Cyclic Square Wave Voltammetry of Single and Consecutive

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Anal. Chem. 2009, 81, 9041–9047

Cyclic Square Wave Voltammetry of Single and Consecutive Reversible Electron Transfer Reactions John C. Helfrick, Jr. and Lawrence A. Bottomley* School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 In this report, theory for cyclic square wave voltammetry for single and consecutive reversible electron transfer reactions is presented and experimentally verified. The impact of empirical parameters on the shape of the current-voltage curve is examined. Diagnostic criteria enabling the use of this waveform as a tool for mechanistic analysis of electrode reaction processes are also presented. Since this waveform effectively discriminates against capacitance currents, cyclic square wave voltammetry will enable acquisition of mechanistic information at analyte concentration levels lower than that possible with cyclic voltammetry. Cyclic voltammetry has been the electrochemical method of choice for the evaluation of the mechanism of electron transfer for more than four decades.1,2 Advantages of this method include the wide availability of low cost instrumentation and extensive theory available to guide the experimentalist in the interpretation of empirical results. These advantages have contributed to its widespread popularity especially among those who are not specialists in electrochemistry. Numerous applications of this method have been published. However, this method has two shortcomings. First, the determination of the mechanism of the second of two or more closely spaced charge transfer reactions (along the potential axis) is often difficult. This poor resolution is a result of the current-voltage peak asymmetry. Second, the concentration of the analyte must be at least 10 µM for the attainment of reliable mechanistic information (except when the analyte is confined to the electrode surface). This lower concentration limit is not a reflection of the poor sensitivity of the method but rather the result of the high capacitance current resulting from sweeping the potential linearly with time. Square wave voltammetry is an important electroanalytical method. In comparison to both linear sweep and cyclic voltammetry, square wave voltammetry has a much broader dynamic range and lower limit of detection because of its efficient discrimination of capacitance current. Analytical determinations can be made at concentrations as low as 10 nM. The application of square wave to problems in analysis has been critically * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Adams, R. N. Electrochemistry at Solid Electrodes; Marcel Dekker: New York, 1969. (2) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2000. 10.1021/ac9016874 CCC: $40.75  2009 American Chemical Society Published on Web 10/02/2009

