Application of Power Spectra Patterns in Fourier Transform Square

Mar 25, 2006 - Transform Square Wave Voltammetry To Evaluate. Electrode Kinetics of Surface-Confined Proteins. Barry D. Fleming,† Nicola L. Barlow,â...
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Anal. Chem. 2006, 78, 2948-2956

Application of Power Spectra Patterns in Fourier Transform Square Wave Voltammetry To Evaluate Electrode Kinetics of Surface-Confined Proteins Barry D. Fleming,† Nicola L. Barlow,‡ Jie Zhang,† Alan M. Bond,*,† and Fraser A. Armstrong‡

School of Chemistry, Monash University, Victoria 3800, Australia, and Inorganic Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QR, U.K.

This paper describes an application of Fourier transform (FT) voltammetry that provides a quantitative evaluation of the electron-transfer kinetics of protein molecules attached to electrode surfaces. The potential waveform applied in these experiments consists of a large-amplitude square wave of frequency f superimposed onto the traditional triangular voltage used in dc cyclic voltammetry. The resultant current-time response, when Fourier transformed into the frequency domain, provides patterns of data at the even harmonic frequencies that arise from nonlinearity in the Faradaic response. These even harmonic contributions are ideally suited for kinetic evaluation of electron-transfer processes because they are highly selective to quasi-reversible behavior (insensitive to reversible or irreversible processes) and almost devoid of background charging current. Inverse FT methods can then be used to provide the wave shapes of the dc as well as the ac voltammetric components and other characteristics employed to detect the level of nonideality present relative to theoretical models based upon noninteracting surface-confined molecules. The new form of data evaluation has been applied to the electron-transfer properties of a typical biological electron carrier, the blue copper protein azurin, immobilized on polycrystalline gold electrodes modified with self-assembled monolayers of different length alkanethiols. Details of the electrode kinetics (rates of electron transfer, dispersion, and charge-transfer coefficients) as a function of alkanethiol, apparent surface coverage, and capacitance are all deduced from the square wave (FT-inverse FT) protocol, and the implications of these findings are considered. Electrochemical studies with redox-active proteins (and particularly enzymes) that are attached to an electrode surface are attracting much attention, both through the ability to gain particularly detailed insight into mechanisms of chemical reactions coupled to electron transfer, including enzyme catalysis, and * Corresponding author. E-mail: [email protected]. † Monash University. ‡ Oxford University.

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because of important applications in sensing technology.1-10 A surface-confined process

Ox(surface confined) f Red(surface confined) + e-

(1)

taking place on a chemically modified working electrode interfaced with a solvent (electrolyte) should represent a simpler theoretical problem than the long-studied solution-phase process

Ox(solution) f Red(solution) + e-

(2)

in which the Oxidant and Reductant are soluble in the solvent (electrolyte). This apparent theoretical simplification in the surfaceconfined process arises from the absence of the complications of mass transport of electroactive species to and from the electrode surface.11 In practice, there are experimental artifacts and nonidealities that complicate matters. In principle, one should be able to design an experiment in which the active site undergoes a well-defined one-electron chargetransfer process which, if it obeys the Butler-Volmer type model, should be characterized by a reversible formal potential E0′, and a standard rate constant k0′ at E0′ that is a function of distance of the active site to the electrode surface. Analogous considerations will apply if other theoretical models are used, e.g., Marcus theory. The surface is assumed to be well-defined, such as those provided by a self-assembled monolayer (SAM) of alkanethiol molecules on gold. However, in reality, nonidealities present with even these (1) Armstrong, F. A.; Wilson, G. S. Electrochim. Acta 2000, 45, 2623-2645. (2) Le´ger, C.; Elliot, S. J.; Hoke, K. R.; Jeuken, L. J. C.; Jones, A. K.; Armstrong, F. A. Biochemistry 2003, 42, 8653-8662. (3) Rusling, J. F.; Zhang, Z. In Biomolecular Films: Design, Function and Applications; Rusling, J. F., Ed.; Marcel Dekker Inc: New York, 2003; pp 1-64. (4) Willner, I.; Katz, E. Angew. Chem., Int. Ed. 2000, 39, 1180-1218. (5) Jeuken, L. J. C.; Armstrong, F. A. J. Phys. Chem. B 2001, 105, 5271-5282. (6) Jeuken, L. J. C.; Wisson, L.-J.; Armstrong, F. A. Inorg. Chim. Acta 2002, 331, 216-223. (7) Armstrong, F. A.; Camba, R.; Heering, H. A.; Hirst, J.; Jeuken, L. J. C.; Jones, A. K.; Le´ger, C.; McEvoy, J. P. Faraday Discuss. 2000, 116, 191-203. (8) Le´ger, C.; Jones, A. K.; Albracht, S. P. J.; Armstrong, F. A. J. Phys. Chem. B 2002, 106, 13058-13063. (9) Armstrong, F. A.; Barlow, N. L.; Burn, P. L.; Hoke, K. R.; Jeuken, L. J. C.; Shenton, C.; Webster, G. R. Chem. Commun. 2004, 3, 316-317. (10) Hudson, J. M.; Heffron, K.; Kotlyar, V.; Sher, Y.; Maklashina, E.; Cecchini, G.; Armstrong, F. A. J. Am. Chem. Soc. 2005, 127, 6977-6989. (11) Chidsey, C. E. D. Science 1991, 251, 919-922. 10.1021/ac051823f CCC: $33.50

