Effects of Coupled Homogeneous Chemical Reactions on the

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Effects of Coupled Homogeneous Chemical Reactions on the Response of Large-Amplitude AC Voltammetry: Extraction of Kinetic and Mechanistic Information by Fourier Transform Analysis of Higher Harmonic Data Chong-Yong Lee,† John P. Bullock,‡ Gareth F. Kennedy,† and Alan M. Bond*,† School of Chemistry, Monash UniVersity, Clayton, Victoria 3800, Australia, and DiVision of Natural Sciences & Mathematics, Bennington College, Bennington, Vermont 05201 USA ReceiVed: June 18, 2010; ReVised Manuscript ReceiVed: August 13, 2010

Large-amplitude ac voltammograms contain a wealth of kinetic information concerning electrode processes and can provide unique mechanistic insights compared to other techniques. This paper describes the effects homogeneous chemical processes have on ac voltammetry in general and provides experimental examples using two well-known chemical systems: one simple and one complex. Oxidation of [Cp*Fe(CO)2]2 (Cp* ) η5-pentamethylcyclopentadienyl) in noncoordinating media is a reversible one-electron process; in the presence of nucleophiles, however, the resulting ligand-induced disproportionation changes the process to a multiple step regeneration. The chemical kinetic parameters of the regeneration mechanism were discerned via analysis of the third and higher harmonics of Fourier-transformed ac voltammetry data. Comparison of experimental data to digital simulations provides clear evidence that the reaction proceeds via a rapid pre-equilibrium between the electrogenerated monocation and the coordinating ligand; simultaneous fitting of the first nine harmonics indicates that kf ) 7500 M-1 s-1 and kr ) 100 s-1, and that the unimolecular decomposition of the corresponding intermediate occurs with a rate constant of 2.2 s-1. The rapid cis+ f trans+ isomerization of the electrogenerated cis-[W(CO)2(dpe)2]+, where dpe ) 1,2-diphenylphosphinoethane, was examined to illustrate the effects of a simpler EC mechanism on the higher harmonics; a rate constant of 280 s-1 was determined. These results not only shed new light on the chemistry of these systems, but provide a clear demonstration that the higher harmonics of ac voltammetry provide mechanistic insights into coupled homogeneous processes far more detailed than those that are readily accessible with dc techniques. Introduction The use of digital simulation to model electrochemical phenomena has been widely employed over the past few decades.1 This is particularly true with respect to the simulation of dc cyclic voltammetric responses2 owing to the widespread use of the technique to examine rates of heterogeneous electron transfer as well as homogeneous reactions coupled to electron transfer processes.3,4 There are currently several commercially available software packages that will model the response of userdefined mechanisms. Access to this user-friendly software has greatly simplified the ease of undertaking a comparison of simulated and experimental data, and access to quantitative study via this approach has proven to be an invaluable tool in electrochemical research.5 Although dc cyclic voltammetry has emerged as the most commonly used approach to investigate mechanisms arising from the coupling of electron transfer and chemical processes, ac voltammetric techniques are in principle more powerful for this purpose than their dc counterparts.6 It has been more than 40 years since the first papers examining the effect of homogeneous chemical processes on ac voltammetric responses were published.7-9 Typically, these experiments employed a small amplitude sinusoidal potential superimposed on a linear dc potential sweep. However, theoretical solutions relevant to the ac technique were limited, and those that did exist generally * To whom correspondence should be addressed. Fax: +61 3 9905 4597. E-mail: [email protected]. † Monash University. ‡ Bennington College.

required relatively small amplitudes of the ac signal to facilitate the theoretical analysis. The exception to this was the provision of a general analytical expression by Oldham and co-workers10 for a reversible process with large-amplitude conditions. This emphasis on linearization of the analysis limited the access to second and higher order harmonic Faradaic currents. Developments in the field were therefore only intermittent11 until about 10 years ago when numerical methods were devised for the accurate simulation of large-amplitude ac voltammetry.12 With the theoretical groundwork in place and the widespread availability of powerful computing hardware that made routine use of Fourier transformations (FT) possible, there has since been growing interest in ac voltammetry.13 We have performed a number of studies that examine various aspects of these techniques, including, for example, the effects of non-Faradaic processes on ac voltammetric responses,14 analytical applications,15 and application to the study of surface-confined substrates16 and mediated electrode processes.17 In this paper we focus on the effects that homogeneous chemical reactions have on the higher harmonics (third and higher) of the ac voltammetric response. Our primary focus on the higher harmonics is due to the fact that these have very small contributions from non-Faradaic currents, thereby allowing the observation of subtle features of the Faradaic processes. The systems we examine are an EC mechanism, the cis+ f trans+ isomerization that follows the one-electron oxidation of cisW(CO)2(dpe)2,18 where dpe ) 1,2-diphenylphosphinoethane, and the far more complex multistep mechanism of the ligandinduced disproportionation of [Cp*Fe(CO)2]2+, where Cp* )

10.1021/jp105626z  2010 American Chemical Society Published on Web 08/30/2010

Mechanistic Insights from ac Voltammetry

J. Phys. Chem. A, Vol. 114, No. 37, 2010 10123

pentamethylcyclopentadienyl.19 Both studies reveal new insights into the relevant chemistry and serve as examples for the application of large-amplitude ac voltammetry to the study of electrode mechanisms involving chemical reactions coupled to electron transfer.

in the usual way.3,4 Homogeneous reactions are coupled to the electron transfer according to the following example. For a simple first order process (eq 3), kf

