Combining Impedance Spectroscopy with Cyclic Voltammetry

The technique of time-resolved impedance spectroscopy can be combined with dc cyclic voltammetry (CV) to study mechanisms and kinetics of electrochemi...
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Anal. Chem. 2006, 78, 3723-3729

Combining Impedance Spectroscopy with Cyclic Voltammetry: Measurement and Analysis of Kinetic Parameters for Faradaic and Nonfaradaic Reactions on Thin-Film Gold C. M. Pettit, P. C. Goonetilleke, C. M. Sulyma, and D. Roy*

Department of Physics, Clarkson University, Potsdam, New York 13699-5820

The technique of time-resolved impedance spectroscopy can be combined with dc cyclic voltammetry (CV) to study mechanisms and kinetics of electrochemical reactions at solid-liquid interfaces. Utilization of these techniques in a combined framework, however, is based on a number of specific considerations of measurement procedures and data analysis. The present work discusses certain essential elements of this topic, focusing primarily on the analysis of time-resolved impedance spectra where interdependent dc and ac effects of parallel faradaic and nonfaradaic reactions are present under potentiodynamic conditions. A thin gold film is used as a model experimental system where oxidation and reduction of the sample surface is voltage-controlled both in the presence and in the absence of specifically adsorbing Cl- ions in neutral background electrolytes of NaF. Impedance spectra are recorded under transient conditions of CV, and kinetic parameters based on electrode-equivalent circuit models are obtained as functions of CV scans. Electrochemical impedance spectroscopy (EIS) is an efficient analytical tool for studying a variety of chemical, electrochemical, and biological surface reactions.1-10 Usually traditional EIS is performed under potentiostatic conditions at fixed dc potentials where only steady state or no dc currents are allowed.1-5 This method, which often also requires several minutes to record a * Corresponding author. E-mail: [email protected]. (1) Barsoukov, E., Macdonald, J. R., Eds. Impedance Spectroscopy; Wiley: New York. 2005. (2) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; Wiley: New York, 2001. (3) Sluyters-Rebach, M.; Sluyters, J. H. In Comprehensive Treatise of Electrochemistry; Yeager, E, Bockris, J. O’M., Conway, B. E., Sarangapani, S., Eds.; Plenum Press: New York, 1980; Vol. 9, p 177. (4) Macdonald, D. D.; Sikora, E.; Engelhardt, G. Electrochim. Acta 1998, 43, 87-107. (5) Coster, H. G. L.; Chilcott, T. C.; Coster, A. C. F. Bioelectrochem. Bioenerg. 1996, 40, 79-98. (6) Pettit, C. M.; Garland, J. E.; Walters, M. J.; Roy, D. Electrochim. Acta 2004, 49, 3293-3304. (7) Garland, J. E.; Pettit, C. M.; Roy, D. Electrochim. Acta 2004, 49, 26232635. (8) Assiongbon, K. A.; Roy, D. Surf. Sci. 2005, 594, 99-119. (9) Emery, S. B.; Hubbley J. L.; Roy, D. Electrochim. Acta 2005, 50, 56595672. (10) Assiongbon, K. A.; Emery, S. B.; Pettit, C. M.; Babu, S. V.; Roy, D. Mater. Chem. Phys. 2004, 86, 347-357. 10.1021/ac052157l CCC: $33.50 Published on Web 04/25/2006