© 2006 American Chemical Society Published on Web 03/25/2006

Figure 1. Models of (a) ideal and (b) nonideal surface-confined processes in which a redox protein with a single active site is bound to a gold electrode modified with a self-assembled monolayer.

systems, versus the model given in Figure 1a, make “theory versus experiment” comparisons potentially subject to significant uncertainty.12-14 Initial problems are that individual protein molecules can adopt many different orientations on an electrode, or the chemically modified (thiol) layers are not perfectly uniform (Figure 1b). Thus, all protein molecules need not have the same thermodynamic (E0′) or kinetic (k0′, R) values, which gives rise to the possibility of thermodynamic or kinetic dispersion. Furthermore, the proteins may interact with each other rather than remain isolated moieties, again a feature that can give rise to nonideality. To date, these surface-confined metalloprotein electron-transfer reactions have been most commonly characterized by the technique of dc cyclic voltammetry in which current-potential plots are obtained from application of a triangular waveform as a function of scan rate. Typically, only the peak potential (just one single specific datum point of the thousands of data points collected) is analyzed by reference against models.5,15,16 Some consideration has been given to surface coverage and peak width.7,17 However, high molecular weight proteins and enzymes give rise only to small surface coverages, of the order of tens of picomoles per centimeter squared or lower. This leads to unfavorable Faradaic-to-background current ratios, which compromises the quality of the data analysis. Several alternative approaches to dc cyclic voltammetry have been used to study electrode kinetics.15,18-21 To obtain the truest evaluation of a surface-confined process, a very efficient level of (12) Rowe, G. K.; Carter, M. T.; Richardson, J. N.; Murray, R. W. Langmuir 1995, 11, 1797-1806. (13) Nahir, T. M.; Bowden, E. F. J. Electroanal. Chem. 1996, 410, 9-13. (14) Honeychurch, M. J.; Rechnitz, G. A. Electroanalysis 1998, 10, 285-293. (15) Gaigalas, A. K.; Niaura, G. J. Colloid Interface Sci. 1997, 193, 60-70. (16) Chi, Q.; Zhang, J.; Andersen, J. E. T.; Ulstrup, J. J. Phys. Chem. B 2001, 105, 4669-4679. (17) Baymann, F.; Barlow, N. L.; Aubert, C.; Schoepp-Cothenet, B.; Leroy, G.; Armstrong, F. A. FEBS Lett. 2003, 539, 91-94. (18) Heering, H. A.; Mondal, M. S.; Armstrong, F. A. Anal. Chem. 1999, 71, 174-182. (19) Guo, S.-X.; Zhang, J.; Elton, D. M.; Bond, A. M. Anal. Chem. 2004, 76, 166-177. (20) Jeuken, L. J. C.; McEvoy, J. P.; Armstrong, F. A. J. Phys. Chem. B 2002, 106, 2304-2313.