O y\z P

(3)

kr

Experimental Section Materials. Cobaltocenium hexafluorophosphate, [CoCp2]PF6, and bis(η5-pentamethylcyclopentadienyl)irondicarbonyl, [Cp*Fe(CO)2]2, were purchased from Strem and used as received. cisW(CO)2(dpe)2 was prepared according to literature methods.20-22 Solvents dichloromethane, acetone, and acetonitrile (Merck, HPLC grade) were dried over activated 4 Å molecular sieves prior to use. Tetrabutylammonium hexafluorophosphate (GFS Chemicals), Bu4NPF6, was recrystallized twice from ethanol prior to use as a supporting electrolyte. Methods and Instrumentation. Standard three-electrode cells were used for all studies described in this work. A platinum wire and a silver wire coated with silver chloride served as the auxiliary and quasi-reference electrodes, respectively. Potentials are reported relative to the reversible reduction of colbaltocenium, Cc+, which was used as an internal standard. The working electrodes employed depended on the system under investigation: those of cisW(CO)2(dpe)2 were conducted with a 1 mm diameter platinum electrode (BAS); those of [Cp*Fe(CO)2]2 used a 3 mm glassy carbon electrode (Pine Instruments). Working electrodes were polished with 0.3 µm alumina (Buehler) and thoroughly rinsed with water and acetone prior to use. Unless otherwise stated, experiments were performed at room temperature (20 ( 1 °C). Studies of [Cp*Fe(CO)2]2 were performed under a blanket of nitrogen presaturated with dichloromethane solvent. Dc cyclic voltammetric experiments were undertaken with a BAS-100B Electrochemical workstation (Bio-Analytical Systems). Large-amplitude ac voltammetry was performed using previously described instrumentation.13 Digital Simulations of AC Voltammetry. Dc and ac cyclic voltammetry results were simulated using MECSim (Monash Electrochemical Simulator), an internally developed program. This simulation package is written in Fortran 77 and is based on the matrix formulation outlined in refs 2 and 23. Output for the dc simulations was obtained by using a zero amplitude (∆E ) 0 V) ac component and routinely compared to that obtained from commercially available software such as Digisim or DigiElch for confirmation. Excellent agreement was always achieved. The approach used to generate the ac output is briefly outlined below. The waveform applied in the ac voltammetric experiments, E(t), consists of the sum of the dc voltage ramp used in cyclic voltammetry, Edc(t), and the sinusoidal component (eq 1),

E(t) ) Edc(t) + ∆E sin(2πft)

(1)

where f and ∆E are the frequency (Hz) and amplitude (V) of the applied sine wave, respectively. Butler-Volmer kinetics are assumed to apply for the electron-transfer processes. Thus, for a one-electron oxidation (eq 2), kET,f

R y\z O + e-

(2)

kET,r

kET,f and kET,r, the forward and reverse rate constants for the electron transfer, depend on potential and the charge transfer coefficient, R, and are related to the standard rate constant, k°,

the forward and reverse homogeneous rate constants are given by kf and kr, respectively. Mass transport under linear diffusion conditions for all diffusing species of interest follows the relationships given below in eqs 4 and 5,

∂[R] ∂2[R] ) DR 2 ∂t ∂x

(4)

∂[O] ∂2[O] ) DO 2 - kf[O] + kr[P] ∂t ∂x

(5)

where DR/O refers to the diffusion coefficients for each species, the bracketed terms represent concentrations, and x is the distance from the electrode. Additional terms are generated and included as necessary on the basis of user-defined mechanisms to calculate the time/concentration relationships for species generated homogeneously.2,23 The mass transport equations are solved according to previously described methods24,25 and application of the following initial and boundary conditions (eqs 6-8), where [R]* is the concentration of the reduced form in the bulk solution:

t ) 0, all x: [O] ) [P] ) 0, and [R] ) [R]* t > 0, x ) 0 (electrode/solution interface)

(6)

∂[O] ∂[R] ) DR ) kET,f[R] - kET,b[O] ∂x ∂x

(7)

-DO

t > 0, x ) ∞: [O] ) [P] ) 0, and [R] ) [R]*

(8)

Once the time and space dependent concentration relationships are generated, the Faradaic current, I, is then calculated according to eq 9,

I ) nFADR

( ∂[R] ∂x )

x)0

(9)

where n, F, and A have their usual meanings. To improve both the efficiency and accuracy of the simulation, an expanding grid originally introduced by Feldberg was adopted.25 The effects of double layer capacitance, Cdl, and uncompensated resistance, Ru, are also taken into account using widely adopted methods.2 Unless otherwise stated, simulations described in this work employed the following parameters: k° ) 0.1 cm s-1, R ) 0.5, Di ) 1.0 × 10-5 cm2 s-1, f ) 13.78 Hz, ∆E ) 100 mV, A ) 0.0079 cm2, Cdl ) 0 µF cm-2, R ) 200 Ω, and T ) 293 K. For reasons previously described,13 simulations were carried out with 2n data points to match the format of experimental data; typically 216 data points were used as these allowed reasonable computing time with no distortion of the voltammetric features. In some cases, such as in simulations of higher frequency experiments, more data points were required to prevent distortion so 218 data points were used. The k° value of 0.1 cm s-1 implies that the electron transfer step is close

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Lee et al.

Figure 1. Simulated (a) dc cyclic (ν ) 59.6 mV s-1) and (b-h) fundamental to seventh harmonic Fourier transformed ac cyclic voltammograms for an EC mechanism (eq 10, 11). First-order rate constants following charge transfer employed are 0 (black), 0.10 (red), 0.32 (magenta), 1.0 (blue), 3.2 (green), and 10 s-1 (orange). Simulation parameters used: [A] ) 1.00 mM, ν ) 59.6 mV s-1, f ) 13.78 Hz, ∆E ) 100 mV, E° ) 0.00 mV, Einit ) -0.400 V, and Eswitch ) 0.400 V, and others provided in the Experimental section.

to, but not fully, reversible under ac conditions, which is a typical situation encountered experimentally. The individual ac harmonic currents are extracted from raw current data, whether obtained experimentally or generated by simulation, as follows. The time domain data is converted to a frequency domain power spectrum by taking the Fourier transform (FT). The frequencies corresponding to individual harmonics are selected and treated with an inverse FT algorithm to generate the current data as a function of time. Although other presentation formats are possible, the figures in this paper plot the magnitudes of the harmonic currents against time; this format essentially provides the current envelope defined by the maxima of successive current oscillations in the ac experiment or simulation. Results and Discussion Simulations of an EC Mechanism. The effects of a simple first order homogeneous reaction coupled to a nearly reversible

(k° ) 0.1 cm s-1) one-electron transfer on ac and dc cyclic voltammograms are illustrated by the simulations presented in Figure 1; the first through seventh harmonics of the ac cyclic voltammograms are shown. The specific mechanism is an EC process and is described by eqs 10 and 11.

