An Experimental Evaluation of Cyclic Voltammetry of Multicharged

Anal. Chem. 2001, 73, 352-359

An Experimental Evaluation of Cyclic Voltammetry of Multicharged Species at Macrodisk Electrodes in the Absence of Added Supporting Electrolyte Alan M. Bond,* Darren C. Coomber, Stephen W. Feldberg,† Keith B. Oldham,‡ and Truc Vu

Department of Chemistry, Monash University, Clayton, Victoria, 3800, Australia

The reversible reduction of [S2Mo18O62]4- to [S2Mo18O62]5and [S2Mo18O62]6- at a glassy carbon macrodisk electrode has been studied by cyclic voltammetry in acetonitrile as a function of the concentration of [(C6H13)4N]4[S2Mo18O62] in the absence and presence of [(C6H13)4N]ClO4 as the added supporting electrolyte. Consideration is given to the influence of scan rate, reference-working electrode distance, [(C6H13)4N]4[S2Mo18O62], and electrolyte concentrations. Experimental data confirm theoretical predictions that cyclic voltammetry at a macrodisk electrode is a viable technique for studies of multiply charged electroactive species without added electrolyte, provided the influence of enhanced complexities associated with effects of increased solution resistance, the mass transport contribution from migration, and convection arising from enhanced density gradients are considered. Enhanced density gradients present in the absence of added supporting electrolyte give rise to a more marked dependence of voltammograms on the angle of the electrode and hence lead to significant distortion of wave shapes at low scan rates. The summation of all these obstacles implies that quantitative evaluation of cyclic voltammograms of multiply charged species requires significantly greater care in the absence than in the presence of added supporting electrolyte. Supporting electrolyte is routinely added in voltammetric studies to increase the electrical conductivity of the solvent, to suppress mass transport by migration and convection, to minimize Frumkin effects by establishing a compact rather than diffuse double layer, and to enforce constant activity coefficients.1-3 However, supporting electrolyte addition may not be necessary for voltammetry of highly charged electroactive species as the electroreactant ion and its counterion can provide the means * Corresponding author: (tel) +61 3 99051338; (fax) +61 3 99054597; (e-mail) [email protected]. † On leave from Department of Applied Science, Brookhaven National Laboratory, Upton, NY 11972. ‡ On leave from Chemistry Department, Trent University, Peterborough, Ontario K9J 7B8, Canada. (1) Heyrovsky´, J.; Ku˚ta, J. Principles of Polarography; Academic Press: New York, 1966. (2) Oldham, K. B.; Myland, J. C. Fundamentals of Electrochemical Science; Academic Press: San Diego, 1994. (3) Oldham, K. B.; Feldberg, S. W. J. Phys. Chem. B 1999, 103, 1699-704.

352 Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

whereby current may be carried through the cell. From the definition

µ)

∑z

1 2

2 i

ci

(1)

of ionic strength, where zi is the charge and ci is the concentration of the ith ion, it follows that even millimolar solutions of multiply charged ionic species can have appreciable ionic strengths. Nevertheless, uncompensated resistance and mass transport by migration and convection are enhanced, relative to the situation prevailing when the usual 0.1 M, or greater, concentration of supporting electrolyte is present. It has been well documented, both experimentally and theoretically, that problems associated with high resistance and migration in the absence of deliberately added supporting electrolyte can be tolerated under polarographic conditions at a dropping mercury electrode1 and also under steady-state conditions at microelectrodes,4-8 when charged species undergo reduction or oxidation to other charged species. An exception to this is the special case in which the product of the electrode reaction is an ion of a sign opposite to that of the ionic reactant. In such cases, fundamental complications4b,e,5 arise which are not addressed here. In contrast to steady-state studies, the far more widely used and mechanistically valuable transient experiments at macrodisk electrodes are almost invariably undertaken with a large (e.g., 50-100-fold) concentration excess of added inert supporting electrolyte.9 However, despite the greater influence of resistance, relative to that encountered under steady-state (4) (a) Bond, A. M.; Fleischmann, M.; Robinson, J. J. Electroanal. Chem. 1984, 168, 299-312. (b) Amatore, C.; Deakin, M. R.; Wightman, R. M. J. Electroanal. Chem. 1987, 225, 49-63. (c) Oldham, K. B. J. Electroanal. Chem. 1988, 250, 1-21. (d) Cooper, J. B.; Bond, A. M.; Oldham, K. B. J. Electroanal. Chem. 1992, 331, 877-95. (e) Palys, M.; Stojek, Z.; Bos, M.; van der Linden, W. E. J. Electroanal. Chem. 1995, 383, 105. (5) Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 1993, 347, 49-91. (6) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 15, pp 267-353 and references therein. (7) Amatore, C. A. In Physical Chemistry, Principles, Methods and Applications; Rubenstein, I., Ed.; Marcel Dekker: New York, 1995; pp 131-208 and references therein. (8) Montenegro, M. I., Queiros, M. A., Daschbach, J. L., Eds. Microelectrodes. Theory and Applications; NATO ASI Series 197; Kluwer: Dordrecht, 1991 and references therein. (9) Bard A. J.; Faulkner, L. R. Electrochemical Methods Fundamentals and Applications; John Wiley and Sons Inc.: New York, 1980. 10.1021/ac000732+ CCC: $20.00