data analysis is required over a wide range of time (or frequency) domains, and methods of rejection of background current terms need to be available. The technique of square wave voltammetry, when implemented by periodic superimposition of a square wave onto the dc ramp used in cyclic voltammetry and analyzed by the Fourier transform (FT) method in the frequency domain, has recently been shown to exhibit such properties.22 Use of the FTinverse FT (iFT) form of analysis gives a vast array of data that include dc, even and odd components, power spectra, and impedance data.23 Under ac conditions, the Faradaic component of the response represents a nonlinear system. In contrast, the background current term is predominately capacitative in nature, which ideally operates as a linear system and only exhibits a response at the dc and odd components. It has been shown that the power spectra associated with the even frequency components derived from a square wave signal are ideally devoid of capacitance current, exhibit novel forms of kinetic selectivity (insensitive to reversible and irreversible processes, sensitive to quasi-reversible processes), and also utilize the entire data set in an extremely efficient manner that is not possible with dc methods.22 Finally, the individual dc, even, and odd harmonic components may be deconvoluted from the power spectrum to assess the contribution of nonideality over a range of experimental conditions, truly providing unprecedented levels of use of data obtained in a voltammetric experiment. The benefits of analyzing power spectra and some features derived from the nonlinearity have been shown for a sinusoidal form of voltammetric pertubation,24 but not with the highly information-rich square wave version that is of interest in the present paper. The system examined experimentally in the present study is the reduction and oxidation of the blue copper center in the bacterial electron-carrier protein azurin. To provide electrode/ protein interface conditions that are reasonably well defined, we have adsorbed azurin at close to monolayer coverage on a polycrystalline gold electrode modified with a self-assembled monolayer of either 1-octanethiol, 1-decanethiol, or 1-dodecanethiol, as shown schematically in Figure 1. The reason for choosing a hydrophobic SAM is that the copper center in azurin lies just below the surface of the protein in an area that is predominantly hydrophobic. Thus, as shown previously,5,15,16 azurin is expected to bind to the hydrophobic SAM surface in an orientation that is suitable for efficient electron transfer across the shortest possible intra-protein distance. The results confirm the expected distance dependence of k0′ for these long-chain alkanethiol SAMs; that is, k0′ decreases exponentially with increasing chain length.16 Insights are provided into the significance of thermodynamic and kinetic data that ignore nonidealities present even with this relatively welldefined and almost ideal system. (21) Chi, Q.; Zhang, J.; Nielsen, J. U.; Friis, E. P.; Chorkendorff, I.; Canters, G. W.; Andersen, J. E. T.; Ulstrup, J. J. Am. Chem. Soc. 2000, 122, 40474055. (22) Zhang, J.; Guo, S.-X.; Bond, A. M.; Honeychurch, M. J.; Oldham, K. B. J. Phys. Chem. B 2005, 109, 8935-8947. (23) Sher, A. A.; Bond, A. M.; Gavaghan, D. J.; Gillow, K.; Duffy, N. W.; Guo, S.-X.; Zhang, J. Electroanalysis 2005, 17, 1450-1462. (24) Brazil, S. A.; Bender, S. E.; Hebert, N. E.; Cullison, J. K.; Kristensen, E. W.; Kuhr, W. G. J. Electroanal. Chem. 2002, 531, 119-132.

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EXPERIMENTAL SECTION Reagents. Pseudomonas aeruginosa azurin was generously provided by Professor Gerard Canters (Leiden University).25 The protein solution, azurin (9.6 mg/mL) in HEPES buffer (20 mM, pH 7) was stored at -80 °C. A buffer solution (pH 4.0) containing 20 mM sodium acetate (AnalaR, BDH) and 100 mM sodium sulfate (AnalaR, BDH) was used as the electrolyte. The pH value was adjusted using an aqueous sulfuric acid (AR, Ajax Chemicals) solution and measured with a Metrohm 744 pH meter, equipped with a Metrohm pH glass electrode (Metrohm Ltd.). The alkanethiols 1-octanethiol, 1-decanethiol, and 1-dodecanethiol (g97%, Fluka) were used as received. Deionized water from a MilliQ-MilliRho purification system (resistivity 18 MΩ cm) was used for all solutions. Apparatus and Procedures. A description of the FT voltammetric instrumentation used in these studies is available elsewhere.26 Fast-scan rate cyclic voltammetry was carried out using an Autolab electrochemical analyzer (Ecochemie, Utrecht, The Netherlands) equipped with a PGSTAT 30 potentiostat module, a fast-scan analog generator (Scangen), and a fast AD converter (ADC750). Uncompensated cell resistance effects were minimized by using the positive-feedback iR compensation function of the potentiostat. A standard three-electrode cell was employed in all electrochemical measurements, with an Ag/AgCl (3 M KCl) electrode as the reference electrode and a platinum wire as the auxiliary electrode. Gold working electrodes used were either commercially available (r ) 0.08 cm radius, Bioanalytical Systems, West Lafayette, IN) or were constructed in a Teflon sheath using gold wire (99.9985%, Alfa; r ) 0.1 cm) attached to a brass rod with silver-loaded epoxy adhesive (RS components), which was embedded in epoxy resin. Prior to use in voltammetric experiments, the gold electrodes were cleaned by successively polishing with 1and 0.3-µm alumina suspensions on a clean polishing cloth (Buehler). After each polish, the electrode was rinsed with deionized water and then sonicated thoroughly in deionized water. The surface was then cleaned electrochemically by cycling five times between 0.244 and 1.044 V in 0.1 M H2SO4 solution, starting and ending at 0.444 V. The upper potential limit was then increased to 1.394 V and another 15 cycles were performed. With the second set of cycles, the surface atoms of the gold electrode are oxidized and reduced during each scan. After rinsing with water, the gold electrode was immersed in a solution of 1 mM alkanethiol in ethanol for 6 h and then rinsed with ethanol and deionized water. A protein film was applied by immersion in a 100-µL solution of azurin (2.4 mM) for 16 h at 22 °C. All voltammetric experiments were performed at 5 ( 1 °C in solutions that were degassed with high-purity nitrogen. All potentials quoted are with respect to the standard hydrogen electrode (SHE). (25) van de Kamp, M.; Hali, F. C.; Rosato, N.; Agro, A. F.; Canters, G. W. Biochim. Biophys. Acta 1990, 1019, 283-292. (26) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. M. Anal. Chem. 2005, 77, 186A-196A.

