Anal. Chem. 2004, 76, 3607-3611
Use of ac Admittance Voltammetry To Study Very Fast Electron-Transfer Reactions. The [Ru(NH3)6]3+/2+ System in Water Martin Muzika´rˇ and W. Ronald Fawcett*
Department of Chemistry, University of California, Davis, California 95616
The kinetics of electroreduction of Ru(NH3)63+ has been studied at a polycrystalline gold electrode using highfrequency ac admittance voltammetry. It is shown that precise kinetic data may be obtained for a very fast electron-transfer reaction using this technique. The kinetic data show a small double layer effect when the concentration of HClO4 used as background electrolyte is varied. This is discussed in terms of the point of zero charge, which is very close to the standard potential for the studied reaction. Several experimental techniques have been employed to study the kinetics of very fast electron-transfer reactions.1 These methods include fast-scan cyclic voltammetry, scanning electrochemical microscopy, and ac admittance voltammetry. The latter technique was developed by Baranski,2 who showed that the optimum frequency range for obtaining kinetic data changes with the value of the standard rate constant. Ac admittance techniques are especially well suited to work with ultramicroelectrodes, which are normally used in these studies. For example, the presence of a leak between a wire electrode and the surrounding glass insulation is easily detected using ac methods. The electroreduction of Ru(NH3)63+ is an example of a very fast electron-transfer reaction whose kinetics are difficult to measure on electrodes of normal dimensions. Using a mercury electrode, Wipf et al.3 found a standard rate constant of 0.45 cm‚s-1 and an experimental transfer coefficient of 0.63 for this system using 0.1 M sodium trifluoroacetate as electrolyte in water. More recently, Birkin and Silva-Martinez4 obtained a standard rate constant of 0.36 cm‚s-1 at a Pt microelectrode in 0.1 M KCl. However, a systematic study of the effects of electrolyte nature and concentration has not been carried out for this system. In the present paper, the kinetic parameters of the [Ru(NH3)6]3+ system are studied on a polycrystalline gold electrode in dilute solutions of HClO4. The purpose of this study is to assess the precision of the ac admittance technique applied at * Corresponding author. Tel.: + 1-530-7521105. Fax: + 1-530-7528995. E-mail:
[email protected]. (1) Fawcett, W. R.; Opallo, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 2131. (2) Baranski, A. S. J. Electroanal. Chem. 1991, 300, 309. (3) Wipf, D. O.; Kristensen, E. W.; Deakin, M. R.; Wightman, R. M. Anal. Chem.1988, 60, 306. (4) Birkin, P. R.; Silva-Martinez, S. Anal. Chem. 1997, 69, 2055. 10.1021/ac0499524 CCC: $27.50 Published on Web 06/03/2004
© 2004 American Chemical Society
high frequencies. In addition, a qualitative examination of double layer effects for this system is made. EXPERIMENTAL SECTION Reagents. All substances were analytical grade and were used without further purification. Hexaammineruthenium chloride and perchloric acid, (70%, redistilled and 99.999% purity) were purchased from Aldrich Chemical Co., and potassium chloride from Fisher Scientific. Electrolyte solutions were prepared with the Barnstead NANOpure water system with a resistivity 17.9-18.1 MΩ‚cm. Electrolyte solutions were purged with argon (PraxairInc.) before and kept under argon during the measurements. Alumina (1, 0.3, and 0.05 µm; Buehler) was used to polish the surface of the electrodes. Electrochemical Measurements. All electrochemical measurements were performed using a three-electrode system placed in Pyrex glass cell with a Teflon cap. The cell was enclosed in a Faraday cage, which was connected to a common ground. Experiments were carried out at 25 ( 0.1 °C. The electrolyte solution was purged for 30 min with argon before electrochemical measurements and kept under the argon atmosphere during the experiment. A gold ultramicroelectrode (ume) of 6.25-µm radius was used as the working electrode in the kinetic studies; it was manufactured by sealing a gold wire into a glass capillary. The capillary was then cut to an appropriate length, and the surface was polished using extrafine carborundum paper followed by alumina powder of successfully smaller sizes down to 0.05 µm. The same procedure was applied for the preparation of a gold electrode of normal size with a radius of 0.25 mm. The latter electrode was using for the determination of the diffusion coefficient and formal