© 2001 American Chemical Society Published on Web 12/15/2000

microelectrode conditions, simulations have suggested the potential viability of transient cyclic voltammetric experiments in the absence of supporting electrolyte for reduction and oxidation of electroactive ionic species.10 Very recently, transient cyclic voltammograms were, in fact, reported for the reduction of hydrogen ions present in aqueous 2 mM HCl.11 However, no studies are available to confirm the validity of previously published theoretical predictions.10 The systems used in this paper to establish the experimental feasibility and practical limitations of undertaking transient cyclic voltammetric experiments in the absence of added electrolyte are the two initial reduction processes of the multiply charged polyoxomolybdate anion [S2Mo18O62]4- at a glassy carbon macrodisk electrode

[S2Mo18O62]4- + e- h [S2Mo18O62]5-

(A)

[S2Mo18O62]5- + e- h [S2Mo18O62]6-

(B)

and

The voltammetry of [S2Mo18O62]4- has been examined in detail in acetonitrile containing excess supporting electrolyte and produces a series of chemically and electrochemically reversible one-electron-reduction processes.12,13 Studies without added electrolyte under steady-state conditions at a platinum microdisk electrode have shown that the first, but not the second, process exhibits almost ideal diffusion-migration behavior.4d EXPERIMENTAL SECTION The synthesis of [(C6H13)4N]4[S2Mo18O62] was based upon published procedures.12 This compound is very light sensitive, and solutions become contaminated with small concentrations of [S2Mo18O62]5- which contribute to the potential of the platinum quasi-reference electrode. Potential differences in figures and tables predominantly reflect the [S2Mo18O62]5- variability associated with experiments undertaken on different solutions. [(C6H13)4N]ClO4 (GFS Chemicals, Colombus, OH) was of puriss grade. UltimAR grade acetonitrile (Mallinckrodt Chemical Inc.) was used as the solvent for all voltammetric studies. Voltammetric experiments were undertaken with a BAS 100A electrochemistry system (Bioanalytical Systems, West Lafayette, IN) in a three-electrode configuration at 21 ( 2 °C. The uncompensated (Ru) resistance9,14-17 was measured14,15 in a potential region ∼200 mV more positive than the peak potential (10) Bond, A. M.; Feldberg, S. W. J. Phys. Chem. B. 1998, 102, 9966-74. (11) Aoki, K.; Baars, A.; Jaworski A.; Osteryoung, J. J. Electroanal. Chem. 1999, 472, 1-6. (12) Way, D. M.; Bond, A. M.; Wedd, A. G. Inorg. Chem. 1997, 36, 2826-33 and references therein. (13) Cooper, J. B.; Way, D. M.; Bond A. M.; Wedd, A. G. Inorg. Chem. 1993, 32, 2416-20. (14) Kissinger, P. T. In Laboratory Techniques in Electroanalytical Chemistry; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1984; Chapter 6. (15) He, P.; Avery, J. P.; Faulkner, L. R. Anal. Chem. 1982, 54, 1313A. (16) Roe, D. K. In Laboratory Techniques in Electroanalytical Chemistry; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1984; Chapter 7. (17) Southampton Electrochemistry Group. Instrumental Methods in Electrochemistry; Ellis Horwood: London, 1990.

