Anal. Chem. 2004, 76, 3619-3629
Large-Amplitude Fourier Transformed High-Harmonic Alternating Current Cyclic Voltammetry: Kinetic Discrimination of Interfering Faradaic Processes at Glassy Carbon and at Boron-Doped Diamond Electrodes Jie Zhang, Si-Xuan Guo, and Alan M. Bond*
School of Chemistry, Monash University, Clayton, Victoria 3800, Australia Frank Marken*
Department of Chemistry, Loughborough University, Loughborough, Leics LE11 3TU, U.K.
Significant advantages of Fourier transformed largeamplitude ac higher (second to eighth) harmonics relative to responses obtained with conventional small-amplitude ac or dc cyclic voltammetric methods have been demonstrated with respect to (i) the suppression of capacitive background currents, (ii) the separation of the reversible reduction of [Ru(NH3)6]3+ from the overlapping irreversible oxygen reduction process under conditions where aerobic oxygen remains present in the electrochemical cell, and (iii) the kinetic resolution of the reversible [Ru(NH3)6]3+/2+ process in mixtures of [Fe(CN)6]3and [Ru(NH3)6]3+ at appropriately treated boron-doped diamond electrodes, even when highly unfavorable [Fe(CN)6]3- to [Ru(NH3)6]3+ concentration ratios are employed. Theoretical support for the basis of kinetic discrimination in large-amplitude higher harmonic ac cyclic voltammetry is provided. Alternating current (ac) voltammetry (polarography), which was invented in the 1950s,1 and intensively developed by Smith and co-workers for studies at a dropping mercury electrode,2 is a powerful technique for quantitative evaluation of electrode processes and for analysis of trace concentrations of electroactive species.1-3 Conventionally, when stationary rather than dropping mercury electrodes are employed, a small-amplitude sine wave is superimposed onto the waveform used in dc linear or cyclic voltammetry (see Figure 1), and the fundamental harmonic ac response is measured as a function of dc potential and frequency.1-3 Unfortunately, the use of the ac voltammetric method remains * Corresponding authors. E-mail:
[email protected]; f.marken@ lboro.ac.uk. (1) Bond, A. M. Modern Polarographic Methods in Analytical Chemistry; Marcel Dekker: New York, 1980 and references therein. (2) Smith, D. E. In Electroanalytical Chemistry, Bard, A. J., Ed.; Marcel Dekker: New York, 1966; Vol. 1. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001. 10.1021/ac049744b CCC: $27.50 Published on Web 05/15/2004
© 2004 American Chemical Society
Figure 1. Waveform employed in large-amplitude ac voltammetry (for simplicity only the forward sweep direction of a reduction process shown). In experimental studies, both the forward (reduction) and backward (oxidation) potential scan directions are considered and current data are plotted as a function of time rather than potential using the foillowing relationship: E(t) ) Estart - vt(0 < t < ts) and E(t) ) Estart - 2vts + vt (ts < t < 2ts).
somewhat restricted in fundamental applications of voltammetry because the range of theoretical solutions is very limited compared to the dc case.1,2 Moreover, the majority of the existing theories assume that the amplitude of the applied alternating potential is small (typically less than 10 mV) and the dc and ac time scales are resolvable so that nonlinear second and higher ac components are very small and hence difficult to measure. However, recent theoretical and experimental studies confirm that a great deal of valuable information is contained in the higher harmonics that is readily accessed under large-amplitude conditions.4-10 Kuhr and (4) Engblom, S. O.; Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 2000, 480, 120. (5) Gavaghan, D. J.; Bond, A. M. J. Electroanal. Chem. 2000, 480, 133.
