ARTICLE pubs.acs.org/JPCA
Activation Parameters Derived From a Temperature Dependent Large Amplitude ac Voltammetric Study of the Electrode Kinetics of the Cp2M0/þ Redox Couples (M = Fe, Co) at a Glassy Carbon Electrode John P. Bullock,† Elena Mashkina,‡ and Alan M. Bond*,‡ † ‡
Division of Natural Sciences & Mathematics, Bennington College, Bennington, Vermont 05201, United States School of Chemistry, Monash University, Clayton, Victoria 3800, Australia ABSTRACT: Heterogeneous charge transfer rate constants (k) for the oxidation of ferrocene, Fc (k = 0.21 cm s1 at 20 C), and the reduction of the cobaltocenium cation, Ccþ (k = 0.12 cm s1 at 18 C), in CH2Cl2 (0.5 M Bu4NPF6) at a glassy carbon (GC) electrode were determined as a function of temperature using the higher harmonic components available in Fourier transformed large amplitude ac voltammetry. The measured k values lie at the upper end of the analytically useful range available for the acquisition of meaningful kinetic data for these very fast (i.e., close to reversible) processes. Measurements of the kinetics are facilitated by the ac technique because contributions resulting from uncompensated resistance and slow electrode kinetics, both of which also vary with temperature, can be distinguished via their different contributions to individual harmonics. Values of k measured over the temperature range of 18 to þ20 C for the Fc0/þ and Ccþ/0 processes gave linear Arrhenius plots yielding free energies of activation (ΔG‡) estimates of 17.0 and 18.0 kJ mol1, respectively, in excellent agreement with theoretical values derived from Marcus theory. An analogous temperature dependence is indicated in a study of the Fc0/þ process in acetonitrile (0.1 M Bu4NPF6), but the greater k value evident makes the temperature dependence of these parameters more difficult to quantify as departures from reversibility are minimal, even in the higher harmonics.
’ INTRODUCTION Elucidating the factors that determine the rate of heterogeneous electron transfer at modified and unmodified electrode surfaces remains an area of active interest.1 While in principle the kinetics of all electron transfer processes are explained satisfactorily on the basis of MarcusHush theory,2 in practice experimental data for heterogeneous processes obtained under dynamic electrochemical conditions depend on the material and history of the electrode and are therefore not as readily interpreted as those of solution phase homogeneous processes. Moreover, measuring the electrode kinetics of redox processes that are considered fast, i.e., those for which the standard heterogeneous charge transfer rate constant, k, is greater than 0.1 cm s1, and that also involve diffusion mass transport, presents an array of experimental challenges1d,e and complicates interpretation of the resulting data as predictions of different theoretical models (MarcusHush Chidsey and ButlerVolmer) become difficult to distinguish. The classic example of a fast ideal process is the oxidation of ferrocene (Fc) Fc h Fcþ þ e
ð1Þ
There have been many attempts to measure k for this process in organic solvents over the past thirty years, with values at platinum and gold electrodes having been reported as low as 0.02 cm s1 to as high as 200 cm s1.3 More recent investigations utilizing r 2011 American Chemical Society
techniques particularly well-suited to measuring fast electrode kinetics at metal surfaces have indicated a k value of around 1.0 cm s1 (high speed channel electrode)4a or, perhaps, even greater.4b A similar level of variability has appeared in studies with glassy carbon (GC) electrodes.1e The Fc0/þ system therefore exemplifies the considerable uncertainty that has bedeviled the measurement of rapid heterogeneous electron transfer processes. One consequence of the above uncertainty in k values has been the resultant difficulty in determining activation parameters of rapid electrode processes, and consequently evaluating the validity of theoretical models of heterogeneous electron transfer that are proposed to address the issue.3 One widely used approach to determine k values as a function of the temperature, and hence activation parameters, has been to measure the separation of oxidation and reduction peak potentials of cyclic voltammograms.5,6 However, for relatively fast electrode kinetics the high scan rates required to obtain peak separations that differ meaningfully from values predicted for a reversible process5 introduces considerable uncertainties. The use of microelectrodes minimizes IRu effects (ohmic drop, where Ru is the uncompensated resistance and I is the current) as well as nonFaradaic background current that make interpretation of cyclic Received: March 7, 2011 Revised: May 4, 2011 Published: May 25, 2011 6493
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voltammograms more difficult, but such techniques are not immune from these issues and can introduce other problems such as uncertainty in electrode geometry. Moreover, decreasing the temperature will inevitably change not only the heterogeneous kinetics but also solution resistance and diffusion characteristics of electroactive species. The extraction of accurate kinetic measurements of heterogeneous redox processes therefore requires the ability to distinguish between k and Ru effects and to quantify them in modeling the voltammogramms. We demonstrate in this paper that use of higher harmonics available in Fourier-transformed large amplitude ac voltammetry1e,7 is very well-suited for this task at macrodisk electrodes, even under transient conditions. Over the past decade, studies from our laboratory have demonstrated a variety of advantages that large amplitude ac voltammetry has over dc techniques, one of which is the power to easily and clearly distinguish between contributions to the response arising from electrode kinetics and uncompensated resistance.8 In this paper we describe how this and other features of the ac technique facilitate the acquisition of high quality activation data. Moreover, because non-Faradaic currents are very small for the higher harmonic component (third and above), the use of the ac technique permits the use of macrodisk electrodes with well-defined geometries with mass transport being modeled conveniently by linear diffusion. We employ GC macrodisk electrodes in these studies as the heterogeneous rate constants at this surface are, for reasons we discuss, somewhat lower than at platinum, placing data obtained using this material in a more sensitive kinetic regime with respect to distinguishing the experimental response from that predicted for a fully reversible process.1e Unfortunately, in contrast to the relatively simple fabrication of Pt and Au microelectrodes, production of the well characterized GC microdisk electrodes that would be required for near steady state voltammetry, with mass transport governed by radial diffusion, presents a significant technological challenge. We focus on two well-studied systems in this work: the oxidation of Fc (eq 1) and the reduction of the cobaltocenium cation, Ccþ (eq 2). Interest in these systems remains high as they are both widely used as internal potential calibration standards in a variety of electrochemically important media.9,10 Ccþ þ e h Cc