of the [S2Mo18O62]4- reduction processes and, hence, in a region where no electrolysis occurs. Most experiments were undertaken with a standard cell design containing the usual three electrodes in a linear configuration. The working electrode was a glassy carbon disk (Metrohm, Herisau, Switzerland) with an area of 0.080 cm2, as determined by fitting fully supported cyclic voltammetric peak currents for the reversible one-electron oxidation of ferrocene in acetonitrile to well-established theory9 and assuming a diffusion coefficient18 of 2.4 × 10-5 cm2 s-1. The auxiliary electrode was a 1-mm-diameter platinum wire. The quasi-reference electrode consisted of a hook-shaped platinum wire (0.5-mm diameter) mounted in an adjustable thread with the tip always the closest part of the reference electrode to the working electrode surface. This pseudoreference system was used to eliminate the possibility of ionic species leaking from a conventional reference electrode into the bulk solution and altering the ionic strength. Other electrode formats related to this conventional configuration17,19 but involving coiled reference and gauze auxiliary electrodes and Pt quasi-reference electrodes with Luggin capillaries were tested without any advantage. Attempts at using a conventional electrode (e.g., Ag/Ag+) eventually failed due to leakage of ions into the test solution and hence leading to nonreproducible voltammetry. The measured parameters of interest in this study are the peak potentials (Ep) and currents (Ip), peak-to-peak separations (∆Ep), ox red av and a value Eav p , defined as (Ep + Ep ))/2. The Ep symbol is introduced to distinguish between this average potential and the thermodynamically significant half-wave (Er1/2) potential, although if no uncompensated resistance is present, then Eav p will be virtually identical to Er1/2. Peak potentials and currents were the averages of at least three measurements. Peak current values were measured after estimating the baseline. Standard deviations for the peak potential and peak current averaged (5 mV and ( 0.2 µA, respectively, for repetitive measurements undertaken on the same 1 mM [S2Mo18O62]4- solution. (See above for platinum electrode potential variation with different solutions.) The experimental wave shape has been compared with theories based on diffusion (DigiSim 3.0 software package, Bioanalytical Systems)20 and migration plus diffusion.10 RESULTS AND DISCUSSION Assessment of Data Obtained in the Absence of Electrolyte. Figure 1 shows cyclic voltammograms of reaction A for a 1.0 × 10-3 M solution of [(C6H13)4N]4[S2Mo18O62] in acetonitrile in the presence and absence of [(C6H13)4N]ClO4 electrolyte. Obviously, important differences may exist between the unsupported and supported cases. In the presence of 0.10 M [(C6H13)4N]ClO4 electrolyte, Figure 1a, and without IRu compensation, ∆Ep ) 70 ( 5 mV, Ired p ) -6.4 red ( 0.2 µA, and |Iox p /Ip | ) 1.00 ( 0.07, values being close to those expected for a chemically and electrochemically reversible process. In the absence of [(C6H13)4N]ClO4, Figure 1b, and without IRu compensation, ∆Ep has increased to 145 ( 10 mV, Ired p has red decreased to -5.8 ( 0.1 µA, and |Iox p /Ip | ) 0.93 ( 0.03. The (18) Bond, A. M.; Luscombe, D.; Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 249, 1-14. (19) Hawkridge, F. M. In Laboratory Techniques in Electroanalytical Chemistry; Kissinger, P. T., Heineman, W. R., Eds.; Marcel Dekker: New York, 1984; Chapter 12. (20) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A600A.

Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

353

Table 1. Data Obtaineda by Cyclic Voltammetry in Acetonitrile as a Function of Scan Rate without Added Supporting Electrolyte for the [S2Mo18O62]4-/5Reduction Process (1.0 × 10-3 M [S2Mo18O62]4-) scan rate (mV s-1)

Ered p (mV)

Eox p (mV)

Ired p (µA)

∆Ep (mV)

Eav p (mV)

1/2 b Ired p ν

2 5 10 20 50 100 200 500 1003 2007

-185 -170 -180 -195 -225 -280 -315 -385 -430 -535

-60 -65 -55 -50 -30 -35 -20 20 65 115

-3.1 -3.7 -4.9 -6.4 -9.7 -13.0 -17.1 -24.5 -31.6 -40.0

125 105 125 145 195 245 295 365 495 650

-122 -118 -118 -122 -128 -158 -168 -182 -182 -210

-2.19 -1.65 -1.55 -1.43 -1.37 -1.30 -1.21 -1.10 -1.00 -0.89

a Distance between glassy carbon working and Pt quasi-reference electrode was 2 mm and no IRu compensation was applied. b Potentials are µA mV-1/2 s1/2 vs Pt. (See Experimental Section for significance.)

