Using the Pulsed Nature of Staircase Cyclic Voltammetry To

Staircase cyclic voltammetry (SCV) is the digital counter- part of analog cyclic voltammetry (CV). However, when the redox-active species is adsorbed ...
0 downloads 0 Views 148KB Size
Download PDF
Anal. Chem. 1999, 71, 174-182

Using the Pulsed Nature of Staircase Cyclic Voltammetry To Determine Interfacial Electron-Transfer Rates of Adsorbed Species Hendrik A. Heering,† Madhu S. Mondal,‡ and Fraser A. Armstrong*

Department of Chemistry, Inorganic Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QR, England

Staircase cyclic voltammetry (SCV) is the digital counterpart of analog cyclic voltammetry (CV). However, when the redox-active species is adsorbed at the electrode surface, the voltammetric peak shapes (width, height, area, and to a lesser extent the reduction potentials) obtained with SCV can be very different from those of CV, even when small potential steps are used. Like analog CV, SCV provides a straightforward method to estimate and subtract the background and charging currents from the desired Faradaic current, while the pulsed nature of SCV provides the time-dependent decay of the Faradaic current, similar to chronoamperometry. Thus, electrontransfer rate constants can be directly measured as a function of applied potential, and no a priori model is required. An SCV equivalent of the square wave “quasireversible maximum” of observed peak height versus sampling moment and step size is predicted. The SCV response can only become independent of potential step size and similar to CV at high scan rates (ν > 10 k0Estep), if the current is sampled at half the step interval. The applicability of SCV to studies of redox centers in proteins is illustrated for the two-electron oxidation/reduction of yeast cytochrome c peroxidase, adsorbed at a pyrolytic graphite edge-plane electrode. Interfacial electron-transfer rates of a species adsorbed at the surface of a solid electrode can be determined by applying a potential step and following the decay of the current (chronoamperometry) or accumulation of charge (chronocoulometry) with time. The advantage of chronomethods is that no a priori model for the potential dependence of the electron-transfer rate is required. However, the transients will always contain interfacial charging currents. In many cases, notably when the interfacial charging kinetics are similar to the electron-transfer kinetics or when the interfacial charging current is very high compared to the Faradaic current, the correction for non-Faradaic currents is not at all a trivial problem.1,2 One of the usual problems is that * Corresponding author: (e-mail) [email protected]; (fax) +44-1865-272690. † Current address: Dipartimento di Chimica, Universita ` di Firenze, Via G. Capponi 9, 50121 Firenze, Italy. ‡ Current address: Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, 240 Longwood Avenue, Boston, MA 02115. (1) Lai Miaw, L.-H. L.; Perone, S. P., Anal. Chem. 1979, 51, 1645-1650.

174 Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

the capacitance of the interface changes when a species is absorbed and may further differ between oxidation states,3 thus frustrating the simple subtraction of a separately measured background. Alternatively, electron-transfer kinetics of adsorbed reactants can be determined by analog cyclic voltammetry (i.e., a smooth sawtooth modulation of the applied potential). The advantage is that estimation of the non-Faradaic background is relatively easy, even when the background is very high, because the amount of electroactive reactant at the surface is finite. The scan rate dependences of the shapes and positions of the resulting peaks can be analyzed to determine the electron-transfer characteristics. However, this method does not yield the electron-transfer rates directly but relies on simulation procedures to model the peak shapes and positions as a function of scan rate. Hence, a detailed model which includes the potential dependence of the electrontransfer rates (e.g., Butler-Volmer or Marcus theory) and possible coupled chemical processes has to be provided a priori.3-11 Moreover, it may prove desirable to obtain apparent electron-transfer rates at low scan rates, where chemical processes equilibrate during the potential cycling. Nowadays, cyclic voltammetry (CV) is often performed in digital modesthe smooth voltage ramp being replaced by a series of small steps (typically 0.5-5 mV), hence the name staircase cyclic voltammetry (SCV). Figure 1 shows how the potential is stepped with time for a single direction, along with the parameters that are normally varied (see below). The current-time plot yields a series of chonoamperometrical traces for consecutive potential increments. The voltammogram is derived from this by sampling the current at a fixed time after each potential step. Several papers have been published dealing with the theoretical shapes of SCV on reactants contained in solution and diffusing to and from the (2) Åberg, S., J. Electroanal. Chem. 1996, 419, 99-103. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications: Wiley: New York, 1980. (4) Laviron, E. J. Electroanal. Chem. 1979, 101, 19-28. (5) Chidsey, C. E. D. Science 1991, 251, 919-922. (6) Nahir, T. M.; Clark, R. A.; Bowden, E. F. Anal. Chem. 1994, 66, 25952598. (7) Weber, K.; Creager, S. E. Anal. Chem. 1994, 66, 3164-3172. (8) Tender, L.; Carter, M. T.; Murray, R. W. Anal. Chem. 1994, 66, 31733181. (9) Forster, R. J.; O’Kelly, J. P. J. Phys. Chem. 1996, 100, 3695-3704. (10) Finklea, H. O.; Liu, L.; Ravenscroft, M. S.; Punturi, S. J. Phys. Chem. 1996, 100, 18852-18858. (11) Hirst, J.; Armstrong, F. A. Anal. Chem. 1998, 70, 5062-5071. 10.1021/ac980844p CCC: $18.00