ð2Þ
’ EXPERIMENTAL SECTION Materials and Materials. Ferrocene, Fc, and cobaltocenium hexafluorophosphate, CcPF6, were purchased from Strem Chemicals and used as received. Dichloromethane (Merck, HPLC grade) was dried over activated 4 Å molecular sieves prior to use. Tetrabutylammonium hexafluorophosphate, Bu4NPF6, was obtained from GFS Chemicals and recrystallized twice from ethanol prior to use as a supporting electrolyte. Standard three-electrode cells were used for all experiments described in this paper. For studies performed in dichloromethane, a platinum wire and a silver wire coated with silver chloride, both placed directly in the test solution, served as auxiliary and quasi-reference electrodes, respectively. The 3 mm diameter GC working electrode (Pine Instruments) was polished with 0.3 μm alumina (Buehler) and sonicated in deionized water prior to use; no additional activation or cleaning procedures were employed. Electrode areas were calculated using double potential
step chronocoulometry by employing the Cottrell equation11 and the slope of Anson plots (Q vs t1/2) along with the published diffusion coefficients for Fc and Ccþ (2.3 and 1.9 105 cm2 s1, respectively).4a,12,13 Solutions were degassed and maintained under a blanket of nitrogen presaturated with solvent for all experiments. Low temperature experiments were performed by immersing the electrochemical cell in either an ice/water slurry or a slurry prepared from dry ice and a water/isopropyl alcohol mixture with the desired freezing point. Specific experimental details and protocols used for studies in acetonitrile have been previously published.1e Instrumentation and Digital Simulations. Dc cyclic voltammetric and chronocoulometry experiments were undertaken with a BAS-100B Electrochemical workstation (BioAnalytical Systems). Large-amplitude ac voltammetry was performed using previously described instrumentation.7 Typically 216 (or 65 536) data points were collected. Ac cyclic voltammetry results were simulated using MECSim (Monash Electrochemical Simulator), an internally developed program. This simulation package is written in Fortran 77 and is based on the matrix formulation outlined elsewhere.14,15 The approach used to generate the ac output is briefly described below. The waveform applied in the ac voltammetric experiments, E(t), consists of the sum of the dc voltage ramp used in cyclic voltammetry, Edc(t), and the sinusoidal component (eq 3), EðtÞ ¼ Edc ðtÞ þ ΔE sinð2πftÞ
ð3Þ
where f and ΔE are the frequency (Hz) and amplitude (V) of the applied sine wave, respectively. ButlerVolmer kinetics are assumed to apply for the electron-transfer processes. Thus, for a one-electron oxidation (eq 4), kET;f
Rs F O þ e s R
ð4Þ
kET;r
kET,f and kET,r, the forward and reverse rate constants for the electron transfer, depend on potential and the charge transfer coefficient, R, and are related to the standard rate constant, k, in the usual way.1b,16 In accord with the ButlerVolmer model for electron transfer, we assumed that R is independent of applied potential. Given the imprecision in the measurement of this parameter, the use of the more refined models of electron transfer offered no advantage to this work. Mass transport under linear diffusion conditions for all diffusing species of interest, i, follows the relationships given below in eq 5, D½i D2 ½i ¼ Di 2 Dt Dx
ð5Þ
where Di refers to the diffusion coefficients for each species, the bracketed terms represent concentrations, and x is the distance from the electrode. The mass transport equations are solved according to previously described methods17,18 and application of the following initial and boundary conditions (eqs 68), where [R]* is the concentration of the reduced form in the bulk solution: t ¼ 0; all x: ½O ¼ 0; and ½R ¼ ½R 6494
ð6Þ
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t > 0, x = 0 (electrode/solution interface): DO
D½O D½R ¼ DR ¼ kET;f ½R kET;b ½O Dx Dx
t > 0; x ¼ ¥: ½O ¼ 0; and ½R ¼ ½R
ð7Þ ð8Þ
Once the time and space dependent concentration relationships are generated, the Faradaic current, I, is then calculated according to eq 9, D½R ð9Þ I ¼ nFADR Dx x ¼ 0 where n, F, and A have their usual meanings. To improve both the efficiency and accuracy of the simulation, an expanding grid originally introduced by Feldberg was adopted.18 The effects of double layer capacitance, CDL, and uncompensated resistance, Ru, are also taken into account using widely adopted methods.14 Individual ac harmonic components were extracted from raw currenttime (or currentpotential) data, whether obtained experimentally or generated by simulation. Data in the time domain were converted to the frequency domain by an FT algorithm to give the power spectrum. The frequencies corresponding to the aperiodic dc component and each individual harmonic were progressively selected, band filtered, and treated with an inverse FT algorithm to generate the required harmonic current data as a function of time. Although other data presentation formats are possible, most figures shown in this paper represent plots of the magnitudes of the selected dc or ac harmonic currents against potential; this protocol essentially provides the current envelope defined by the maxima of successive current oscillations in the ac experiment or simulation. Optimal values of the parameters E, Ru, k, R, and double layer capacitance (CDL) were determined by iteratively adjusting these five unknown input values and comparing simulation output to experimental results.1e CDL is modeled by the binomial function, CDL = c0 þ c1(E Ec) þ c2(E Ec)2, where E is the applied potential and Ec, c0, c1, and c2 are constants with appropriate units.8c Values of all parameters used in experiments and simulations are provided in the figure captions and relevant tables.