A h B + ek11

B 98 C

(10) (11)

The rate constants employed in the simulations range from 0.1 to 10 s-1; an additional simulation in which k11 ) 0 s-1 is also presented and represents a simple E-type mechanism. While



the small amplitude case has been examined previously,7-9 that of the large amplitude with the higher order harmonics has not. It is helpful to draw comparisons between the dc and ac responses. The changes in the dc voltammograms are familiar and can be quickly summarized by the following two points: (1) when k11 is relatively low the most obvious effect is a decrease in the peak current ratio, irev/ifor, which results from the consumption of the electrogenerated species, B, by the homogeneous process; and (2) when k11 is relatively large, the oxidation peak shifts to a lower potential and sharpens slightly; these effects are due to the disturbance of the electron transfer equilibrium by the fast coupled homogeneous step.26 The simulations in Figure 1a effectively illustrate that dc voltammetry is most sensitive to changes in rate constants when operating in a time regime where significant return current is present. The influence of the first order C step on dc voltammograms are mirrored in the ac harmonics as evident in Figures 1b-h. The current responses of all the harmonics show two data sets, which correspond to the forward and reverse sweeps of the experiment. For the parameters employed in these simulations of the EC reaction scheme, E ) E° at 6.7 s in the forward sweep and 20.1 s in the reverse sweep; the switching time is 13.4 s. In the E-mechanism (k11 ) 0 s-1) the peaks of the forward and reverse sweeps have equal currents, and each envelope is close to symmetrical about its midpoint. When coupled to a homogeneous chemical step with a relatively small rate constant the most obvious change in the harmonics is a rather marked diminution of the peak currents of the return sweep. For example, when k11 ) 0.1 s-1 the integrated area under the return peaks is only 61% of the value when k11 ) 0 s-1. This is entirely analogous to the decrease in coupled peak current in the dc voltammogram. In contrast, as was true in the dc case, the peak position and shape of the forward sweep is rather insensitive to the effects of the chemical step when the rate constant is fairly low; the integrated area for the forward peak of the third harmonic when k11 ) 0.1 s-1 is 97% of that seen in the E mechanism under the same conditions. At faster reaction rates an obvious asymmetry arises in the forward sweep response: the currents of each peak in a given harmonic envelope become increasingly attenuated with higher values of k11. For example, when k11 ) 10 s-1 the relative attenuation of the peaks in the third harmonic from the simple E mechanism are such that the first peak becomes the largest in the set. In the fundamental harmonic, a similar effect is seen, but because there is only one peak evident in either scan direction higher values of k11 lead to increasing distortion of this process, with the currents becoming more highly attenuated at more positive potentials. The above analysis reveals a potentially valuable application of the higher harmonics of Fourier transformed ac voltammograms. Specifically, whereas dc cyclic voltammetry becomes less sensitive, in terms of measuring rate constants, when the current of the return sweeps is very low, ac voltammetry can remain quite sensitive to changes in k11 so that the kinetic regimes accessible with ac voltammetry are extended considerably (Figure S1 of the Supporting Information). We present an example of this type of rate constant determination later in this paper. Multiple Step Mechanism. We now proceed to consider the more chemically complex half-regeneration mechanism (eqs 12-15) that models the ligand-induced disproportionation we present later.

A h B + e-

(12)

k13f

B + C y\z D

(13)

k13r k14

D 98 E + F

(14)

2E 98 A

(15)

(fast)

In this scheme the electrogenerated species, B, reacts with C, present in the bulk solution, to form a short-lived intermediate, D. Decomposition of D yields two species: E, which dimerizes to regenerate A, and F, the final oxidation product. The regenerated A can then be reoxidized at the electrode, resulting in a net two-electron oxidation (eq 16).

A + 2C f 2F + e-

(16)

The simulated dc and ac harmonic current responses of the EC and multiple step mechanisms described above are compared in Figure 2. The rate constant for the EC mechanism shown in Figure 2 is 3.2 s-1; to provide convenient comparison of the features of the two mechanisms, [C] and k13f were chosen to yield a pseudofirst order rate constant that is also 3.2 s-1; other rate parameters were: k13r ) 0 s-1 and k14 ) 100 s-1. The rationale for choosing these particular parameters in the comparison to those for the EC result is to show how the “switching on” of the second electron-transfer process influences the outcome; the rates of consumption of the electrogenerated species, B, in the two cases is virtually identical. As expected, the dc voltammogram for the multiple step pathway shows significant current enhancement over the EC mechanism; both show very little return current. Also as expected, the ac harmonic currents are higher for the multiple step than the EC mechanism due to the regeneration of the electroactive A. However, perhaps unexpectedly, is the observation that currents obtained in the forward sweep for the multiple step pathway are lower than the simple E-type pathway, despite the obvious current enhancement detected in the dc experiment. This is a direct result of the maximum amplification of Faradaic currents in large-amplitude ac voltammetry being achieved when the electrode process is both electrochemically and chemically reversible. The lack of chemical reversibility in the multiple step mechanism results in lower harmonic currents despite the higher dc current response. One aspect of FT ac voltammetry that is not immediately obvious from the plots in Figure 2 is its ability to distinguish closely related mechanistic pathways. For example, consider two variations of the multiple step scheme above, one featuring a rapid preequilibrium in which k13f and k13r are both much greater than k14, and one involving a rate-determining second-order step in which k14 . k13f, and k13r is negligible. The rate equations for the reactions would be similar: that for the rapid pre-equilibrium case under pseudofirst order conditions is given by,

rate )

1 d[F] 1 1 ) k14[D] ) K13k14[B]eq[C]* 2 dt 2 2

(17)

where [B]eq is the equilibrium concentration of electrogenerated B, and [C]* is the concentration of C in the bulk solution. The