© 1998 American Chemical Society Published on Web 11/19/1998

Figure 1. The staircase wave form, indicating the variables Estep, tstep () Estep/ν), and the definition of τ, the relative sampling time.

electrode surface.12-17 From these papers it is clear that in general SCV is not exactly equal to its analog counterpart. When measuring diffusing reactants, SCV will only yield Faradaic currents approximately equal to those measured by analog CV when the current is sampled either at 1/4 or at 1/2 of the interval between the steps () τ, the relative sampling time) depending on the reaction mechanism. Seralathan et al.15 reported that a value of 1/ is appropriate for mechanisms that can be described by an 4 Abel integral equation. Falling into this category are mainly uncomplicated, fully reversible electron-transfer reactions with semi-infinite linear or spherical diffusion. However, most systems are less ideal (e.g., quasi-reversible and irreversible processes and most mechanisms involving coupled reactions) and require sampling at 1/2 the step interval. An advantage of SCV over analog CV when species are studied in solution is that the background current can be much lower: the interfacial charging processes of (metal) electrodes are often much faster than the diffusion-limited Faradaic processes and are almost equilibrated by the time the current is sampled.14 However, when a redox-active species is adsorbed on the electrode surface, it represents a “pseudocapacitance”.18 Depending on the electrontransfer kinetics, this means that the SCV response of an adsorbed couple depends strongly on scan rate, step size, and current sampling moment. The Faradaic current can be either enhanced or attenuated relative to the current measured with analog CV, and it has been reported that in some cases the response can be totally invisible.19 This implies that electroactive surface coverages apparent from SCV can differ greatly from the true values. On the other hand, the pulsed nature of SCV, in combination with the straightforward baseline correction it has in common with analog CV, makes SCV a powerful alternative to chronoamperometry for determining electron-transfer rates of adsorbed reactants. These advantages are not unique to SCV but are shared by most modern pulse voltammetry methods.20 In particular, square (12) Ferrier, D. R.; Schroeder, R. R. J. Electroanal. Chem. 1973, 45, 343-359. (13) Ferrier, D. R.; Chidester, D. H.; Schroeder, R. R. J. Electroanal. Chem. 1973, 45, 361-376. (14) Ryan, M. D. J. Electroanal. Chem. 1977, 79, 105-119. (15) Seralathan, M.; Osteryoung, R. A.; Osteryoung, J. G. J. Electroanal. Chem. 1987, 222, 69-100. (16) Donten, M.; Stojek, Z. J. Electroanal. Chem. 1996, 405, 183-188 (17) Kalapathy, U.; Tallman, D. E. Anal. Chem. 1992, 64, 2693-2700. (18) Tilak, B. V.; Chen, C.-P.; Rangarajan, S. K. J. Electroanal. Chem. 1992, 324, 405-414. (19) Stojek, Z.; Osteryoung, J. Anal. Chem. 1991, 63, 839-841. (20) Osteryoung, J. Acc. Chem. Res. 1993, 26, 77-83.