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THEORETICAL ANALYSIS OF SQUARE WAVE VOLTAMMETRY FOR A SURFACE-CONFINED PROCESS The basic principles of the theory of square wave voltammetry of surface-confined species in the frequency domain have been described in detail elsewhere.22 In brief, we will consider a oneelectron reduction process as defined earlier in (1), where Ox(surface confined) and Red(surface confined) are the oxidized and reduced species and kf and kb are the forward and backward electron-transfer rate constants, respectively. If the potential dependence of the rate constants is assumed to obey the Butler-Volmer formalism,27 then

kf ) k0′ exp

[

-RF (E - E0′) RT

]

and

kb ) k0′ exp

[

]

(1 - R)F (E - E0′) (3) RT

where k0′ is the formal electron-transfer rate constant at E0′, the formal potential of the surface-confined redox couple; R is the electron-transfer coefficient; E is the applied potential at time t; and R, T, and F have their usual meanings. Provided Ox and Red are both strongly adsorbed on the electrode surface and adsorption follows a Langmuir isotherm, then the Faradaic current, I, is given by

dθ ) FAΓ[kb(1 - θ) - kfθ] dt

I ) FAΓ

(4)

where A is the area of the electrode, Γ is the total surface concentration of the bound electroactive species (oxidized and reduced forms), and θ is the potential-dependent surface coverage of the oxidized form. The potential at time t in ramped square wave voltammetry is given by eq 5 for a reduction process,

E(t) ) Edc(t) + Eac(t) ) Estart - vt + Eac(t)

(5)

where v is the scan rate of the dc ramp and Estart is the starting or initial value of the potential. The ac waveform used experimentally can be represented as a sum of sine waves of angular frequencies which are the odd multiples of ω,

Eac(t) )

4∆E π

K

∑

n)1

sin((2n - 1)ωt) 2n - 1

(6)

where ω ) 2πf, f is frequency, ∆E is the amplitude, and K is an integer. When K becomes sufficiently large (K g 20), an excellent approximation of a square wave signal is generated. Figure 2 shows the case when K ) 40, which is applied to obtain the experimental and theoretical results presented in this paper. The general procedure used in numerical simulations of a surface-confined process is to replace the continuous ramp by a waveform that contains a series of very small potential increments (sufficiently small so that the calculated current is independent of the size of the potential increment). During the course of the (27) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001.

potential increment. An average current is calculated on the basis of the change of the surface concentrations of electroactive species for each small potential increment. In the present numerical simulation, the potential increment within a single potential step is chosen to be small (typically ∼0.01 mV). Therefore, the change in the rate constants is negligible in the brief interval δt, during which θ(t) changes by δθ. Consequently, eq 4 can be integrated to obtain,

θ(t + δt) ) θ(t) + δθ ) θ(t) +

(

)

kb - θ(t) (1 kf + kb exp[-(kf + kb)δt]) (7)

The current is then calculated from,

(

)

Figure 2. Example of the total applied waveform employed in square wave voltammetric measurements. In this case, 40 sine waves are employed to approximate a square wave.

kb (1 - exp[-(kf + kb)δt]) δθ I ) ) (8) - θ(t) FAΓ δt kf + kb δt

simulation, the potential within each individual potential increment is assumed to be constant, and both the potential and potentialdependent surface coverage are updated at the end of each

Equation 8 can be solved numerically by the finite difference method to give the total Faradaic current as a function of time (or potential).

Figure 3. Power spectra (power vs frequency) obtained from simulation of the electron-transfer reaction of the active site of a protein bound to an electrode (reductive sweep only). Fourier transformation of the total current (a) into a power spectrum (b), highlights the large odd harmonic components and relatively small response at even harmonics associated with the nonlinearity of the Faradaic component. In subsequent representations of power spectra, only the outline of the even harmonic profile (c) is presented. A comparison of the profile of the even harmonic components for different values of k0′ is shown in (d). Parameters used in the simulations: k0′, as shown, v ) 0.05 V‚s-1, f ) 38.125 Hz, ∆E ) 0.05 V, Estart ) 0.55 V, Efinish ) -0.25 V, electrode radius r ) 0.1 cm, Γ ) 10 pmol‚cm-2, E0′ ) 0.370 V, R ) 0.5, T ) 278 K.