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Figure 2. Simulated (a) dc cyclic (ν ) 59.6 mV s-1) and (b-h) fundamental to seventh current harmonics of Fourier transformed ac cyclic voltammograms of E (black), EC (eqs 10, 11, red), and multiple step (eqs 12-15, blue) mechanisms. Rate constants and relevant concentrations employed in the simulations are, for the EC mechanism: [A] ) 1.00 mM, k11 ) 3.2 s-1; for the multiple step mechanism [A] ) 1.00 mM, [C] ) 50.0 mM, k13f ) 64 M-1 s-1, k13r ) 0 s-1, k14 ) 100 s-1, k15 ) 1.0 × 107 s-1. Other simulation parameters used: ν ) 59.6 mV s-1, f ) 13.78 Hz, ∆E ) 100 mV, E° ) 0.00 mV, Einit ) -0.400 V, Eswitch ) 0.400 V, and others provided in experimental section.

rate law for the mechanism featuring the rate-determining second order step is given by

rate )

1 d[F] 1 ) k13f[B][C]* 2 dt 2

(18)

These two cases represent extremes of a continuum of kinetic possibilities. However, because of the similarities in the rate laws, conventional dc cyclic voltammetry is poorly suited, relative to the ac version, to identify where along this continuum a given reaction system might lie. A series of simulated dc cyclic voltammograms that illustrate this point are presented in Figure 3a. Kinetic parameters (provided in the figure caption) were chosen to model systems in which the actual rate of product formation is

the same across the series; moreover, the equilibrium constant, K13, is held constant for all simulations involving pre-equilibria. Although these voltammograms show a significant potential shift of the peak maxima as expected from theory,26 this is not helpful in distinguishing these mechanisms in the absence of a reliable measurement of E°, a common problem encountered when examining irreversible chemical pathways. Otherwise, the voltammograms show only very subtle differences in shape. The similarity of the dc results above stand in marked contrast to those obtained by the ac method (Figures 3b-j). The peaks of the third, fourth, and fifth harmonics, for example, of the ac voltammograms show obvious differences in magnitude, symmetry, and resolution. Two particularly interesting trends emerge. When there is no pre-equilibrium (Figure 3b-d) the individual peaks are relatively large in magnitude and well-resolved, showing sharp and



Figure 3. Simulated (a) dc cyclic (ν ) 59.6 mV s-1) and third (b, e, h), fourth (c, f, i), and fifth (d, g, j) current harmonics of Fourier transformed ac cyclic voltammograms showing the effect of pre-equilibrium kinetics on harmonic peak characteristics of the multistep mechanism (eqs 12 - 15). Simulations depict responses by mechanisms involving no prequilibrium (b-d), pre-equilibria in which k13r and k14 are comparable (e-g), and rapid pre-equilibria (h-j). Specific homogeneous rate parameters used in the simulations are given by the following table: Other simulation parameters used: ν ) 59.6 mV s-1, f ) 13.78 Hz, ∆E ) 100 mV, E° ) 0.00 mV, Einit ) -0.400 V, and Eswitch ) 0.400 V, [A] ) 1 × 10-3 M, [C] ) 0.050 M, Cdl ) 0 µF cm-2, Ru ) 200 Ω, T ) 293 K, and others provided in experimental section. Color of Trace black red purple blue green orange

k13f (M-1 s-1) 60 200 2 × 103 2 × 104 2 × 106 2 × 108

well-defined current minima between the peaks. As the rate constant of the reverse reaction of the pre-equilibrium, k13r, becomes comparable to that of the forward rate constant of the subsequent step, k14 (Figures 3e-g), the peaks broaden and become smaller. This trend continues as the rate constants of the pre-equilibrium increase but then reverses when the pre-equilibrium becomes extremely rapid (Figure 3h-j); under such conditions the peak shapes sharpen but show lower symmetry than those seen in the absence of any pre-equilibrium.

K13r (s-1) 1 × 10-5 1 10 100 1 × 104 1 × 106

k14 (s-1) 1 × 105 5 3 3 3 3

A conceptual model to explain the above trends involves the nature of competition between the ac electron transfer kinetics and the homogeneous chemical kinetics. In ac cyclic voltammetry, amplification of the Faradaic current arises from the rapid oscillation of the applied potential; at potentials near E°, reversible redox couples undergo rapid oxidation and reduction cycling, producing currents considerably larger than those obtained from dc voltammetry employing the same scan rate. This gives rise to a kinetic regime related to the frequency of the ac signal. When coupled

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Lee et al. [Cp*Fe(CO)2]2 h [Cp*Fe(CO)2]+ 2 + e

Figure 4. The effect of ac frequency on the fourth harmonic of selected Fourier transformed ac cyclic voltammograms. Simulated ac frequencies, f, are 13.76 (blue), 44.10 (red), and 137.6 Hz (black). Other parameters are the same as those specified in caption to Figure 3.