potential of the reactant. A calomel electrode (0.05 M KCl), CE0.05, connected to the electrolyte through a Luggin capillary, served as a reference electrode, and a gold wire of 1-mm diameter as counter electrode. Cyclic voltammetry was performed with an EG&G PAR potentiostat/galvanostat model 283. The ac admittance measurements were carried out with a 1255 frequency response analyzer (Solatron) connected to the potentiostat using a GPIB PCII 488.2 interface. The data obtained were analyzed with the help of PowerSuite 2.35.2 software (Princeton Applied Research). The experimental setup was tested with an ac impedance dummy cell before starting the experiments. Analytical Chemistry, Vol. 76, No. 13, July 1, 2004 3607
Table 1. Diffusion Coefficients and Formal Redox Potentials of Ru(NH3)63+/2+ in HClO4 Electrolyte at a Gold Electrode (0.25-mm Diameter) Measured versus CE0.05
Figure 1. Cyclic voltammograms for reduction of 5 mM Ru(NH3)63+ in 0.02 M HClO4 electrolyte at a gold standard size electrode (0.25mm diameter) using reference CE0.05. The sweep rates were 30, 40, 50, 60, 75, 100, 150, 200, 300, 400, and 500 mV‚s-1.
Figure 2. Reduction peak current Ip as a function of the square root of sweep rate v1/2 (experimental conditions as in Figure 1).
RESULTS In this study, the diffusion coefficient of the reactant and the standard potential for the Ru(NH3)63+/2+ couple were first determined using cyclic voltammetry. Then the kinetic parameters were obtained using ac admittance voltammetry. Typical cyclic voltammograms for the electroreduction of [Ru(NH3)6]3+ at a gold macroelectrode in 0.02 M HClO4 are shown in Figure 1 for scan rates in the range from 30 to 500 mV‚s-1. The data for the peak current Ip were analyzed using the RandlesSˇ evcˇik equation for a one-electron process at 25 °C:
Ip ) 2.69 × 105ADA1/2cAv1/2
(1)
Here, A is the electrode area (in cm2), DA, the diffusion coefficient of the reactant A (in cm2 s-1), cA, its concentration (in mM), and v, the scan rate (in V‚s-1). The proportionality between Ip and v1/2 is demonstrated by the results presented in Figure 2. To estimate the diffusion coefficient, the electrode area must be determined. This was assumed to be equal to the apparent geometric area, which is reasonable for a well-polished gold electrode. In the present case, the working electrode was a disk 3608
Analytical Chemistry, Vol. 76, No. 13, July 1, 2004
electrolyte, mol‚L-1
D1/2, 1 × 10-3 cm‚s-1/2
formal redox potential, V
0.02 0.05 0.1
2.56 ( 0.02 2.44 ( 0.03 2.26 ( 0.02
-0.31 -0.29 -0.27
with a diameter of 0.25 mm, giving an apparent area of 4.91 × 10-4 cm2. The value of DA1/2 determined from the data in Figure 2 is 2.56 × 10-3 cm‚s-1/2. This corresponds to a diffusion coefficient of 6.55 × 10-6 cm2‚s-1. The present result can be compared with values of 5.48 × 10-6 cm2‚s-1, at a 6-µm platinum disk electrode,5 and 6.00 × 10-6 cm2‚s-1, at a 10-µm carbon disk electrode6 in phosphate buffers. The value of D depends on the medium used in the experiment so that our result looks quite reasonable. Data obtained in three different HClO4 solutions are summarized in Table 1 together with estimates of the experimental error. As expected, the diffusion coefficient decreases with increase in ionic strength because of the effects of ion-ion interactions. The formal redox potential of the Ru(NH3)63+/2+ system was obtained by averaging the cathodic and anodic peak potentials of the recorded cyclic voltammograms (Figure 1). The values obtained against CE0.05 are also presented in Table 1. The change in formal potential with electrolyte concentration is attributed to a corresponding change in the activity of the reactants with ionic strength. For a very fast electrode reaction, the peak potential on the cyclic voltammogram should be independent of sweep rate. The fact that the peak potential moves in the negative direction with increase in sweep rate in attributed to IR drop in the solution (Figure 3). This effect is easily demonstrated by correcting the potential scale according to the equation
E′ ) E - IRs
(2)
