Anal. Chem. 1999, 71, 3650-3656
Coupled Electron- and Proton-Transfer Processes in the Reduction of r-[P2W18O62]6- and r-[H2W12O40]6- As Revealed by Simulation of Cyclic Voltammograms Paul D. Prenzler,*,†,§ Colette Boskovic,† Alan M. Bond,*,‡ and Anthony G. Wedd*,†
School of Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia, and Department of Chemistry, Monash University, Clayton, Victoria 3168, Australia
Quantitative analysis of the complex problem of coupled electron- and proton-transfer steps during reduction of the polyoxo anions r-[P2W18O62]6- and r-[H2W12O40]6- in aqueous NaCl (0.5 M) has been achieved by simulation of cyclic voltammograms (Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A) over wide ranges of anion concentration, pH, and scan rate. Since there are too many unknown parameters to attempt a onestep global form of simulation, a systematic, stepwise approach has been adopted by progressively accessing regimes of increasing voltammetric complexity. This protocol allows experimental behavior in each system over 5 orders of magnitude in proton concentration to be simulated by estimation of three protonation constants combined with experimentally determined reversible halfwave potentials for the two one-electron processes involved. Fast electron transfer and protonation kinetics are assumed. The importance of the values chosen for the diffusion coefficients of the proton and polyoxo anion species is considered. The simulations account for the fact that pairs of one-electron processes coalesce to give an apparent two-electron process in the pH range 1-6 for reduction of both anions.
INTRODUCTION1 Polyoxometalate anions are versatile reagents which exhibit rich acid-base, redox, and photolytic chemistries.2-5 One characteristic feature observed in voltammetric studies in aqueous solutions is the conversion of one-electron reduction processes to complex multielectron processes as the pH is lowered.6-12 * Corresponding author. (Fax): 61-3-9347-5180. (E-mail): t.wedd@ chemistry.unimelb.edu.au.,
[email protected].,
[email protected]. † University of Melbourne. ‡ Monash University. § Present address: School of Science and Technology, Charles Sturt University, P.O. Box 588, Wagga Wagga, New South Wales, 2678, Australia. (1) Abbreviations: d, diameter; CV, cyclic voltammetry; D, diffusion coefficient; ∆Ep, peak-to-peak separation; E, potential; E r1/2, reversible half-wave potential; F, Faraday’s constant; Fc, Fe(η5-C5H5)2; K, equilibrium constant; kb, backward rate constant; kf, forward rate constant; khet, heterogeneous rate constant; n, number of electrons transferred per mole; T, temperature; v, scan rate.
3650 Analytical Chemistry, Vol. 71, No. 17, September 1, 1999
The reduction of anions R-[P2W18O62]6- and R-[H2W12O40]6(Figure 1) in aqueous solution has been described, but no detailed quantitative account of the coupled electron- and proton-transfer processes is available.7,8,13 The advent of powerful simulation packages provides an elegant method of addressing the mathematical complexities of systems with numerous coupled electrochemical and chemical steps. However, they must be used with caution since a large number of potentially adjustable parameters exist in a postulated reaction scheme. In such cases, a systematic iterative protocol must be developed to maximize the probability of obtaining a unique solution. The present paper describes a systematic approach based upon progressive simulations under conditions of increasing voltammetric complexity. A maximum of two adjustable parameters is used under given conditions, and ultimately, the three equilibrium constants are deduced from comparison of the experimental and simulated voltammograms. This approach, based upon an established program for simulation of cyclic voltammograms,14 provides a full thermodynamic description of the redox chemistry and has significant potential for directed electrosynthesis. For example, an initial study of simulation in the R-[S2Mo18O62]4- system as a function of [H+] in MeCN/H2O (95/5 v/v) yielded reduction potentials, protonation constants, and disproportionation constants.15 This information helped define conditions for isolation, in substance, of crystalline salts in different redox and protonation states: (1e-), (2e-), (2e-, H+), (2e-, 2H+), (4e-, 2H+), and (4e-, 4H+). Such salts have application as electron-proton transfer reagents, especially in light-catalyzed reactions.16,17 (2) Pope, M. T. Heteropoly and Isopoly Oxometalates; Springer-Verlag: Berlin, 1983; pp 101-117. (3) Pope, M. T.; Mu ¨ ller, A. Angew. Chem., Int. Ed. Engl. 1991, 30, 34-48. (4) Hill, C. L.; Prosser-McCartha, C. M. Coord. Chem. Rev. 1995, 143, 407455. (5) Hill, C. L. Chem. Rev. 1998, 98 (1), 1-387. (6) Wu, H. J. Biol. Chem. 1920, 43, 189. (7) Pope, M. T.; Varga, G. M. Inorg. Chem. 1966, 5, 1249-1254. (8) Pope, M. T.; Papaconstantinou, E. Inorg. Chem. 1967, 6, 1147-1152. (9) Tourne´, C. Bull. Soc. Chim. Fr. 1967, 3196, 3199, 3214. (10) Contant, R.; Fruchart, J.-M. Rev. Chim. Miner. 1974, 11, 123-140. (11) Keita, B.; Nadjo, L. J. Electroanal. Chem. 1987, 227, 77-98. (12) Way, D. M.; Bond, A. M.; Wedd, A. G. Inorg. Chem. 1997, 36, 2826-2833. (13) Tourne´, C. Bull. Soc. Chim. Fr. 1967, 3196, 3199, 3214. (14) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A. (15) Way, D. M.; Cooper, J. B.; Sadek, M.; Vu, T.; Mahon, P. J.; Bond, A. M.; Brownlee, R. T. C.; Wedd, A. G. Inorg. Chem. 1997, 36, 4227-4233. 10.1021/ac9814290 CCC: $18.00
© 1999 American Chemical Society Published on Web 06/25/1999
Figure 1. Polyhedral representations of (a) R-[H2W12O40]6- and (b) R-[P2W18O62].6- Oxygen and hydrogen atoms are represented by spheres. Tungsten atoms are located near the centers of the octahedra of oxygen atoms. In (a), two protons are trapped in the internal cavity. In (b), the P atoms are located within the internal tetrahedra.