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co-workers, for example, have demonstrated the application of large-amplitude methodology, with lock-in amplifier detection and analysis of higher harmonics with very favorable Faradaic to charging current ratios, for analytical detection purposes.8-10 Studies with large-amplitude ac techniques are advantageous in fundamental studies for the same reason and also because of the well-defined patterns of behaviors that emerge in the higher harmonics that are readily detected by Fourier transform methods of data analysis.7 On these bases, the use of large rather than traditional small-amplitude forms of ac voltammetry is now being advocated.4,5,7-10 Advanced forms of instrumentation for ac voltammetric measurements (sinusoidal, square wave, sawtooth) at a stationary electrode incorporate Fourier transform (FT) and inverse FT or equivalent functions11,12 that enable the dc and ac harmonic terms to be separated. The instrumental format employed in recent studies from this laboratory6,7b mimics the simulation protocols developed for the theoretical studies, thereby allowing theory and experiment comparison to be readily undertaken. In this form of instrumentation, as in the case with theoretical analysis, FT analysis is employed to obtain the power spectrum of largeamplitude ac voltammograms and then inverse FT analysis is used to separate the dc signal and the first and higher harmonics from the total measured current. These FT-based approaches represent an extension of ideas contained in the pioneering studies by Smith.12 In the case where a sinusoidal perturbation is used, both theoretical and experimental results show that the second and higher harmonic components remain essentially free of background charging current under large-amplitude conditions,7b which provides one of the most significant advantages of the largeamplitude method. In this paper, the benefits of second and higher (third to eighth) harmonic large-amplitude ac voltammetry are demonstrated experimentally in the case of kinetic discrimination achieved in voltammetric studies of the reversible [Ru(NH3)6]3+/2+, the quasi-reversible [Fe(CN)6]3-/4-, and the irreversible oxygen reduction processes in aqueous solution at glassy carbon and at boron-doped diamond13 electrodes. The experimental observation of exceptionally high selectivity that may be achieved in the third and higher harmonics for a reversible process in the present of a quasi-reversible process is supported by numerical simulations. (6) Gavaghan, D. J.; Elton, D. M.; Bond, A. M. Collect. Czech. Chem. Commun. 2001, 66, 255. (7) (a) Honeychurch, M. J.; Bond, A. M. J. Electroanal. Chem. 2002, 529, 3. (b) Guo, S.; Zhang, J.; Elton, D. M.; Bond, A. M. Anal. Chem. 2004, 76, 166. (8) Cullison, J. K.; Kuhr, W. G. Electroanalysis 1996, 8, 314. (9) Singhal, P.; Kawagoe, K. T.; Christian, C. N.; Kuhr, W. G. Anal. Chem. 1997. 69, 1662. (10) Singhal, P.; Kuhr, W. G. Anal. Chem. 1997, 69, 3552. (11) (a) Ha´zı`, J.; Elton, D. M.; Czerwinski, W. A.; Schiewe, J.; Vicente-Beckett, V. A.; Bond, A. M. J. Electroanal. Chem. 1997, 437, 1. (b) Schiewe, J.; Ha´zı`, J.; Vicente-Beckett, V. A.; Bond, A. M. J. Electroanal. Chem. 1998, 451, 129 and references therein. (12) (a) Smith, D. E. Anal. Chem. 1976, 48, 517A. (b) Smith, D. E. Anal. Chem. 1976, 48, 221A. (c) Creason, S. C.; Smith, D. E. Anal. Chem. 1973, 45, 2401. (d) Glover, D. E.; Smith, D. E. Anal. Chem. 1973, 45, 1869. (e) Hayes, J. W.; Glover, D. E.; Smith, D. E. Anal. Chem. 1973, 45, 277. (13) (a) Compton, R. G.; Foord, J. S.; Marken, F. Electroanalysis 2003, 15, 1349. (b) Fujishima, A.; Rao, T. N.; Tryk, D. A. Electrochim. Acta 2000, 45, 4683.
3620 Analytical Chemistry, Vol. 76, No. 13, July 1, 2004
Figure 2. Image obtained from a polished polycrystalline borondoped diamond electrode surface by scanning electron microscopy. Crystal grain sizes of 1-20 µm can be seen. Note that differences in brightness in this image are electronic rather than topographic in nature.
