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Attributes of Direct Current Aperiodic and Alternating Current Harmonic Components Derived From Large Amplitude Fourier Transformed Voltammetry Under Microﬂuidic Control in a Channel Electrode Sinéad M. Matthews,† Muhammad J. A. Shiddiky,‡,⊥ Kamran Yunus,† Darrell M. Elton,§ Noel W. Duﬀy,‡,¶ Yunfeng Gu,† Adrian C. Fisher,*,† and Alan M. Bond*,‡ †

Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, United Kingdom ‡ School of Chemistry, Monash University, Clayton, Victoria 3800, Australia § Department of Electronic Engineering, La Trobe University, Bundoora, Victoria 3086, Australia ABSTRACT: The ﬂow rate dependencies of the aperiodic direct current (dc) and fundamental to eighth alternating current (ac) harmonic components derived from large-amplitude Fourier transformed ac (FT-ac) voltammetry have been evaluated in a microﬂuidic ﬂow cell containing a 25 μm gold microband electrode. For the oxidation of ferrocenemethanol ([FcMeOH]/[FcMeOH]+ process) in aqueous 0.1 M KNO3 electrolyte, standard “Levich-like” dc behavior is observed for the aperiodic dc component, which enables the diﬀusion coeﬃcient for FcMeOH to be obtained. In experimental studies, the ﬁrst and second ac harmonic components contain contributions from the double layer capacitance current, thereby allowing details of the non-Faradaic current to be established. In contrast, the higher order harmonics and dc aperiodic component are essentially devoid of double layer capacitance contributions allowing the faradaic current dependence on ﬂow rate to be studied. Signiﬁcantly, ﬂow rate independent data conforming to linear diﬀusion controlled theory are found in the sixth and higher ac harmonics at a frequency of 15 Hz and for all ac harmonics at a frequency of ≥ 90 Hz. Analysis of FT-ac voltammograms by theory based on stationary microband or planar electrode conﬁgurations conﬁrms that stationary microband and planar electrode conﬁgurations and experimental data all converge for the higher order harmonics and establishes that the electrode kinetics are very fast (≥1 cms−1). The ability to locate, from a single experiment, a dc Faradaic component displaying Levich behavior, fundamental and second harmonics that contain details of the double layer capacitance, and Faradaic ac higher order harmonic currents that are devoid of capacitance, independent of the volume ﬂow rate and also conform closely to mass transport by planar diﬀusion, provides enhanced ﬂexibility in mass transport and electrode kinetic analysis and in understanding the performance of hydrodynamic electrochemical cells and reactors.

H

where Cb is the concentration of electroactive species in the bulk solution, n is the number of electrons transferred in the electron transfer step, F is the Faraday constant, D is the diﬀusion coefﬁcient of the electroactive species, and vf is the volume ﬂow rate. The channel parameters, xe (electrode width); h (half cell height); d (cell width); w (electrode length), are deﬁned in Figure 1, with d = w in this case. The development of microfabrication techniques makes possible the production of microelectrochemical reactors with signiﬁcantly enhanced transport rates, resulting in access to faster kinetic regimes,4 as well as improved performance in applications related to the study of processes at an immiscible liquid/ liquid interface,5 biosensing (e.g., glucose detection),6 and gas

ydrodynamic electrodes have been used for many years in electrochemistry.1 The steady-state conditions created by the presence of convection often simplify numerical modeling which facilitates the investigation of physical processes as well as quantitative analysis of relevant thermodynamic and kinetic parameters associated with an electrode process. An important example of a hydrodynamic arrangement is provided by the channel electrode conﬁguration, where an electrode is embedded into one wall of a rectangular duct over which electrolyte containing solution is ﬂowed. This arrangement has been extensively characterized by comparison of experimental data and theory based on numerical and analytical approaches.2 An important theoretical outcome is that a linear relationship between the steady-state limiting current (iL) obtained in direct current (dc) voltammetry and the cube root of the volume ﬂow rate has been established in the so-called Levich relationship (eq 1):3 iL =