reviewed.3,4 Theory to guide in the evaluation of charge transfer mechanisms has been developed by O’Dea, Osteryoung, and Osteryoung.5-8 Their work details the effects of first-order kinetic complications and nonplanar or restricted diffusion on the square wave voltammograms. The applications of this theory for mechanistic analysis have been limited. This may, in part, be due to bias on the part of nonspecialists against techniques that utilize unidirectional potential sweeps for mechanistic analysis. This bias is based on the presumption that the shape of the current-voltage curves is primarily determined by the electrode reactant. In this work, we explore a composite waveform for the evaluation and identification of electron transfer mechanisms, i.e., cyclic square wave voltammetry.9,10 This waveform utilizes a square wave which steps through the region of the formal potential of the electroactive species under study in two directions. Although there is strong literature precedent for cyclic pulse techniques,11-17 only a few reports on CSWV have appeared.9,10,16,18-28 We believe (3) Hawley, M. D. In Laboratory Techniques in Electroanalytical Chemistry; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1984; pp Ch. 17 and references therein. (4) Osteryoung, J. G.; Osteryoung, R. A. Anal. Chem. 1985, 57, 101A–102A, 105A-106A, 108A, 110A. (5) O’Dea, J. J.; Osteryoung, J.; Lane, T. J. Phys. Chem. 1986, 90, 2761. (6) O’Dea, J. J.; Osteryoung, J.; Osteryoung, R. A. Anal. Chem. 1981, 53, 695– 701. (7) O’Dea, J. J.; Osteryoung, J.; Osteryoung, R. A. J. Phys. Chem. 1983, 87, 3911–3918. (8) O’Dea, J. J.; Wikiel, K.; Osteryoung, J. J. Phys. Chem. 1990, 94, 3628– 3636. (9) Chen, X.; Pu, G. Anal. Lett. 1987, 20, 1511–1519. (10) Xinsheng, C.; Guogang, P. Anal. Lett. 1987, 20, 1511. (11) Drake, K. F.; Van Duyne, R. P.; Bond, A. M. J. Electroanal. Chem. 1978, 89, 231–246. (12) Eccles, G. N.; Purdy, W. C. Can. J. Chem. 1987, 65, 1795–1799. (13) Eccles, G. N.; Purdy, W. C. Can. J. Chem. 1987, 65, 1051–1057. (14) Miaw, L. H. L.; Boudreau, P. A.; Pichler, M. A.; Perone, S. P. Anal. Chem. 1978, 50, 1988–1996. (15) Miaw, L. H. L.; Perone, S. P. Anal. Chem. 1979, 51, 1645–1650. (16) Ramaley, L.; Tan, W. T. Can. J. Chem. 1987, 65, 1025–1032. (17) Ryan, M. D. J. Electroanal. Chem. 1977, 79, 105–119. (18) Cai, P.; Miao, W.; Mo, J.; Zhang, R. Fenxi Ceshi Xuebao 1995, 14, 33–38. (19) Camacho, L.; Ruiz, J. J.; Serna, C.; Molina, A.; Gonzalez, J. J. Electroanal. Chem. 1997, 422, 55–60. (20) Eccles, G. N. Crit. Rev. Anal. Chem. 1991, 22, 345–380. (21) Miao, W.; Mo, J.; Cai, P.; Zhang, R. Fenxi Ceshi Xuebao 1995, 14, 1–5. (22) Mo, J.; Cai, P.; Lu, Z.; Zhang, R.; Zou, Y. Fenxi Huaxue 1995, 23, 250–254. (23) Mo, J.; Miao, W.; Cai, P.; Zhang, R. Fenxi Ceshi Xuebao 1993, 12, 16–20. (24) Mo, J.; Miao, W.; Cai, P.; Zhang, R. Fenxi Ceshi Xuebao 1995, 14, 1–6. (25) Mo, J.; Zhang, R.; Lu, Z.; Cai, P.; Zou, Y. Fenxi Huaxue 1995, 23, 255–258. (26) Pu, G.; Cheng, X.; Wang, E. Yingyong Huaxue 1987, 4, 31–36. (27) Pu, G.; Cheng, X.; Wang, E. Yingyong Huaxue 1988, 5, 32–37. (28) Pu, G.; Wu, S.; Cheng, X. Zhongguo Kexue Jishu Daxue Xuebao 1986, 16, 365–366, 364.

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Figure 1. Cyclic square wave voltammetric waveform used throughout this study.

the use of this waveform merits consideration for several reasons. First, the utilization of the square wave potential waveform and the discrete current sampling regimen will permit mechanistic evaluations at trace levels. Second, the reverse potential sweep functions as a probe of the stability of the product generated on the forward potential sweep. Third, the method is readily adaptable to existing instrumentation capable of both square wave and cyclic voltammetry. Fourth, the data display format is familiar to nonelectrochemists who currently make extensive use of cyclic voltammetry for compound characterization. The aim of this paper is to present both the theoretical basis and empirical verification of this electrochemical method and to explore the effect of empirical parameters on the shape of the current-voltage curves obtained for reversible, singular, and consecutive electron transfer reactions. In subsequent reports, we will present applications of CSWV to kinetically controlled and chemically coupled electron transfer reactions at electrode surfaces.29 EXPERIMENTAL SECTION Theoretical voltammograms were calculated using modified versions of the FORTRAN programs previously published by John O’Dea30 and converted to MATLAB format. Two different instruments were used to acquire CSWV data: a home-built computercontrolled voltammographic system31,32 and a PARC model 273 potentiostat interfaced to a personal computer through a National Instruments IEEE-488 general purpose interface board. Headstart software (PARC 1986) was modified to incorporate the cyclic square wave waveform. Voltammograms were acquired at either a Pt button or a hanging mercury drop electrode (EG&G PARC Model 303A). All solutions were sparged for at least 4 min with N2 to remove dissolved O2. The analytes used were reagent grade and used as received from Fisher Scientific. RESULTS AND DISCUSSION Figure 1 depicts the CSWV waveform used throughout this study. Note that the backward potential step sequence is a mirror image of the forward potential step sequence. The current is sampled just prior to the onset of a new applied potential. Individual current readings, or their difference, can be plotted (29) Helfrick, J. C., Jr.; Bottomley, L. A., manuscripts in preparation. (30) O’Dea, J. J. Ph.D. Dissertation, Colorado State University, Fort Collins, CO, 1979. (31) Reardon, P. A.; O’Brien, G. E.; Sturrock, P. E. Anal. Chim. Acta 1984, 166, 175. (32) Sturrock, P. E.; O’Brien, G. E. U.S. Patent 4 628 463, 1986.