© 2006 American Chemical Society

full impedance spectrum, does not generally provide an adequate framework for studying time-dependent systems. The disadvantages of this approach are mostly encountered in studies of faradaic electrochemical reactions that are controlled with cyclic voltammetry (CV).2 In these cases, it is difficult to quantitatively compare potentiodynamic dc data for voltage-dependent currents with potentiostatic ac EIS results. In recent years, a number of time-resolved ac impedance techniques have been reported that can effectively address the aforementioned disadvantages of stationary state EIS.6-18 Fourier transform electrochemical impedance spectroscopy (FT-EIS) is an experimentally convenient technique for such potentiodynamic impedance measurements.7,9,15,19 In this approach, a series of Nyquist (or Bode) spectra are obtained in parallel with the recording of CV data, and dc voltage-dependent electrode equivalent circuit (EEC) models are developed through complex nonlinear leastsquares (CNLS) analysis20 of these impedance spectra; information about surface kinetics is obtained by studying various voltagedependent features of the kinetic circuit parameters.7-10,21 The dc response of the system plays an essential role in dictating the detailed composition of the EECs found in such cases, and these effects become particularly important for faradaic systems where significant dc currents are generated in the CV scans.6,9 Certain aspects of various dc effects on impedance measurements have been discussed in the context of ac voltammetry.11,22,23 However, the roles of dc voltages and currents in ac analysis of EECs are rarely discussed in the context of EIS experiments. In (11) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. M. Anal. Chem. 2005, 77, 186A-196A. (12) Ragoisha, G. A.; Bondarenko, A. S. Surf. Sci. 2004, 315, 566-568. (13) Yoo, J.-S.; Song, I.; Lee, J.-H, Park, S.-M. Anal. Chem. 2003, 75, 32943300. (14) Darowicki, K.; Krakowiak, S.; Œlepski, P. Electrochim. Acta 2004, 49, 29092918. (15) Popkirov, G. S.; Schindler, R. N. Electrochim. Acta 1993, 38, 861-867. (16) Popkirov, G. S.; Schindler, R. N. Electrochim. Acta 1994, 39, 2025-2030. (17) Baltrunas, G.; Popkirov, G. S.; Scindler, R. N. J. Electroanal. Chem. 1997, 435, 95-101. (18) Popkirov, G. S. Electrochim. Acta 1996, 41, 1023-1027. (19) Schwall, R. J.; Bond, A. M.; Loyd, R. J.; Larsen, J. G.; Smith; D. E. Anal. Chem. 1977, 49, 1797-1805. (20) Boukamp, B. A. Solid State Ionics 1986, 20, 31-44. (21) Gorantla, V. R. K.; Assiongbon, K. A.; Babu, S. V.; Roy, D. J. Electrochem. Soc. 2005, 152, G404-G410. (22) Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 2002, 535, 27-35. (23) Harrington, D. A. J. Electroanal. Chem. 1993, 355, 21-35.

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Figure 1. Illustrative examples of circuit models for faradaic and nonfaradaic reactions, showing distribution of dc and ac currents in parallel branches. A general circuit is shown in (A). The circuit containing four branches (I-IV) in (B) shows typical combinations of resistive and capacitive elements for nonfaradaic adsorption (“a”) and faradaic (“f”) reactions. The Rf-Cf branch III in (B) only allows capacitive currents, jı cf (dc) and ˜ıcf (ac), and the pure resistive branch IV allows the current components jı rf (dc) and ˜ırf (ac).

the present work, we focus on further clarification of the dc and ac effects that are simultaneously activated in time-resolved EIS. The experimental system used here is a thin-film Au electrode in neutral electrolytes of NaF (in the absence of anion adsorption) and NaF + NaCl (in the presence of Cl- adsorption), where faradaic formation of gold hydroxides and oxides are controlled with CV in both solutions. Our selection of this model system is based on the consideration that, thin-film gold electrodes are now used in numerous optoelectrochemical sensors where faradaic and nonfaradaic surface reactions such as those investigated here are often encountered.24-28 THEORETICAL CONSIDERATIONS Criteria for Combining FT-EIS with dc Cyclic Voltammetry. If FT-EIS is combined with CV, it becomes necessary to simultaneously measure (and analyze) both dc and ac parameters, which we denote here with a “bar” and a “tilde”, respectively. FTEIS utilizes a single noiselike ac perturbation input typically containing 50-200 frequency-selected, sinusoidal, phase-randomized small voltages.7 For each angular frequency (ω) in the spectrum we have E ˜ ) E0 sin(ωt + φ0), where E0, φ0, and t represent the voltage amplitude, a reference phase, and time in the perturbation voltage E ˜ , respectively. The ac voltage is superimposed on the dc voltage E h of CV, and E h is linearly scanned at a rate of v. The resulting current i contains both dc (ıj) and ac (ı˜) components, i ) jı + ˜ı. Figure 1A shows a general EEC representing a faradaic reaction of impedance Zf, operative in parallel with a nonfaradaic anion adsorption of impedance Za. Ru and Cd are the uncompensated solution resistance and double (24) Pronkin, S.; Wandlowski, Th. Surf. Sci. 2004, 573, 109-127. (25) Roy, D.; Fendler, J. H. Adv. Mater. 2004, 16, 479-508. (26) Dugo, G.; La Pera, L.; Turco, V. L.; Bella, G. D. Chemosphere 2005, 61, 1093-1101. (27) Kim, S. D.; Chung, J. W.; Kim, J. T.; Krause, H.; Pyun, J. C. Sens. Actuators, B 2005, 111-112, 463-469. (28) Ligler, F. S., Taitt, C. A. R., Eds. Optical Biosensors: Present and Future, Elsevier: Amsterdam, 2002.