’ RESULTS AND DISCUSSION Kinetics for Oxidation of Ferrocene at a Glassy Carbon Electrode at 20 C in dichloromethane. While there have been
many determinations of the electrode kinetics for the oxidation of Fc at platinum electrodes, there have been far fewer at GC electrodes, despite the fact this electrode material is widely employed in analytical, physical, and mechanistic electrochemical studies.19 The study in dichloromethane described in this paper was initiated from observations made in a related kinetic study of homogeneous processes coupled to electron transfer in this solvent at GC electrodes.20 In the course of that work, we noted that k for the oxidation of Fc in this solvent was consistently lower at GC working electrodes than the approximately 1 cm s1 value established using hydrodynamic techniques at platinum electrodes.4 Results for one such experiment using Fourier-transformed large amplitude ac cyclic voltammetry of 1.0 mM Fc in dichloromethane (0.5 M Bu4NPF6) are presented in Figure 1 (ΔE = 100 mV, f = 14.31 Hz, dc component scan rate = 74.51 mV s1); shown are the fundamental to eighth
harmonics along with the corresponding simulated voltammograms. As can be readily observed, agreement between experiment and simulation is excellent; the only exception is seen in the seventh harmonic, in which second harmonic 100 Hz line noise (from the main frequency of 50 Hz used in Australia) interferes with the seventh ac harmonic signal (7f = 100.17 Hz). While the data show effects attributable to uncompensated resistance, they closely correspond to predictions for a reversible redox couple. A k value of 0.21 cm s1 is estimated from detailed comparison of experimental and simulated data based on the ButlerVolmer model of electron transfer. This value is larger than that estimated from analysis of cyclic voltammetry21 but is similar to the value in acetonitrile (0.1 M Bu4NPF6) we recently determined by detailed analysis of ac large amplitude voltammograms.1e All the calculations provided in that study, concerning the extraction of heterogeneous rate parameters of processes near the reversible limit, for the oxidation of Fc in acetonitrile, also apply to this study in dichloromethane. Specifically, the lower harmonics (the fundamental through the fourth) of these ac voltammograms are difficult to distinguish from those predicted for genuinely reversible systems; deviations from reversible behavior are much more apparent in the fifth through eighth harmonics (see below) and, accordingly, these are more heavily weighted in the determination of k. It has long been recognized that heterogeneous rate constants for many systems are a function of the electrode material, a phenomenon that has been examined extensively. According to the semiclassical encounter pre-equilibrium model,22 the standard rate constant is given by eq 10, ‡
k ¼ kel Kp νn Γn eΔGET =RT
ð10Þ
where ΔG‡ET is the electron transfer free energy activation barrier, kel is the electronic transmission factor, usually taken to be 1 for metallocene electron transfer reactions (i.e., perfect adiabaticity is assumed), Kp is the equilibrium constant for the precursor complex, νn is the nuclear barrier-crossing frequency, and Γn is the nuclear tunneling factor. This model is commonly employed for redox processes at metal electrodes, the density of states (DOS) of which is high enough such that the assumption of perfect adiabaticity for metallocene electron transfer does not introduce significant error. Data for metallocenes are assumed to parallel the example of the [Ru(NH3)6]3þ/2þ couple, considered a “benchmark” for fast electrode kinetics, which has k values that are high, but apparently similar at different metal electrodes such as Au, Pt, Pd, and others,23 as predicted for genuinely adiabatic electron transfer. In contrast, k for the [Ru(NH3)6]3þ/2þ couple is reported to be somewhat lower at GC and several orders of magnitude lower still at highly ordered pyrolytic graphite (HOPG) electrodes.24 The lower k values at carbon are attributed to the nonadiabaticity of the electron transfer at electrodes with lower DOS.1b The higher k at GC compared to HOPG for the [Ru(NH3)6]2þ/3þ couple is attributed primarily to a significantly higher and more evenly distributed DOS values in GC, which is considered more metallic in character. Nevertheless, the DOS values for GC is still lower than that of metals, thereby accounting for the lower k relative to those electrode materials. An additional demonstration of this effect was provided by Lewis and co-workers who observed a roughly 1 order of magnitude decrease in k for the reduction of Ccþ at n-Si semiconductor electrodes, normally considered “metallic in character”, relative to data obtained at mercury.25 They attributed the 6495
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Figure 1. Comparison of experimental and simulated fundamental to eighth harmonics derived from the oxidation of ferrocene in CH2Cl2 (0.5 M Bu4NPF6) at a 3mm diameter GC electrode at 20 C. Experimental data are shown in black; simulations are in red. Experimental conditions: [Fc] = 0.99 mM, ν = 74.51 mV s1, f = 14.31 Hz, ΔE = 100 mV, and A = 0.0527 cm2. CDL parameters for the simulation were Ec = 0.20 V, c0 = 4.5 105 F cm2, c1 = 2.5 105 F cm2 V1, and c2 = 1.6 105 F cm2 V2; other parameters employed in experiment and simulation are summarized in Table 1.