Figure 1. Cyclic voltammograms obtained for the reduction of 1.0 × 10-3 M [(C6H13)4N]4[S2Mo18O62] at a glassy carbon macrodisk electrode in acetonitrile with a scan rate of 20 mV s-1 and a workingreference electrode separation of 2 mm: (a) 0.10 M [(C6H13)4N]ClO4 and without IRu compensation; (b) without supporting electrolyte and without IRu compensation; (c) without supporting electrolyte and with instrumental IRu compensation.

increased solution resistance associated with the withdrawal of supporting electrolyte is the dominant cause of the large increase in the ∆Ep value. After application of instrumental IRu compensation (nominally 100%,14-16 but perfect compensation is very unlikely to have been achieved16), ∆Ep ) 70 ( 5 mV, Ired p ) -6.5 ( 0.1 red µA, and |Iox /I | ) 1.00 ( 0.02. That is, the measured ∆Ep and | p p red Iox /I | values after instrumental IR compensation are indistinu p p guishable within experimental error from those obtained without IRu compensation in the presence of 0.10 M added electrolyte. This is in agreement with the theory for a 4-/5- ([S2Mo18O62]4-/5-) reduction process.10 The cyclic voltammograms shown in Figure 1 demonstrate that qualitatively useful data can be obtained in the absence of added electrolyte for the reduction of [S2Mo18O62]4- at macrodisk electrodes in nonaqueous solvents. However, the following investigations reveal the existence of significant limitations in quantifying data, some of which are not accounted for by use of available diffusion plus migration theory.10 Scan Rate Dependence. In quantitative cyclic voltammetric studies, in the presence of added electrolyte, the scan rate (ν) dependence is of considerable significance.9 For a reversible red process, ∆Ep ) 57 mV (25 °C) and |Iox p /Ip | is unity at all scan 1/2 rates, while Ip is proportional to ν . Cyclic voltammograms for the [S2Mo18O62]4-/5- reduction process in the absence of added electrolyte were studied over the range of ν from 2 to 2007 mV s-1, with the reference electrode tip placed 2 mm from the working electrode surface. Data collated in Table 1 at a range of scan rates 354 Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

show substantial differences from the close-to-ideal data obtained in the presence of 0.10 M [(C6H13)4N]ClO4 supporting electrolyte under otherwise identical conditions. Thus, in the absence of added supporting electrolyte and as the scan rate increases, Ered p shifts to more negative values, Eox p shifts to less negative values, a negative shift is observed in Eav p , and ∆Ep increases significantly. In contrast, ideally for a reversible process, all these parameters should be independent of scan rate, as was the case when 0.1 M supporting electrolyte was present or when IRu compensation was applied. In the absence of added supporting electrolyte, Table 1, Ired p vs ν1/2 is nonlinear, which is attributable to the scan rate-dependent IRu drop. With instrumental IRu compensation, linearity is still not achieved, presumably due to enhanced problems with achieving truly 100% compensation at the higher scan rates.14-16 Consequently, a scan rate of 20 mV s-1 will be used in most data described below due to the lessened effect of IRu drop and the higher precision of peak potential measurements at this scan rate. The problems introduced by the presence of natural convection at this low scan rate also will be addressed. Reference Electrode Position. The distance of the tip of the platinum quasi-reference electrode from the working electrode surface was varied, and cyclic voltammetric data were obtained with and without IRu compensation, Table S1. As theoretically expected,9 the resistance decreases as the tip of the quasireference electrode is placed closer to the working electrode. However, nominally 100% compensation of Ru, as detected by the potentiostat circuitry, was most readily achieved with the reference tip at 2 mm. Voltammetric experiments show that ∆Ep decreases from 165 to 145 mV as the reference electrode is moved from 8 to 0.5 mm. With nominally 100% IRu compensation, a ∆Ep value of 70 ( 5 mV, identical to the value observed in the presence of excess electrolyte, was obtained routinely with the reference tip at a distance of 2 mm from the working electrode. When the reference was placed closer, the value of ∆Ep became variable from experiment to experiment but was always g70 mV and small increases in peak current values were observed relative to the case when the distance is g2 mm. This inconsistency may be associated with shielding of the current19 or disturbance of the

Figure 2. Cyclic voltammograms obtained a scan rate of 20 mV s-1 without IRu compensation for the reduction of 1.0 × 10-3 M [(C6H13)4N]4[S2Mo18O62] at a glassy carbon electrode in acetonitrile: (a) 1.0 × 10-1, (b) 1.0 × 10-2, (c) 1.0 × 10-3, (d) 1.0 × 10-4, and (e) 0 M added [(C6H13)4N]ClO4, supporting electrolyte. Working-reference electrode separation of 2 mm.