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layer capacitance, respectively. The total current is distributed in three branches; i ) ic + ia + if. The double layer charging current is ic, and the currents in the anion adsorption and faradaic reaction branches are ia and if, respectively. Each current has a dc and an ac component; ic ) jıc + ˜ıc, ia ) jıa + ˜ıa, and if ) jıf + ˜ıf. The net impedance (Z) of the EEC is, Z ) Z′ + jZ′′; j ) (-1)1/2; Z′ and Z′′ are the real and imaginary parts of Z, respectively. Also, in this notation, Za ) Za′ + jZa′′, and Zf ) Zf′ + jZf′′. The general criteria for EIS measurements include causality, current-voltage linearity, and system stability.1 In addition, the experimental system must exhibit “short-term” stationary behavior18 so that the surface conditions do not vary during the maximum time period (1/fmin) of the ac voltages (fmin being the lowest frequency in the spectrum, and f ) ω/2π). The main criteria for potentiodynamic EIS can be briefly summarized as follows:6-8 (i) E0 e (RT/nF); (ii) fmin . [v/((2)1/2πE0)]; (iii) fmin . [(dıj/dt)/((2)1/2πi0)], where i0 is the amplitude of ˜ı, n is the charge number of the electrode reaction under study, and (RT/ nF) is the characteristic electrochemical voltage in usual notation. Validation of recorded impedance spectra usually requires the Kramers-Kronig transformation test,1,29 which is commonly used in frequency-domain EIS studies. Popkirov et al. have developed an alternate method for validation of time domain FT-EIS data that involves a detailed frequency-matching comparison between the ac input voltage and the corresponding current response spectra.15-18 This latter method has also been illustrated in our earlier reports6,7 and is used in the present work for checking the validity of EIS results. Dc and ac Current Paths in Electrode Equivalent Circuits. Figure 1B is a more detailed version of Figure 1A, showing an illustrative example of a commonly found circuit arrangement for nonfaradaic and faradaic adsorption reactions. The currents through pure resistance and capacitance-resistance combination branches are labeled with superscripts “r” and “c”, respectively. Mass-transfer-limited diffusion effects9,23 are excluded from this simple example. Ra and Ca are adsorption resistance and pseudocapacitance of the nonfaradaic adsorption reaction, respectively; Rf and Cf are faradaic resistance and pseudocapacitance of a faradaic charge-transfer reaction, respectively. In branches I, II, and III, dc currents can only flow through charging-discharging of the capacitors contained in these branches. Such capacitive currents usually are too small to support strong faradaic reactions at high overpotentials, and the resistance Rdc f provides the pathway for these faradaic currents.9 Like the dc double layer current in branch I, usually the dc capacitive current in branch II (ıja ≡ jıac) also is small compared to jıf.31 In branches III and IV, jıf ) jı cf + jı rf , and ˜ıf ) ˜ı cf + ˜ı rf , where jı cf and jı rf (or ˜ı cf and ˜ı rf ) are the dc (or ac) capacitive and resistive currents allowed by Cf and Rdc f , respectively. The dc resistance Rdc f is critical in determining the relative dc and ac current paths in the EEC. To consider experimental measurement of this quantity, we note that the dc polarization resistance (Rp), commonly found in the literature of corrosion electrochemistry1,30 is h ]-1, where E h m is the mixed defined as Rp ) LimEh fEh m[d(ıjrf )/dE (29) Lasia, A. In Modern Aspects of Electrochemistry; Conway, B. E., Bockris, J. O’M., White, R. E., Eds.; Kluwer: New York, 1999; Vol. 32, p 236. (30) Fontana, M. G. Corrosion Engineering; McGraw-Hill: New York, 1986; p 462. (31) Pettit, C. M.; Goonetilleke, P. C.; Roy, D. J. Electroanal. Chem. In press.