slower kinetics to the lower DOS of the semiconductor and outlined a theoretical framework to compare metallic and semiconductor electrodes based on the Fermi Golden Rule expression for the heterogeneous rate constant. Similarly, the slower electrode kinetics of the Fc0/þ couple observed at GC relative to Pt may be due to the lower DOS at GC at the relevant potentials. The k data surveyed above implies that the rate constants may be directly correlated with DOS. However, great care has to be made in attributing difference solely to this. For example, surface preparation can also strongly influence heterogeneous kinetics, especially with carbon electrodes, the surfaces of which can be functionalized (e.g., with carboxylic acid groups), and consequently activated, during polishing. This dependence on electrode history is particularly important for inner-sphere electron transfer processes, as they involve substantial interaction between the electroactive species and the electrode. The k values for [Fe(CN)6]4 oxidation at GC electrodes, for example, can vary by orders of magnitude depending on electrode history.26 The kinetics of outer sphere processes, on the other hand, should be considerably less sensitive to electrode material or history. Indeed, it has been shown that the kinetics for the oxidation of [Ru(NH3)6]2þ, an outer-sphere process, is remarkably insensitive to surface preparation of the electrode.27 Similarly,
the metallocene couples examined in this work, also generally considered to be outer sphere in nature, yielded quite reproducible k values when measured by large amplitude ac voltammetry; routine differences in electrode cleaning procedures and analyte concentrations notwithstanding. This reproducibility provides supplemental evidence that the slower kinetics observed at GC are primarily due to an inherent characteristic of the electrode material itself and not to factors related to its history or preparation. Another potentially complicating factor in comparing kinetics at different electrode materials is that, ideally, k should be corrected for double layer effects. The correction required is a function of the potential of zero charge28 and hence likely to be a function of electrode material. Unfortunately, neither the potential of zero charge at the heterogeneous glassy carbon electrode, nor the dependence of the double layer on potential, is known accurately. Consequently, we have not been able to take the double layer corrections into account in the present work. However, because all of our kinetic measurements were made at GC, the lack of this correction should not influence the resulting activation parameters even if direct comparison to rate constants made at other electrode materials may not be straightforward. Another issue that needs to be carefully considered in relatively rapid electrode processes is whether or not the observed 6496
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Figure 2. (a)(f). Simulated third (a) to eighth (f) harmonic components derived from large amplitude ac voltammograms for the oxidation process, R = O þ e, when k is 1000 (black), 1 (red), 0.1 (violet), and 0.01 cm s1 (blue). Other simulation parameters were E = 0.000 V, DO = DR = 2.3 105 cm2 s1, where subscripts R and O represent the reduced and oxidized forms of the couple, [R] = 1.0 mM, [O] = 0 mM, R = 0.50, Ru = 250 Ω, CDL = 5.0 105 F cm2, ν = 74.51 mV s1, f = 14.31 Hz, ΔE = 100 mV, and A = 0.05 cm2. (g) Charge ratios, Qn/Qn,rev, for the third through eighth harmonics of fifteen simulations for which 0.001 cm s1 < k < 10 cm s1. Charges for the reversible system were approximated by using k = 1000 cm s1.