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Table 1. Dependence of the Kinetically Sensitive Regions (k0′min to k0′max) of Simulated Even Harmonic Power Spectra Profiles on the Applied Perturbation Frequency (Simulation Parameters as for Figure 3) frequency/Hz

k0′min/s-1

k0′max/s-1

9.5 38.125 127.55

30 150 500

300 1500 3500

A power spectrum is obtained by performing a Fourier transformation on the total current (Figure 3a) obtained by either simulation or experiment. The power spectrum contains, in the frequency domain, the relative contributions generated by the dc (minimal in this case) and ac components (observed at the applied frequency and harmonics thereof) of the waveform. In the power spectrum, power (P) is calculated according to

P ) xRe2 + Im2

(9)

where Re and Im are the real and imaginary parts of the data after Fourier transformation, respectively.28 An example of a power spectrum obtained for the simulated reduction of a surface-bound protein at a given value of k0′ is shown in Figure 3b. In the present report, we are particularly interested in the even harmonics because they have been shown to exhibit novel forms of kinetic selectivity.22 Also, unlike the odd harmonics that have a large contribution from the background current, the even harmonics are almost void of charging current. As such, power spectra presented in this report will contain the general profile of the even harmonic contributions only, as shown in Figure 3c. The power spectra obtained for the simulated reduction of a surface-bound protein at different values of k0′ (50-3000 s-1) are shown in Figure 3d. As can be seen from these simulated data, the profile of the even harmonic components of the power spectra is very sensitive to the kinetics of the electron-transfer process. However, a minimum and maximum value of k0′ could be identified, below and above which the even harmonic power spectra profile did not significantly change. This kinetic sensitivity window was found to be dependent on the applied perturbation frequency as expected. For example, when the perturbation frequency of the applied waveform was increased (reduced time scale of ac measurement), the kinetic sensitivity window was shifted to a faster kinetic region. Table 1 highlights the kinetic range (k0′ values) for three applied frequencies. These frequencies were chosen because they are most relevant to the azurin/SAM systems being studied experimentally. In addition, it should be noted that the magnitude of the power spectrum is sensitive to Γ and ∆Esincreasing either of these would shift the entire power spectrum profile up the power axis. In principle, odd harmonic components could be used in an analogous manner, but correction for a significant level of non-Faradaic current would be needed. The above attributes and dependencies of the power spectra profiles means that, upon successful experiment-simulation comparison (using the same parameters), we can obtain estimates for the values of k0′ and Γ for the experimentally acquired data. EXPERIMENTAL STUDIES WITH AZURIN Dc Voltammetry. Dc cyclic voltammetric studies were undertaken for azurin bound to each of the alkanethiol-modified gold 2952

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Figure 4. Dc cyclic voltammogram of azurin bound to a 1-decanethiol-modified gold electrode (pH 4.0, 20 mM sodium acetate, 100 mM Na2SO4) at a scan rate of 0.05 V‚s-1, starting from an oxidizing potential.

electrodes using the FT ac instrument (in this case, obviously ∆E ) 0 mV) and employing slow scan rates. Figure 4 shows a typical dc cyclic voltammogram obtained this way at a scan rate of 0.05 V‚s-1, for azurin bound to a 1-decanethiol-modified gold electrode in contact with 20 mM sodium acetate and 100 mM Na2SO4 solution buffered at pH 4.0. The reduction potential value, E0′ calculated as (Epοx + Epred)/2, where Epοx and Epred are the oxidation and reduction peak potentials, respectively, was 0.364 ( 0.010 V (vs SHE), which agreed well with a previously published value of 0.368 V for azurin adsorbed at 1-decanethiol.5 Additionally, the average peak-to-peak separation (∆Ep) calculated as Epοx Epred was 8 ( 3 mV and the peak width at half-height (W1/2) values of 100 ( 10 mV were slightly broader than the Nernstian value of 84.5 mV predicted for a one-electron reversible process at 5 °C.29 The area under the peak was used to determine the electroactive protein coverage Γ using the relationship

Γ ) (area under peak)/nFAv

(10)

where n is the number of electrons transferred () 1), F is Faraday’s constant, A is the geometric area of the electrode, and v is the scan rate. Typically, Γ values lay in the range of 14 ( 6 pmol‚cm-2, with only ∼20% loss observed after 2 h for a given alkanethiol modified electrode in contact with the electrolyte. The rate of interfacial electron transfer, k0′, was initially estimated in the conventional manner using fast-scan cyclic voltammetry by fitting a plot of peak position, Epοx and Epred vs (log) scan rate with theoretical values based on Butler-Volmer equations.7 The dc method is relatively insensitive to R so its value was assumed to be 0.5 in this theory, rather than being evaluated. Figure 5 shows the trumpet plots (peak position as a function of scan rate) for azurin on each of the modified gold electrodes. The k0′ value acquired by analysis of the fast scan rate data gave rate (28) Chapra, S. C.; Canale, R. P. Numerical Methods for Engineers: With Programming and Software Applications, 3rd ed.; WCB/McGraw-Hill: Singapore, 1998. (29) Laviron, E. In Electronanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1982; Vol. 12, p 53.

