Higher Harmonic Large-Amplitude Fourier Transformed Alternating

Anal. Chem. 2008, 80, 4614–4626

Articles Higher Harmonic Large-Amplitude Fourier Transformed Alternating Current Voltammetry: Analytical Attributes Derived from Studies of the Oxidation of Ferrocenemethanol and Uric Acid at a Glassy Carbon Electrode Anthony P. O’Mullane,† Jie Zhang,‡ Anna Brajter-Toth,§ and Alan M. Bond*,† School of Chemistry, Monash University, Clayton, Victoria 3800, Australia, Institute of Bioengineering and Nanotechnology, 31 Biopolis Way, The Nanos, Singapore 138669, and Department of Chemistry, University of Florida, P.O. Box 117200, Gainesville, Florida 32611 An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s-1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e- rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast. Second and higher harmonic ac components, derived from large amplitude forms of Fourier transformed alternating current * To whom correspondence [email protected] † Monash University.

4614

should

be

addressed.

Analytical Chemistry, Vol. 80, No. 12, June 15, 2008

E-mail:

(FT-ac) voltammetry, may offer significant advantages relative to outcomes achievable with dc or ac fundamental harmonic approaches. In terms of kinetic discrimination, enhanced ability to resolve reversible from irreversible electron transfer processes is possible with higher harmonics using a sinusoidal waveform,1 whereas full discrimination against reversible processes may be achieved using a second order form of a square wave perturbation.2 Furthermore, almost complete separation of an underlying reversible electron transfer process from a coupled catalytic chemical reaction is achieved with the higher harmonics in the case of mediated glucose oxidation.3 Another area of potentially significant advantage of the higher harmonic components is the minimal contribution from background capacitive current which has been exploited in studies of solution phase4,5 and surface confined processes.2,6,7 Traditionally, the theory for the background current has been derived from a double layer model of the electrode–solution interface that behaves like an ideal capacitor, which is assumed to behave as an electronically linear element that only gives rise to a fundamental harmonic signal upon application of an ac perturbation.8 However, at most electrode surfaces, experimental studies reveal that complete elimination of background is not achieved by use of the second harmonic. Removal of capacitive background current down to the instrumental noise level may in fact require the use of third or even higher harmonics. ‡

Institute of Bioengineering and Nanotechnology. University of Florida. (1) Zhang, J.; Guo, S.-X.; Bond, A. M.; Marken, F. Anal. Chem. 2004, 76, 3619. (2) Zhang, J.; Guo, S.-X.; Bond, A. M.; Honeychurch, M. J.; Oldham, K. B. J. Phys. Chem. B 2005, 109, 8935. (3) Fleming, B. D.; Zhang, J.; Bond, A. M.; Bell, S. G.; Wong, L.-L. Anal. Chem. 2005, 77, 3502. (4) Sher, A. A.; Bond, A. M.; Gavaghan, D. J.; Harriman, K.; Feldberg, S. W.; Duffy, N. W.; Guo, S.-X.; Zhang, J. Anal. Chem. 2004, 76, 6214. (5) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. Anal. Chem. 2005, 77, 186A (6) Guo, S.-X.; Zhang, J.; Elton, D. M.; Bond, A. M. Anal. Chem. 2004, 76, 166. (7) Fleming, B. D.; Barlow, N. L.; Zhang, J.; Bond, A. M.; Armstrong, F. A. Anal. Chem. 2006, 78, 2948. (8) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; John Wiley and Sons: New York, 2001. §

10.1021/ac0715221 CCC: $40.75  2008 American Chemical Society Published on Web 05/17/2008