voltammetry differs significantly from predictions for reversible systems. In general, when operating close to the reversible limit, optimized k values from simulations could represent a lower limit rather then an absolute value.1e Specifically, the measured current of higher order harmonics derived from large amplitude ac voltammetry under conditions used in this study reach a limiting response when k approaches 1 cm s1; increases in k beyond this value have relatively little impact. This is illustrated in Figure 2af, which shows simulated voltammograms for a system in which k values are varied from 0.01 to 1000 cm s1 with f = 14 Hz, ν = 100 mV s1, and ΔE = 100 mV; other simulation parameters were chosen to be experimentally realistic and are provided in the figure caption. As can be seen, the current when k = 1 cm s1 is only marginally smaller than that seen when it is 1000 cm s1. This would inevitably give rise to very large relative uncertainties in any kinetic measurements made in the k g 1 cm s1 regime. Below 1 cm s1, the current magnitude in the higher harmonics becomes a much more sensitive function of k. Of particular relevance is the degree to which the current decreases among the different harmonics as a result of the slower electrode kinetics; while all harmonics shown in Figure 2 show diminished current with smaller k values, the magnitude of the diminution increases regularly with the order of the harmonic, as illustrated in Figure 2g. Here, the total charges for each individual harmonic, Qn (calculated by integration of the corresponding current vs time curves, not shown), of electrode processes
for which 0.001 < k < 10 cm s1, expressed as a ratio to the corresponding charge for the fully reversible system (approximated by k = 1000 cm s1), Qn,rev, are plotted against log k; each harmonic gives a unique response, resulting in a nest of sigmoidal curves. It is clear from this presentation that statistically significant deviations from reversible behavior will be more readily apparent in the higher harmonics. Thus, for the oxidation of Fc in acetonitrile, we have previously shown that k is high enough such that only the fifth and higher harmonics show statistically significant deviations from reversible behavior.1e The 0.21 cm s1 value of k for the oxidation of Fc in dichloromethane at GC at 20 C found in the present study is low enough to place it in a more analytically useful range. In principle if the same level of kinetic sensitivity is retained at lower temperature it would make possible the determination of the relevant electrochemical activation parameters. Determination of Fc0/þ Activation Parameters in Dichloromethane. The ability to measure the kinetics at a GC electrode for the Fc0/þ process presents an opportunity to acquire quantitatively reliable activation data for the heterogeneous electron transfer. The fundamental to eighth harmonics for the oxidation of Fc at þ20, þ1, and 18 C are superimposed in Figure 3. The most obvious trend observed in the voltammograms is the regular decrease in current as the temperature is lowered. This is due to three independent factors: lower diffusion coefficients (D) and k values, and higher Ru. Double potential-step 6497
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Figure 3. First to eighth harmonics for the oxidation of ferrocene in CH2Cl2 (0.5 M Bu4NPF6) at a 3mm diameter GC electrode at þ20 (black), þ1 (red), and 18 C (blue). Other experimental conditions are as indicated in Figure 1. Potentials shown are relative to the E value for the process at each temperature.
Table 1. Parameters Used To Simulate ac Voltammograms for Oxidation of Ferrocene and Reduction of Cobaltocenium in Dichloromethane (0.5 M Bu4NPF6) and Oxidation of Ferrocene in Acetonitrile (0.1 M Bu4NPF6) analyte/medium Fc in CH2Cl2 (0.5 M Bu4NPF6)
T (C)
Fc in CH3CN (0.1 M Bu4NPF6)a a
105D (cm2 s1)
Ru (Ω)
R
20
0.21
2.3
270
0.50
1
0.14
1.9
315
0.50
0.075
1.4
390
0.47
18
0.12
1.9
230
0.45
2
0.07
1.4
275
0.45
18
0.04
1.0
400
0.45
0.250.50 0.2
2.4 1.8
130 180
0.250.75 0.50
18 Ccþ in CH2Cl2 (0.5 M Bu4NPF6)
k (cm s1)
20 0
Data from ref 1e.
chronocoulometry was used to measure the diffusion coefficients at subambient temperatures from the slopes of Anson plots (Q vs t1/2), which are proportional to D1/2 according to the Cottrell equation.11 The calculated diffusion coefficients at the temperatures examined (Table 1) are in reasonable agreement with those reported previously in other solvents over similar temperature ranges.5,29 Moreover, we found the diffusion coefficient of Fc to follow Arrhenius behavior with an activation energy of 8.2 kJ mol1, in reasonable agreement with the 7.2 kJ mol1 recently reported in acetonitrile (0.1 M Bu4NPF6).29c
Values for Ru and k were estimated by fitting simulated voltammograms to those obtained experimentally; the optimized parameters obtained from the fits are included in Table 1 and the best fit simulations at þ1 and 18 C (Figures 4 and 5, respectively) are in excellent agreement with the experimental data. The higher Ru values at low temperature are attributed to an increase in ion-pairing of the supporting electrolyte, which decreases the total number of charge carriers, as well as lower mobility of ions. The estimates of Ru in Table 1 are in good agreement with the values measured directly from the RC time constant (using a feature 6498
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Figure 4. Fundamental (a) to eighth (h) harmonics for the oxidation of ferrocene in CH2Cl2 (0.5 M Bu4NPF6) at a 3mm diameter GC electrode at 1 C: experimental data (black); simulated (red). Experimental conditions are as indicated in Figure 1. Simulation parameters Ru, k, and R are summarized in Table 1; CDL parameters were Ec = 0.20 V, c0 = 3.6 105 F cm2, c1 = 2.5 105 F cm2 V1, and c2 = 1.2 105 F cm2 V2.