potential30 of different active surface reactions. This definition of Rp corresponds to a limited voltage region in the immediate neighborhood on both anodic and cathodic sides of the mixed potential, where |ıjrf | is small and linear in E h . Rp is independent of variations in E h within this range and does not necessarily provide an adequate measure of the dc resistance at voltages away from E h m. A differential form of the E h -dependent resistance Rdc can be f introduced by generalizing the above definition of Rp, that is by (assuming that jı ≈ jıf, and) calculating the voltage-dependent local slopes [d(ıj)/dE h ]-1 of experimentally obtained (ıj - E h ) voltammograms. The individual circuit elements contained in Za and Zf also are defined in similar differential forms.3 However, to evaluate the overall ac and dc response characteristics of the EEC, usually it is only necessary to compare Rdc f with the dc voltage-dependent composite impedance term Zf. Simple order of magnitude estimates are often sufficient for such comparisons,9 and for this purpose, it is useful to introduce a simple integral form of Rdc f as follows:30 Rdc h -E h m|/|ıjrf |) for |E h -E h m| > 0. For predomif ≈ (|E nantly faradaic systems (ıj ≈ jıf), this Rdc f can be easily obtained from the recorded dc voltammograms. Rdc f is a representative empirical parameter of the dc faradaic response of the electrode at E h *E h m, where |ıjrf | is nonzero and not necessarily linear in E h. At E h ) E h m, one has jı rf ) 0, and in this limit according to L’Hospital’s rule, the above empirical formula of Rdc f takes the usual differential form of Rp. Thus, the integral quantity Rdc f is consistent with the definition of Rp, and the relationship between Rdc f and Rp can be phenomenologically characterized by considering the limit of zero dc current at the mixed potential. We note in this context that straightforward determination of the differential form of Rdc h ) by using CV can often be difficult, because taking f (E direct point-to-point derivative of a given dc voltammogram can lead to significant amplification of even minor noises associated with such data. This problem can be largely avoided by using the integral form of Rdc as described above. Moreover, at large f overpotentials and for small values of v, Cd and Cf, order of magnitude estimates for Rdc f can be made for some systems simply in terms of the ratio (E h /ıj). For moderately strong faradaic reactions (|E h -E h m| ranging between 0.1 and 1.0 V, and jıf between 10 and 50 µA cm-2) Rdc f varies between 2 and 0.1 MΩ cm2. In comparison, even at the minimum perturbation frequency (usually 100 Hz) available for time-resolved FT-EIS, the corresponding ac impedance (|Zf| ) |Rf + (jωCf)-1 | in Figure 1B) of the same faradaic reactions usually is several orders of magnitude smaller than these values of 6-10 This forces ˜ Rdc ıf to essentially bypass the current branch of f . dc r Rf (that is, ˜ı f 0) outside those of linear polarization are shown in (C) and (D), respectively. The values of E h m (listed in Table 1) used to determine Rdc f in (C) and (D) are obtained from Figure 3B and C, respectively. Table 1. Dc Parameters for Faradaic Oxidation-Reduction of Au Q h tfa (µC cm-2)

Q h tfc (µC cm-2)

E hm (V vs SCE)

jım (µA cm-2)

M NaF + 1 mM NaCl

351

400

-0.22a

0.29a

0. 1 M NaF

329

355

-0.14b -0.20a 0.03b

0.20b 0.21a 0.12b

solution

a For positive voltage scan from -0.5 to 0.5 V. b For negative voltage scan from 0.5 to -0.5 V.

faradaic reaction in both solutions used here has the form39-44

Au + H2O ) Au-OHads + H+ + e-

(1)

where OHads represents adsorbed hydroxide species and e- is the electron charge. Depending on the electrolyte composition, the Au-OHads may also retain a partial negative charge.43 On Au thin films in neutral solutions, the anodic current of reaction 1 typically becomes measurable between -0.2 and 0 V.38-40,45 At higher positive potentials (g-0.05 V) some of the Au-OHads sites generated via reaction 1 can be oxidized further to AuO:38,45

Au-OHads ) AuO + H+ + e-

(2)

The reverse (reduction) steps of reactions 1 and 2 occur in negative voltage scans of CV between -0.2 and -0.5 V.42,43 3726 Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