EXPERIMENTAL SECTION Reagents. R-K6[P2W18O62]‚14H2O was synthesized from Na2WO4‚2H2O (Ajax).18 R-(NH4)6[H2W12O40] (Aldrich) was used as received. Instrumentation. Cyclic voltammograms at stationary electrodes were acquired with a Cypress Systems model CYSR-IR potentiostat interfaced to an IBM-compatible PC running Cypress Systems software version 6.1/2V. The working electrode was a glassy carbon disk. Before each experiment, the electrode was polished on a polishing pad (LECO Inc.) using slurries of 0.3 µm alumina (Buehler Ltd.) in deionized water, washed with water, polished again on the polishing pad with water only, washed again, and dried in air. A Ag/AgCl (3.5 M KCl) reference electrode was used and its potential checked against a solution of potassium ferricyanide (0.5 mM in 0.5 M KCl) before each run. The Er1/2 value of the [Fe(CN)6]3-/4- couple was +0.227(3) V vs Ag/AgCl. Potentials are quoted relative to Ag/AgCl. The pH was measured (16) Bond, A. M.; Way, D. M.; Wedd, A. G.; Compton, R. G.; Booth, J.; Eklund, J. C. Inorg. Chem. 1995, 34, 3378-3384. (17) Bond, A. M.; Eklund, J. C.; Tedesco, V.; Vu, T.; Wedd, A. G. Inorg. Chem. 1998, 37, 2366-2372. (18) Contant, R. Inorg. Synth. 1990, 27, 105-106.
with a glass electrode using a TPS Digital pH meter. The electrode was calibrated with pH 7.00 and pH 4.00 buffers prior to each run. The diffusion coefficient Danion was determined in 1 mM solutions of aqueous NaCl (0.5 M) via application of the Levich Equation to data obtained by rotating disk voltammetry at pH 5.19 These results were obtained using a variable speed Metrohm 62810 rotator. Simulation of Cyclic Voltammograms. The simulation package DIGISIM V 2.0 (Bioanalytical Systems, West Lafayette, IN) is described in ref 14. It was run on a 150 MHz Pentium PC. Each simulation required about 5 s. A number of background input parameters are common and are defined here: (1) Experimental solutions: Polyoxometalate salt (1 or 5 mM) was dissolved in an aqueous solution of NaCl (0.5 M). The pH was adjusted with aqueous NaOH or HCl. With this electrolyte combination, no evidence of adsorption was encountered in the anion concentration range of 1-5 mM, as indicated by the linear dependence of peak current on concentration and on the square root of scan rate (50-1000 mVs-1). Adsorption phenomena are evident under other conditions.20 (2) Er1/2 values for simple one-electron steps: These were estimated from CV data (uncertainty, (5 mV) as the average of reduction and oxidation peak potentials in solutions of sufficiently high pH (Table 1). (3)Uncompensated resistance arising from IR drop between the working and reference electrodes: A value of 200 ((10) ohm was found to be suitable over the scan-rate range v ) 50-1000 mV s-1 and was obtained as described in ref 21. The distinction between slow electron transfer and uncompensated resistance is notoriously difficult to make. However, concentration-dependent studies revealed that the same values of uncompensated resistance could be incorporated into the simulation to obtain an excellent fit to the data, implying that the value was suitable for the purpose of the present simulations. (4) Double-layer capacitance: A value of 2 × 10-6 F was used in all calculations. This value was determined by cyclic voltammetry in the absence of electrolyte and comparison of simulated14 and experimental background currents. However, because the concentration of polyoxo anion was always >10-3M, contributions from background current or double-layer capacitance are not significant. Parameters 3 and 4 were both obtained from measurement in the electrolyte at pH > 5 where protonation effects were minimal. (5) Temperature: This was monitored throughout the CV experiments and was 23.5 ( 1.5 °C. The simulation temperature was set to 298.2 K. The difference with experiment had virtually no effect upon simulation (