provided in BAS instrumentation) and follow Arrhenius behavior; a plot of ln Ru vs 1/T is linear (Eact = 6.0 kJ mol1). The smaller k values observed at low temperature arise from the exponential term in eq 10, ΔG‡ET/RT. Because this is an outer sphere process, the major component of this activation barrier is the solvent reorganization around the electron transfer product1a and should be amenable to the following theoretical treatment. The activation energy for any electron transfer process is the sum of the inner and outer sphere components (eq 11). Metallocene redox ΔG‡ET ¼ ΔG‡is þ ΔG‡os
ð11Þ
processes have long been considered classic cases of outer sphere processes because the inner sphere component, ΔG‡is, is quite small; on the basis of measured bond length changes between the neutral and cationic forms of Fc, Weaver and co-workers estimated ΔG‡is ∼ 0.6 kJ mol1 for the oxidation.30 The outer sphere component can be calculated using the Born equation (eq 12),2 ! e2 1 1 1 1 ‡ ΔGos ¼ N ð12Þ εop;r εs;r 32πεo rA re
where N is the Avogadro constant, e is the charge on the electron, εo, εop,r, and εs,r, are the permittivity of free space, the relative permittivity of the solvent at optical frequencies and the corresponding relative static permittivity, respectively. The temperature dependence of the latter two terms has been shown to be small and is neglected in the following analysis.6 The terms rA and re are the radius of the reactive species and the imaging distance to the electrode, usually assumed to be ¥.3 We employed the following constants30 in eq 5: for dichloromethane, εop,r = 2.03, and εs,r = 9.0, and for Fc (and Ccþ, see below) rA = 0.38 nm; a theoretical value, ΔG‡os = 17.4 kJ mol1 is thereby obtained. Thus, given the estimated inner sphere component, eq 11 then yields, ΔG‡ET = 18.0 kJ mol1. This is in very good agreement with the value obtained from the slope of the Arrhenius plot (Figure 6, inset), which gives ΔG‡ = 17.0 ( 1.2 kJ mol1. This compares to values of 19.5 (in acetone)5 and 22.4 kJ mol1 (in methanol)31 for Fc oxidation previously reported. An alternative approach for the extraction of other activation parameters that has not been often employed for electrode kinetics is via an Eyring plot (Figure 6), ln kT1 vs T1. With our data, an activation enthalpy, ΔH‡, of 14.7 ( 1.2 kJ mol1 is obtained from the slope and an activation entropy, ΔS‡ of 210 ( 10 J K1 mol1 is obtained from the intercept. While previous 6499
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Figure 5. Fundamental (a) to eighth (h) harmonics for the oxidation of ferrocene in CH2Cl2 (0.5 M Bu4NPF6) at a 3mm diameter GC electrode at 18 C: experimental data (black); simulated (red). Experimental conditions are as indicated in Figure 1. Simulation parameters Ru, k, and R are summarized in Table 1; CDL parameters were Ec = 0.18 V, c0 = 2.6 105 F cm2, c1 = 2.2 105 F cm2 V1, and c2 = 0.8 105 F cm2 V2.
Figure 6. Arrhenius (inset) and Eyring plots obtained for the oxidation of Fc (O) and the reduction of Ccþ (b) in 0.5 M CH2Cl2 (Bu4NPF6) at 3mm diameter GC electrode. Slopes, m, and intercepts, b, of the linear least-squares fit lines are as follows: Arrhenius plots Fc (m = 2040 ( 140 K, b = 5.4 ( 0.5), Ccþ (m = 2160 ( 140 K, b = 5.2 ( 0.5); Eyring plots Fc (m = 1770 ( 150 K, b = 1.2 ( 0.5), Ccþ (m = 1890 ( 140 K, b = 1.4 ( 0.5).
studies of ferrocene did not report these particular activation parameters, they can be calculated using the published data: in acetone, ΔH‡ = 17.2 kJ mol1, ΔS‡ = 170 J K1 mol1;5 in methanol, ΔH‡ = 16 kJ mol1, ΔS‡ = 170 J K1 mol1.31 Despite
considerable differences in the absolute values for k obtained in these studies, the similarity in activation parameters is notable. We speculate that the negative ΔS‡ values reflect a reordering of the electrolyte and solvent around the redox active species necessary to facilitate the electron transfer. Determination of Ccþ/0 Activation Parameters in Dichloromethane. Despite the fact that Ccþ, like Fc, has been widely employed as an electrochemical standard for reference potential scale calibration, its electrode kinetics have not been examined nearly as thoroughly. The one electron reduction to Cc (eq 2) is widely considered to be a “fast” process and, as such, there has also been difficulty in measuring this k value accurately. Values in the literature range from 0.01 to >3 cm s1 at metal electrodes.25,32 Given the widespread interest in the Cc0/þ couple, and the dearth of kinetic studies performed at GC for this process, we performed large amplitude ac voltammetric experiments under the same conditions used for the oxidation of Fc to better characterize the electrode kinetics and determine the relevant activation parameters. Selected harmonics of the ac voltammograms at 20 C and lower temperatures, along with optimized simulations, are shown in Figure 7. Diffusion coefficients for Ccþ were determined in the same manner as that described above for ferrocene; these values, as well as corresponding R, Ru, and k estimates that were used in the simulations, are summarized in Table 1. As expected, these data show a decrease in current at lower temperature which mimics the behavior observed for Fc oxidation. The Arrhenius plot (Figure 6, inset) for the kinetic data in Table 1 yields ΔG‡ = 18.0 ( 1.2 kJ, in excellent agreement with the Marcus prediction 6500
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Figure 7. Third to sixth harmonics (top to bottom) for the reduction of Ccþ in CH2Cl2 (0.5 M Bu4NPF6) at a 3mm diameter GC electrode at þ18, þ2, and 18 C: experimental data (black); simulated data (red). Experimental conditions: [Ccþ] = 0.46 mM, ν = 74.51 mV s1, f = 14.31 Hz, ΔE = 100 mV, and A = 0.0442 cm2. Simulation parameters Ru, k, and R are summarized in Table 1.