EXPERIMENTAL SECTION Chemicals. [Ru(NH3)6]Cl3 (Strem Chemicals), K3[Fe(CN)]6, HNO3, and KCl (AR, BDH) were used as received. Triply distilled water was used to prepare aqueous solutions used in the voltammetric studies. Apparatus and Procedures. The essential features of the instrumentation employed for the FT ac voltammetric measurements are available in ref 7b. A conventional three-electrode cell was employed for all electrochemical measurements, with an Ag/AgCl (saturated KCl) electrode as the reference electrode and a platinum wire auxiliary electrode. A 3-mm-diameter glassy carbon electrode (Bioanalytical Systems) or a 3-mm-diameter polished polycrystalline boron-doped diamond (BDD) electrode (Windsor Scientific Ltd., Slough, U.K.) was used as the working electrode. The boron-doped diamond electrode surface was polished (topographically featureless down to nanometer scale), but an SEM image (see Figure 2) clearly shows the electronic heterogeneity associated with the polycrystalline structure. The working electrodes were polished with 0.3µm alumina on a clean polishing cloth (Buehler) and thoroughly rinsed with water before use. In some experiments, the BDD electrode also was “activated” following a literature procedure14 in which (i) the electrode potential was held at +5 V versus Ag/ AgCl for 20 s (anodic pretreatment) or (ii) the electrode potential was held at -2 V versus Ag/AgCl for 20 s (cathodic pretreatment) in 1 M aqueous HNO3. All voltammetric measurements were undertaken at 20 ( 1 °C, and unless stated otherwise, the solutions were degassed with high-purity nitrogen for at least 5 min prior to the electrochemical measurements in order to remove oxygen. Dc cyclic voltammograms were simulated using DigiSim.15 Simulations of largeamplitude ac voltammograms are described in the text. The diffusion coefficients used in the simulations of 6.7 × 10-6 cm2 s-1 for [Ru(NH3)6]3+ and 7.6 × 10-6 cm2 s-1 for [Fe(CN)6]3- were taken from the literature.3 (14) Marken, F.; Paddon, C. A.; Asogan, D. Electrochem. Comm. 2002, 4, 62. (15) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A.
For field emission gun scanning electron microscopy (SEM) imaging of the diamond electrode surface, a Leo 1530 field emission gun SEM system was employed without gold coating of the diamond sample. RESULTS AND DISCUSSION Reduction of [Ru(NH3)6]3+ at Glassy Carbon and BoronDoped Diamond Electrodes. [Ru(NH3)6]3+ undergoes a fast outer-sphere electron-transfer process (see eq 1). Since the
[Ru(NH3)6]3+(aq) + e- a [Ru(NH3)6]2+(aq)
(1)
process is reversible on the time scale of the experiments reported in this paper, Fourier transformed large-amplitude ac voltammograms are insensitive to the electrode material or electrode surface pretreatment. The essentially ideal reversible [Ru(NH3)6]3+/2+ process was initially studied in 0.5 M KCl aqueous electrolyte at a glassy carbon working electrode using a range of amplitudes, ∆E (30, 50, and 80 mV), for the sine wave modulation, a frequency, f ) 9.54 Hz, and a (dc ramp) scan rate, v ) 50 mV s-1. The large amplitudes employed induce a large level of nonlinearity in the system. Consequently, well-defined and symmetrically shaped ac cyclic voltammograms up to the eighth harmonic component were readily obtained when a 0.5 mM [Ru(NH3)6]3+ solution was employed (see Figure 3). For ease of presentation, the ac cyclic voltammograms in this and other figures are presented as a plot of current versus time, t. This form of presentation leads to well-separated reduction and oxidation features rather than overlapped components that arise when the more conventional current versus potential, E(t), plots are used. The two forms of presentation may be transformed from one to the other by the relationship (for a reduction process), E(t) ) Estart - vt(0 < t < ts) and E(t) ) Estart - 2vts + vt (ts < t < 2ts), where Estart is the starting potential, v is scan rate, and ts is the time required to complete one sweep. In contrast, with experiments undertaken with conventionally used conditions (amplitudes of 0, X ) 0 (electrode/solution interface):