Figure 3. (A) Diagram (not drawn to scale) illustrating the essential elements of the mixed potential concept for analyzing dc parameters of two simultaneously operative faradaic reactions. The schematic Tafel plots for two reactions with two different equilibrium potentials (E h (1) h (2) h m and jım are the mixed eq < E eq ) in (A) are labeled as (1) and (2); E potential and current, respectively. Corresponding experimental data are shown in (B) and (C) for positive (from -0.5 to 0.5 V) and negative (from 0.5 to -0.5 V) voltage scans at 5 mV s-1, respectively. Plots a and b correspond to electrolytes of 0.1 M NaF + 1 mM NaCl and 0.1 M NaF, respectively.

In the 0.05-0.1 M concentration range of Cl-, and in the absence of other competing adsorption processes, chemisorption of Cl- dominates the surface electrochemistry of Au films between -0.5 and 0.5 V.9 In our present experiments, however, Cl- is either completely absent (0.1 M NaF) or is only present at a considerably smaller concentration (0.1 M NaF + 1 mM NaCl) than the aforementioned values. In these cases, F- from the supporting electrolyte is unlikely to adsorb on Au in any measurable amounts,46 and chemisorption of Cl- in the NaF + NaCl system is constrained due to competing faradaic reactions. This is indicated by the strikingly similar voltammograms for the Clcontaining and Cl- free solutions in Figure 2B. Dissolution of Au as Au(Cl2)- (in the presence of Cl-), Au+, or Au3+ and formation of higher oxides of Au are prevented within the anodic voltage limit used here.47 By integrating the currents in Figure 2B, we obtain the total anodic and cathodic charges (averaged between positive and negative cycles), Q h tfa and Q h tfc, listed in the first two columns of (43) Hsiao, M. W.; Adzˇic´, R. R.; Yeager, E. B. J. Electrochem. Soc. 1996, 143, 759-767. (44) Chen, A.; Lipkowski, J. J. Phys. Chem. B 1999, 103, 682-691. (45) Ye, S.; Ishibashi, C.; Shimazu, K.; Uosaki, K. J. Electroaanal. Chem. 1998, 145, 1614-1623. (46) Habib, M. A.; Bockris, J. O’M. In Comprehensive Treatise of Electrochemistry; Bockris, J. O’.M., Conway, B. E., Yeager, E., Eds.; Plenum: New York, 1980; Vol. 1, p 135. (47) Milazzo, G.; Caroli, S. Tables of Standard Electrode Potentials; John Wiley: New York, 1978.

Table 1. These charges are associated with the forward and reverse steps of the combined reaction [(1) + (2)], respectively. In both solutions used, |Q h tfc| is somewhat larger than |Q h tfa|. This t suggests that Q h fc may contain a measurable contribution of the hydrogen evolution reaction48 at the cathodic extreme of the voltage range used here. The total charge density (Q h s) necessary to faradaically form a full layer of adsorbates by |e| amount of charge-transfer per site on the Au surface can be estimated as Q h s ≈ No|e|, where No is the surface density of bare Au sites. Taking8 No ) 12 × 1014 cm-2, we obtain Q h s ≈ 192 µC cm-2. If all the charges contained in Q h tfa in Table 1 are attributed to reaction 1, then the number of AuOH layers formed should be (Q h tfa/Q h s) ≈ 1.8 and 1.7, for the NaF + NaCl and NaF, solutions, respectively. In practice, however, the charge contained in Q h tfa is likely to be divided between reactions 1 and 2, which implies that the anodically formed films on Au probably are thinner than the aforementioned values and that these films contain both AuOH and AuO species. Moreover, the relative amounts of AuOH and AuO in the anodic films could be different in the different solutions. Mixed Potentials and Currents. The dc parameters at E h) E h m for the presently studied surface reactions are examined using the Tafel plots in Figure 3. The underlying framework for this analysis is based on the considerations of mixed potential theory30 and is schematically shown in Figure 3A. We assume here that the net dc current is caused primarily by the faradaic reactions 1 and 2, and that these reactions have the same Tafel slopes, but have two different equilibrium potentials, E h (1) h (2) eq and E eq . In Figure 3A, the schematic Tafel plots for these two reactions are labeled as (1) and (2), respectively. The net polarization plot is labeled as (1) + (2). The mixed potential (E h m) and mixed current (ıjm) for the net reaction are also indicated in Figure 3A. Here jım represents the anodic current of the forward step of reaction 1, which also is equal to the cathodic current of the reverse step of reaction 2. Here E h m and jım are equivalent to what are commonly referred to as corrosion voltage and current for certain systems, h )E h m, the rate of the forward step of reaction respectively.30 At E 1 becomes equal to the rate of the reverse step of reaction 2, and then the net reaction takes the form, Au + AuO + H2O ) 2(AuOHads). The experimental data in Figure 3B and C correspond to the positive (-0.5 to 0.5 V) and negative (0.5 to -0.5 V) voltage scans, respectively. Plots a and b represent electrolytes of 0.1 M NaF + NaCl and 0.1 M NaF, respectively. The dc parameters obtained from Figure 3B and C are summarized in Table 1. In Figure 3B, the values of E h m are similar between the Cl--containing and Cl-free solutions, which reinforces the point we made earlier that the faradaic reactions dominate here over nonfaradaic anion adsorption in dictating the overall surface conditions. In Figure 3B, the value of jım for plot a is larger than that for (b), which implies that the Au surface is relatively less oxidized (passivated) in (a) as a result of Cl- adsorption.21 This also is indicated in the slightly lower value of E h m for plot a than for plot b. In addition, if adsorption of Cl- on Au is not strictly nonfaradaic, the partial charge transfer for Cl- adsorption would also contribute to the measured value of jım.49 A feature containing the characteristic (48) Lovell, M. A.; Roy, D. Appl. Surf. Sci. 1998, 135, 46-52.