wave voltammetry (SWV) is becoming increasingly popular for determining electron-transfer kinetics of adsorbed reactants. The theory of SWV on quasi-reversible redox reactions of adsorbed reactants is well developed and experimentally verified.21-27 It has been shown that the current response exhibits a “quasi-reversible maximum” when the frequency matches the electron-transfer rate. The reason for the disappearance of the response at short pulse times is that when the reaction is very rapid, redox equilibrium is restored before the current is sampled. As mentioned above, a similar phenomenon can be expected for other pulsed methods such as differential pulse voltammetry (DPV). Brown and Anson28 demonstrated this for DPV on adsorbed reactants by decreasing electron-transfer rates through the addition of artificial uncompensated resistance. The major advantage of SCV over DPV or SWV is that, despite its stepped nature, it is very similar to analog CV. In particular, the cyclic nature and relatively uncomplicated potential/time function offers the possibility to determine the reversibility of the redox reaction and to detect potential- and timedependent changes of the reactants (e.g., square schemes) in the same way as with analog CV. However, the theoretical basis for the SCV response when reactant and product are adsorbed is poorly developed. In this paper, we provide this theoretical basis, predicting that SCV provides two ways to determine interfacial electron-transfer rates: one based on its similarity to chronoamperometry due to the pulsed nature of SCV and the other based on its similarity to analog CV. The applicability of SCV to determine (apparent) electron-transfer rate constants and their potential dependence will be illustrated for the reversible twoelectron oxidation of the resting Fe(III) state of yeast cytochrome c peroxidase adsorbed on a pyrolytic graphite edge (PGE) electrode. This system provides an interesting example of how the relatively new technique of protein film voltammetry is used to probe complex biological redox chemistry, in this case enabling access to highly oxidizing, catalytic intermediates. THEORY The solution for staircase cyclic voltammetry of adsorbed redox molecules presented below is based partly on the formulism for square wave voltammetry presented by Reeves et al.24 For the strongly adsorbed couple kf

Oxads + ne- {\ } Redads k b

(1)

the rate of the reaction is given by

u)-

∂ΓOx ) kfΓOx - kbΓRed ) (kf + kb)ΓOx - kbΓtotal ∂t

(2)

where ΓOx and ΓRed are the surface concentrations of the oxidized (21) Lovric´, M.; Branica, M. J. Electroanal. Chem. 1987, 226, 239-251. (22) Lovric´, M.; Komorsky-Lovric´, Sˇ . J. Electroanal. Chem. 1988, 248, 239253. (23) Lovric´, M.; Komorsky-Lovric´, Sˇ .; Bond, A. M. J. Electroanal. Chem. 1991, 319, 1-18. (24) Reeves, J. H.; Song, S.; Bowden, E. F. Anal. Chem. 1993, 65, 683-688. (25) O’Dea, J. J.; Osteryoung, J. G. Anal. Chem. 1993, 65, 3090-3097. (26) Komorsky-Lovric´, Sˇ .; Lovric´, M. J. Electroanal. Chem. 1995, 384, 115122. (27) Komorsky-Lovric´, Sˇ .; Lovric´, M. Electrochim. Acta 1995, 40, 1781-1784. (28) Brown, A. P.; Anson, F. C. Anal. Chem. 1977, 49, 1589-1595.

Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

175

and reduced species and Γtotal is the constant sum of ΓOx and ΓRed. At constant potential (thus constant kf and kb), the solution of this equation is given by

ΓOx )

kbΓtotal + c exp{-(kf + kb)t} kf + kb

(3)

of the complete staircase voltammogram is obtained, expressing the current as a function of potential at a chosen relative sampling time τ.30 It is convenient to express the SCV equations in terms of dimensionless parameters: dimensionless relative potentials

and thus

u)-

∂ΓOx ) c(kf + kb) exp{-(kf + kb)t} ∂t

(4)

where the constant c depends on the boundary conditions for ΓOx. In the interval between two potential steps of height Estep, from t ) t0 to t ) t0 + tstep (where tstep ) Estep/ν, with ν being the potential scan rate), the time can be expressed as

t ) t0 + τtstep

(0 e τ e 1)

P ) nF(E - E0)/RT

(10a)

Pstep ) nFEstep/RT

(10b)

and

fractional surface concentration

ΦOx ) ΓOx/Γtotal

(11)

(5) dimensionless rate constants

where τ is the relative current sampling time.29 With a given surface concentration ΓOx at the beginning of the step interval and replacing t by τ, the constant c can be eliminated and the full solution becomes

ΓOx(τ) )

kbΓtotal + u(τ) kf + kb

(7)