In order to better understand the analytical utility of the approach, detailed studies now have been undertaken for the first time on the background current present in higher harmonic ac voltammetry with the widely used glassy carbon (GC) electrode. It is well-known that pretreatment of this electrode surface by chemical, mechanical, heating, laser irradiation, or electrochemical methods can influence its electrochemical activity.9–15 Such pretreatments affect the formation and coverage of functional groups such as alcohols, phenols, carbonyls, carboxylates, esters, acid anhydrides, ketones, and quinone groups on the GC surface9–17 and hence the analytical performance. In this study, a routinely used surface pretreatment protocol is employed that involves polishing the GC electrode with an alumina slurry followed by sonication in distilled water. Such a pretreatment produces surface functional groups, and hence a background current, similar to those found on a GC surface generated by chemical or electrochemical oxidation.18 Clearly, the nature of the GC surface also is a function of pH, and the electrolyte chosen in the present study was a pH 7.4 phosphate buffer. In order to assess whether the faradaic to background current ratio and hence analytical sensitivity obtained can be improved by using higher harmonic conditions than usually employed, the limits of detection available from the oxidation of ferrocenemethanol (FcMeOH) and uric acid at a GC electrode have been evaluated for each of the initial five harmonics. FcMeOH oxidation to FcMeOH+ was chosen as the model system as it is known as a reversible one-electron system that does not significantly modify the background current or result in electrode fouling. For these reasons, the FcMeOH0/+ process is routinely employed as a redox mediator in scanning electrochemical microscopy.19,20 Uric acid was chosen as a contrasting case study because of its importance in diseases such as gout, hyperuricaemia, Lesch-Nyhan syndrome and its antioxidant properties21–23 (and references cited therein) and also because of its more typical level of electrochemical complexity. The determination of uric acid by dc voltammetry has been studied at an extensive range of electrodes which include GC, modified GC, composite carbon paste, sol–gel composites, modified clay and ceramic, diamond, carbon nanotube, and nanostructured carbon fiber electrodes.21,24–26 Electrochemical oxidation of uric acid at carbon based electrodes in aqueous (9) McCreery, R. L., Ed.; Electroanalytical Chemistry; Marcel Dekker: New York, 1991. (10) Fagan, D. T.; Hu, I. F.; Kuwana, T. Anal. Chem. 1985, 57, 2759. (11) Hu, I. F.; Kuwana, T. Anal. Chem. 1986, 58, 3235. (12) Chandrasekaran, M.; Noel, M.; Krishnan, V. J. Electroanal. Chem. 1991, 303, 185. (13) Chen, P.; McCreery, R. L. Anal. Chem. 1996, 68, 3958. (14) Dai, H.-P.; Shiu, K.-K. J. Electroanal. Chem. 1996, 419, 7. (15) Ray, K. G.; McCreery, R. L. J. Electroanal. Chem. 1999, 469, 150. (16) Zhou, J.; Wipf, D. O. J. Electroanal. Chem. 2001, 499, 121. (17) Antoine, O.; Augustynski, J. Electrochem. Commun. 2001, 3, 195. (18) Yi, S.-Y.; Chang, H.-Y.; Cho, H.-h.; Park, Y. C.; Lee, S. H.; Bae, Z.-U. J. Electroanal. Chem. 2007, 602, 217. (19) O’Mullane, A. P.; Neufeld, A. K.; Bond, A. M. Anal. Chem. 2005, 77, 5447. (20) Sun, P.; Mirkin, M. V. Anal. Chem. 2006, 78, 6526. (21) Salimi, A.; MamKhezri, H.; Hallaj, R. Talanta 2006, 70, 823. (22) Bravo, R.; Stickle, D.; Brajter-Toth, A. In Oxidative Stress Biomarkers and Antioxidant Protocols; Armstrong, D., Ed.; Humana Press: Totowa, NJ, 2002. (23) Bravo, R.; Hsueh, C.; Brajter-Toth, A.; Jaramillo, A. Analyst 1998, 123, 1625. (24) Brajter-Toth, A.; Abou El-Nour, K.; Cavalheiro, E. T.; Bravo, R. Anal. Chem. 2000, 72, 1576. (25) Shi, K.; Shiu, K.-K. Electroanalysis 2001, 13, 1319. (26) Hsueh, C. C.; Brajter-Toth, A. Anal. Chem. 1993, 65, 1570.