current density or potential distribution.19 The possibility of working electrode products reaching the quasi-reference electrode and causing a change in the reference potential when a 2-mm distance is used can be dismissed by using the error function complement of the concentration profile.9 For a cyclic voltammetric experimental time of 120 s (maximum time used in this study), a value12 of D of 6.2 × 10-6 cm2 s-1, and a [S2Mo18O62]4concentration of 1 × 10-3 M, the concentration of the reduced [S2Mo18O62]5- species at the reference electrode will be only 2.2 × 10-10 M at a distance of 2 mm. The concentration of electrochemically generated reduced species present under this condition is too low to alter the platinum quasi-reference electrode potential. At the faster scan rate of 100 mV s-1, ∆Ep values are always g100 mV, regardless of the position of the reference electrode or application of nominally 100% IRu compensation. Thus, for the cell design used in this study, a reference distance of 2 mm is considered optimal for voltammetric measurements in the absence of supporting electrolyte and, unless noted otherwise, was the distance used in data reported in this paper. Dependence on Added Supporting Electrolyte Concentration. Resistance uncompensated and compensated cyclic voltammograms were obtained over the concentration range of added electrolyte from 0 to 0.10 M [(C6H13)4NClO4] for both Reactions A and B, Figure 2. Data obtained are summarized in Table S2 red1 with the term |Iox2 p /Ip | representing the ratio of the oxidation current for the second process and the reduction current for the first process. In view of the proximity of the two processes, Iox2 p

Figure 3. Resistance in acetonitrile at a working-reference electrode separation of 2 mm against (a) concentration of added [(C6H13)4N]ClO4 for 1.0 × 10-3M [(C6H13)4N]4[S2Mo18O62]. Resistance obtained at a potential of +100 mV vs Pt; (b) concentration of [(C6H13)4N]4[S2Mo18O62]. Resistance measured at 0 mV vs Pt.

could be more precisely measured than Ired2 or Iox1 p p , both of which are strongly influenced by the current from the neighboring process. It is assumed that Iox2 is equal in magnitude to Ired2 p p since both reduction processes have been shown to be electrochemically reversible. As mentioned previously, many features associated with decreasing the concentration of added supporting electrolyte are attributable to an increase in solution resistance. Figure 3a illustrates the dependence of the solution resistance on the added electrolyte concentration. For both the [S2Mo18O62]4-/5- and [S2Mo18O62]5-/6- processes, an increase is observed in ∆Ep from 65 and 70 mV, in the fully supported case, to 185 and 145 mV, respectively, in the unsupported case. The large distortion in ∆Ep values can be minimized with IRu compensation, to give a range of 65-85 mV across all electrolyte concentrations, which is close to the values observed in the presence of excess electrolyte. The shift in both Eav p values to more negative potentials with decreasing concentrations of the electrolyte is independent of resistance compensation and is attributed to the change in solution composition altering the reference potential of the platinum quasi-reference electrode. The value of Ired1 is not strongly dependent on added p Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

355

Figure 4. Cyclic voltammograms obtained in acetonitrile at a scan rate of 20 mV s-1, with no added supporting electrolyte or IRu compensation and a working-reference electrode separation of 2 mm for the reduction of (a) 4.9 × 10-4, (b) 5.0 × 10-3, and (c) 3.0 × 10-2 M [(C6H13)4N]4[S2Mo18O62].

electrolyte concentration. In contrast, the value of Iox2 p increases with increasing supporting electrolyte concentration for concentrared1 tions below 5 mM. Thus, the ratio |Iox2 p /Ip | approaches the 9 expected value of unity when the added electrolyte concentration is ∼0.10 M but has a significantly lower value in the absence of added supporting electrolyte concentration. With IRu compensation, both measured currents are larger than the uncompensated case at electrolyte concentrations below 5 mM, and as noted above, under these circumstances, Ired1 in p the absence of supporting electrolyte is very similar to the current obtained with 0.10 M electrolyte. Although IRu compensation results in higher currents at lower supporting concentrations, it red1 does not dramatically alter the |Iox2 p /Ip | ratio. Dependence on [(C6H13)4N]4[S2Mo18O62] Concentration. Cyclic voltammograms were obtained over a [(C6H13)4N]4[S2Mo18O62] concentration range of 5.0 × 10-4-3.0 × 10-2 M in acetonitrile without added electrolyte, as reported in Figure 4 and Table 2. Ideally,10 in the absence of added supporting electrolyte, current magnitudes (I) should scale with bulk [S2Mo18O62]4solution concentration (cb), whereas terms related to IR drop should be independent of concentration (I ∝ cb, R ∝ 1/cb). The value of R (Table 2, Figure 3b) decreases with increasing [S2Mo18O62]4- concentration but not as the reciprocal of concentration, as would be expected if complete dissociation of the tetran-hexylammonium salt occurred in acetonitrile. Thus, significant ion pairing can be assumed to be present at higher concentrations. 356 Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