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versus potential. In the terminology of Osteryoung,33 the currents measured on each upward potential excursion are deemed forward currents; those measured on each downward excursion are deemed reverse currents. Traditionally, cyclic techniques involve a forward and reverse sweep. When this terminology is applied to CSWV, there should exist a forward sweep forward current, forward sweep reverse current, reverse sweep forward current, and reverse sweep reverse current. To avoid the confusion that this terminology would generate, we have adopted the terminology of Sturrock and Carter.34 Examination of the potential waveform (Figure 1) reveals the origin of the nomenclature to be used. The initial potential is designated as Einitial. The second potential value is simply the addition of a pulse to Einitial, while the third potential is the addition of the Estep to the initial potential. Thus, the odd numbered potentials can be calculated by Em ) Einitial + (m - 1)Estep + Epulse

(1)

whereas the even numbered potentials can be calculated by Em ) Einitial + mEstep

(2)

where Em is the potential on step number m. The current which flows during the application of an odd numbered potential is designated as a pulse current, ipulse, whereas the current which flows during the application of an even numbered potential is designated as step current, istep. The difference current, ∆I is determined by subtracting ipulse from istep and is plotted versus the average of the potentials at which both current acquisitions were made. Throughout this work the forward difference current, ∆If will denote the difference currents acquired over the interval Ei to the switching potential Esw and the backward difference current, ∆Ib will denote difference currents acquired over the backward potential sweep from Esw to the final potential, Efinal. The plotting convention used herein is ∆If are displayed as positive currents and ∆Ib are displayed as negative currents. The waveform depicted in Figure 1 is similar to the waveform suggested by Xinsheng and Guogang.10 In our waveform, the additional pulse prior to sweep reversal has been removed. This modification produces a display matching that of cyclic voltammetry and also produces a bidirectional probe of the charge transfer process over the same potential intervals. Since several commercial computer-based instruments are capable of CSWV, the reader is advised to look closely at the specific CSWV format before applying the theory described herein. Reversible Charge Transfer. A reversible electron transfer (i.e., Ox + ne- T Red) is limited only by the rate of mass transport of the electroactive species to the electrode surface. Under semi-infinite linear diffusion conditions, the concentration of Ox and Red at the electrode surface is related to the applied potential through the Nernst Equation

Eapplied ) E0 -

RT CRed(0, t) ln nF COx(0, t)

(3)

(33) Osteryoung, J. G.; O’Dea, J. J. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1986; Vol. 14, pp 209-224. (34) Sturrock, P. E.; Carter, R. J. Crit. Rev. Anal. Chem. 1975, 5, 201–223.

where Eapplied is the applied potential, E0 is the formal potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred, F is Faraday’s constant, and COx(0, t) and CRed(0, t) are the concentrations of Ox and Red, respectively, at the electrode surface at any time t after the potential is applied. On the basis of this equation, the integral equations from Smith,35 and the numerical approximation of Nicholson and Olmstead,36 Osteryoung and O’Dea developed a theory for reversible charge transfer monitored by square wave voltammetry.33 To compute theoretical voltammograms for CSWV, we modified O’Dea’s SWV program for a reversible reaction, incorporating reverse sweep potentials. Cyclic square wave voltammograms were calculated, and the effects of the step time, step height, switching potential and pulse height on the peak currents, peak potentials, peak widths, peak current ratio, and peak separations were investigated and are itemized below. Effect of Step Time. The current on each step or pulse is related to step time by

i(t) )

ψ(t)nFAD1/2C*o (πt)1/2

Figure 2. Impact of pulse (A), step (B), and difference (C) currents as step height is increased. Solid line ) 5 mV; dotted line ) 15 mV; dashed line ) 25 mV.