chemical processes are slow compared to the kinetics of the electron transfer there is relatively little attenuation or distortion of the alternating current; this accounts for the relatively limited influence the lower rate constants have on the forward sweep shown in Figure 1. At the other end of the kinetic continuum, if all coupled kinetics are much faster than the electron transfer step then the overall process remains in equilibrium and a close to “ideal” response is retained. In contrast, when the chemical kinetics are of the same order as those of the electron transfer, significant peak broadening is observed. Thus, the system in Figure 3 that exhibits the poorest resolution (k13f ) 2 × 104 M-1 s-1; k13r ) 1 × 102 s-1; k14 ) 3 s-1; blue trace in Figures 3h-j), exhibits better resolved processes when the frequency is increased. This is illustrated by the simulations in Figure 4, which depict the ac response of the same chemical system when the ac frequency increases from 13.76 Hz to 44.10 and 137.6 Hz. In the latter two simulations, the applied frequency is high enough to make the chemical kinetics appear “slower”, giving harmonics with greater resolution. Similar loss of resolution is observed at high reactions rates in the EC mechanism (Figure S1). Finally, the well resolved ac harmonics depicted in Figure 2 are due to the relatively long-lived nature of electrogenerated product under the homogeneous kinetic parameters employed. These simulations clearly indicate that there is a wealth of kinetic information available from the higher harmonics of the ac method. Taken as an ensemble, the magnitude and shape of the various harmonics serve as a “kinetic signature” for a given mechanism. Moreover, since each harmonic corresponds to a different time regime, one can, by carefully fitting the peaks shapes for multiple harmonics simultaneously, estimate the accessible rate constants for coupled equilibria with substantially greater certainty than is possible with dc techniques. Comparison of Simulated and Experimental Data. Oxidation of [Cp*Fe(CO)2]2: An E Mechanism. In relatively noncoordinating media such as CH2Cl2/Bu4NPF6, [Cp*2Fe(CO)2]2, like its unmethylated analog, undergoes a chemically reversible one-electron oxidation to the corresponding binuclear radical cation (eq 19).19,27,28 The dc cyclic voltammogram derived from oxidation of 0.85 mM [Cp*Fe(CO)2]2 in CH2Cl2/0.5 M Bu4NF6 is presented in Figure 5a; the reversible potential, E°′, was measured to be 1.26 V vs Cc/Cc+ under these conditions.

(19)

The fundamental through ninth ac harmonic components for this oxidation, along with the corresponding simulations, are presented in Figures 5b-h. Fits between simulated and experimental data were optimized by iteratively adjusting relevant parameters (k0, Ru, and Cdl in this case) until no further improvement could be achieved.14a These results exhibit signs of uncompensated resistance but are otherwise typical of those expected for a nearly reversible electron transfer process. Simulations indicate that Ru is about 275 Ω, similar to the value measured directly from the RC time constant. Comparison of experimental data to simulations also indicates that k° ) 0.12 cm s-1, similar to the value found for the Fc/Fc+ process (Fc ) ferrocene) under similar conditions. However, since this value is close to the upper limit detectable under the experimental conditions used, this may be considered to be a minimum value. The data shown in Figure 5 exhibit exceptional agreement between theory and observation. Thus, even in the very weak ninth harmonic the major features are simulated satisfactorily. In this particular harmonic, the mean current within the forward sweep envelope is approximately only 25 nA. Nevertheless, the average difference with simulated currents is less than 15%. The ninth harmonic example, therefore, demonstrates the substantial noise filtering capability of the FT-inverse-FT approach in ac voltammetric data analysis. Simulations of higher current values detected in the lower harmonics show considerably better agreement with experimental measurements. Oxidation of [Cp*Fe(CO)2]2: A Multiple Step Mechanism. The product of the one-electron oxidation of [Cp*Fe(CO)2]2 is highly reactive toward nucleophiles, resulting in complex electrochemical behavior in coordinating solvents. For example, in acetonitrile, [Cp*Fe(CO)2]2 undergoes an irreversible net twoelectron oxidation (eq 20) to the monomeric iron(II) acetonitrile adduct, [Cp*Fe(CO)2(CH3CN)]+.

[Cp*Fe(CO)2]2 + 2CH3CN f 2[Cp*Fe(CO)2(CH3CN)]+ + 2e-

(20)

The mechanism of the above reaction was previously examined in detail by dc cyclic voltammetry and double-potential step chronocoulometry over the course of an acetonitrile titration, as well as by stopped-flow spectroscopy performed using solutions of the radical cation that were generated via bulk electrolysis of the neutral parent.19 These studies indicated that the electrogenerated cation undergoes a ligand-induced disproportionation described by the following scheme (eqs 21-23). + [Cp*Fe(CO)2]+ 2 + CH3CN h {[Cp*Fe(CO)2]2(CH3CN)} (21)

{[Cp*Fe(CO)2]2(CH3CN)}+ h [Cp*Fe(CO)2(CH3CN)]+ + Cp*Fe(CO)2 2Cp*Fe(CO)2 h [Cp*Fe(CO)2]2

(22) (23)

The overall scheme represents a half-regeneration mechanism and exhibits the expected dc current enhancement when performed in a noncoordinating medium in the presence of acetonitrile. Stopped-flow experiments indicated that the overall



Figure 5. Dc cyclic voltammetry (a) and the first through fifth (b-f), sixth and eighth (g), and seventh and ninth harmonic voltammograms (h) obtained for the oxidation of 0.85 mM [Cp*Fe(CO)2]2 in 0.5 M CH2Cl2/Bu4NPF6. Experimental data is in black, simulated in red. Experimental parameters: ν ) 59.6 mV s-1, f ) 13.71 Hz, ∆E ) 0.1 V, Estart ) 0.856 V, Eswitch ) 1.656 V. Simulation parameters: D (all species) ) 1.4 × 10-5 cm2 s-1, E° ) 1.256 V, k° ) 0.12 cm s-1, R ) 0.5, Ru ) 275 Ω, A ) 0.0521 cm2, and Cdl ) [2.9 × 10-5 F cm-2 + 3.2 × 10-5 (E - Ec) F V-1 cm-2 + 1.4 × 10-5 (E - Ec)2 F V-2 cm-2], where Ec ) 0.958 V.

disproportionation is first order with respect to acetonitrile and the radical cation and takes place with a second-order rate constant of 120 M-1 s-1,19 although a subsequent analysis of the dc voltammograms was later published that indicated a slower value of 40-50 M-1 s-1.29 Regardless of the rate constant, however, is the fact that neither of these analyses reveal whether the reaction proceeds via a rate-determining secondorder step or if a rapid pre-equilibrium involving the purported intermediate, {[Cp*Fe(CO)2]2(CH3CN)}+, is involved. Moreover, the dependence of the reaction rate on acetonitrile provides for a system in which the level of influence of the chemical steps coupled to electron transfer can be controlled quite easily. For these reasons, oxidation of [Cp*Fe(CO)2]2 provides an

excellent system with which to examine the types of kinetic insights obtainable using large-amplitude ac voltammetry. The dc cyclic voltammograms and third through seventh ac harmonics of 0.85 mM [Cp*Fe(CO)2]2 in 0.5 M CH2Cl2/TBAPF6 obtained in the presence of 0, 1.2, 4.7, 14, 29, 58, and 120 equivalents of acetonitrile are shown in Figure 6. These data clearly show the effect of the increasing rate of reactions with some of the trends resembling those discussed earlier for the effect of k on the EC mechanism response. Specifically, as the dc voltammograms show a decrease in the return current magnitude, the ac harmonic peaks in the return sweeps get progressively smaller as the rate of product formation increases. The dc results also show the current enhancement of the forward