Figure 4. Illustrative dc voltage-dependent Nyquist plots recorded in 0.1 M NaF + 1 mM NaCl (A and B) and 0.1 M NaF (C and D) at -0.2 V during the positive voltage scan (A and C) and at -0.5 V at the end of the triangular voltage sweep (B and D). The symbols are data points, and the lines represent CNLS fits to the data using the circuits shown in Figure 5A (for the data in Figure 4A and B) or 6A (for the data in Figure 4C and D).

signature of surface passivation30 is observed at ∼0.3 V in Figure 3C. The differences observed in Figure 3B between the dc parameters of the Cl--containing and Cl--free systems are enhanced further in Figure 3C. This is a result of higher (site passivating) AuO content of the Au surface during negative voltage scans following the positive oxidation scans. The presence of these oxide layers is also manifested in the noticeably higher values of E h m in Figure 3C in comparison with their respective counterparts in Figure 3B (Table 1). These same effects are responsible for the observed lowering (Table 1) of the values of jım as we go from positive (Figure 3B) to negative (Figure 3C) voltage scans. The anodic current branch of Figure 3B(b) contains a distinct structure (indicated by a vertical arrow) at E h ) -0.05 V where the current exhibits a noticeable abrupt increase. The same structure is also present but is considerably weaker in Figure 3B(a). According to the illustration of Figure 2A, this feature most probably corresponds to activation of reaction 2. Thus, the net reactions that are activated during the CV cycle can be divided in two voltage zones. In the first zone, between -0.50 and -0.05 V, the main faradaic step is reaction 1. In the second zone, between -0.05 and 0.50 V, both reactions 1 and 2 contribute to jı. dc Voltage-Dependent Nyquist Plots and Impedance Parameters. Figure 4 shows illustrative examples of time-resolved Nyquist plots recorded during CV of the Au film electrode in 0.1 M NaF + 1 mM NaCl (A and B) and 0.1 M NaF (C and D). The sampling voltages are indicated in the figure caption. The symbols and the solid lines in Figure 4A-D represent experimental data and CNLS fits to the data, respectively. An animated compilation of the full set of Nyquist plots, recorded at 1-s intervals during the CV scans is currently displayed at our research group’s web site.50 The EECs in Figures 5A and 6A fit consistently to all Nyquist plots recorded during CV in 0.1 M NaF + 1 mM NaCl and 0.1 M (49) Walters, M. J.; Garland, J. E. Pettit, C. M., Zimmerman, D. S.; Marr, D. R.; Roy, D. J. Electroanal. Chem. 2001, 499, 48-60. Addition and corrections: 2002, 526, 142-142. (50) http://people.clarkson.edu/∼surop/.