(4)

where i(t) is the current at time t (mA), Ψ(t) is the current function at time t, n is the number of electrons transferred, F is the Faraday, A is the electrode area (cm2), D is the diffusion coefficient (cm2/s), C*0 is the bulk concentration of Ox (mol/ L), and t is the step time (s). Thus, the peak current will decrease with t-1/2. Since the current is sampled at the end of the step and the step time is constant throughout the sweep, the peak current on the forward and reverse sweeps will be equally affected; therefore, the peak ratio will remain unity regardless of step time. The peak widths at half height are also unaffected with step time. Likewise, the step time has no effect on the peak potentials. Thus, the step time is one factor that can be utilized to increase the peak current without increasing the peak width. The reversible mechanism is the only mechanism in which the peak ratio, potentials, and widths are unaffected by the step time. Effect of Step Height. The sweep rate for square wave techniques is given by step height divided by step time. Increasing the step height therefore increases the sweep rate. In cyclic voltammetry the peak current for diffusion-controlled processes increases with the square root of the sweep rate. In CSWV, the maximum of the dimensionless difference current, ∆Ψpk,f or ∆Ψpk,r, decreases slightly with increasing step height. An increase in step height decreases the potential difference between the step and pulse potentials and, consequently, decreases the difference current as illustrated in Figure 2. For example, when the step height is varied from 2-30 mV while the pulse height is held constant at 100 mV, the decrease in ∆Ψpk,f decreases from 1.344 at a step height of 2 mV to 1.260 at 25 mV. ∆Ψpk,r behaves similarly. The peak ratio ∆Ψpk,r/∆Ψpk,f remains unity throughout the range of step heights investi(35) Smith, D. E. Anal. Chem. 1963, 35, 602–609. (36) Nicholson, R. S.; Olmstead, M. L. In Electrochemistry: Calculations, Simulation and Instrumentation; Mattson, J. S., Marks, H. B., MacDonald, H. C., Eds.; Marcel Dekker: New York, 1972; Vol. 2, pp Ch. 5.

Figure 3. Effect of step height on the number of points defining peak potentials.

gated. This trend compares with that found in CV where for a reversible mechanism the peak ratio is unity regardless of sweep rate.37 Osteryoung33 has shown that the peak potentials in SWV are equal to the formal potential. For a reversible charge transfer process studied by CSWV, both the forward and backward peak potentials are independent of pulse amplitude, step time, and switching potential. The peak potentials are also independent of step amplitude so long as a sufficient number of samplings are taken to adequately define the current-voltage curve. Thus, step height is limited experimentally to about 25-30 mV. At larger step heights, the number of data points defining the peak becomes small. This is shown graphically in Figure 3. As well as being aesthetically unpleasing, large step heights lead to greater uncertainty in peak current and potential measurement. For the (37) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706–723.

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Figure 4. Impact of pulse height on the shape of the cyclic square wave voltammogram. Pulse height: (A-D) 100, 80, 60, and 40 mV, respectively.

Figure 5. Impact of pulse height on peak width for both the forward (A) and reverse (B) sweeps.

reversible mechanism, Epk,f and Epk,r equal E0 and are invariant with changes in step height. However, the peak width, W1/2, decreases slightly for the peaks on both the forward and reverse sweeps with increasing step height. For example, the ∆W1/2 is only about 7 mV as the step height increases from 2 to 20 mV. Effect of Pulse Height. A series of calculated voltammograms in which the pulse height is varied is shown in Figure 4. The individual peak currents increase proportionately with Epulse; the peak current ratio is equal to unity and independent of Epulse as long as Epulse > Estep. As Epulse approaches Estep, Epk,f shifts to negative potentials and Epk,r shifts to positive potentials; e.g., at an Epulse of 20 mV and an Estep of 10 mV, the separation between Epk,f and Epk,r is only 4 mV. This trend has been reported by previous workers using the same theory.16 When Epulse ) Estep, a staircase potential waveform results and a nonzero peak separation is expected. Thus, Epulse should be maintained at a sufficiently large value (Epulse > 5 Estep) to ensure that any peak potential separation is the result of chemical or electron transfer kinetics. Under that condition, Epk for the reversible mechanism is independent of Epulse. Figure 5 depicts the dependence of W1/2 on Epulse. As Epulse increases, the potential of the pulse crosses the formal potential 9044

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Figure 6. Effect of switching potential on shape of the cyclic square wave voltammogram. Esw - E0 ) 160 mV (A); 120 mV (B); 80 mV (C); 40 mV (D).