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Figure 6. Dc cyclic voltammetry (a) and the first through fifth (b-f), sixth and eighth (g), and seventh and ninth harmonic voltammograms (h) obtained for the oxidation of 0.85 mM [Cp*Fe(CO)2]2 in CH2Cl2 (0.5 M Bu4NPF6) in the presence of 0 (black), 1.2 (magenta), 4.7 (violet), 14 (blue), 29 (green), 58 (orange), and 120 (red) equivalents of acetonitrile. Experimental parameters: ν ) 59.6 mV s-1, f ) 13.71 Hz, ∆E ) 0.100 V, Estart ) 0.874 V, and Eswitch ) 1.674 V.

sweep, expected for a regeneration mechanism. However, it is important to note that the changes among the various sets of harmonics are qualitatively different from each other and are not nearly as simple as the serial signal attenuations that characterize the EC simulations in Figure 1. So, while the first, second (neither shown) and third harmonics (Figure 6b) do not show major shape changes over the course of the titration, the same cannot be said of the higher harmonics (Figure 6c-f). The peaks of the fifth harmonic, for example, show substantial increases and sharpening at low levels of acetonitrile. Peaks of the sixth and seventh harmonics show even more complex changes in shape. Importantly, these changes are modeled exceptionally well by simulation and, given the high sensitivity of the higher harmonics to coupled homogeneous processes, the resulting estimates of kinetic parameters are quite reliable, albeit subject to some rather tight coupling, as discussed below. The complexity of the harmonic signals seen in Figure 6 provide clear evidence that the ligand-induced disproportion of [Cp*Fe(CO)2]2+ proceeds via a pre-equilibrium, as a simple ratedetermining second-order step would result in series of welldefined peaks of the type seen in Figures 2 and 3(a-c). To explain how the specific kinetic parameters of the multiple step mechanism are extracted from the ac data, a detailed examination of one of the data sets from Figure 6 is described presently.

The first through ninth harmonics obtained from the solution with 29 equivalents of acetonitrile are shown along with the corresponding digital simulations in Figure 7; the specific kinetic rate constants employed in the simulations were: k21f ) 7500 M-1 s-1, k21r ) 100 s-1, k22f ) 2.2 s-1, k22r ) k23r ) 1 × 10-7 s-1, k23f ) 1 × 107 M-1 s-1. These parameters correspond to an apparent second-order rate constant of 165 M-1 s-1, in reasonable agreement with the result obtained by stopped-flow experiments. However, note that the values of these parameters are tightly coupled, that is, changes in any one of them can be largely offset by corresponding changes in others. For example, under pseudo-first order conditions, the apparent rate constant is given by [CH3CN]K21k22, where K21 ) k21f/k21r. In terms of the overall reaction rate, a decrease in k22 can be exactly balanced by a corresponding increase in K21. Although the harmonics for two such cases will not be identical, they will of course remain similar if the relative changes are small. Moreover, because K21 is a ratio, the effect on the ac harmonics of a change in k21f can be very small if accompanied by a proportional change in k21r. That said, however, we estimate the reported values to be correct within a factor of 2 since greater changes in any parameter lead to obvious deviations from experimental data. Finally, the reliability of the above-mentioned rate parameters was confirmed by using the values obtained from



Figure 7. Dc cyclic voltammetry (a) and the first through fifth (b-f) and sixth through ninth (g-h) ac current harmonics obtained for the oxidation of 0.85 mM [Cp*Fe(CO)2]2 in CH2Cl2 (0.5 M Bu4NPF6) in the presence of 29 equivalents of acetonitrile; the sixth and eighth (g, top and bottom traces, respectively), and seventh and ninth (h, top and bottom traces, respectively) harmonics are plotted on the same axes. Experimental data are in black, simulated data are in red. Experimental parameters: ν ) 59.6 mV s-1, f ) 13.71 Hz, ∆E ) 0.1 V, Estart ) 0.874 V, Eswitch ) 1.674 V, and [CH3CN] ) 25 mM. Simulation parameters: D (all species except CH3CN) ) 1.4 × 10-5 cm2 s-1, DCH3CN ) 2.5 × 10-5 cm2 s-1, E° ) 1.256 V, k° ) 0.12 cm sec-1, Ru ) 250 Ω, A ) 0.0521 cm2, and Cdl ) [2.2 × 10-5 F cm-2 + 3.4 × 10-5 (E - Ec) F V-1 cm-2 + 0.8 × 10-5 (E - Ec)2 F V-2 cm-2], where Ec ) 0.958 V; homogeneous kinetic parameters are provided in the text.

data shown in Figure 7 to simulate the responses derived from other concentrations in the series; the resulting simulations were in very good agreement with experimental data. Oxidation of cis-W(CO)2(dpe)2: An EC Mechanism. Oxidation of many metal carbonyl compounds leads to geometric isomerization30 owing to changes in the relative stabilities in the oxidized and reduced forms.31 If the isomerization is rapid on the cyclic voltammetric time-scale, the oxidation process will appear irreversible. A good example is the rapid cis+ f trans+ isomerization upon oxidation of W(CO)2(dpe)2, described by eqs 24 and 25.

cis - W(CO)2(dpe)2 h cis - [W(CO)2(dpe)2]+ + e(24) k25

cis - [W(CO)2(dpe)2]+ 98 trans - [W(CO)2(dpe)2]+

(25) No room temperature kinetic measurements of the isomerization have been reported as the reaction was too fast to accurately measure using the equipment available when the initial studies were performed more than 30 years ago,32 although measure-

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Figure 8. Comparison of experimental (black) and simulated (red) dc cyclic voltammograms for the oxidation of cis-[W(CO)2(dpe)2] at a Pt electrode in acetone (0.1 M Bu4NPF6). Scan rates are (a) 1 V s-1, (b) 10 V s-1, (c) 25 V s-1 and (d) 50 V s-1. Parameters used in the simulations: kf ) 70 s-1, E°′ ) 1.02 V, k° ) 1.0 cm s-1, R ) 0.5, Dox ) Dred ) 1.4 × 10-5 cm s-2, [R] ) 0.12 mM (where R is the analyte), Ru ) 200 Ω, Cdl ) 3.5 × 10-5 F cm-2, and A ) 0.02 cm2.