In view of the high molecular weight of [(C6H13)4N]4[S2Mo18O62], the quantity of the salt added in grams per liter (Table 2) is large and this may lead to significant viscosity changes, which also may be important. Examination of Ired1 and Iox2 p p , Table 2, shows that both peak current values increase with concentration. At higher concentrations, significant deviations from linearity are evident for the first process, which again is attributable to the effect of ion pairing or viscosity. As the concentration of [(C6H13)4N]4[S2Mo18O62] inred1 creases, the ratio |Iox2 p /Ip | tends toward unity and a significant change in wave shape occurs. If [(C6H13)4N]4[S2Mo18O62] were wholly ionized into 4- anions and 1+ cations, then a 10 mM solution would have an ionic strength of 100 mM. The conductivity of such a solution should then be comparable (though probably somewhat less on account of the large size of the anion) with that of 100 mM (C6H13)4NClO4. In fact, the conductance of 10 mM [(C6H13)4N]4[S2Mo18O62] is 1.1 mS, while that of 100 mM (C6H13)4NClO4 under similar conditions is 4.9 mS (conductance calculated from data in Figure 3). When ion-pairing and viscosity effects are small, well-defined voltammograms that obey the diffusion-migration theory are predicted at high concentration in the absence of supporting electrolyte, as observed in the cases of potassium ferrocyanide and ferricyanide in water.21 A further effect of increased IRu observed at high [(C6H13)4N)4av1 - Eav2 [S2Mo18O62] concentrations is that ∆Eav p ) Ep p , which should be independent of [(C6H13)4N]4[S2Mo18O62] concentration in the absence of ion pairing, increases as the concentration increases. Comparison with Theoretical Predictions. To assess to what extent mass transport by diffusion plus migration accounts for the shapes of the curves at low concentrations where ion pairing is minimized, cyclic voltammograms obtained for the reduction of 1.05 × 10-3 M [(C6H13)4N]4[S2Mo18O62], at a scan rate of 20 mV s-1 and with a reference-working electrode distance of 2 mm in the absence of added supporting electrolyte, were compared with those obtained theoretically using both the DigiSim software package20 with mass transport solely by diffusion and a numerical method10 which incorporates both diffusion and migration. Both simulation packages can include resistance effects. The measured value of D for [S2Mo18O62]4- in acetonitrile12 of 6.2 × 10-6 cm2 s-1 was used for all species in the simulations. It has been shown that the D values of the one- and two-electron-reduced polyoxometalate species are essentially identical.12 The dependence of diffusion coefficients on ionic strength1 was neglected. D for the (C6H13)4N+ counterion is unknown, although variation in the simulation10 by a factor of 5 led to only small changes in the theoretically predicted voltammograms. Both reduction processes were assumed to be electrochemically reversible in all simulations. A comparison of simulated voltammograms incorporating only diffusion and resistance with those obtained experimentally in the absence of electrolyte, with and without resistance compensation, is shown in Figure S1. Simulation provides reasonable agreement with experiment only in the region of the initial reduction wave. As expected, incorporation of migration into the theory enables superior agreement to be obtained with experiment for the peak (21) Rooney, M. B.; Coomber, D. C.; Bond, A. M. Anal. Chem. 2000, 72, 3486.

Table 2. Cyclic Voltammetric Dataa Obtained for the Reduction of Variable Concentrations of [S2Mo18O62]4- in Acetonitrile at a Glassy Carbon Electrode without Added Supporting Electrolyte at a Scan Rate of 20 mV s-1 and with a Working-Reference Electrode Distance of 2 mm first process Ired1 p

Eox1 p

Iox1 p

second process

conc (10-4 M)

g L-1

R (Ω)

(mV)

(µA)

(mV)

(µA)

(mV)

(mV)

(mV)

(µA)

Eox2 p (mV)

Iox2 p (µA)

Eav2 p (mV)

∆E2p (mV)

red1 |iox2 p /ip |

∆Eav p (mV)

5 10 20 50 100 200 300

2.1 4.2 8.4 21 42 84 126

8025 4585 2780 1480 925 635 520

-260 -255 -240 -245 -255 -265 -280

-2.8 -5.6 -11.1 -26.9 -50.7 -83.4 -101

-105 -85 -70 -70 -65 -60 -65

2.5 5.0 9.9 25.7 52.6 98.7 134

-185 -170 -155 -160 -160 -165 -175

155 170 170 175 190 200 215

-500 -495 -480 -495 -510 -535 -560

-1.6 -3.4 -6.9 -17.6 -36.1 -68.8 -95.2

-370 -350 -340 -345 -350 -355 -360

2.0 4.2 8.8 22.1 43.3 75.1 93.4

-435 -425 -410 -420 -430 -445 -460

130 145 140 150 160 180 200

0.72 0.75 0.79 0.82 0.85 0.90 0.92

255 255 255 260 270 280 290

a

Ered1 p

Eavl p

∆E1p

Ered2 p

Ired2 p

Potentials are vs Pt. See Experimental Section for significance.