earlier in the sweep, resulting in larger pulse and step currents and therefore larger ∆i values earlier in the sweep. Consequently, large values of Epulse increases W1/2 and may result in poor resolution of two closely spaced peaks along the potential axis (vide infra). Since the major effect of changes in Epulse are on ∆I and W1/ 2, the main consideration when selecting pulse height is to obtain an adequately large signal-to-noise ratio while minimizing W1/2. Osteryoung and O’Dea have found that for the reversible mechanism, the maximum peak current to width ratio occurs at a pulse height of 100 mV for a 2.5, 10, or 25 mV step and a one-electron transfer.33 Effect of Switching Potential. A series of voltammograms in which the switching potential is varied is shown in Figure 6. Variation of switching potential impacts only the reverse sweep. Note that ipk,f remains constant, while ipk,r has decreased by less than 1% when the switching potential is only 40 mV past the formal potential. The peak ratio decreases by less than 1% when the switching potential is as little as 20 mV past the formal potential. Similarly, the peak potentials are independent of switching potential at values greater than one-half the pulse height. Thus, the switching potential may be greater than or equal to E0 - Ep/2 without introduction of artifacts. The reversible mechanism is the only one examined in which the switching potential has no visible effect on the voltammograms. Diagnostic criteria for the reversible mechanism are given in Table 1. Note that we have also examined the impact of heterogeneous electron transfer kinetics as well as the impact of coupled chemical reactions on both singular and consecutive electron transfer reactions. The mechanistic criteria for the identification of these electron transfer mechanisms from CSWV data differ significantly from that listed in Table 1. Manuscripts describing these will be forthcoming.29 Experimental Verification. Two well-known reversible redox couples were selected to compare theory and experiment: the reduction of Ti(IV) to Ti(III) and Cd(II) to Cd(0) in 0.1 M oxalic

Table 1. Diagnostic Criteria for a Reversible Electrode Reaction by CSWV waveform parameters empirical variable step height, Es step time switching potential, Esw pulse height, Ep

peak currents Ipk,f and Ipk,r decrease with increasing Es Ipk,f and Ipk,r decrease with increasing step time independent of Esw

peak ratiosa

peak potentials

equals unity at all Es values independent of Es

peak separation

peak widths

equals zero at all Es values independent of Es

equals unity at all step times independent of step equals zero at all step times independent of step time time independent of Esw independent of Esw equals zero at all Esw values

Ipk,f and Ipk,r increase with Ep equals unity at all Ep values independent of Ep

equals zero at all Ep values W1/2 increases with Ep

a Peak ratios for chemically coupled electron transfer reactions deviate from unity. b Peak potential separations for kinetically controlled electron transfer reactions are larger than zero.

Figure 7. Theoretical (line) and experimental (square) voltammograms for Ti(IV)/Ti(III) couple. Ep ) 100 (A); 80 (B); 60 (C); 40 mV (D).

acid at a hanging mercury drop.38 Test solutions were 0.01 mM in either TiCl4 or Cd(NO3)2 and 0.1 M in oxalic acid. A PARC model 303A mercury electrode stand was used to provide a hanging mercury drop working electrode. Figure 7 shows the excellent agreement found between experimental and theoretical voltammograms. Each voltammogram depicted is the raw data obtained during the first sweep on a new drop. Data collected for both redox couples were consistent with the diagnostic criteria presented in Table 1 for a reversible electrode reaction. It should be noted that our theoretical voltammograms are computed from a planar diffusion model. At the hanging mercury drop electrode, however, radial diffusion is the mode of transport and slightly larger currents are both anticipated and observed. We chose these redox systems specifically to evaluate the empirical parameter trends listed in Table 1. The diagnostic criteria for a reversible reaction put forth herein holds for both planar and radial diffusion. Consecutive Electron Transfers. The theory for CSWV is extended to the case of consecutive, reversible electron transfers, commonly known as the EE mechanism, i.e., Ox1 + n1e- T Red1 Red1 + n2e- T Red2

(5)

Ox1, the electroactive species in bulk solution, is reduced to Red1 at a formal potential of E01 and subsequently to Red2 at a (38) Saveant, J. M.; Vianello, E. Electrochim. Acta 1965, 10, 905–920.