0 < t < ts:
Cox )
0
Kb ) Knorm exp[(1 - R)(E(t)norm - Enorm )]
For a reduction process,
cox/c/ox
Kf ) Knorm0 exp[-R(E(t)norm - Enorm0)] 0
where k0 is the standard electron-transfer rate constant, R is the electron-transfer coefficient, E0′ is the formal potential of the redox process, E(t) is the applied potential, t is the time, and R, T, and F have their usual meanings. The waveform employed is a combination of a sine wave and a ramped dc waveform. Consequently, the potential at time t, E(t) is given by eq 5
E(t) ) Edc(t) + Eac(t)
where Dox and Dred are the diffusion coefficients of the oxidized and reduced forms, respectively. D is the larger one of Dox and Dred. c/ox is the bulk concentration of the oxidized form. Consequently, eqs 3, 4, and 9 can be cast into the dimensionless formats
and
Dred,r ) Dred/D
(17)
(23) Timmer, B.; Sluyters-Rehbach, M.; Sluyters, J. H. J. Electroanal. Chem. 1967, 14, 169. (24) Bond, A. M.; O’Halloran, R. J.; Ruzic, I.; Smith, D. E. Anal. Chem. 1976, 48, 872.
-Dox,r
∂Cox ∂Cred ) Dred,r ) KfCox - KbCred ∂X ∂X
τ > 0, X ) ∞:
Cox ) 1
and
Cred ) 0
To improve both the efficiency and accuracy of the simulation, an expanding grid originally introduced by Feldberg27 was adopted. The dc component and the ac harmonics are obtained by application of FT and inverse FT algorithm written in Fortran 77. The theoretical model outlined above involves several key parameters, including f, ∆E, k0, and R. However, in this paper, we only need to consider the influence of k0 on the characteristics of high-harmonic large-amplitude ac voltammetry. Simulated currents, I, are obtained at 293 K and are presented in the dimensionless form, Inorm ) I/FAc/ox(DvF/(RT))1/2, where A is the electrode area. The results refer to use of the following parameters: v ) 50 mV s-1, f ) 10 Hz, and Dox ) Dred ) 7 × 10-6 cm2 s-1 and do not take into account the contribution of background charging current as the second and higher harmonic ac components of major interest in this paper are essentially free from this problem.7b Typical ac voltammograms (first to third harmonics) of reversible and quasi-reversible systems with R ) 0.5 are presented in Figure 10. Symmetrically shaped lobes (Figure 10a-c) with a clear separation between each lobe are obtained when the electrode process is reversible. In contrast, for a quasi-reversible process, the lobe shapes (especially in the higher harmonic ac components) are nonsymmetrical and they are not necessarily resolved. Importantly, the peak current magnitude in the ac components drastically decreases when the electrode process changes from fully reversible to quasi-reversible to fully irreversible. This dependency on the level of reversibility is most significant in the (25) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (26) Britz, D. Digital Simulation in Electrochemistry, 2nd ed.; Springer-Verlag: New York, 1988. (27) Feldberg, S. W. J. Electroanal. Chem. 1981, 127, 1.
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3627
Figure 10. Simulated large amplitude first (a-a2), second (b-b2), and third (c-c2) harmonic Fourier transformed ac cyclic voltammograms of reversible (a-c) and quasi-reversible processes with k0 ) 0.01 (a1-c1) and 0.001 (a2-c2) cm s-1. Other parameters used in the simulations are provided in the text. Table 2. Influence of ∆E on [I(nωt)]max (n ) 2-5) for the Reduction Component of [Fe(CN)6]3-/4- Processa at a BDD Electrode under Conditions of Large-Amplitude Fourier Transformed ac Cyclic Voltammetry electrode pretreatment
a
polish with Al2O3
cathodic
∆E/mV
30
50
80
30
50
80
30
50
80
[I(2ωt)]max/µA [I(3ωt)]max/µA [I(4ωt)]max/µA [I(5ωt)]max/µA [I(6ωt)]max/µA
11.7 1.68 0.16 b b
29.4 6.92 1.10 0.17 b
63.5 23.3 5.65 1.44 0.34
2.00 0.29 b b b
5.10 1.12 0.25 0.08 b
15.0 3.50 1.11 0.48 0.17
12.4 1.78 0.184 b b
31.1 7.42 1.29 0.19 b
66.2 24.8 6.38 1.62 0.44
Experimental conditions are the same as those described in the caption to Figure 7. b Data not given because of poor signal-to-noise ratio.