Here E′ is the corrected potential, I is the current (negative for the forward reaction and positive for the backward reaction), and Rs is the effective solution resistance between the working and reference electrodes. The effect of this correction at the slowest sweep rate (30 mV‚s-1) is negligible. However, at 500 mV‚s-1, the peak potential shifts by 45 mV in the positive direction on the corrected potential scale when the solution resistance is assumed to be 10050 Ω. In addition, it is independent of sweep rate, confirming that the electrode reaction is fast with respect to the conditions used in the cyclic voltammetric experiments. Kinetic Studies. The kinetic data were obtained using highfrequency ac admittance voltammetry. The data analysis is based on the Randles equivalent circuit for the interfacial impedance (Figure 4). Determination of the heterogeneous rate constant involves finding the solution resistance Rs and the double layer (5) Baur, J. E.; Wightman, R. M. J. Electroanal. Chem. 1991, 305, 73-81. (6) Wehmeyer, K. R.; Deakin, M. R.; Wightman, R. M. Anal. Chem. 1985, 57, 1913.
Table 2. Kinetic Parameters of Charge-Transfer Processes for 5 mM Ru(NH3)63+/2+ System at a Gold ume (6.25-µm Diameter) in Perchloric Acid Supporting Electrolyte electrolyte, mol L-1
frequency range, kHz
solution resistance, Ω
0.02 0.05 0.1
45-70 62-88 75-110
11230 ( 180 9895 ( 70 4960 ( 50
standard rate constant, cm‚s-1 Randles Baranski 0.54 0.85 1.43
Figure 3. Comparison of cyclic voltammograms uncompensated (30, 500) and compensated (500′) for IR drop. The numbers represent sweep rate in mV‚s-1. Other experimental conditions are given in the caption for Figure 1.
Figure 4. Equivalent circuit of the cell according to Randles with Rs, the solution resistance, Rfar, the faradaic impedance, Zwar, the Warburg impedance, and Cdl, the double layer capacitance.
capacity Cdl in the absence of faradaic process and subtracting them vectorally from the total admittance to obtain the faradaic impedance for the reaction. To obtain an ideal response, the admittance due to the reaction, 1/Rfar, must be equal to the double layer admittance, ωCdl. The experimental parameters that are most easily adjusted to achieve ideal conditions are the electrode area A and the angular frequency of the ac signal, ω. By using a ume, the faradaic admittance for a fast electron-transfer reaction is brought into a range where precise measurements can be made for frequencies of the order of 100 kHz. For example, consider a reaction with a standard rate constant of 1 cm‚s-1. The corresponding faradaic impedance is given by
Rfar ) RT/n2F2AcAks
(3)
0.56 ( 0.02 0.81 ( 0.04 1.44 ( 0.05
exptl transfer coefficient 0.55 ( 0.02 0.52 ( 0.03 0.48 ( 0.02
Figure 5. Ac admittance curves obtained for a gold ultramicroelectrode (6.25-µm radius) in 0.1 M HClO4 solution containing 5 mM Ru(NH3)63+. The ac frequency was 94 kHz.
where ks is the standard rate constant. Using an electrode area of 1 × 10-6 cm2 and a reactant concentration of 0.5 mM, the corresponding faradaic impedance for a one-electron process is 53 kΩ. Assuming that the double layer capacity of the ume is 20 pF (20 µF‚cm-2), the frequency at which the double layer admittance is equal to the faradaic admittance is 94 kHz. The magnitude of the solution resistance Rs also plays a role in determining optimum conditions for the experiment. In the present study, Rs did not play an important role because the experiments were carried out in aqueous media of reasonable conductivity. At first, the solution resistance was determined from admittance data measured in the absence of the faradaic process for several potentials in the range from -0.55 to -0.05 V. Admittance was converted to impedance and the solution resistance, which is the real component of the impedance, which is independent of frequency and potential, was then calculated as an average of the results (see Table 2). Then admittance data were obtained as a function of potential for 15 different frequencies in the potential range of the faradaic process. An example of typical curves for the real and imaginary components of the admittance as a function of potential are presented in Figure 5. The admittance data were then corrected for solution resistance by converting them first to the corresponding impedance data. The solution resistance determined earlier was then subtracted from the real component of the impedance. The corrected data were then converted back to admittance. The resulting ac admittance curves obtained from the data in Figure 5 are shown in Figure 6. The presence of the faradaic process is now clearly visible as a maximum for both the real and imaginary components. These data must still be corrected for the double Analytical Chemistry, Vol. 76, No. 13, July 1, 2004
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Figure 6. Ac admittance curves after subtraction of the solution resistance (experimental conditions as in Figure 4).