(using rA = 0.38 nm and the estimated ΔG‡is of 1 kJ mol1)30 of 18.4 kJ mol1. The corresponding Eyring plots yield ΔH‡ = 15.7 ( 1.2 kJ mol1 and ΔS‡ = 210 ( 10 J K1 mol1, very similar to the corresponding values we measured for the oxidation of ferrocene. The results summarized above are notable for several reasons. First, we find that the k for Ccþ (0.12 cm s1) at a GC electrode in dichloromethane (0.5 M Bu4NPF6) is lower than that for Fc by about a factor of 2 over the temperature range examined. Because the activation parameters of the two processes appear to be very similar, the cause of the different rate constants may lie in the preexponential term of eq 3. The most likely origin for the difference would be in the electronic transmission factor, kel, which is related to the degree of adiabaticity of the process and, ultimately, to the DOS of the GC electrode. We speculate that a lower DOS at GC near the Ccþ reduction potential relative to that near the Fc oxidation potential makes the electron transfer relatively less facile. Second, our results indicate that lower DOS for the electrode material, while it may affect the magnitude of k, does not appear to alter the activation parameters appreciably; our results are within experimental error of the theoretical values. That said, such an interpretation must be tempered by the fact we explicitly neglected any temperature dependence of the preexponential term, the magnitude of which has been the subject of considerable speculation.6,33,34 Moreover, the use of GC may, in fact, result in somewhat different solvation energetics than would occur at a metal electrode due to the lack of ideal adiabaticity,26 so the agreement between our results and those predicted by Marcus theory do not definitively validate the model. Finally, the similarity in the Fc and Ccþ electron transfer activation parameters, while theoretically not surprising, is striking given the oft reported challenges associated with making such measurements.
’ CONCLUSIONS The results presented in this paper provide a further demonstration of the utility of large amplitude ac voltammetry to clearly distinguish between the effects of changes in Ru and k and address problems with CDL. In the present study we have used the technique to determine k and to facilitate the estimation of activation parameters for the Fc0/þ and Ccþ/0 electrode processes at GC electrodes. The kinetics appears to be markedly slower than at Pt electrodes for these outer sphere mechanisms. Both the Fc0/þ and Ccþ/0 metallocene couples give activation parameters that are within experimental error of predictions based on Marcus theory. These data should be of value in the ongoing investigation that is needed to further refine models of heterogeneous electron transfer. Finally, it is worth noting that we recently employed large amplitude ac voltammetry to examine the electrode kinetics for oxidation of Fc in acetonitrile (0.1 M Bu4NPF6) and found that k at 20 C most probably lies in the range 0.250.5 cm s1,1e even greater than that measured in CH2Cl2(0.5 M Bu4NPF6) in this current work. We performed additional experiments in acetonitrile at 0 C to give the electrode kinetics and other parameters included Table 1. This temperature dependence closely mimics the behavior observed in dichloromethane, but uncertainties are higher due to even closer proximity to the reversible limit of the electrode process. As we have stressed, there is always concern in reports of measurements of fast processes that k values determined at or near the limit of reversibility actually represent minimum values, and this applies to oxidation of Fc in acetonitrile. Of course, the upper limit measurable is governed by the level of deviation from reversibility, which is a function of k, D, Ru, and hence, temperature. In summary, the k data and the temperature dependence obtained in this study appear to be both statistically 6501
dx.doi.org/10.1021/jp2021787 |J. Phys. Chem. A 2011, 115, 6493–6502
The Journal of Physical Chemistry A significant and obey theoretical predictions, implying that conclusions are based on genuine variation of k values, rather than temperature dependence of apparent values, which would instead represent the lower limits measurable by the FT-ac voltammetric method.
’ AUTHOR INFORMATION Corresponding Author
*Fax: þ61 3 9905 4597. E-mail:
[email protected].