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Figure 5. (A) EEC used to fit time-resolved Nyquist plots recorded during CV between -0.5 and 0.5 V at 5 mV s-1 of a thin-film Au electrode in 0.1 M NaF + 1 mM NaCl. (B) and (C) dc voltagedependent kinetic impedance parameters measured with FT-EIS for the faradaic (Rf and Cf) and nonfaradaic (Ra and Ca) reaction branches, respectively. To maintain clarity of the graphs, we have used every fourth data point from the full data set to plot Rf and Cf, and every other data point to plot Ra and Ca.

Figure 6. (A) EEC used to fit time-resolved Nyquist plots recorded during CV (between -0.5 and 0.5 V at 5 mV s-1) of a thin-film Au electrode in 0.1 M NaF. (B) Dc voltage-dependent kinetic impedance parameters (Rf and Cf) measured with FT-EIS for the faradaic reaction branch. To maintain clarity of the graphs, we have used every fourth data point from the full data set to plot Rf and Cf.

NaF, respectively. The circuit parameters in each case are dc voltage dependent, as shown in Figure 5B and C (for NaF + NaCl) and in Figure 6B (for NaF). Ru and Cd are not included in Figures 5 and 6; Ru is voltage independent with values remaining close to 0.6 Ω cm2 in both solutions used. Cd also is voltage independent, about 7 and 5 µF cm-2, in NaF + NaCl and NaF, respectively. The two lower branches in Figure 5A are identical in terms of their representative circuit elements, but these elements have considerably different values and different dc voltage dependencies between the two branches. Moreover, the circuit elements (Rf and Cf) having the larger values are more sensitive to variations in E h than the elements (Ra and Ca) of lower values. Because the faradaic steps of eqs 1 and 2 dominate the dc response of the interface 3728 Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

(Figures 2 and 3), it is expected that these reactions would also dominate the ac impedance characteristics of the Au electrode. Based on this consideration, we associate the relatively more voltage sensitive circuit branch (Rf -Cf) in Figure 5A with reactions 1 and 2; the branch of Ra and Ca is then attributed to the relatively weaker reaction of anion adsorption. More compelling basis for these branch assignments can be noted by comparing the results of Figures 5 and 6. In Cl--free NaF (Figure 6), anion adsorption is negligible and the faradaic steps of eqs 1 and 2 are the only detectable reactions using EIS. Therefore, the single reaction branch containing Rf and Cf in Figure 6 should be associated with the faradaic reactions and not with anion adsorption. At the same time, both in terms of their voltage dependencies and overall magnitudes, Rf and Cf in Figure 6 are comparable to Rf and Cf (but not with Ra and Ca) in Figure 5. This indicates that the circuit branch labeled with “f” in Figure 5A indeed represents the faradaic reactions. Dc voltage-dependent analytical formulas for resistive and capacitive elements of nonfaradaic adsorption and faradaic charge transfer have been reported previously.3,6,9,51,52 Certain general predictions about the voltage-dependent trends of these impedance parameters can be made based on these previously known formulas. If a faradaic adsorption step is characterized by a Langmuir-type equilibrium isotherm, then the adsorption capacitance would exhibit a peak-shaped dependence with respect to variations in the dc voltage,9,51 and the corresponding resistance would show an opposite trend; this capacitance peak would occur at the formal potential of the reaction.9 For fast reactions, this equilibrium voltage dependence of the pseudocapacitance might be largely retained even at voltages away from equilibrium.40,52,53 On the other hand, for slow reactions, voltage dependencies of the impedance parameters could resemble those of irreversible reactions.6,9 In the latter case, the capacitance would monotonically decrease (and the resistance would increase) with increasing adsorbate coverages (that is, with increasing positive voltages for anion adsorption).6 The impedance parameters in Figure 5B contain characteristic features of both reactions 1 and 2. Because these two reactions occur sequentially (in series), Cf as well as Rf can be considered as21 (Cf)-1 ) (Cf1)-1 + (Cf2)-1, and Rf ) (Rf1 + Rf2), where subscripts “1” and “2” correspond to reactions 1 and 2, respectively. According to the observations made in Figure 3B, anodic reaction 1 dominates between -0.50 and -0.05 V, where Cf1 and Rf1 should dominate the voltage dependencies of Cf and Rf, respectively. If these elements for reaction 1 contain the characteristic features of irreversible systems, Cf would decreases with an accompanying increase in Rf in this voltage range. If Cf2 and Rf2 dominate the observed faradaic impedance in the next reaction zone between -0.05 and 0.50 V, and if these elements result from a Langmuir-type adsorption, then the capacitance-voltage graph should be approximately bell-shaped, with the corresponding resistance plot being inverted bell-shaped. The Cf and Rf graphs in Figure 5B are consistent with this scenario. The plots in Figure 5B also are associated with a measurable hysteresis with respect to the voltage scan directions. This hyteresis is consistent with (51) Conway, B. E. Prog. Surf. Sci. 1984, 16, 1-137. (52) Los, P.; Laviron, E. J. Electroanal. Chem. 1997, 432, 85-99. (53) Jovic´, B. M.; Jovic´, V. D.; Drazˇic´, D. M. J. Electroanal. Chem. 1995, 399, 197-206.