0.925nFC bD2/3vf 1/3h−2/3dd−1/3wxe 2/3 © 2012 American Chemical Society

Received: April 27, 2012 Accepted: July 6, 2012 Published: July 6, 2012

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colleagues and others have demonstrated the advantages of the use of large amplitude ac voltammetric methods (sinusoidal, square wave, sawtooth).10 The use of Fourier transform (FT) forms of data analysis10 enable the dc and ac harmonic terms to be separated and analyzed independently. The FT algorithm is employed to obtain the power spectrum. If a large amplitude perturbation is superimposed onto the same dc ramp as used in dc voltammetry, the use of the inverse FT algorithm then allows the aperiodic dc response and an extensive series of harmonic components to be resolved. Advantages include access to enhanced kinetic sensitivity and, from the experimental perspective, the third and higher harmonic components that are essentially free of background charging current.11 The present study explores the application of the large amplitude Fourier transformed ac (FT-ac) voltammetric technique to the microelectrochemical reactor regime. In particular, the inﬂuence of the applied frequency and volume ﬂow rates on the aperiodic dc and fundamental to eighth harmonics has been investigated in order to understand how the interplay of the two forms of mass transport, namely, diﬀusion and convection, apply as a function of harmonic component and applied frequency. In particular, we were interested to ascertain if Levich type ﬂow rate dependence as well as ﬂow rate independent regimes could be established from a single experiment, as is the case at a rotating disk electrode.12

Figure 1. Schematic illustration of the microﬂuidic channel electrode conﬁguration used in this study with all electrodes being gold (xe = 25 μm; h = 45 μm; d = w = 500 μm). Spacing between working and reference electrodes is 50 μm. Dimensions of working and quasireference gold electrodes are the same. The gold counter electrode is much larger in the area and located downstream.

sensing.7 In order to enhance the sensitivity, selectivity, and mechanistic understanding of microreactors performance in electroanalytical chemistry, new voltammetric waveforms and data analysis strategies are being introduced; the one of interest in the present study being based on Fourier transformed large amplitude alternating current (ac) voltammetry. Following the introduction of sinusoidal waveforms in the 1950s,8 sophisticated extensions of ac methodology were introduced by Smith and co-workers.9 ac voltammetry is now a well established technique for the quantitative evaluation of electrode kinetics, at least in the small amplitude limit where the theory is moderately simple. More recently, Bond and

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EXPERIMENTAL SECTION The microelectrochemical reactors used in this study were fabricated using standard photolithography and soft lithography

Figure 2. (A) Levich analysis of the limiting current data for the oxidation of 1, 0.5, and 0.1 mM ferrocenemethanol (FcMeOH) in 1, 0.05, and 0.01 M aqueous KNO3 electrolyte versus cube root of the volume ﬂow rate observed with the channel electrode. (B) dc voltammograms for the oxidation of 1, 0.5, and 0.1 mM FcMeOH in 0.1, 0.05, and 0.01 M aqueous KNO3 electrolyte, respectively, with Vf = 0.5 cm3 min−1. (C) Comparison of dc limiting current and aperiodic dc limiting current derived from the dc components of a large amplitude FT-ac voltammetric experiment at designated frequencies (ΔE = 80 mV) when 1.0 mM FcMeOH is oxidized in aqueous 0.1 M KNO3. 6687

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Figure 3. Total current (center) and ac harmonic responses for oxidation of 1.0 mM FcMeOH in aqueous 0.1 M KNO3 electrolyte (conditions: Vf = 0.25 cm3 min−1, ΔE = 80 mV, f = 105 Hz). For clarity, only the current magnitudes of the harmonic components are shown.

techniques.13 The electrodes were constructed on a glass wafer, and the microchannel conﬁguration accurately aligned to provide the features shown in the microﬂuidic device depicted schematically in Figure 1. Electrode Fabrication. Glass wafers were cleaned using Piranha solution, rinsed in deionized water, and dried with nitrogen. (Caution: Piranha solution is a strong oxidant and should be handled with care.) A positive photoresist (Shipley, S1828) was then spin coated (Karl Suss, Delta 10TT) onto the wafer and prebaked at 115 °C as per the manufacturer’s guidelines. Next, the photoresist was exposed to UV light through a computer designed mask; subsequent development in EC 351 solution (Microposit, Rohm and Haas) removed any photoresist which had been exposed, thus revealing the electrode design. The wafer was then coated with thin layers of titanium and gold (approximately 50 and 150 nm, respectively) using a thermal evaporator (Edwards Auto 306). Development of the wafer in acetone removed any remaining photoresist and ﬁnally exposed the electrodes. Microchannel Fabrication. A 500 μm wide, 90 μm high channel mold was constructed on a clean glass wafer using a negative photoresist (Microchem, SU-8 2100). The photoresist was spin coated onto the wafer, prebaked at 65 and 95 °C as per the manufacturer’s guidelines, and then exposed to UV light (Karl Suss, MJB3). Following a postbake at 65 and 95 °C, development of the wafer in EC solvent (Microposit, Rohm and Haas) removed any unexposed photoresist to reveal the microchannel mold, which was subsequently covered in