layer admittance, which was accomplished in the present case by a graphical method. The fundamental idea of the graphical method is to estimate the nonfaradaic admittance directly using results obtained sufficiently far from the potential region where the reaction affects the admittance. Values of the real and imaginary components of the admittance obtained in the potential regions E < (Es - 0.1 V) and E > (Es + 0.1 V) were fitted to a polynomial curve (see Figure 6), which provided an estimate of the nonfaradaic admittance at potentials where the faradaic process occurred. Finally, the remaining faradaic admittances obtained after subtracting the estimates of the nonfaradaic components were converted into impedances. These data provide the information from which the kinetic parameters are obtained. Two different approaches are presented here. The first is based on the Randles circuit and applied at the standard potential. The second method following Baranski2 uses impedance data obtained as a function of potential near the admittance maximum to obtain both the standard rate constant and the apparent transfer coefficient. Randles Analysis. The Randles analysis is based on plots of the real and the imaginary components of the faradaic impedance at the formal potential versus the reciprocal of the square root of the angular frequency. A typical Randles plot from the present results is shown in Figure 7. Two parallel straight lines are obtained with the value of Rfar being obtained from the intercept of the plot of the real component of the impedance. The slope of the plots was determined from a one-parameter least-squares fit of the imaginary component of the faradaic impedance, which goes to zero at infinite frequency. Using this value of the slope, the intercept for the plot of the real component was determined in a second one-parameter least-squares fit. The value of the standard rate constant was then estimated using eq 3. From the results recorded in Table 2, the standard rate constant increases from a value of 0.54 cm‚s-1 in 0.02 M HClO4 to 1.43 cm‚s-1 in 0.1 M HClO4. This increase corresponds to a repulsive double layer effect in which the role of the double layer becomes less important with increase in ionic strength. The present results are consistent with those obtained earlier at ume’s.3,4 They also fall in the same range as results obtained by extrapolation of data 3610
Analytical Chemistry, Vol. 76, No. 13, July 1, 2004
Figure 7. Randles plot of real and imaginary faradaic impedance for 5 mM Ru(NH3)63+ at a gold ultramicroelectrode (6.25-µm radius) in 0.1 M HClO4. The frequency range was 75-110 kHz, and the measurements were carried out at the standard potential of the Ru(NH3)63+/2+ redox couple versus CE0.05. Rfar ) 30450 Ω.
at electrodes modified by self-assembled monolayers (1.7 7 and 1.8 cm‚s-1 8). Baranski Analysis. In the Baranski analysis,2 the rate constant for electron transfer is calculated at potentials close to the formal potential so that the potential dependence of this quantity can be determined. The equations giving the faradaic impedance Rfar are the following:
Rfar ) ZR -
aRnl(Rnl + 2a)
(4)
(Rnl + a)2 + a2
where
Rnl )
2RT cosh2[(nF/2RT)(E - E0f)] πn2F 2rDAcA
(5)
and
a)-
Rnl ( R 2 + 4ZIRnl - 4ZI2 - Rnl - Rnl - 2ZI) (6) 4ZI x nl
ZR and ZI are the real and imaginary parts of the faradaic impedance and Rnl is nonlinear mass transport resistance. Then, the forward rate constant kf was calculated from eq 7.
kf )
[
)]
RT nF (E - E0f ) 1 + exp RT 2n2F 2ARfarcA
(
(7)
where n is the number of electrons involved in the electrochemical reaction, A is the electrode surface area (in cm2), cA is the bulk concentration of reactant (in mol‚cm-3), and (E - Eof ) is the overpotential. (7) Sabatini, E.; Rubinstein, I. J. Phys. Chem. 1987, 91, 6663. (8) Prostailo, L. V.; Fawcett, W. R. Electrochim. Acta 2000, 45, 3497.