the upward shifts of equilibrium potentials observed in going from Figure 3B (positive CV scan) to C (negative CV scan), and as we already stated in the context of Figure 3, these shifts could be explained in terms of different oxide contents of the Au surface in the positive and negative voltage scans. Close inspection of the data in Figure 5C indicates that both Ca and Ra contain a slight trend of Langmuir-like adsorption behavior as observed in earlier studies of Cl- adsorption on Ag.53 Nevertheless, these plots are distorted in the region between -0.05 and 0.50 V due to interference of reactions 1 and 2, and therefore, it is difficult to examine the shapes of these plots quantitatively. Similar interfering effects of faradaic and nonfaradaic reactions have been observed previously.9 The overall values of Cf and Rf in Figure 6B for NaF are comparable to those observed in Figure 5B for NaF + NaCl. This finding is consistent with the comparable voltammograms seen for the two systems in Figure 2B. The detailed features of the impedance parameters, however, are different between the two solutions. From -0.50 to -0.05 V (region of reaction 1), the voltage dependencies of Cf and Rf in Figure 6B are similar to those of Cf and Rf in the same region of Figure 5B, respectively. Between -0.05 and 0.50 V (region of both reactions 1 and 2), Cf and Rf in Figure 6B continue their respective established trends from the more cathodic region, even though these parameters in Figure 5B exhibit rather different voltage dependencies in the two voltage regions. The different effects of the two voltage regions in the two solutions have already been observed in Figure 3B, where contribution of reaction 2 (marked by the feature at -0.05 V) was more prominently seen in the NaF + NaCl solution (plot a) than in NaF (plot b) alone. To examine the possible origin(s) of this effect, we note that, in the presence of Cl-, adsorption of water molecules on Au could be favored around the Cl--containing surface sites.54 Thus, it is possible that reaction 1, which uses adsorbed water on Au as a reactant, occurs in the Cl--containing electrolyte at preferential surface regions surrounding the Cladsorption sites. As these “water-enriched” Au sites begin to be exhausted through their conversion to AuOH, reaction 2 starts to dominate the faradaic response of the electrode surface. Because this transition occurs around -0.05 V, both the dc (Figure 3B(a)) and ac (Figure 5B) faradaic parameters of the Cl-containing system tend to exhibit the different adsorption features of reactions 1 and 2 on two sides of the transition voltage. In the absence of Cl- adsorption, surface coverage of water should be more uniform throughout the Au surface. Therefore, anodic reaction 1, now occurring at more delocalized sites, and having a relatively lower equilibrium potential, can have a stronger role than reaction 2 in dictating the overall faradaic response of the electrode at E h >E h (2) eq . In this case of Cl -free NaF, the kinetics of reaction 1 should primarily control the voltage dependencies of both the dc and ac faradaic parameters in the full voltage range of CV. The results of Figures 6B and 3B(b) are consistent with this description. Furthermore, according to the reaction mechanisms proposed above, the Au surface should be relatively more passivated in NaF alone than in NaF + NaCl. This is expected, because the active Au sites for reaction 1, which eventually turn into AuOH and AuO, should be relatively more widespread

across the (Cl--free chemically uniform) surface in the latter solution. The consistently higher values of E h m measured in the absence of Cl- (Table 1) are in full agreement with this description. Relative Values of dc Resistance and ac Impedance for Faradaic Reactions. The values of Cd (e7 µF cm-2) and Cf (