Figure 8. Calculated voltammograms for EE mechanism when n1 ) n2 ) 1. Ep ) 100 mV, Es ) 10 mV and E01 - E02 ranges from 500 to -500 mV in increments of 100 mV. The inset depicts voltammograms E01 - E02 from 200 to -200 mV in increments of 20 mV.

formal potential of E02. The formal potential for the conversion of Red1 to Red2 may be negative, equal, to or positive of the formal potential for the conversion of Ox to Red1. We define the difference in formal potentials, δ, as δ ) E01 - E02

(6)

A theoretical treatment of the EE mechanism has been previously reported by Polcyn and Shain39 for CV and by Richardson and Taube for differential pulse voltammetry.40 In the following section, the effect of δ, step height, pulse height, and step time on CSWV peak currents, potentials and half-widths is presented. Full details of our theoretical development are provided as Supporting Information. The resolution of CSWV peaks along the potential axis depends on the value of δ and pulse height. Figure 8 depicts a series of calculated voltammograms for the case where the pulse height is 100 mV, n1 ) n2 ) 1 and δ varies from +500 to -500 mV. When δ is greater than 250 mV, two independent, single-electron transfer processes are observed. Peak widths, heights, and potentials are essentially invariant with increasing formal potential separation. The impact of step time, step height, and pulse height on the individual peak currents and potentials parallels that seen for the reversible case presented above. When δ is less than -200 mV, a single, two-electron transfer (39) Polcyn, D. S.; Shain, I. Anal. Chem. 1966, 38, 370–375. (40) Richardson, D. E.; Taube, H. Inorg. Chem. 1981, 20, 1278–1285.

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Figure 9. Impact of pulse height on sequential electron transfers separated by 100 mV. Pulse heights ranged from 30 to 100 mV; step height ) 10 mV.

process is observed; peak potentials are found midway between E01 and E02. The peak width and height is independent of δ. When -100 < δ < 250 mV, peak currents and potentials depend markedly on the value of δ. The inset of Figure 8 contains an expanded series of calculated voltammograms in which δ is systematically varied from +200 to -200 mV in increments of 20 mV. At δ ) 120 mV, the peak current for the first reduction process has increased by greater than 10%, the peak potential has shifted by 20 mV, and the peak widths have increased dramatically. Polcyn and Shain39 have stated that for two CV waves to be independent of each other, a potential separation of ∼118 mV is required. This difference between CSWV and CV is attributed to the presence of the pulse potential in square wave. As δ becomes smaller, the pulse potential becomes sufficiently negative to initiate the conversion of Red1 to Red2 before the difference current returns to zero. As δ becomes increasingly negative, the voltammogram becomes identical to a reversible two-electron transfer. For a given value of δ, peak currents, half-widths, and potentials are independent of step height but are strongly dependent on pulse height. Figure 9 shows a set of calculated voltammograms (for n1 ) n2 ) 1, δ ) 100 mV, and step height ) 10 mV) as a function of pulse magnitude. At a pulse height of 30 mV, two peaks are readily discernible on both the forward and reverse sweeps. As the pulse height increases, the peak currents and W1/2 for each process increase. When δ ∼ pulse height, the two process merge into a single peak on both the forward and reverse sweeps. The peak potential for this process is -50 mV vs E01, half the value of δ and W1/2 is 297 mV. The minimum value of δ for which two peaks can be distinguished depends upon Epulse and, to some extent, Estep. Figure 10 presents the relationship between the computed values of δmin and Epulse for Estep ) 4 mV. Least squares fitting of a polynomial function to the data presented in Figure 10 resulted in the following empirical relationship: δmin(mV) )

Estep + (3.81 × 10-3)E2pulse(1.18 × 10-2)Epulse + 2 71.2 (7)

Variation in Estep was found to add to the minimum value of δ by exactly 1/2 the value of Estep. We have also examined consecutive electron transfer reactions with n1 * n2. For the case where n1 ) 1 and n2 ) 2, a series of voltammograms at several values of δ were computed and 9046

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Figure 10. Impact of Epulse on the minimum value of δ for which two sequential redox processes can be discerned.

Figure 11. Calculated voltammograms for EE mechanism when the n1 ) 1 and n2 ) 2. Ep ) 100 mV, Es ) 10 mV and E01 - E02 ranges from 500 to -500 mV in increments of 100 mV.