(12)

and dimensionless reaction rate

1 ∂ΦOx RT )U)u nFνΓtotal Pstep ∂τ

(6)

with

u(τ) ) u(τ ) 0) exp{-(kf + kb)τtstep}

Λi ) kiRT/nFν

(13)

where E0 is the standard potential of the reaction in eq 1, R is the molar gas constant, and T the absolute temperature. This yields

ΦOx(τ) ) Φeq Ox + U(τ)/(Λf + Λb)

(14)

and

u(τ ) 0) ) (kf + kb)ΓOx(τ ) 0) - kbΓtotal

(8)

Assuming that the system is equilibrated at the starting potential, the Nernstian equilibrium value of ΓOx at this potential can be used as the boundary condition for the first step. Using an interfacial electron-transfer model which describes the dependence of kf and kb on applied potential (e.g., Butler-Volmer or Marcus theory), the rate at the beginning of the step interval u(τ ) 0) is calculated, and from this is determined the rate at any given τ. The current at τ then follows directly from this rate:

i(τ) ) -nFAu(τ)

(9)

where F is the Faraday constant and A is the electrode area. Finally, ΓOx at the end of the step interval is calculated from the rate u at τ ) 1 and used as the initial value for the next interval (an instantaneous change of the potential with Estep, i.e., a perfect step, is assumed). Continuing in this way, the analytical solution (29) The relative current sampling time in staircase cyclic voltammetry is usually represented by the symbol R or sometimes β ) 1 - R. Unfortunately, these symbols are also commonly used for the transfer coefficient in ButlerVolmer theory (eq 18). To avoid confusion, the SCV sampling time will be represented by the symbol τ in this paper, while R is reserved for the ButlerVolmer transfer coefficient.

176

Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

and

U(τ) ) (Λf + Λb)(ΦOx(τ ) 0) - Φeq Ox) × exp{-(Λf + Λb)Pstepτ} (15) where

Φeq Ox )

Λb 1 ≡ Λf + Λb 1 + exp(-P)

(16)

is the fractional surface concentration of the oxidized species when equilibrated at the applied potential. The current, relative to the peak height predicted for a totally reversible analog CV, is then given by

I(τ) ) i(τ)4RT/n2F 2AΓν ) -4U(τ)

(17)

This shows that a normalized voltammogram (normalized current versus dimensionless relative potential), starting from equilibrium, (30) Note that the use of this method to predict the current as a function of applied potential at a given sampling moment is not restricted to staircase CV but can be applied to any sequence of potential steps with equal intervals.

is fully defined by the two dimensionless SCV parameters τ and Pstep and by the sum of dimensionless rate constants Λf + Λb. The latter sum is determined by the dependence of the electron-transfer rate constants on applied potential, and the Butler-Volmer equation provides a semiempirical exponential relationship:3 for reduction

{

}

{

nRF nR (E - E0) ) k0 exp -R P RT n

kf ) k0 exp -R

}

(18a)

and for oxidation

{

}

{

nRF nR (E - E0) ) k0 exp (1 - R) P RT n

kb ) k0 exp (1 - R)

}

(18b) The parameter R is the transfer coefficient,29 nR is the number of electrons involved in the rate-determining step, and k0 is the standard rate constant: kf(E ) E0) ) kb(E ) E0) ) k0. The sum Λf + Λb at any potential is proportional to Λ0 ) k0RT/nFν. PREDICTIONS Figures 2-5 illustrate the forms of the staircase voltammograms predicted by the theory. A series of simulations at different Λ0, Pstep, and τ are shown, using Butler-Volmer theory (with R ) 0.5 and nR ) n) to calculate the potential dependence of the interfacial electron-transfer rate constants. The predicted peak characteristics (height, area, width, position) of a single oxidative sweep are plotted in Figures 2A, 3A, 4A, and 5, as functions of Λ0. Note that the two values of Pstep are extreme cases, chosen for clarity: Pstep ) 0.005 and 1.0 will give Estep ) 0.13 and 25 mV, respectively at 295 K for n ) 1. More realistic step values will give results lying within the plotted lines. For Pstep f 0, the large differences occur at Λ0 f ∞; thus the staircase CV peak characteristics will become equal to those of CV peaks, plotted in bold. Taken together, the plots show that the SCV peak characteristics are similar to analog CV only at low electrontransfer rates and either with small step sizes or when τ ≈ 0.5. In general, dramatic differences between analog CV and digital SCV are predicted, including the large range where the electrontransfer rates are high relative to the scan rate, and no peak is observed at all. As shown in Figures 2B, 3B, and 4B, plotting the peak height, area, and width as functions of the product Λ0Pstep ) k0Estep/ν removes the large positional changes due to the step size and so highlights the relative differences. For low values of τ, a clear maximum is predicted for the peak height and area. At τ ) 0.1, the peak currents are predicted to be 3.6 times larger than the corresponding analog CV peaks, and the maximum height will increase further exponentially with decreasing τ (although τ < 0.1 may not be feasible due to instrumental limitations). The maximum current is predicted to occur when the product Λ0Pstepτ ) k0t (i.e., the exponential term in eqs 7 and 15) is equal to 0.5. The maximum value thus indicates the conditions where the sampling time matches the standard electron-transfer rate and is the staircase equivalent of the square wave “quasi-reversible maximum”.21-27 For τ g 0.5, no maximum