Figure 5. Comparison of experimental and simulated (diffusion plus migration) cyclic voltammograms obtained in acetonitrile in the absence of added supporting electrolyte and with a workingreference electrode separation of 2 mm for the reduction of 1.05 × 10-3 M [S2Mo18O62]4-: (a) experimental (without IRu compensation) and simulated (migration, without IRu compensation) voltammograms at a scan rate of 20 mV s-1, (b) experimental (with IRu compensation) and simulated (migration, with 100% IR compensation) voltammograms at a scan rate of 20 mV s-1, and (c) experimental (with IRu compensation) and simulated (migration, with 100% IRu compensation) at a scan rate of 100 mV s-1.

current of the reduction component of the second process, Figure 5, but significant discrepancies still exist. Incorporation of spherical diffusion that can be important at long times (scan rate 20 mV s-1, electrode radius 0.16 cm) into these simulations made only a small difference and certainly does not account for more than a minor fraction of the discrepancy between experiment and theory. The variation of resistance as a function of potential was considered in this simulation10 but found to have a negligible influence for the highly charged (4-/5-) system. The differences between experimental and simulated voltammograms even after

inclusion of migration and Ru may be explained by a combination of factors that include the following: the [S2Mo18O62]4- anion having a slightly different diffusion coefficient in the absence of excess added supporting electrolyte; the absence of charging current in the simulation; small variations in reference-working electrode distance from the simulated value of 2.0 mm; small departures from reversibility, i.e., small components of spherical diffusion and diffuse double-layer Frumkin effects. However, most critically, the diffusion plus migration simulation predicts a significantly different mass transport-limited current from that obtained experimentally at potentials beyond Ered2 and at all p potentials on the entire reverse scan, regardless of the extent of IRu compensation. This discrepancy is most readily observed as a large current “offset” when comparing experimental and simulated voltammograms, Figure 5a. Thus, it is concluded that incorporation of migration into the theory fails to provide a completely adequate description of the cyclic voltammetry of [S2Mo18O62]4- in the absence of added supporting electrolyte. Simulations incorporating a very fast (diffusion-controlled) crossredox reaction for comproportionation of [S2Mo18O62]4- and [S2Mo18O62]6- with both diffusion and migration were shown to have virtually no effect upon the shape of the voltammogram, so that this does not account for the discrepancy. Additionally, it should be noted that ion pairing would not be predicted to give an increased current at potentials beyond Ered2 p . The major feature excluded from the simulations is a possible contribution from convection, which appears to be enhanced by both the absence of added supporting electrolyte and high [S2Mo18O62]4- concentrations. Thus, voltammograms obtained at a [S2Mo18O62]4- concentration of 3.0 × 10-2 M, Figure 4c, show such pronounced evidence of convection that characteristics of a steady-state response are exhibited. If the origin of the problem is convection, then use of higher scan rates should minimize the relative importance of convection. Indeed, superior agreement between experiment and simulation (diffusion and migration) was obtained at a scan rate of 100 mV s-1, Figure 5c. However, a slightly enhanced current is still observed in the experimental voltammogram at potentials beyond Ered2 p , and despite the employment of nominally IRu compensation, fitting the peak potentials now requires the inclusion of significant resistance to the simulation. Simulations involving diffusion, migration, and convection are not presently available, so a detailed comparison of theory Analytical Chemistry, Vol. 73, No. 2, January 15, 2001

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Figure 7. Current ratio (current divided by the current obtained at 0°) against electrode angle for the reduction of 1.0 mM [(C6H13)4N]4[S2Mo18O62] in the absence of electrolyte (measured at -800 mV vs Pt) and in the presence of 0.10 M [(C6H13)4N]ClO4 (measured at -650 mV vs Pt).

Figure 6. Cyclic voltammograms obtained in acetonitrile at a scan rate of 20 mV s-1 at a range of electrode angles for the reduction of 1.0 × 10-3 M [(C6H13)4N]4[S2Mo18O62] with (a) no added supporting electrolyte and (b) 0.10 M [(C6H13)4N]ClO4.