poly(dimethylsiloxane) (PDMS-Dow Corning, Sylgard 184) that was allowed to cure for 24 h. The PDMS was then removed from the mold and exposed to air plasma along with the electrode wafer. Next, the microchannel and electrodes were accurately aligned and brought into contact, to give a device which was then baked at 65 °C for 2 h to ensure a mechanically robust seal. A height/width ratio of approximately 1:5 was chosen to ensure that conditions relevant to a uniform convection proﬁle across the width of the channel were achieved. Inlets and outlets were created using a biopsy punch to allow silicone tubing to be inserted and secured using a silicone sealant (Dow Corning, 734). Flow to the device was controlled with a syringe pump (Harvard PHD 2000). All experiments were undertaken at 25 ± 1 °C. Aqueous solutions of 1, 0.5, and 0.1 mM ferrocenemethanol (Aldrich, 97%) with 0.1, 0.05, and 0.01 M potassium nitrate (Aldrich ≥99%) were pumped through the channels at volume ﬂow rates varying from 0 to 1 cm3 min−1. The potential was cycled from −150 mV to 400 mV (versus the gold pseudoreference electrode) at a scan rate of 163 mV s−1. Initial studies used the conventional dc voltammetric techniques to obtain limiting currents for comparison with the Levich equation. Following characterization of the channel electrode device under purely dc conditions, an ac perturbation of 80 mV amplitude with frequencies ranging from 15 to 165 Hz was applied using homebuilt instrumentation.10 A software package developed in-house called MECSim (Monash Electrochemistry Simulator)11 was 6688

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Figure 4. Peak current (current for lobe with maximum value) dependence on the cube root of the volume ﬂow rate for the ﬁrst 6 harmonics at an applied frequency of 15 Hz (ΔE = 80 mV) for oxidation of 1.0 (■) and 0.5 mM (red ⧫) FcMeOH in 0.1 or 0.05 M aqueous KNO3, respectively.

chosen to be suﬃciently fast to minimize experimental times but slow enough to allow the dc response to lie in the steadystate regime so that the dc limiting current is independent of scan rate. Thus, no peak associated with transient forms of dc voltammetry is detected under cyclic voltammetric conditions. Figure 2 shows the linear dependence of the steady-state limiting current derived from oxidation of FcMeOH on the cube root of the volume ﬂow rate. These data and eq 1 were then used to determine the value of diﬀusion coeﬃcient. The best ﬁt to the dc limiting current experimental data was obtained with DFcMeOH = 7.6 ± 0.1 × 10−6 cm2s−1 (Figure 2A) for 1 mM FcMeOH with aqueous 0.1 M KNO3 as supporting electrolyte: a value which is consistent with the literature.15 Examples of dc voltammograms for the three diﬀerent concentrations of FcMeOH and supporting electrolyte concentrations are shown in Figure 2B.

used to simulate the FT-ac responses using theory based on reversible electron transfer with mass transport occurring solely by planar diﬀusion. The MECSim package is written in Fortran 77 and is based on the matrix formulation outlined in ref 14. Simulations of the stationary microband electrode geometry were undertaken with the commercially available Digi Elch software. No simulations of the entire convective−diﬀusion problem were undertaken. Thus, the simulations were used solely to extract information available from the ﬂow rate independent higher order ac harmonics.