Figure 2. SCV peak heights relative to the reversible analog CV peak height n2F2AΓν/4RT, predicted when the electron-transfer rate constants conform to the Butler-Volmer model with R ) 0.5 and nR ) n. (A) Ipeak as a function of the dimensionless standard rate constant for electron transfer Λ0 ) k0RT/nFν. The bold line is the peak height predicted for analog CV and for Pstep f 0. Conditions: Pstep ) 0.005 and 1.0 (i.e., the extreme cases of 0.13 and 25 mV at 295 K for n ) 1) and τ ) 0.1, 0.2, 0.5, and 1.0. (B) Ipeak as a function of Λ0Pstep ) k0Estep/ν for the same step sizes as in panel A (traces for Pstep ) 1.0 are in gray) and τ ) 0.1, 0.15, 0.2, 0.30, 0.5, 0.70, and 1.0.

is predicted, and the peak height decreases sigmoidally with increasing log(k0Estep/ν) (apart from the coincidence at certain values of Pstep for which the sigmoidal occurs at Λ0 values where the transition between reversible and irreversible peaks occur). For very large k0Estep/ν, i.e., at low scan rate or high electrontransfer rate, the response disappears completely, as expected when the current is measured only after equilibrium is reestablished. Figure 3 shows that the changes in peak area are similar to those of the peak height, but the maximum occurs at slightly lower values of Λ0. The difference implies that the peak shapes also depend on Pstep and τ. The peak shape can be conveniently summarized by the width at half-height, and Figure 4 shows that considerable changes are predicted as the staircase parameters are varied. At low k0Estep/ν, the predicted trends are independent of τ and depend on the potential step size as a result of the altered range of k0/ν. However, at high k0Estep/ν, the width is independent of step size and fully determined by the sampling moment τ. The peak is predicted to be considerably sharper as compared to analog CV peaks. This is a consequence of the exponentially Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

177

Figure 3. Normalized SCV peak areas Q/nFAΓ, predicted when the electron-transfer rate constants conform to the Butler-Volmer model with R ) 0.5 and nR ) n. (A) Area as a function of the dimensionless standard rate constant for electron transfer Λ0 ) k0RT/ nFν. The bold line is the peak area predicted for analog CV (≡ 1) and for Pstep f 0. (B) Area as a function of Λ0Pstep ) k0Estep/ν. Conditions are as given in Figure 2.

increasing sum of electron-transfer rate constants with overpotential and, thus, a more rapid decay to zero current in the wings of the peak. In principle, this can be exploited to enhance resolution of overlapping peaks; however, its practical use may be limited since the peak height rapidly decreases with increasing k0Estep/ν. With small potential steps and at k0Estep/ν < 0.01, the shape of a digitally measured peak approaches that of an analog peak and will no longer be influenced by the sampling moment. This is to be expected because at very long half-life times of the exponential decay relative to the step time Estep/ν, the current becomes constant and thus independent of τ. Under these conditions, the peak area also becomes equal to nFAΓtotal and thus enables calculation of the surface coverage. Figure 5 shows that, in addition to the peak shape and area, the peak potential is also predicted to become equal to those expected for analog CV when Pstep is small. In fact, all traces except those for the high Pstep and τ * 0.5 coincide with the bold line for analog CV. The equivalence of SCV and analog CV that is predicted with small potential steps and high scan rates enables the use of SCV to determine electrontransfer characteristics from the peak shapes and potentials in 178 Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