Figure 9. Comparison of experimental (black) and simulated (red) ac fundamental to sixth harmonic voltammograms for the oxidation of cis[W(CO)2(dpe)2] at a Pt electrode in acetone (0.1 M Bu4NPF6). Parameters used in the simulations: ∆E ) 100 mV, f ) 9.0 Hz, Estart ) 0.778 V, Eswitch ) 1.30 V, k° ) 0.13 cm s-1, R ) 0.50, kf ) 280 s-1, T ) 293 K, Dox) Dred ) 1.5 × 10-5 cm s-2, [R] ) 0.18 mM, ν ) 0.1490 V s-1, E°′ ) 1.017 V, Ru ) 200 Ω, Cdl ) [1.22 × 10-5 F cm-2 + 0.20 × 10-5 (E - Ec) F V-1 cm-2 + 0.22 × 10-5 (E - Ec)2 F V-2 cm-2], where Ec ) 0.758 V and A ) 0.02 cm2.

ments of the reaction were made at lower temperatures using double potential step chronoamperometery.33 We have measured the rate constant, k25, using both dc and ac cyclic voltammetry. Results of a scan rate study where dc cylic voltammetry conditions for the one-electron oxidation of cis-W(CO)2(dpe)2 in acetone (0.1 M Bu4NPF6) are presented in Figure 8. Note

that at 1.0 V s-1 (Figure 8a) the oxidation is virtually completely irreversible due to the rapid isomerization. At 50 V s-1 (Figure 8d) there is still little definition of the return wave. Moreover, due to the higher scan rate, the non-Faradaic contribution to the current, primarily due to double-layer capacitance, becomes quite large, obscuring the Faradaic component to the total



Figure 10. Comparison of experimental (black) and simulated (red) ac fourth to sixth harmonic voltammograms for the oxidation of cis-[W(CO)2(dpe)2] at a Pt electrode in acetone (0.1 M Bu4NPF6). Scan rates employed: (a1-a3) 0.0745 V s-1 and (b1-b3) 0.298 V s-1. Other parameters used in the simulations are as defined in Figure 9.

Figure 11. Comparison of experimental (black) and simulated (red) ac fourth to seventh harmonic voltammograms (a-d) for the oxidation of cis-[W(CO)2(dpe)2] at a Pt electrode in acetone containing 0.1 M TBAPF6 at 0 °C. Parameters used in the simulations: ∆E ) 100 mV and f ) 9.0 Hz, Estart ) 0.8567 V, Eswitch ) 1.30 V, k° ) 0.10 cm s-1, R ) 0.50, kf ) 70 s-1, T ) 273 K, Dox ) Dred ) 1.4 × 10-5 cm s-2, [R] ) 0.12 mM, ν ) 0.2533 V s-1, E°′ ) 1.028 V, Ru ) 200 Ω, Cdl ) [1.22 × 10-5 F cm-2 + 0.20 × 10-5 (E - Ec) F V-1 cm-2 + 0.22 × 10-5 (E - Ec)2 F V-2 cm-2], where Ec ) 0.758 V and A ) 0.02 cm2.

current, and the oxidation peak maximum shifts to higher potential. Clearly, any kinetic parameters extracted from the dc data would be subject to considerable uncertainty. The isomerization rate constant, k25, is considerably greater than any of those used in the simulations shown in Figure 1. However, trends established above at lower rate constants continue as k increases. This can be seen in Figure S1, which depicts the simulated dc cyclic voltammograms and the fundamental through seventh harmonics of an EC mechanism with homogeneous rate constants ranging from 10 to 1000 s-1. Note that the asymmetry described earlier for lower rate constants becomes even more pronounced at higher reaction rates; other

changes include peak broadening and a shift to less positive potential with high values of k25. Results of ac voltammetric oxidation of cis-W(CO)2(dpe)2 are presented along with optimized simulation data in Figure 9; the homogeneous rate constant, k25, employed in the simulation was 280 s-1. This is considerably higher than the estimate of 45 s-1 made on the basis of low temperature chronoamperometry studies.33 However, based on the sensitivity of the ac technique and the fact that these are direct measurements, as opposed to calculations based on activation parameters obtained at low temperature, as well as to the introduction of iR correction in this work, we expect the higher value to be a considerably