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RESULTS AND DISCUSSION Initial experiments focused on the characterization of the microﬂuidic device using standard dc voltammetric techniques. The dc scan rate of 163 mVs−1 used in these experiments was 6689

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Figure 5. Dependence of peak current at designated frequencies (ΔE = 80 mV) for the fundamental ac harmonic component on the cube root of the volume ﬂow rate for the oxidation of 1.0 (■) and 0.5 mM (red ⧫) FcMeOH in 0.1 or 0.05 M aqueous KNO3, respectively.

aperiodic dc component may be directly used to characterize the hydrodynamic behavior of a channel electrode. Having established that the dc aperiodic component responded to changes in the volume ﬂow rate in the same manner as a pure dc voltammetric measurement, attention was then focused on the response of the FT recovered harmonic components. Figure 3 contains the ﬁrst to eighth ac harmonic components for the oxidation of 1.0 mM FcMeOH in aqueous 0.1 M KNO3 electrolyte solution with Vf = 0.25 cm3 min−1, f = 105 Hz, and ΔE = 80 mV. Under these conditions, excellent Faradaic current to noise ratio were obtained for all eight ac harmonics irrespective of volume ﬂow rate up to 1 cm3 min−1. A similar outcome applied to the 0.5 mM FcMeOH oxidation in 0.05 M KNO3 aqueous electrolyte. However, signal-to-noise issues meant that, at 0.1 mM FcMeOH concentrations with 0.01 M KNO3 electrolyte, only up to the sixth harmonic could be readily detected above background noise under the conditions of Figure 3.

The Levich analysis under purely dc conditions, with identical current values being obtained irrespective of the potential scan direction, demonstrated that the microﬂuidic device was performing in accordance with the expected dc theory; subsequently, the device was then employed for ac voltammetric measurements using the same volume ﬂow rates used in the dc study. A range of applied frequencies (15−165 Hz) with an amplitude (ΔE = 80 mV) was used. Initial data analysis focused on the relationship between the FT recovered aperiodic dc component and the purely dc voltammetric response (see above). Figure 2C shows a comparison of the aperiodic dc components as a function of cube root of volume ﬂow rate at designated frequencies with ΔE = 80 mV; it emerges that the dc steady-state limiting current is not aﬀected by the ac perturbation, within experimental error. The value of the DFcMeOH calculated from the aperiodic dc component with 0.1 M KNO3 as the supporting electrolyte was 7.6 ± 0.1 × 10−6 cm2s−1 as also found when a purely dc perturbation was employed (see above). This is an important outcome as it means the 6690

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thickness of this depletion layer is deﬁned by the solution velocity and under these convective controlled conditions there is a linear relationship between the cube root of the volume ﬂow rate and dc limiting current (eq 1). Deviation from this relationship occurs at slow ﬂow rate when mass transport via diﬀusion (ﬂow rate independent) becomes relatively signiﬁcant. The depletion layer arising from the ac perturbation in much thinner than the convective diﬀusion layer thickness. Thus, under ac conditions, application of higher frequencies and use of higher order ac harmonic components will increase the extent to which “Levich-like” behavior breaks down, and mass transport becomes dominated by diﬀusion rather than convection. The geometry of the microchannel will also be an important factor to deﬁne the exact size of the depletion layer and, hence, conditions where ﬂow rate independence is achieved. In this study, an approximately 1:5 height to width ratio ensures that a uniform convective proﬁle applies across the width of the channel. Thus, the higher order ac harmonics become diﬀusion rather than convective controlled in the channel electrode examined in this study. Under these conditions, microband electrode theory should apply (radial type diﬀusion), but the thinness of the ac depletion layer implies that planar diﬀusion may provide a very good approximation to that for radial diﬀusion at a microband electrode. Thus, as shown in Figure 6, theory for a reversible process based on a microband