Figure 4. Dimensionless SCV peak widths at half-height (δnF/RT), predicted when the electron-transfer rate constants conform to the Butler-Volmer model with R ) 0.5 and nR ) n. (A) Width as a function of the dimensionless standard rate constant for electron transfer Λ0 ) k0RT/nFν. The bold line is the peak width predicted for analog CV and for Pstep f 0. (B) Width as a function of Λ0Pstep ) k0Estep/ν. Conditions are as given in Figure 2. Note that the traces could not be completed at high Λ0 due to peak heights below the precision of the calculations (10-39).

the conventional manner. However, when the potential steps are too large, the peak shifts markedly with τ, changes shape and height under all conditions, and hence would yield incorrect electron-transfer rates if interpreted in the usual way for analog CV. Figures 2-5 show clearly that the effect of increasing step size on the shape, area, and potential of the peak at high scan rates is smallest at values of τ around 0.5. Consequently, under experimental conditions where a step size below 1 mV may be impractical due to storage space or computer speed, use of τ ≈ 0.5 will minimize the staircase “errors” just as for most diffusioncontrolled systems. However, for adsorbed species, this “remedy” is limited to scan rates ν > 10k0Estep.31 In addition to predicting the differences and similarities between CV and SCV, the theory also suggests that SCV can provide a three-dimensional data set (i-E-t) that can be applied to elucidate electrochemical reactions.32 Recording the same film (31) A value of 0.5 works for small steps. For very large steps, SCV will approach CV at values of τ slightly lower than 0.5 (e.g., 0.45 for Pstep ) 1).

Figure 5. Dimensionless relative SCV peak potentials Ppeak ) nF(Epeak - E0)/RT, predicted when the electron-transfer rate constants conform to the Butler-Volmer model with R ) 0.5 and nR ) n. The potentials are plotted as a function of the dimensionless standard rate constant for electron transfer Λ0 ) k0RT/nFν. The bold line is the peak potential predicted for analog CV and for Pstep f 0. Conditions are as given for Figure 2A, but note that for τ ) 0.5 at Pstep ) 1.0, and for all τ at Pstep ) 0.005, the traces are hidden by the analog CV trace in bold.

of molecules at given scan rate and Estep, but different values of τ, a logarithmic plot of the current (at fixed potential and corrected for baseline) versus τtstep yields a line with a slope of -(kf + kb) at that potential:

ln|i| ) ln{nFAu(τ ) 0)} - (kf + kb)τtstep

(19)

For the normalized current, this yields

ln|I| ) ln{4(Λf + Λb)(ΦOx(τ ) 0) - Φeq Ox)} (Λf + Λb)τPstep (20) When the current at zero overpotential is used (approximately equal to the peak current under conditions where the effect of τ is large and Estep is small), the slope is -2k0. Log plots for different Estep or scan rates will result in series of parallel lines because the initial surface concentration for each potential step, and thus the offset of the current, depends on the height and frequency of all previous steps. This is illustrated in Figure 6 in normalized form: the plot of ln|I| at P ) 0 versus τPstep ) nFν(t - t0)/RT for different Pstep results in a series of parallel lines with slopes -2Λ0. This method is independent of the particular model used to describe the rate constants as a function of potential. The important implication is that electron-transfer rate constants can be obtained directly from the measured SCV current, instead of indirectly by constructing models to simulate the voltammograms at different scan rates. Although it would be sensible, theoretically, to plot the peak height and width as functions of Λ0Pstepτ, this does not yield the (32) The general advantage of constructing three-dimensional i-E-t profiles in elucidating electrochemical reactions is described by: Papadopoulos, N.; Hasiotis, C.; Kokkinidis, G.; Papanastasiou, G. J. Electroanal. Chem. 1991, 308, 83-96.

Figure 6. Logarithmic plot of the normalized current at P ) 0 (i.e., at E ) E0), as a function of the normalized current sampling time τPstep ) nFν(t - t0)/RT, for Λ0 ) 10, and Pstep ) 0.05, 0.15, and 0.25. The symbols are values derived from simulated voltammograms at τ ) 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. The lines show the predicted and extrapolated trends.