Figure 8. Tafel plot of electron-transfer rate constant versus overpotential. The ac frequency was 94 kHz, and the supporting electrolyte was 0.1 M HClO4.
Figure 7 shows a typical plot of ln kf against overpotential. Excellent linear plots were obtained at different frequencies and concentrations of the supporting electrolyte. The standard rate constant ks and the experimental transfer coefficient Rex were calculated from the intercept and the slope of these plots. All experimental results are summarized in Table 2. Very good agreement between data from the Randles and Baranski analyses was observed. DISCUSSION It is clear from the data presented that very precise data for fast rate constants may be obtained using high-frequency ac admittance voltammetry at a ume. One of the purposes of this paper is to illustrate in detail what we consider the best way to analyze the results. An important aspect of this involves separation of the Warburg or mass-transfer impedance from the overall impedance for the system. The graphical technique seems to be the best way to achieve this separation. The cyclic voltammetric study is an important prelude to the faradaic admittance experiments because it provides diffusion coefficient data that are relevant to the solution composition used. Since the diffusion coefficient changes significantly with ionic strength, these data are reported here as the square root D1/2. In this way, estimated errors from each experiment may be compared directly. In the present case, the level of error does not change with ionic strength. (9) Hromadova, M.; Fawcett, W. R. J. Phys. Chem. A 2000, 104, 4356. (10) Fawcett, W. R.; Hromadova, M.; Tsirlina, G. A.; Nazmutdinov, R. R. J. Electroanal. Chem. 2001, 498, 93. (11) Komanicky, V.; Fawcett, W. R. Angew. Chem., Int. Ed. 2001, 40, 563. (12) Komanicky, V.; Fawcett, W. R. Anal. Chem. 2003, 75, 4534.
The double layer effect observed is consistent with that for a positively charged reactant reacting at an electrode close to the pzc. The pzc on polycrystalline gold is estimated to be -0.23 V on the potential scale used in this study versus a calomel electrode with 0.05 M KCl. This is slightly more positive than the standard potential for the reaction (see Table 1). Thus, at the most positive potentials, the reactant is repelled from the double layer. However, this rapidly decreases and becomes attraction for the most negative potentials. The net double layer effect decreases with increase in ionic strength so that the standard rate constant increases by a factor of 3 when the concentration of HClO4 increases from 0.02 to 0.1 M. At the same time, the experimental transfer coefficient decreases from 0.55 to 0.48. The relationship between the experimental transfer coefficient Rex and the true transfer coefficient R is
Rex ) R + (zA - R)(dφr/dE)
(8)
where dφr/dE is the coefficient describing the change in the effective potential at the reaction site with electrode potential9,10 and zA is the charge on the reactant. The coefficient dφr/dE is the order of 0.1 when the reaction site is on the outer Helmholtz plane, and it decreases with increase in ionic strength. Assuming that zA is 2+ because of ion pairing,9 and that R is 0.5, the second term on the right-hand site of eq 8 is equal to 0.15. As a result, Rex would be 0.65. Since the experiments’ values are significantly smaller, the charge center of the reactant is probably located further from the outer Helmholtz plane in the diffuse layer. The distribution of charge within the reactant is also important in determining the magnitude of this term and of the double layer effect.9,10 Further analysis of the double layer effect was not attempted because the structure of a polycrystalline electrode depends on the metallurgical history of the gold and is not easily reproduced. For this reason, we have developed single crystal ume’s.11,12 This system will be studied at Au(111) and Au(100) so that a more quantitative analysis of the double layer effect may be presented. This will provide valuable information to those interested in the theory of electron transfer. It will also allow us to examine effects related to the distribution of charge in this polyatomic reactant.9,10
ACKNOWLEDGMENT This research was supported by a grant from the National Science Foundation, Washington (CHE-0133758). Received for review January 8, 2004. Accepted March 11, 2004. AC0499524
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