and experiment is not possible. Dependence of Cyclic Voltammograms on Electrode Angle. The occurrence of a redox process at an electrode surface leads to density gradients within the depletion layer resulting in natural convective mass transfer, which causes current measurements to be dependent on the relative densities of the redox species, the angle of the electrode (with the subsequent influence of gravity), and the type of diffusion (planar/spherical).17-19 Natural convection when supporting electrolyte is present has been studied transiently at electrodes of millimeter dimensions and during steady-state voltammetry at microelectrodes22-24 at an electrode surface. Added supporting electrolyte has been present in all these studies and usually in large excess. However, in ref 24, the microelectrode voltammetry of 0.5 M [Fe(CN)6]3-/4- in the presence of 0.2 M KCl was examined, which represents a situation where the added (KCl) supporting electrolyte is only present in a relatively small concentration. The situation in the complete absence of added electrolyte is more complex than when exess added supporting electrolyte is present as density gradients may be generated by transport of the counterion as well as by the oxidized and reduced forms of the electroactive moieties. Cyclic voltammograms have been obtained for the reduction of [(C6H13)4N]4[S2Mo18O62] in acetonitrile in the absence of added electrolyte at electrode angles from vertical (electrode downward, defined as 0°) to horizontal (defined as 90°) at a scan rate of 20 mV s-1. Inspection of data in Figure 6a reveals that the peak potential and current values of the initial reduction process are (22) Laitinen, H. A.; Kolthoff, I. M. J. Am. Chem. Soc. 1939, 61, 3344-9. (23) Bard, A. J. Anal. Chem. 1961, 33, 11-5. (24) Gao, X.; Lee J.; White, H. S. Anal. Chem. 1995, 67, 1541-5.

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independent of the electrode angle. In contrast, while peak potential values are identical for the second reduction process, the peak current values significantly increase as the angle approaches 90°. Furthermore, it is obvious that currents in the mass transport-limited, more negative potential, region are strongly electrode-angle dependent and have many of the characteristics of a steady-state response. Figure 7 contains plots of the ratio of the current at a potential of -800 mV vs Pt against that at an angle of 0°, for a range of angles. For electrode angles greater than 45°, the value of the current at -800 mV vs Pt remains constant, within experimental error, but at a significantly greater value than at 0°. Angles above 0° and below 45° show increased, but intermediate, current values. On the reverse potential sweep, the peak potential values are shifted slightly to more negative potentials as the angle increases. Although the peak current values (corrected for the baseline current) are similar on the reverse scan, the absolute current values are markedly different, with lower values observed at larger angles. Thus, density-induced convection provides a credible explanation for the major part of the current offset observed when comparing experimental and theoretical voltammograms. At the faster scan rate of 100 mV s-1, no dependence on electrode angle is observed in cyclic voltammograms at a [S2Mo18O62]4- concentration of 1.0 mM in the absence of added supporting electrolyte, indicating that the duration of the voltammetry is now brief enough to inhibit the extent of the influence of the natural convection process. At a scan rate of 50 mV s-1, the reductive sweeps are similar at both 0 and 90° electrode orientations. However, on the oxidative scan, the absolute current values are more positive at 0°. Voltammograms obtained for the reduction of [S2Mo18O62]4in the presence of 0.10 M (C6H13)4NClO4 electrolyte show a much lower dependence on electrode angle over the range 0-90°, when a scan rate of 20 mV s-1 is employed, Figure 6b. In the added electrolyte case, peak potentials are independent of angle for all processes. A plot of reductive current measured at -650 mV vs Pt, Figure 7, shows no dependence on electrode angle, within experimental error. However, the current values associated with the oxidative sweep scan direction decrease as the electrode angle

is increased over the range 0-90°. At a scan rate of 100 mV s-1, the entire voltammetric response is independent of the electrode angle, when 0.10 M (C6H13)4NClO4 is present as the added electrolyte. CONCLUSIONS The quantitative evaluation of cyclic voltammograms obtained for the reduction of [(C6H13)4N]4[S2Mo18O62] at a glassy carbon macrodisk electrode in acetonitrile in the absence of added supporting electrolyte requires care. For example, voltammograms obtained at slow scan rates that are less affected by IRu drop and hence are more readily resistance compensated, but they are more severely influenced by convection. The reverse situation applies at high scan rates. As expected, careful placement of the reference electrode assists in lowering the uncompensated resistance. Theory based on mass transport by diffusion and migration provides good agreement with experimental peak potentials for IRu-compensated voltammograms obtained at slow scan rates. However, convection associated with density gradients is enhanced in the absence of added supporting electrolyte and this

factor results in divergence of the current magnitude from theory based solely on diffusion and migration, particularly when low scan rates are employed. ACKNOWLEDGMENT A.M.B. acknowledges the Australian Research Council for financial support in the form of a Special Investigator Award. K.B.O. is grateful for support by the Natural Sciences and Engineering Research Council of Canada. S.W.F. gratefully acknowledges the U.S. Department of Energy for support under Contract DE-AC02-98CH10886. SUPPORTING INFORMATION AVAILABLE Figure S1 and Tables S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review June 26, 2000. Accepted October 19, 2000. AC000732+

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