most convenient plots for the experimentalist who wishes to determine k0 or minimize peak widths for enhanced resolution. As a guide, the plots shown in Figures 2B, 3B, and 4B are more useful: for a given τ, the maximum peak heights occur at constant Λ0Pstep ) k0Estep/ν ) k0tstep. This means that, for any given k0, the optimum ratio Estep/ν can be determined by maximizing the change of the voltammetric peak height with τ. This ratio, predicted to be approximately 5/k0 for τ g 0.1, will give the maximum kinetic sensitivity and will also yield sharp peaks, especially for τ g 0.5. Although a higher ratio Estep/ν or a higher τ will further decrease the width of the peak, the current will drop dramatically, which will naturally decrease the sensitivity of the measurement. A step size of 3-5 mV will usually give a good compromise between voltammetric and kinetic resolution, but when a larger Estep is required (e.g., more than 5 mV), the resolution can be enhanced by overlaying several scans with slightly different initial potentials (as has, in fact, been done to derive the Pstep ) 1.0 traces in Figures 2-5 with sufficient accuracy). The optimum scan rate can be much lower than that used to determine electron-transfer rates from the shape and potential of the peaks as a function of scan rate. Electrochemical reversibility, and thus a small separation between oxidative and reductive peaks, can therefore be maintained, especially when Estep is small. Over the potential range where the peak current is sufficiently above the baseline to be measured (approximately 200 mV for a oneelectron peak, depending on the signal-to-noise ratio), the complete profile of kf + kb can be obtained from a sample of voltammograms recorded at different τ. When both the scan rate and Estep are increased proportionally, the effect of changing τ will remain, but the oxidation peak will shift to positive potential and the reduction peak will shift in a negative direction relative to E0. This enables extension of the potential range beyond the boundaries of the peak at low scan rates. In addition, a higher scan rate decreases the overall time scale of the experiment: in the case of unstable oxidized or reduced species, this may “outrun” Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

179

coupled reactions and thus measure isolated redox reactions of intermediates or select specific populations of reactant(s) with different electron-transfer rates. The latter will give rise to multiphasic log plots, and different subpopulations can be selected by adjusting tstep ) Estep/ν.33 EXPERIMENTAL SECTION A three-electrode electrochemical cell was used as described previously.34,35 The sample compartment was thermostated and the entire cell was housed in a Faraday cage. The rotating disk PGE working electrode (geometric area 0.03 cm2) was used in conjunction with an EG&G M636 electrode rotator. A platinum wire was used as counter electrode, and a saturated calomel electrode (SCE), held in a Luggin sidearm containing 0.1 M NaCl, was used as reference. Voltammograms were recorded using an Autolab electrochemical analyzer (Eco Chemie, Utrecht, The Netherlands) controlled by GPES 3.3 software (allowing values of τ down to 0.1) and equipped with an electrochemical detection (ECD) module for increased sensitivity. All potentials are reported with reference to the standard hydrogen electrode (SHE), based on a potential of 242 mV for SCE at 20 °C.3 The PGE electrode was polished with an aqueous aluminum oxide slurry (Buehler, 1 µm) and sonicated thoroughly. Bakers’ yeast cytochrome c peroxidase (CcP) was purified as described previously.36 Protein films were obtained by introducing a freshly polished electrode to a 0.13 µM solution of CcP in 20 mM sodium acetate buffer at pH 5.45 and 0 °C and rotating the electrode. Measurements were performed without noise filtering. Instead, each scan was repeated four times and the averaged voltammograms were used for analysis. Baseline corrections were carried out using an in-house routine which involved constructing a smooth cubic spline background interpolation, based on the parts of the voltammograms where the Faradaic current is negligible. To facilitate measurement of low Faradaic currents, the voltammograms were smoothed using an in-house fast-Fourier transform routine. The resulting peaks were always verified to have the same shape as the original data. RESULTS AND DISCUSSION Our main interest is to study reactions of redox-active centers in proteins. Here, a minuscule sample (usually between 3 and 15 pmol/cm2) can be studied with high sensitivity and optimal control. Direct voltammetric observation of the catalytic and nonturnover electron-transfer reactions provides opportunities to (33) Other interfacial processes, such as ion migration, may accompany electron transfer (Biniak, S.; Dzielen´dziak, B.; Siedlewski, J. Carbon 1995, 33, 12551263). These processes become more important at higher current densities. One of the consequences may be that the current does not decrease purely exponentially with time, so that current transients will persist beyond the predicted limits. Addition of resistance in the circuit (e.g., in the form of an analog RC noise filter or uncompensated resistance in the electrolyte solution) will also disturb the pure SCV response by flattening the exponential decay: It is reported that filtering may render the SCV response equivalent to analog CV (He, P. Anal. Chem. 1995, 67, 986-992). The absence of supporting electrolyte also makes the SCV peaks less sensitive to sampling time.16 (34) Mondal, M. S.; Fuller, H. A.; Armstrong, F. A. J. Am. Chem. Soc. 1996, 118, 263-264. (35) Mondal, M. S.; Goodin, D. B.; Armstrong, F. A. J. Am. Chem. Soc. 1998, 120, 6270-6276. (36) English, A. M.; Laberge, M.; Walsh, M. Inorg. Chim. Acta 1986, 123, 113116.