buffers proceeds initially via a coupled two electron, two proton (2e-, 2H+) process to give an unstable quininoid diimine which reacts further to give final products that are dependent on the solution pH and the nature and concentration of the buffer.27 The process can therefore be represented simplistically by an EEC scheme but with surface interaction also being important.21,28 To better understand the analytical implications, the ac harmonic responses for both FcMeOH and uric acid oxidation were initially simulated to provide data relevant to detection limits for an ideal one electron versus a two electron type process of a kind that is common for oxidation of biologically important molecules. The higher ac harmonic responses of a GC electrode in pure phosphate buffer have also been investigated to determine the contribution of capacitive and faradaic currents to the total background current and how it impacts the limit of detection for both FcMeOH and uric acid. Finally, it has been noted that the oxidative detection of biologically important molecules such as uric acid, ascorbic acid, and dopamine suffer from lack of resolution arising from the presence of overlapping oxidation processes which makes their individual quantitative determination extremely difficult in samples such as urine and serum.23,29 Thus studies also have been undertaken to ascertain if uric acid and dopamine oxidation processes can be resolved at a GC electrode by direct and simple use of higher ac harmonic components. EXPERIMENTAL SECTION Chemicals. Ferrocenemethanol (FcMeOH) from Sigma-Aldrich and uric acid from BDH were used as received. A 124 mM phosphate buffer solution (pH 7.4) was prepared from NaH2PO4 · H2O (AnalaR, BDH) and Na2HPO4 (AnalaR, BDH) in deionized water (resistivity of 18.2 MΩ cm) purified by use of a Milli-Q reagent deionizer (Millipore). The buffer pH was adjusted using aqueous NaOH (AnalaR, BDH) solution and measured with a Metrohm model 744 pH meter, equipped with a Metrohm glass pH electrode. Apparatus and Procedures. A detailed description of the FT voltammetric instrumentation is available elsewhere.5 Sine waves of frequencies f ) 11.03, 21.46, 41.13, and 61.09 Hz and amplitudes of ∆E ) 80-120 mV were employed as the ac perturbation source. Direct current voltammetric experiments were carried out with the FT form of instrumentation by using a zero amplitude perturbation or a CH Instruments (model CHI910B) electrochemical analyzer. The diffusion coefficient of FcMeOH was determined using linear sweep voltammetry and applying the Randles-Sevcik equation.8 Uncompensated resistance (Ru) was obtained using a BAS-Epsilon potentiostat and applying a small potential step in a region where no faradaic reaction occurs. Analysis of the charging current versus time curve allows the Ru and double layer capacitance (Cdl) to be extracted.8 All voltammetric experiments were undertaken at (20 ± 2) °C in an electrochemical cell that allowed reproducible positioning of the working, reference, and auxiliary electrodes and a nitrogen inlet tube. The GC working electrode (BAS) (geometric area of 0.071 cm2) was polished with an aqueous 0.3 µm alumina slurry (27) Goyal, R. N.; Brajter-Toth, A.; Dryhurst, G. J. Electroanal. Chem. 1982, 131, 181. (28) Ernst, H.; Knoll, M. Anal. Chim. Acta 2001, 449, 129. (29) Hsueh, C.; Bravo, R.; Jaramillo, A. J.; Brajter-Toth, A. Anal. Chim. Acta 1997, 349, 67.

Analytical Chemistry, Vol. 80, No. 12, June 15, 2008

4615

on a polishing cloth (Microcloth, Buehler), sonicated in deionized water for 5 min, and dried with tissue paper (Kimwipe) prior to use. The reference electrode was Ag/AgCl (aqueous 3 M KCl), and the auxiliary electrode was a coiled platinum wire. Voltammetric experiments were commenced after degassing the electrolyte solutions with nitrogen for at least 10 min, in order to remove oxygen. THEORY The oxidation of uric acid is usually considered to involve the overall reaction (eq 1)

- R)nF ( E(t) - E° )] [ -(1 RT

kb ) k°′ exp

′

(5)

where k°′ is the formal electron transfer rate constant, R is the electron transfer coefficient, E°′ is the formal potential of the redox process, E(t) is the applied potential, t is the time, and n, R, T and F have their usual meanings. The waveform employed in this study is a combination of a sine wave and a ramped dc waveform, given by eq 6, E(t))Edc(t)+Eac(t)

(6)