Figure 5. Peak positions vs log scan rate (trumpet plots) for azurin bound to octanethiol- (9), decanethiol- (b), and dodecanethiol (2)modified gold electrodes (pH 4.0, 20 mM sodium acetate, 100 mM Na2SO4). Solid lines show theoretical fits based on Butler-Volmer models with R ) 0.5 and k0′ values given in text. Scans were initiated from the oxidizing regime.

constants of the order of 2700 ( 500, 440 ( 80, and 40 ( 8 s-1 (error estimates assume random error) for 1-octanethiol, 1-decanethiol, and 1-dodecanethiol, respectively. However, it was noted that varying degrees of deviation from theory were present in each case (Figure 5). These deviations were scan-rate dependent; in particular, ∆Ep does not approach zero at low scan rates, W1/2 values are broader than predicted using k0′ values calculated from Ep values, and fits to data are better in certain scan rate ranges. These data, like those obtained from ac measurements that form the focus of this paper are also likely to contain systematic errors associated with kinetic (and thermodynamic) dispersion or the presence of interacting centers. Square Wave ac Voltammetry. To probe the azurin system more systematically, the square wave ac method was applied. This only requires a single experiment measured at the correct perturbation frequency (Table 1) versus ∼40 experiments to obtain the dc data (Figure 5). As predicted theoretically, the dc and all odd harmonic components of square wave voltammograms for surface-bound azurin are dominated by background charging current. Charging current only minimally affects the intensity of the even harmonic power spectra. As mentioned earlier, the contributions from the even components are of particular interest in this report, not just because they are devoid of charging current but also because they have been shown to be sensitive to the electrode kinetics, including the charge-transfer coefficient R,22 which is difficult to estimate from dc cyclic voltammograms. 1. Dc Component. Fourier analysis was used to deconvolve the dc component from the total current spectrum of a square wave experiment. Analysis of the deconvolved dc data revealed similar E0′ and Γ values, as obtained under purely dc conditions. However, the presence of a large-amplitude ac signal resulted in increased ∆Ep and W1/2 values, as theoretically expected. For example, with the 1-decanethiol-modified electrode under conditions where v ) 0.05 V‚s-1, f ) 38.15 Hz, and ∆E ) 0.05 V these parameters had values of 20 ( 5 and 170 ( 10 mV respectively, compared to values of 8 ( 3 and 100 ( 10 mV obtained in the absence of the ac perturbation.

2. Even Harmonic Power Spectra. The even harmonic power spectra profiles for the reduction of azurin at 1-octanethiol, 1-decanethiol, and 1-dodecanethiol modified gold electrodes are shown in Figure 6. For each of the azurin-alkanethiol systems studied, a good simulation-experiment comparison was obtained. However, the theoretical fit to the data reveals systematic deviations at the low- and high-frequency regimes. The k0′ values determined by the power spectrum method for all the alkanethiolmodified gold electrodes studied are summarized in Table 2. Consistent levels of agreement of k0′ values were obtained in repeat experiments and with different gold electrodes. Notably, as deduced from fast scan rate dc experiments, k0′ values decrease exponentially with increasing alkane chain length of the SAM. This behavior was also reported previously for azurin reduction on octanethiol, decanethiol, and dodecanethiol and other SAMs.16,30 It should be noted, however, that deviation from this distance dependence occurs for shorter chain alkanethiol SAMs.16,30 Qualitatively, but not quantitatively, k0′ values obtained via this method of analysis agree with those obtained from fast-scan dc data. However, there is an apparent inconsistency with respect to the value of the surface coverage relative to that obtained by the dc method. For the data shown in Figure 6, and in all other experiments, it was noted that the surface concentration values, Γapp, estimated from simulated power spectra were consistently lower (20-40%) than those calculated from dc voltammetry. This is not due to a real decrease in azurin surface coverage via film loss, as dc voltammetrically determined values calculated after the ac scans, or values calculated from the dc component of the ac square wave experiment, still gave uniformly higher coverage than deduced via power spectra. Rather, the origin of the difference is believed to be associated with systematic error. Given that the azurin molecules in the film are unlikely to exhibit identical rates of electron transfer, it follows that the time or frequency window used to observe these molecules become significant. Thus, at different frequencies, detection of molecules undergoing certain ranges of rates of electron transfer is emphasized, and as a consequence, analysis of coverage based on the power spectra peak magnitude need not be the same as that predicted from a model that assumes all molecules are kinetically and thermodynamically equivalent (cf. different situation prevailing at slower scan rates or lower frequency).17 The actual method of calculating Γ (or k0′ or E0′) can therefore contribute to the apparent technique-dependent differences observed in their value when kinetic or thermodynamic dispersion is present, because of differences in sensitivity to the nonideality. The dc voltammetric method typically uses the total area under the curve to estimate Γ, whereas the profile of the power spectra method, as used in Figure 6, relies on the power spectra peak current magnitude to calculate this parameter. As an alternative, fitting the peak width at half-height or the total area under the peak of the power spectra could have been used instead of fitting the peak current magnitude. In dc techniques, k0′ is usually calculated from measurement of peak potential (Figure 5). However, the experimental dc response, when compared with an ideal dc response based on the value of k0′, has a broader shape than theoretically predicted. Analogously, the power spectra deviate between theory and experiment on the basis of Γ and k0′ deduced by using the profile of power spectra, so that nonideality Analytical Chemistry, Vol. 78, No. 9, May 1, 2006