Table 3. Influence of k0 on Dimensionless Peak Current Magnitude [Inorm(nωt)]max (n ) 1-8) Deduced by Analysis of the Reduction Component of Simulated Large-Amplitude Fourier Transformed ac Voltmmograms k0/cm s-1 first harmonic second harmonic third harmonic fourth harmonic fifth harmonic sixth harmonic seventh harmonic eighth harmonic a
[Inorm(ωt)]max tp,ωtb [Inorm(2ωt)]max tp,2ωtb [Inorm(3ωt)]max tp,3ωtb [Inorm(4ωt)]max tp,4ωtb [Inorm(5ωt)]max tp,5ωtb [Inorm(6ωt)]max tp,6ωtb [Inorm(7ωt)]max tp,6ωtb [Inorm(8ωt)]max tp,6ωtb
reversible
0.01a
0.001a
2.911 8.012 1.057 6.894 0.6526 8.004 0.2654 7.347 0.1424 8.002 0.05806 7.515 0.02902 8.002 0.01171 7.611
2.568 8.015 0.7733 6.946 0.3998 8.007 0.1306 7.325 0.05600 8.005 0.01780 7.501 6.850 × 10-3 8.005 2.120 × 10-3 7.577
1.183 8.222 0.1576 7.052 0.06537 8.119 0.01135 7.135 4.300 × 10-3 8.196 6.687 × 10-4 7.244 voltammograms are not well-defined
Simulations undertaken with ∆E ) 80 mV, v ) 50 mV s-1, and R ) 0.5. b tp,nωt (n ) 1-8) is the time corresponding to [Inorm(nωt)]max.
highest harmonic components that correspond to the shortest time scales. Simulated voltammograms in Figure 10 also clearly show that the current magnitude of ac harmonics is only significant 3628 Analytical Chemistry, Vol. 76, No. 13, July 1, 2004
when the electrode potential is relatively close to the formal potential, regardless of the reversibility of the electrode process. In contrast, in the case of dc cyclic voltammograms, a significant
current response is obtained over a much wider potential range when the reversibility of electrode process decreases. A summary of the dependence of peak currents and peak positions of the reduction process on reversibility is given in Table 3. All the features predicted theoretically were observed experimentally in this paper. However, direct comparison between theory and experiment was not feasible because the irreversibility for [Fe(CN)6]3-/4- process at a BDD electrode is not the result of a single process and the reduction of O2 involves a complex sequence of electron-transfer and coupled chemical reactions. CONCLUSIONS Advantages of employing higher harmonic components that are easily measured in large-amplitude ac voltammetry have been demonstrated experimentally with respect to (i) the suppression of capacitive background currents, (ii) the separation of the reversible reduction of [Ru(NH3)6]3+ from an overlapping irrevers-
ible oxygen reduction process, and (iii) the kinetic resolution of the reversible [Ru(NH3)6]3+ reduction from the complex nonreversible [Fe(CN)6]3- reduction at a boron-doped diamond electrode. ACKNOWLEDGMENT F.M. thanks the Royal Society (London) for the Award of a University Research Fellowship and the Royal Society of Chemistry for financial support of his visit to Monash University that made this collaborative study possible. A.M.B. and J.Z. also kindly acknowledge the Australian Research Council and the Monash University Research Fund for financial support.
Received for review February 13, 2004. Accepted April 12, 2004. AC049744B
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