’ ACKNOWLEDGMENT The financial support of the Australian Research Council is gratefully acknowledged. ’ REFERENCES
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(24) McCreery, R. L. Chem. Rev. 2008, 108, 2646–2687. (25) Tan, M. X.; Lewis, N. S. Inorg. Chim. Acta 1996, 242, 311–321. (26) Rice, R. J.; Pontikos, N.; McCreery, R. L. J. Am. Chem. Soc. 1990, 112, 4617–4622. (27) Chen, P.; McCreery, R. L. Anal. Chem. 1996, 68, 3958–3965. (28) See Chapter 13 in ref. 1b. (29) (a) Tsierkezos, N. G. J. Solution Chem. 2007, 63, 289–302. (b) Xiao, L.; Dickinson, E. J. F.; Wildgoose, G. G.; Compton, R. G. Electroanalysis 2010, 22, 269–276. (c) Wang, Y.; Rogers, E. I.; Compton, R. G. J. Electroanal. Chem. 2010, 648, 15–19. (30) Gennett, T.; Milner, D. F.; Weaver, M. J. J. Phys. Chem. 1985, 89, 2787–2794. (31) Baranski, A. S.; Winkler, K.; Fawcett, W. R. J. Electroanal. Chem. 1991, 313, 367–375. (32) (a) Winkler, K; Baranski, A. J. Electroanal. Chem. 1993, 346, 197–210. (b) Tsierkezos, N. G. J. Mol. Liq. 2008, 138, 1–8. (33) McManis, G. E.; Weaver, M. J. J. Chem. Phys. 1989, 90, 1720–1729. (34) Fawcett, W. R.; Kovacova, Z. J. Electroanal. Chem. 1990, 292, 9–32.
(1) (a) Weaver, M. J. Chem. Rev. 1992, 92, 463–480.(b) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001; Chapter 3 (c) Smalley, J. F.; Sachs, S. B.; Chidsey, C. E. D.; Dudek, S. P.; Sikes, H. D.; Creager, S. E.; Yu, C. J.; Feldberg, S. W.; Newton, M. D. J. Am. Chem. Soc. 2004, 126, 14620–14630. (d) Swaddle, T. W. Chem. Rev. 2005, 105, 2573–2608. (e) Mashkina, E.; Bond, A. M. Anal. Chem. 2011, 83, 1791–1799. (2) Marcus, R. A. J. Chem. Phys. 1965, 43, 679–701. (3) Fawcett, W. R.; Opallo, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 2131–2143. (4) (a) Clegg, A. D.; Rees, N. V.; Klymenko, O. V.; Coles, B. A.; Compton, R. G. J. Electroanal. Chem. 2005, 580, 78–86. (b) Mirkin, M. V.; Richards, T. C.; Bard, A. J. J. Phys. Chem. 1993, 97, 7672–7677. (5) Safford, L. K.; Weaver, M. J. J. Electroanal. Chem. 1992, 331, 857–876. (6) J. N. Richardson, J. N.; Harvey, J.; Murray, R. W. J. Phys. Chem. 1994, 98, 13396–13402. (7) Bond, A. M.; Duffy, N. W.; Guo, S.-X.; Zhang, J.; Elton, D. Anal. Chem. 2005, 77, 186A–195A. (8) (a) Sher, A. A.; Bond, A. M.; Gavaghan, D. J.; Harriman, K.; Feldberg, S. W.; Duffy, N. W.; Guo, S.-X.; Zhang, J. Anal. Chem. 2004, 76, 6214–6228. (b) Zhang, J.; Guo, S.-X.; Bond, A. M. Anal. Chem. 2007, 79, 2276–2288. (c) Bond, A. M.; Duffy, N. W.; Elton, D. M.; Fleming, B. D. Anal. Chem. 2009, 81, 8801–8808. (9) Gritzner, G.; Kuta, J. Pure Appl. Chem. 1984, 56, 461–466. (10) Stojanovic, R. S.; Bond, A. M. Anal. Chem. 1993, 65, 56–64. (11) Heineman, W. R.; Kissinger, P. T. Laboratory Techniques in Electroanalytical Chemistry, 2nd ed.; Dekker: New York, 1996; Chapter 3. (12) Sharp, M. Electrochim. Acta 1983, 28, 301–308. (13) Hultgren, V. M.; Mariotti, A. W. A.; Bond, A. M.; Wedd, A. G. Anal. Chem. 2002, 74, 3151–3156. (14) Rudolph, M.; Reddy, D. P.; Feldberg, S. W. Anal. Chem. 1994, 66, 589A–600A. (15) Rudolph, M. In Physical Electrochemistry: Principles, Methods, and Applications; Rubinstein, I., Ed.; Marcel Dekker: New York, 1995; Chapter 3. (16) Gosser, D. K., Jr. Cyclic Voltammetry: Simulation and Analysis of Reaction Mechanisms; VCH: New York, 1993. (17) Mocak, J.; Feldberg, S. W. J. Electroanal. Chem. 1994, 378, 31–37. (18) Feldberg, S. W. J. Electroanal. Chem. 1981, 127, 1. (19) McCreery, R. L.; Cline, K. K. In ref 11, Chapter 10. (20) Lee, C.-Y.; Bullock, J. P.; Kennedy, G. F.; Bond, A. M. J. Phys. Chem. A 2010, 114 (37), 10122–10134. (21) Xiao, L.; Dickinson, E. J. F.; Wildgoose, G. G.; Compton, R. G. Electroanalysis 2010, 22, 269–276. (22) Weaver, M. J. In Comprehensive Chemical Kinetics; Compton, R. G., Ed.; Elsevier, 1987; Vol. 27, pp 160. (23) Iwasita, T.; Schmickler, W.; Schultze, J. W. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 138–142. 6502
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