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Figure 6. Determination of k0′ by comparison of experimental (×) and simulated (b) even harmonic power spectra for the reduction of azurin bound to an (a) 1-octanethiol-, (b) a 1-decanethiol-, and (c) a 1-dodecanethiol-modified gold electrode (reductive sweep only). For octanethiol, experimental conditions were v ) 0.477 V‚s-1, f ) 127.55 Hz, ∆E ) 0.05 V, Estart ) 0.55 V, Efinish ) -0.25 V, and r ) 0.08 cm, and simulation parameters were as per experimental conditions and k0′ ) 1600 s-1, Γapp ) 10.4 pmol‚cm-2, E0′ ) 0.369 V, R ) 0.5, and T ) 278 K. For decanethiol, experimental conditions were v ) 0.05 V‚s-1, f ) 38.15 Hz, ∆E ) 0.05 V, Estart ) 0.55 V, Efinish ) -0.25 V, and r ) 0.1 cm, and simulation parameters were as per experimental conditions and k0′ ) 330 s-1, Γapp ) 10.0 pmol‚cm-2, E0′ ) 0.369 V, R ) 0.5, and T ) 278 K. For dodecanethiol, experimental conditions were v ) 0.05 V‚s-1, f ) 9.54 Hz, ∆E ) 0.05 V, Estart ) 0.55 V, Efinish ) -0.25 V, and r ) 0.1 cm, and simulation parameters were as per experimental conditions and k0′ ) 68 s-1, Γapp ) 12.5 pmol‚cm-2, E0′ ) 0.340 V, R ) 0.5, and T ) 278 K. Table 2. Comparison of k0′ Values Derived from Various Evaluation Methods for the Reduction of Azurin Bound to a Gold Electrode Modified with Different Length Alkanethiols k0′/s-1 SAM

power spectraa

second second harmonic harmonicb sine/square ratioc

1-octanethiol 1750 ( 250 1850 ( 150 1-decanethiol 340 ( 50 390 ( 60 1-dodecanethiol 70 ( 10 80 ( 10

2100 ( 150 430 ( 90 90 ( 10

fast scan dcd 2700 ( 500 440 ( 80 40 ( 8

a Based on simulation/experiment comparison of even harmonic components of power spectra. b Based on simulation/experiment comparison of individual second harmonic peaks. c Based on the ratio of the magnitude of the second harmonic sine wave to the second harmonic square wave. d Values calculated using data in Figure 5.

resulting from dispersion is detected under both dc and ac conditions. Analysis of individual components also highlights the importance of systematic error. 2954 Analytical Chemistry, Vol. 78, No. 9, May 1, 2006

3. Second Harmonic Components. Comparisons of individual second harmonic components, obtained by performing the FT-iFT operation on simulated and experimental square wave data, were also made (Figure 7). This form of data analysis provides another method for estimation of the kinetics, but ideally also allows the value of R to be determined. The asymmetry in the peak lobes detected for the second harmonic components implies that R is not exactly 0.5. A value of R ) 0.48 ( 0.01 is therefore deduced on the basis of the shape of individual components and neglecting frequency dispersion or other form of nonideality. The very sensitive nature of the ac method to R is revealed by this analysis. The k0′ values determined by this approach are also summarized in Table 2. The magnitude of these values also decreases with increasing alkanethiol chain length and are similar in magnitude to those derived from the power spectrum (30) Fujita, K.; Nakamura, N.; Ohno, H.; Leigh, B. S.; Niki, K.; Gray, H. B.; Richards, J. H. J. Am. Chem. Soc. 2004, 126, 13954-13961.

Figure 7. Comparison of experimental (b) and simulated (solid line) second harmonic voltammograms for azurin bound to (a) an 1-octanethioland (b) a 1-decanethiol-modified gold electrode (reductive sweep only). Experimental conditions: As for Figure 6. Simulation parameters: As for Figure 6, except for (a) k0′ ) 1750 s-1, R ) 0.48; and (b) k0′ ) 390 s-1, R ) 0.48.