For an oxidation process,

In terms of deriving the theory for large amplitude FT-ac voltammetry, the oxidation of uric acid is most conveniently simulated as a reaction scheme frequently encountered in the oxidation of biologically important molecules18 which involves the initial heterogeneous electron transfer of n electrons (n ) 2) (eq 2) followed by an irreversible first order homogeneous chemical reaction (eq 3). kf

R 98 O + ne-

(2)

kb

khom

O 98 P

(3)

In these equations, O is the oxidized form and R is the reduced form of the redox couple, in which R and O may exist in rapid acid–base equilibrium with protonated and nonprotonated forms, P is the electroinactive product of the homogeneous reaction, kf and kb are the forward and backward electron transfer rate constants, respectively, and khom is the rate constant for the homogeneous chemical reaction taking place in the solution phase. In principle, transference of multiple electrons is highly unlikely to occur in an elementary single reaction step. However, if the transfer of a second or subsequent electrons is both thermodynamically and kinetically more favorable than the transfer of the initial electron, then multiple steps of single heterogeneous electron transfer can be perfectly treated as a single step of multiple electron transfer in the time scale of the voltammetric measurements. This equivalency was confirmed with regard to dc cyclic voltammetry by comparison of simulations derived in this work (zero amplitude case) and ones generated from the commercial simulation packages, such as DigiSim and DigiElch. If Butler–Volmer kinetics are obeyed, then

(E(t) - E° )] [ RnF RT

kf ) k°′ exp 4616

′

Analytical Chemistry, Vol. 80, No. 12, June 15, 2008

(4)

0 e t e ts: Edc(t) ) Estart + vt

(7)

ts 0, x ) 0 (electrode/solution interface): -DO

∂cO ∂cR ) DR ) kfcR - kbcO ∂x ∂x

t > 0, x ) ∞: cO ) 0 and cR ) c/

(13) (14)

where c/ is the bulk concentration of the reduced form. To improve both the efficiency and accuracy of the simulation, an expanding grid originally introduced by Feldberg31 was adopted. (30) Mocak, J.; Feldberg, S. W. J. Electroanal. Chem. 1994, 378, 31. (31) Feldberg, S. W. J. Electroanal. Chem. 1981, 127, 1.

The current, I, once the space and time dependent concentration relationship is known, can be calculated according to eq 15

( )

I ) nFADR

∂cR ∂x

x)0

(15)

where A is the electrode area. The effects of double layer capacitance (Cdl) and uncompensated resistance (Ru) are also taken into account in the simulation using widely adopted procedures.32 The dc component as well as the ac harmonics are obtained by application of the FT and inverse FT algorithms written in Fortran 77. In brief, the FT algorithm is used to convert the time domain data to frequency domain to give the power spectrum. Then, dc, fundamental, second, and higher harmonic components are obtained by selecting the frequency region of interest in the power spectrum and employing the inverse FT procedure. Many forms of ac harmonic data presentation are available, but in this study, the total or magnitude of the current for the fundamental and the magnitude of the second to fifth ac harmonic components are plotted as a function of time or potential. The theoretical model outlined above involves consideration of a range of key parameters, that include n, Cdl, Ru, f, ∆E, v, k°′, R, and khom. However, in this paper, the influence of n on the magnitude of the faradaic current is of particular significance. Thus, the presence of the chemical step is temporarily ignored in initial discussions so as to clearly illustrate the influence of n, while the homogeneous reaction step will be taken into account when experiment/theory comparisons are presented for the oxidation of uric acid. Simulated currents, I, when considering the role of n, refer to use of the following arbitrary parameters: v ) 100 mV s-1, f ) 21 Hz, ∆E ) 80 mV, A ) 0.0079 cm2, c/ ) 1.0 mM, DO = DR ) 1.0 × 10-5 cm2 s-1, E′ ) 400 mV, Estart ) 0.000 mV, R ) 0.50, and T ) 293 K. Reversible charge transfer processes, as encountered experimentally for the oxidation of FcMeOH (n ) 1) or approximately for uric acid (n ) 2), are first considered. The simulated results shown in Figure 1 produce symmetrical ac harmonic components. The peak width is always narrower when n ) 2, which is useful in a resolution context, but more significantly, the peak currents are strongly influenced by the number of electrons transferred, especially the higher harmonic ac components. This trend also has been established using analytical solutions.33 However, calculations have yet to be provided to establish the details of the influence of the amplitude (∆E). The results of simulations contained in Table 1 clearly reveal in the case of reversible processes that (a) the peak current ratio for the n ) 2:1 case of interest in this paper is very much larger for the higher harmonic components, especially when ∆E is small where Ip ∝ n2∆E, n3∆E2, n4∆E3, n5∆E4, n6∆E5 for the first five harmonics, respectively;33,34 (b) the peak current ratio decreases for both dc and ac components when the amplitude of the applied ac waveform increases, but the decrease is much more rapid for the higher harmonic components; and (c) the current ratio enhancement becomes modest when ∆E is large. (32) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A (33) Engblom, S. O.; Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 2000, 480, 120. (34) Smith, D. E., Bard, A. J., Eds.; Marcel Dekker: New York, 1966; Vol. 1.