Ideally, no dc background charging current would be present under truly steady-state conditions, and this situation applies to the dc (Figure 2A) and aperiodic dc (Figure 2C) data. However, FT-ac components correspond to transient forms of voltammetry, and Figure 3 clearly shows a substantial baseline oﬀset is present in the fundamental harmonic ac component; this oﬀset reﬂects the background current generated from double layer capacitance under transient conditions. The fundamental harmonic charging current, ic, exhibited a close to linear dependence on frequency, and there was no signiﬁcant contribution from volume ﬂow rate to this background current term. The capacitance of the double layer, Cdl, obtained under conditions of Figure 3A and use of the relationship Cdl = ic/ AΔEω1/2 (ω = angular frequency) was 30 μFcm−2 for a dc potential of −0.1 V. A very small level of background current is present in the second harmonic but not detected in third and higher harmonics. A full analysis of the dependence of ic on dc potential is available using MECSim simulation software. Thus, potential dependent capacitance data may also be obtained via simulation under channel electrode conditions. The role of uncompensated resistance, Ru, in FT-ac voltammetry was examined initially by analyzing the width at halfpeak height (W1/2) of the fundamental ac harmonic component and wave-shape parameters for the other harmonics based on peak-to-peak separation. iRu drop gives rise to broadening of the ac harmonic components. The experimentally determined peak width parameters for the ﬁrst to eight harmonics were compared with those simulated for a stagnant system with zero uncompensated resistance assuming the [FcMeOH]0/+ process is reversible. Deviation of experimental and simulated values was only found with very dilute 0.01 M electrolyte where the experimental wave shape parameters increased with applied frequency (at frequencies greater than 75 Hz) and volume ﬂow rate. With either 0.1 or 0.05 M KNO3 electrolyte concentrations, there was no signiﬁcant dependence of the peak width parameters on either the applied frequency (15 to 165 Hz) or the volume ﬂow rate (0 to 1 cm3min−1). Consequently, only data obtained at the higher electrolyte concentrations were assumed to be devoid of distortion from iRu drop and hence were used in the quantitative analysis of ac data. Figure 4 shows the variation in peak current response with the cube root of the volume ﬂow rate for the ﬁrst 6 harmonics at an applied frequency of 15 Hz with 0.1 or 0.05 M aqueous KNO3 as the supporting electrolyte. Under these low frequency conditions, the fundamental harmonics exhibits a linear dependence on the cube root of the volume ﬂow rate in a similar manner to the aperiodic dc component (“Levich-like” behavior). However, as the harmonic order increases, the dependence of the peak current response on volume ﬂow rate diminishes and is eventually independent of ﬂow rate in the sixth and higher order harmonics. A decrease in the ﬂow rate dependence, and hence deviation from “Levich-like” behavior, can also be obtained in the fundamental ac harmonic current by increasing the frequency (Figure 5). That is, an approximately linear relationship of peak current on the cube root of ﬂow rate is exhibited only at low frequencies. Flow rate independent data for all ac harmonics is achieved at high frequency (≥90 Hz), as in the case with the higher harmonics at low frequencies. The origin of the increasing departure from “Levich-like” behavior found at lower ﬂow rate, higher ac harmonics, and higher applied frequencies can be understood by considering the nature of the depletion layer generated immediately adjacent to the electrode surface. At suﬃciently high ﬂow rates, the

Figure 6. Comparison of the simulated (both planar and microband geometries) and experimental peak currents derived from the fundamental to eighth harmonic FT-ac components for oxidation of 1.0 mM FcMeOH in aqueous 0.1 M KNO3 electrolyte (Vf = 0.25 cm3 min−1, f = 15 Hz, ΔE = 80 mV). Parameters used in simulation: electrode area = 1.25 × 10−4 cm2, reversibility achieved by used of heterogeneous electron transfer rate of 1500 cm s−1 and charge transfer coeﬃcient of 0.50; formal potential, E0′ = 53 mV; T = 298 K; uncompensated resistance, Ru = 0; scan rate, ν = 163 mVs−1; double layer capacitance, Cdl = 0.

electrode of dimension 25 μm × 500 μm with a radial diﬀusion component or a planar electrode of the same area as the microband (1.25 × 10−4 cm2) with planar diﬀusion converge with experimental data for the higher harmonics. In the case of the FcMeOH0/+ process, analysis of data in the ﬂow rate independent regime using theory derived for a microband or planar electrode conﬁguration under zero ﬂow rate condition (Figure 6) reveals that the process exhibits reversible behavior under the experimental conditions employed. That is, the electrode kinetics are very fast with use of a charge transfer rate constant of ≥1 cm s−1 in stationary planar or microband diﬀusion scenarios providing an excellent match to experimental data for the fourth and higher order harmonics as shown in Figure 6. Thus, ability to use simple planar electrode theory in a channel 6691

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ACKNOWLEDGMENTS Financial support from the Australian Research Council is gratefully acknowledged.

electrode for higher order ac harmonics is therefore veriﬁed for a reversible process, but this should also apply to quasireversible processes and other mechanisms. An analogous situation prevails in an ac voltammetry at a rotating disk electrode where the ac component is also very insensitive to convection and hence to electrode rotation rate. In this case, experimental data comply with planar diﬀusion theory for both reversible and quasi-reversible process.12