profile approach. Clearly, the most significant discrepancy between experiment and simulation of the individual components shown in Figure 7 is the peak broadness (peak width at half-height). In comparison, solution-phase simulation-experiment comparisons for reversible or quasi-reversible systems show no analogous peak broadening. The use of individual components to provide kinetic values should provide a “snapshot” of kinetic data at a specific frequency, compared with analysis via the power spectrum profile approach, which gives rise to a weighted value arising from a frequency range. Again, Γ values obtained from second harmonic component peak heights are lower than values obtained from dc cyclic voltammetric areas. One could choose to use the peak area of the even ac harmonic components as the basis of estimation of Γ values, rather than the peak current magnitudes, and this generates values more closely related to those obtained from dc voltammetric area measurements. 4. Sine/Square Ratio Method. Another approach available to estimate k0′, that has the advantage of avoiding the need to assume a value for Γ and E0′, is to measure the ratio of the magnitude of the peak current obtained from the second harmonic of a single sine wave experiment relative to that obtained for the second component for a square wave (40 sine waves) of the same amplitude and frequency and then to compare this value with the simulated ratios.22 By applying this protocol to a series of experiments, k0′ values for each of the alkanethiol-modified electrodes were obtained (Table 2). When the k0′ value derived from this approach is used in the simulation of the second harmonic, the resultant Γapp value is similar to that obtained from the power spectra approach. 5. Odd Harmonic Voltammograms. Figure 8 illustrates the fundamental harmonic components detected experimentally compared with those determined by simulation (for a given set of parameters) for azurin electron transfer at a 1-decanethiol-modified Au electrode. There is a large contribution from the background capacitance current, Idl to the first (and other odd) harmonic terms (nonzero baseline). The capacitance of the double layer, Cdl, was

Figure 8. Comparison of experimental (points) and simulated (solid line) first harmonic voltammogram for the electron-transfer reaction of azurin bound to a 1-decanethiol-modified gold electrode (reductive sweep only). Experimental conditions: As for Figure 6b. Simulation parameters: As for Figure 6b, except for R ) 0.48, Γapp ) 16 pmol‚cm-2, and Cdl ) 6.6 µF‚cm-2.

calculated on the basis of the first harmonic data for each of the alkanethiol-modified electrodes using the expression

Cdl ) Idl/8f∆EA

(11)

over the dc potential ranges 0.755-0.605 V and 0.105 to -0.045 V for the experimental conditions shown in Figure 6b. The capacitance calculated in this manner depends slightly on potential and frequency, but the average value of Cdl calculated for the 1-octanethiol-, 1-decanethiol-, and 1-dodecanethiol-modified electrodes was 7.5 ( 1.9 µF‚cm-2. Electrochemical ac impedance spectroscopy revealed Cdl values of 17.5 and 1.5 µF‚cm-2 for bare gold and decanethiol SAM gold, respectively, under solution conditions similar to those used to obtain Figure 8 (without the presence of azurin).31 Presumably, the presence of the azurin (31) Boubour, E.; Lennox, R. B. Langmuir 2000, 16, 4222-4228.

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molecules bound at the surface of the SAM accounts for the additional capacitance component, either by increasing the apparent dielectric constant or causing structural changes in the SAM.16 Inclusion of Cdl into simulations based on kinetics deduced from fundamental harmonic values results in much better agreement with the experimental data although, again, the experimental voltammograms are broader than simulated ones. The value for Γapp obtained from analyses emphasizing the peak heights of the first harmonic components are closer to that derived from dc experiments. Under these low-frequency conditions, the response is close to reversible, serving to minimize the influence of frequency dispersion. However, the charging current component adds additional uncertainty into a data analysis problem already made complex by nonideality associated with frequency dispersion, so caution is needed in making deductions of this kind. CONCLUSIONS Even harmonic power spectra of square wave ac voltammetric data provide a powerful approach to analyzing the electron-transfer kinetics of a typical electron-carrier protein, azurin, at a gold electrode modified with different length alkanethiols. In the presence of nonideality associated with frequency or thermodynamic dispersion or interaction of molecules, the results reflect a weighted average associated with the sensitivities to different time or frequency regions. The k0′ values are qualitatively consistent with those derived from traditional dc voltammetric approaches but highlight the difficulties encountered by what is presumed to be nonideality attributed to kinetic and thermodynamic dispersion. The major benefits of the FT square wave approach are that it

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efficiently utilizes virtually all the large amount of data available, from each experiment, and provides results that are essentially devoid of background charging current. These features, plus the fact that individual dc and ac components are all accessible, provide a realistic basis on which to make detailed evaluations of the nature and contributions of the nonidealities. Further studies will be directed toward this important aspect of metalloprotein and enzyme electrochemistry; particularly for rapid electrontransfer systems obtained at high frequencies or fast scan rates. However, this is an inherently complex problem, since in addition to nonidealities identified above, the possibility of Marcusian or other models versus Butler-Volmer, and contributions from uncompensated resistance and local field fluctuations due to polycrystalline electrodes also need to be considered and distinguished from influences of kinetic and thermodynamic dispersion or other forms of nonideality. ACKNOWLEDGMENT Financial support from the Australian Research Council, a Monash University Research Fund Postdoctoral Fellowship for B.D.F., and the award of a Vallee Visiting Professorship to A.M.B. that facilitated this Monash and Oxford University collaboration are gratefully acknowledged. The research in Oxford was funded by grants to F.A.A. from the EPSRC and BBSRC (43/B19096).

Received for review October 11, 2005. Accepted February 27, 2006. AC051823F