These results lead to the prediction of significantly improved detection limits for uric acid (n ) 2) relative to the detection of FcMeOH (n ) 1) in the higher harmonics provided the homogeneous reaction (eq 3) is not critical, background currents are negligible, and ∆E is not too large. The presence of the homogeneous reaction does not significantly affect the peak currents (with n ) 2) for the forward reaction over a range of khom from 0 to 1 s-1 (Figure S1, Supporting Information). While the data imply that use of small values of ∆E would produce the greater relative enhancement in peak current, in practice amplitudes in the range of about g80 mV are needed to obtain the higher harmonics with good signal-to-noise ratios. Thus, in this study, ∆E values in the range of 80-120 mV were employed. In the case of a quasi-reversible process, despite the fact that the magnitude of the peak currents are smaller,1 the peak current ratio for the n ) 2 versus n ) 1 cases is even larger than found for a reversible process (Figure S2). RESULTS AND DISCUSSION Large Amplitude FT-ac Voltammetry of Ferrocenemethanol. First to Fifth Harmonics. The one electron FcMeOH0/+ redox couple at a GC electrode in pH 7.4 phosphate buffer is essentially reversible on the time scale of the present ac measurements. Initial studies were conducted by superimposing a sine wave of frequency f ) 21.46 Hz and an amplitude of ∆E ) 100 mV onto the dc waveform. The large amplitude induces a significant level of nonlinearity in the faradaic component which allows well defined second, third, fourth, and fifth harmonics and even higher components to be obtained when the potential is scanned over the range of -150 to 600 mV. For convenience, the first five harmonics are discussed in detail, and the sixth and higher ones, when analytical performance starts to deteriorate, are considered in the next section. At the 1.0 mM FcMeOH concentration level (Figure 2), the background current is not significant relative to faradaic current in any of the second to fifth harmonics or dc term but is responsible for the current commencing and finishing at nonzero values in the fundamental harmonic component. Also contained in Figure 2 are the simulated fundamental to fifth harmonic responses for a reversible process (k°′ g 1 cm s-1, R ) 0.5). Studies using a range of electrode surfaces have reported k°′ values between 0.2 and 2 cm s-1 for the FcMeOH0/+ system in aqueous media.35,36 The E°′ value used in the simulation was 214 mV, as obtained experimentally (standard deviation was 2 mV) by analysis of the peak potential (first, third, and fifth harmonic) and current minima (second and fourth harmonic). This value is in good agreement with the E°′ value of 213 mV calculated from dc cyclic voltammograms as the average of the oxidation and reduction dc peak potentials. The diffusion coefficient of 7.6 × 10-6 cm2 s-1 used in simulations represents the experimentally determined value (dc cyclic voltammetry and the Randles-Sevcik equation) which also agrees well with values reported in other studies.37 An uncompensated resistance value of Ru ) 80 Ω provided the best fit between simulated and experimental data. This value is in satisfactory agreement with a measured Ru value (35) Miao, W.; Ding, Z.; Bard, A. J. J. Phys. Chem. B 2002, 106, 1392. (36) Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J.-M. J. Am. Chem. Soc. 1995, 117, 11499. (37) Cannes, C.; Kanoufi, F.; Bard, A. J. J. Electroanal. Chem. 2003, 547, 83.