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more accurate estimate. This contention is supported by additional measurements. An ac voltammetry scan rate study (Figure 10) was performed and the results match those obtained by simulations performed using the value of k25 specified above (280 s-1). The kinetic parameters obtained by comparison of experimental data to simulations, therefore, appear to be quite robust. Another advantage of the ac technique is the fact that, unlike the peak potentials of irreversible cyclic voltammetric peaks, those of ac harmonics peaks may provide a direct estimate of the reversible electron-transfer potential.16d Specifically, we find that the location of the minimum current at the midpoint of even-numbered harmonics is to be very close to E°, at least when the electron transfer rate is close to reversible and homogeneous reaction rates are less than about 100 s-1. In the present case, the rate constant is so fast that the minima will be slightly shifted from E°, based on the simulation results. However, we estimate that the reversible potential for the electron transfer described in eq 24 is 1.02 V versus Cc/Cc+. Finally, just as low temperature dc voltammetric studies have become routine for studying reaction mechanisms, ac voltammetry can be performed advantageously under similar conditions. The fourth through seventh ac harmonics obtained for the oxidation of cis-W(CO)2(dpe)2 at 0 °C are presented in Figure 11. These data show sharper peak shapes than those seen at 20 °C, as would be expected with a slower coupled homogeneous step. Comparison of simulation results to experimental data indicate that k25 ) 70 s-1 and E° ) 1.03 V versus Cc/Cc+ under these conditions. Also note that the electrontransfer kinetics at the electrode are also affected by the lower temperature, with simulations indicating that k0 is 0.10 cm s-1, rather than the 0.13 cm s-1 observed at room temperature. Conclusion The case studies described in this paper demonstrate the utility of large-amplitude ac voltammetry toward the study of coupled homogeneous electrode processes. Although the technique does not negate the necessity of performing standard experiments in electrochemical kinetic investigations, such as concentration or scan rate studies, it is clear that there is a wealth of information available in the higher harmonics that is simply lacking in the results of the analogous dc method. These studies provide a more accurate rate constant determination of the cis+ f trans+ isomerization of W(CO)2(dpe)2 than previously available, and considerably deeper insight into the mechanism of the ligandinduced disproportionation of electrogenerated [Cp*Fe(CO)2]2+. The simulation tools we have developed are flexible enough to accommodate a wide range of mechanisms so the examples provided are by no means an exhaustive demonstration of the capabilities of the approach. We are currently exploring strategies to automate the fitting routines to more effectively facilitate analysis of experimental data. Acknowledgment. We thank Dr. Steven Feldberg and Dr. Angel Torriero for many valuable and helpful discussions. The financial support of the Australian Research Council and the award of Monash University postgraduate scholarships (MGS and MPPA) to C. Y. L. are also gratefully acknowledged.

Lee et al. Supporting Information Available: Digital simulations of the EC mechanism employing rate constants ranging from 10 to 1000 s-1. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Maloy, J. T. In Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Marcel Dekker: New York, 1997; Ch 20. (2) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; John Wiley & Sons: New York, 2001. (4) Gosser, D. K., Jr. Cyclic Voltammetry: Simulation and Analysis of Reaction Mechanisms; VCH: New York, 1993. (5) Saveant, J.-M. Elements of Molecular and Biomolecular Electrochemistry; Wiley: New York, 2006; Ch 4. (6) Bond, A. M. Modern Polarographic Methods in Analytical Chemistry; Marcel Dekker: New York, 1980; p 341. (7) McCord, T. G.; Smith, D. E. Anal. Chem. 1968, 40, 1959. (8) McCord, T. G.; Smith, D. E. Anal. Chem. 1969, 41, 116. (9) Bullock, K. R.; Smith, D. E. Anal. Chem. 1974, 46, 1567. (10) Engblom, S. O.; Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 2000, 480, 120. (11) Bond, A. M. J. Electroanal. Chem. 1974, 50, 285. (12) Gavaghan, D. J.; Bond, A. M. J. Electroanal. Chem. 2000, 480, 133. (13) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. Anal. Chem. 2005, 77, 186A–195A. (14) (a) 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. (b) Zhang, J.; Guo, S.-X.; Bond, A. M. Anal. Chem. 2007, 79, 2276. (15) O’Mullane, A. P.; Zhang, J.; Brajter-Toth, A.; Bond, A. M. Anal. Chem. 2008, 80, 4614. (16) (a) Guo, S.; Zhang, J.; Elton, D. M.; Bond, A. M. Anal. Chem. 2004, 76, 166. (b) Fleming, B. D.; Barlow, N. L.; Zhang, J.; Bond, A. M.; Armstrong, F. A. Anal. Chem. 2006, 78, 2948. (c) Lee, C. Y.; Fleming, B. D.; Zhang, J.; Guo, S.-X.; Elton, D. M.; Bond, A. M. Anal. Chim. Acta 2009, 652, 205. (d) Fleming, B. D.; Zhang, J.; Elton, D. M.; Bond, A. M. Anal. Chem. 2007, 79, 6516. (17) Lertanantawong, B.; O’Mullane, A. P.; Zhang, J.; Surareungchai, W.; Somasudrum, M.; Bond, A. M. Anal. Chem. 2008, 80, 6515. (18) Bond, A. M.; Grabaric, B. S.; Jackowski, J. J. Inorg. Chem. 1978, 17, 2153. (19) Bullock, J. P.; Palazotto, M. C.; Mann, K. R. Inorg. Chem. 1991, 30, 1284. (20) Chatt, J.; Watson, H. R. J. Chem. Soc. 1961, 4980. (21) Wimmer, F. L.; Snow, M. R.; Bond, A. M. Inorg. Chem. 1974, 13, 1617. (22) Hogan, C. F.; Bond, A. M.; Neufeld, N. K.; Connelly, N. G.; Llamas-Rey, E. J. Phys. Chem. A 2003, 107, 1274. (23) Rudolph, M. In Physical Electrochemistry: Principles, Methods, and Applications; Rubinstein, I., Ed.; Marcel Dekker: New York, 1995; Ch 3. (24) Mocak, J.; Feldberg, S. W. J. Electroanal. Chem. 1994, 378, 31. (25) Feldberg, S. W. J. Electroanal. Chem. 1981, 127, 1. (26) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (27) Legzdins, P.; Wassink, B. Organometallics 1984, 3, 1811. (28) Torriero, A. A. J.; Shiddiky, M. J. A.; Bullock, J. P.; Boas, J. F.; MacFarlane, D. R.; Bond, A. M. Inorg. Chem. 2010, 49, 2502. (29) Geiger, W. E. In Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Marcel Dekker: New York, 1996; pp 706-708. (30) Bond, A. M.; Colton, R. Coord. Chem. ReV. 1997, 166, 161. (31) Mingos, D. M. P. J. Organomet. Chem. 1979, 179, C29. (32) Bond, A. M.; Colton, R.; Jackowski, J. J. Inorg. Chem. 1975, 17, 274. (33) Bond, A. M.; Grabaric, B. S.; Jackowski, J. J. Inorg. Chem. 1978, 17, 2153.

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