REFERENCES

(1) See for example Bard, A. J.; Faulkner, L. R. Electrochemical Methods Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001; Chapter 9. (2) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J. Phys. Chem. 1993, 97, 10410. (3) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Upper Saddle River, NJ, 1962. (4) Zhang, W.; Stone, H. A.; Sherwood, J. D. J. Phys. Chem. 1996, 100, 9462. (5) Yunus, K.; Marks, C. B.; Allsopp, D. W. E.; Ryan, T. J.; Dryfe, R. A. W.; Roberts, E. P. L.; Fisher, A. C. Electrochem. Commun. 2002, 579, 4. (6) Lindsay, S.; Vasquez, T.; Egatz-Gomez, A.; Loyprasert, S.; Garcia, A. A.; Wang, J. Analyst 2006, 132, 412. (7) Wang, J. Electroanalysis 2007, 19, 415. (8) Bond, A. M. Modern Polarographic Methods in Analytical Chemistry; Marcel Dekker: New York, 1980 and references therein. (9) Smith, D. E. In Electroanalytical Chemistry, Bard, A. J., Ed.; Marcel Dekker: New York, 1966; Vol. 1. (10) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. Anal. Chem. 2005, 77, 186A. (11) (a) Shiddiky, M. J. A.; Torriero, A. A. J.; Zhao, C.; Burgar, I.; Kennedy, G.; Bond, A. M. J. Am. Chem. Soc. 2009, 131, 7976. (b) Shiddiky, M. J. A.; Torriero, A. A. J.; Reyna-González, J. M.; Bond, A. M. Anal. Chem. 2010, 82, 1680. (12) Bano, K.; Kennedy, G. F.; Zhang, J.; Bond, A. M. Phys. Chem. Chem. Phys. 2012, 14, 4742. (13) Liu, S.; Gu, Y.; Le Roux, R. B.; Matthews, S. M.; Bratton, D.; Yunus, K.; Fisher, A. C.; Huck, W. T. S. Lab Chip 2008, 8, 1937. (14) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A. (15) O’Mullane, A. P.; Zhang, J.; Brajter-Toth, A.; Bond, A. M. Anal. Chem. 2008, 80, 4614.

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CONCLUSIONS The technique of Fourier transformed ac voltammetry can be advantageously applied to assist in the understanding of the mass transport, electrode kinetic, and double layer capacitance behavior of a microﬂuidic electrode device. The aperiodic dc limiting current component is not aﬀected by the imposition of an ac perturbation and hence obeys the Levich relationship, allowing the diﬀusion coeﬃcient to be easily evaluated. Even in the presence of solution ﬂow, ac harmonic responses retain excellent signal-to-noise ratio allowing higher order harmonics to be accessed, up to at least the eighth harmonic in the case of oxidation of FcMeOH. The experimentally measured third and higher harmonic components, along with the aperiodic dc component, are essentially devoid of background capacitance current and, hence, allow Faradaic current and electrode kinetics to be evaluated with high signal-to-noise ratios. The fundamental harmonic contains a background current that is ﬂow rate independent and hence may be used to calculate the double layer capacitance. The relationship between the ac harmonic current response and the volume ﬂow rate has been established in a channel electrode for the [FcMeOH]0/+ process. At a low applied frequency of 15 Hz, the lower order harmonics exhibit a ﬂow rate dependence which diminishes with increasing harmonic order and becomes negligible in the sixth and higher order harmonics. At applied frequencies of ≥90 Hz, all ac harmonics were found to be independent of the volume ﬂow rate. This study shows that large amplitude ac voltammetry under limiting cases can be used to investigate both convective and diﬀusive aspects of mass transport within a microﬂuidic device; the “relative signiﬁcance” of either form of mass transport can be altered by varying the applied frequency, harmonic analyzed, and volume ﬂow rate. Thus, Levich theory can be applied to the aperiodic dc component and simple planar or microband diﬀusion theory to the high order harmonics in the ﬂow rate independent regime. The fundamental harmonic component provides double layer capacitance data, with all forms of behavior being contained in data derived from a single experiment.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.M.B.); [email protected] (A.C.F.). Present Addresses ⊥

Australian Institute for Bioengineering and Nanotechnology (AIBN), The University of Queensland, St Lucia, QLD 4072, Australia. ¶ CSIRO Energy Technology, Clayton, Victoria 3169, Australia. Notes

The authors declare no competing ﬁnancial interest. 6692

dx.doi.org/10.1021/ac3017554 | Anal. Chem. 2012, 84, 6686−6692