Analytical Chemistry, Vol. 80, No. 12, June 15, 2008

4617

Figure 1. Simulated (a) large amplitude dc and (b-f ) fundamental to fifth harmonic Fourier transformed ac cyclic voltammograms of a one (black) and two electron (red) reversible electron transfer process. Parameters used, v ) 100 mV s-1, f ) 21 Hz, ∆E ) 80 mV, A ) 0.0079 cm2, c/ ) 1.0 mM, DO ) DR ) 1.0 × 10-5 cm2 s-1, E°′ ) 400 mV, Estart ) 0.000 mV, and T ) 293 K.

of 100 Ω (see Experimental Section). A potential independent double layer capacitance (Cdl) value of 8.5 µF cm-2 included in the simulation produced a reasonable fit to the fundamental harmonic background current data. The value of Cdl at a GC electrode is highly dependent on polishing, the origin of the electrode material, the electrolyte, the potential, and the analyte.9 A large fraction of the background may even arise from the presence of surface functional groups and their faradaic processes.9 McCreery9 has revealed the complex nature of apparent values of Cdl as measured voltammetrically at a GC electrode. It will emerge that the apparent value of Cdl determined in the present study may be minimally suppressed by the presence of FcMeOH but significantly enhanced by the addition of uric acid. As expected, decreasing the concentration of FcMeOH from 1.0 mM to 65 µM significantly decreases the dc and fundamental harmonic faradaic to background current ratio (compare Figures 4618

Analytical Chemistry, Vol. 80, No. 12, June 15, 2008

2a and 3a). The background current now contributes noticeably to even the second and third harmonic current thereby confirming that this term is complex9 and cannot be modeled perfectly by an ideal linear capacitor, which is predicted to only generate dc and fundamental harmonic double layer capacitance responses. Nevertheless, the fourth and fifth harmonic faradaic background components remain negligible in comparison to those for the FcMeOH0/+ faradaic process and consequently may exhibit better analytical sensitivity than the second harmonic which is usually assumed to have the optimal sensitivity. Also included in Figure 3 are the simulated ac harmonic components generated with the same parameters used for the simulation of the oxidation of 1.0 mM FcMeOH except that a Cdl value of 5 µF cm-2 was used to best fit the entire fundamental harmonic current response. Again generally, excellent agreement of experimental and simulated data is achieved. At even lower concentrations of FcMeOH (25-10

Table 1. Dependence on ∆E of the Simulated Ratio of Peak Currents (PR) when n ) 2:1 for the dc and ac Components of the Fourier Transformed ac Voltammograms for a Reversible Process a PR first second third fourth fifth ∆E/mV dc harmonic harmonic harmonic harmonic harmonic 0 2.828 N/A N/A N/A N/A N/A 5 10 25 50 75 100 150

2.812 2.764 2.549 2.344 2.293 2.274 2.253

3.967 3.888 3.453 2.790 2.396 2.220 2.086

7.898 7.695 6.536 4.669 3.624 3.074 2.567

b

b

b

15.10 11.80 7.022 4.693 3.595 2.708

b

b

22.55 12.22 7.39 5.193 3.447

41.42 19.32 10.36 6.688 4.003

a Ratio derived from the peak current with a maximum value (see Figure 1) in the case of the second and higher harmonics. Other parameters used in the simulations are available in the text. b A welldefined voltammogram is not obtained, especially when n ) 1.

µM), the faradaic dc and fundamental to third harmonic responses become progressively more affected by background, while the fourth and fifth harmonics remain minimally perturbed. At FcMeOH concentrations below 10 µM (e.g., Figure 4), the symmetry of the fourth and fifth harmonic responses is subtly affected by background contribution. However, the magnitude of faradaic signal remains well above the background until a concentration of 2 µM FcMeOH is reached, where the ratio becomes about 3:1 and approaches the limit of detection. It should be noted that the noise level in the FT instrument of