couple in acetonitrile has a very high self-exchange rate constant ((3.3 ÷ 4.3) × 109 M-1 s-1).42 Highly reproducible kinetic parameters extracted from nearly ideal steady-state voltammograms of the reduction of TCNQ (Table 4) give the average values, k° ) 1.1 ( 0.04 cm/s and R ) 0.42 ( 0.025. In contrast to a fast self-exchange rate constant, the measured k° is lower than the rate constants of other ET reactions studied here. However, it is still higher than the value measured at microelectrodes (0.23 ( 0.01 cm/s).43 Comparison of the measured rate constants with the theoretical values is difficult because very different k° values have been calculated for the same ET reaction using different theoretical assumptions.44 There is no apparent correlation between electrochemical rate constants measured here and corresponding selfexchange rate constants: the lowest k° was measured for the (42) (a) Komarynsky, M. A.; Wahl, A. C. J. Phys. Chem. 1975, 79, 695. (b) Ganesan, V.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2003, 125, 2559. (43) Russell, A.; Repka, K.; Dibble, T.; Ghoroghchian, J.; Smith, J. J.; Fleischmann, M.; Pons, S. Anal. Chem. 1986, 58, 2961. (44) Swaddle, T. W. Chem. Rev. 2005, 105, 2573.

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redox couple with the fastest kex (TCNQ/TCNQ-), and vice versa, the fastest heterogeneous rate constant was obtained for Ru(NH3)63+/2+ in 0.5 M KCl whose kex is the lowest among the studied couples. The latter reaction exemplifies the difficulties in comparing the rates of homogeneous and heterogeneous ET reactions. Unlike Fc, FcCH2OH, and TCNQ, Ru(NH3)63+ is a triplecharged cation. The magnitude of the Frumkin correction for such species is hard to evaluate quantitatively.44,45 Another factor is a significant increase in k° of Ru(NH3)63+ reduction in the presence of chloride ions.18 These factors and the essential adiabaticity of this reaction44,46 should be responsible for the unusually high k°. The measured standard rate constants of Fc and FcCH2OH oxidation reactions are comparable to those obtained at micrometersized electrodes. A slightly larger k° value obtained for Fc (8.4 vs 6.8 cm/s) is in line with the shorter longitudinal relaxation time of acetonitrile as compared to water and somewhat larger Pekar factor (op-1 -  s-1).41 The lower rate of TCNQ reduction in acetonitrile is probably due to the lower degree of adiabaticity. CONCLUSIONS The polished Pt electrodes (g10-nm radius) were prepared and routinely used as tips for SECM experiments, so that a number of current versus distance curves and voltammograms were obtained at the same tip without damaging it. This allowed us to characterize the tip geometry and then use it to obtain an extensive set of experimental data. In this way, nanoelectrochemical measurements of ET kinetics were made with reproducibility similar to that reported previously for micrometer-sized electrodes. The SECM current versus distance curves showed high feedback response indicating that the prepared tips were flat on the nanometer scale and not recessed. The steady-state voltammograms and approach curves obtained were in agreement with conventional electrochemical theory at all a and d values. (45) Muzika´, M.; Fawcett W. R. Anal. Chem. 2004, 76, 3607. (46) (a) Iwasita, T.; Schmickler, W.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 138. (b) Iwasita, T.; Schmickler, W.; Schultze, J. W. J. Electroanal. Chem. 1985, 194, 355.

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The kinetic parameters obtained for three rapid heterogeneous ET reactions were reproducible within ∼10% error margin. The mass-transfer rate was changed by more than 2 orders of magnitude by varying both the tip radius and the tip/substrate separation distance, and the measured k° and R values were essentially independent of both a and d. For three fast ET reactions (the oxidation of ferrocenemethanol in water and ferrocene in acetonitrile, and the reduction of TCNQ in acetonitrile), the standard rate constants measured at nanoelectrodes were similar to or slightly higher than the values obtained previously at larger electrodes. The standard rate constant of Ru(NH3)63+ reduction in KCl is very fast (17.0 ( 0.9 cm/s) and hard to measure by other electrochemical techniques. Overall, there is no major difference between ET rate measured at nanoelectrodes and at larger interfaces. At the same time, the upper limit for the rate constant measurable at nanoelectrodes under steady-state conditions is as high as ∼200 cm/s. ACKNOWLEDGMENT The support of this work by the National Science Foundation (CHE-0315558), the donors of the Petroleum Research Fund administrated by the American Chemical Society, and a grant from PSC-CUNY are gratefully acknowledged. We thank Dr. Alexander Vaskevich (Weizmann Institute of Science) for generously providing evaporated Au substrates for SECM experiments, and Franc¸ ois Laforge and James Carpino for producing an electronic circuit for the SECM instrument. SUPPORTING INFORMATION AVAILABLE Additional details of the analysis of steady-state SECM voltammograms. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review May 19, 2006. Accepted June 26, 2006. AC060924Q