180

Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

investigate the mechanism and energetics associated with interfacial electron transfer, intramolecular electron relays, coupled reactions that may be induced by or “gate” the primary electronexchange processes, and potential-dependent switches that modulate the catalytic activity. Reactive states and catalytic intermediates may also be detected.11,34,35,37-40 As electrochemical models, redox proteins may approach the status of ideal systems because the protein matrix provides a uniform and constant local environment for all redox centers by shielding them from direct interaction with the electrode surface and from lateral interactions with each other. The application of SCV to measure apparent electron-transfer rate constants as a function of potential is illustrated for yeast CcP. Although not the simplest of systems, this is a important and much studied enzyme and we have collected a large voltammetric database. CcP catalyses the two-electron reduction of H2O2 to water. The mechanism is believed to involve reaction of peroxide with the Fe(III) state (resting CcP) to produce a two-electron oxidized Fe(IV)dO/Trp•+ state known as compound I.34,35,41 The resting enzyme is regenerated by one-electron transfers from two Fe(II) cytochrome c molecules. Cytochrome c peroxidase adsorbs spontaneously at a PGE electrode from dilute solutions at low ionic strength (20 mM phosphate).34,35 On the electrode, the enzyme displays a single signal consisting of sharp and symmetric oxidation and reduction peaks (half-height widths 10 k0Estep), provided that the potential steps are small or that τ ≈ 0.5, the Faradaic SCV response is predicted to become equal to that of analog CV. This implies that SCV also offers the full analytical power of its analog counterpart, with the possibility to obtain surface coverage, to observe intermediate species, and to “outrun” reactions that may be induced by the primary electron transfer. The kinetic constants obtained for a film of cytochrome c peroxidase are in good agreement with previous more conventional measurements. Finally, the use of SCV can provide enhanced resolution for the detection of redox centers in adsorbed proteins. This may be useful either if several redox centers appear at similar potential or if the protein electroactive coverage is low. LIST OF SYMBOLS

R

molar gas constant

Red

reduced species

t

time

t0

time at the start of an interval between two potential steps

tstep

duration of the interval between two potential steps

T

absolute temperature

u

rate of the reaction in direction of reduction

U

dimensionless rate of the reaction in direction of reduction

ν

potential scan rate

R

transfer coefficient in Butler-Volmer theory

ΦOx

fractional surface concentration of the oxidized species

Φeq Ox

fractional surface concentration of the oxidized species when equilibrated at the applied potential

ΓOx

surface concentrations of the oxidized species

ΓRed

surface concentrations of the reduced species

A

electrode area

Γtotal

total surface concentration (ΓOx + ΓRed)

c

arbitrary constant

Λ0

dimensionless standard electron-transfer rate constant

E

applied potential

E0

Λf

standard reduction potential

dimensionless electron-transfer rate constant for reduction

Estep

potential step height

Λb

F

Faraday constant

dimensionless electron-transfer rate constant for oxidation

i

current

τ

relative current sampling time

I

normalized current (current relative to the reversible analog peak height)

k0

standard electron-transfer rate constant

kf

electron-transfer rate constant for reduction

kb

electron-transfer rate constant for oxidation

n

total number of electrons involved in the redox reaction

nR

number of electrons involved in the rate-determining step

Ox

oxidized species

P

dimensionless relative potential

Received for review July 30, 1998. Accepted October 12, 1998.

Pstep

dimensionless potential step height

AC980844P

182

Analytical Chemistry, Vol. 71, No. 1, January 1, 1999

ACKNOWLEDGMENT This work was supported by the Wellcome Trust (Grant 042109) and by the UK Engineering and Physical Sciences Research Council (Grant GR/J84809). We thank Judy Hirst for useful discussions, and Harsh Pershad for proof reading of the manuscript.