Figure 12. Calculated voltammograms for EE mechanism when the n1 ) 2 and n2 ) 1. Ep ) 100 mV, Es ) 10 mV, and E01 - E02 ranges from 500 to -500 mV in increments of 100 mV.

presented in Figure 11. Examination of the results presented in this figure reveals that the two waves behave as independent oneand two-electron transfers when the separation is greater than 180 mV. At separations of -100 mV or more negative, one peak results which has the peak current and width of a reversible threeelectron transfer. Peak potentials are weighted toward the formal potential of the two-electron transfer and occur two-thirds of the way toward E02 from E01. For example, if E01 is 0 mV and E02 is +300 mV, then the peak potential will occur at +200 mV. As δ becomes more negative than -100 mV, the peak current and width become constant at values equal to those of a reversible three-electron transfer. Similarly, for the case where n1 ) 2 and n2 ) 1, a series of voltammograms at several values of δ were computed and presented in Figure 12. Once again, the peaks are independent electron transfers when δ is larger than +180 mV. When δ is less than -100 mV, the voltammograms become equivalent to reversible three-electron transfers. The peak potential is again biased toward the second electron transfer.

Figure 13. Cyclic square wave voltammogram obtained at a Pt electrode for nitrido manganese p-methoxytetraphenylporphyrin dissolved in CH2Cl2 (0.1 M TBAP). The blocks are the experimentally obtained difference currents at each potential; the line is the simulated values.

Examination of the three cases for the EE mechanism leads to the conclusion that when δ is less than -100, the peak potential is found at the weighted average of the potentials for the individual electron transfer steps, i.e.

E0apparent )

(n1E01 + n2E02) (n1 + n2)

(8)

where E0apparent is the single peak potential for the EE process. An obvious implication of eq 8 is that if δ is less than -100 mV, there is no way to determine E01 or E02. Furthermore, n1 and n2 cannot be determined unless a second electron transfer is observed (in which case n1 and n2 must be equal to 1). Of course, these limitations are also present in CV and certainly in SWV. Experimental Verification. Nitrido manganese p-methoxytetraphenylporphyrin undergoes two sequential one-electron oxidations in nonaqueous supporting electrolyte.41 Figure 13 shows a cyclic square wave voltammogram obtained on this compound; the simulated voltammogram is overlaid on the experimental data. The first and second oxidations are separated by 310 mV and the two redox processes behave independently of each other. The peak ratio for each process is unity, and the peak potential for the forward sweep is identical to that of the reverse sweep for both redox processes. Varying the sweep rate has no effect on the peak potential or ratio. These criteria are indicative of reversible electron transfers. Agreement between the experimental and theoretical voltammograms is excellent. CONCLUSION In summary, CSWV voltammetry is a technique that merits strong consideration for mechanistic analysis of electrode reactions at low solute concentrations. Reversible electron transfer reactions can be identified by examination of peak currents, potentials, and half-widths following systematic variation in pulse height, step height, and step time. The resolution along the potential axis afforded by CSWV is significantly better than that (41) Bottomley, L. A.; Neely, F. L.; Gorce, J.-N. Inorg. Chem. 1988, 27, 1300– 1303.

Figure 14. Cyclic square wave (upper trace) and cyclic (lower trace) voltammograms obtained at a Pt button electrode for the consecutive oxidations of cobalt tetraphenylporphyrin dissolved in CH2Cl2 (0.1 M TBAP).

found with CV. As an illustration, Figure 14 compares the cyclic square wave and cyclic voltammograms for cobalt tetraphenylporphyrin dissolved in methylene chloride (0.1 M tetrabutylammonium perchlorate at the supporting electrolyte). This compound is known to undergo three successive one-electron transfers which are closely spaced along the potential axis. Inspection of the cyclic square wave voltammogram reveals that the peak ratio for each process is unity and the potentials are same on the forward and reverse sweep for each of the three processes. Similar evaluation by CV is hampered by the close proximity of the three processes and peak asymmetry. The increased sensitivity of CSWV is also exemplified by the larger peak currents. Clearly, determination of peak currents and potentials is much easier for the cyclic square wave voltammogram compared to the cyclic voltammogram. We have also examined the impact of heterogeneous electron transfer kinetics as well as the impact of coupled chemical reactions on both singular and consecutive electron transfer reactions. Mechanistic criteria for the identification of these electron transfer mechanisms from CSWV data will be forthcoming. ACKNOWLEDGMENT This manuscript is dedicated to the memory of Profs. Peter E. Sturrock and Robert A. Osteryoung who, by their teachings and scholarship, inspired this work. We also acknowledge instrumental modifications made by Mr. Gerald O’Brien and the software modifications made by Dr. Dale S. Owens. We are grateful for the partial support of this research by DHHS. SUPPORTING INFORMATION AVAILABLE Theory for consecutive electron transfers by CSWV is provided. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review July 28, 2009. Accepted September 19, 2009. AC9016874

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