A Facile Measurement of Heterogeneous Electron Transfer Kinetics

Article pubs.acs.org/ac

A Facile Measurement of Heterogeneous Electron Transfer Kinetics Paulo R. Bueno,*,† Tiago Azevedo Benites,† Márcio Sousa Góes,‡ and Jason J. Davis*,§ †

Instituto de Química, Universidade Estadual Paulista, CP 355, 14800-900, Araraquara, São Paulo, Brazil Universidade Federal da Integraçaõ Latino-Americana, CP 2044, 85867-970 Foz do Iguaçu, Paraná, Brazil. § Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom. ‡

ABSTRACT: This work introduces a simple, single-step, impedance-derived capacitance spectroscopic approach as a convenient and direct way of reporting the heterogeneous rate of electron-transfer between an electrode and solution-phase redox species. The proposed methodology requires no equivalent circuit analysis or data fitting and is equally applicable to the strong coupling (diffusion-mediated) or weak coupling electron-transfer regimes.

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present work is to present a new, simple, single-step protocol to calculate effective heterogeneous electron-transfer rate (kr), equally applicable to surface-bound or diffusion-mediated processes (herein bare metallic or passivated metallic surfaces, respectively).

xaminations of charge transfer between molecular systems and man-made metal or semiconductor interfaces, electrochemistry,1 underpin not only fundamental developments in our understanding of electron transport but also a vast array of energy capture, sensor, data storage, and electronic technologies.2−7 Within such analyses, the rate of electron exchange between molecule and electrode remains a fundamental parameter, sensitively dependent on thermodynamic, mechanistic, and electronic coupling parameters, the latter readily tuned experimentally.1,8,9 At metallic electrodes in particular, the rate of electron transfer from either surface-confined or solution-diffusive redox centers is sensitively dependent on the thickness and composition of any intervening self-assembled monolayer (SAM) (Figure 1) and is informative of both electronic coupling and, in many cases, biologically or technologically relevant characteristics.4,7,10−12 The reaction free energy of a single-step electron-transfer process can be described as1 ΔG = e(V − V 0) = E F − Er

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EXPERIMENTAL PROCEDURES Materials and Sample Preparation. All working electrodes were 2 mm diameter polycrystalline gold disks (GDE, Edaq, ET076), prepared as previously reported13 by a series of mechanical and electrochemical polishing steps, separated by sonication for short intervals in Milli-Q water. Realistic electrode areas were evaluated by integration of the cathodic peak from gold electropolishing voltammograms, acquired by cycling the potential between −0.25 V and +1.25 V (versus Ag/ AgCl reference electrode) in 0.1 M aqueous sulfuric acid at 100 mV/s. Typically, areas of 0.032−0.035 cm2 were obtained. Prior to thiol passivation, all electrodes were treated with hot piranha solution (70% H2SO4/30% H2O2) followed by mechanical polishing to a mirror finish by use of aluminum oxide disks (Buehler, Fibrmet Discs) with polishing progressing from coarse (0.3 μm) to fine (0.05 μm). CAUTION: Piranha solution can react violently with organic materials and should be handled with extreme caution! Piranha solution should not be stored in tightly sealed containers. This was followed by electrochemical polishing in 0.1 M sulfuric acid and potential scanning from −0.5 V to ca. 1.3 V versus Ag/AgCl at a sweep rate of 100 mV· s−1. After incubation, electrodes were thoroughly rinsed in ethanol and ultrapure water and inserted in the electrochemical

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where e is the elementary charge, V is electrode potential, and V0 is the formal or redox potential of the redox site. EF is the Fermi energy of the electrode, and Er the formal potential of the redox state. When EF = Er the electrode potential is V0 (ΔG = 0), such that the forward and backward electron-transfer rates have the same value, which is the standard electron-transfer rate of the redox reaction; that is, kf = kb = kr0.1 [Electron transfer quantified at the half-wave potential corresponds to the standard electron-transfer rate constant.] Though numerous methods exist for the experimental determination of heterogeneous electron-transfer rate, none are fast and many require the acquisition of numerous data points prior to analysis/curve fitting.1 The main purpose of the © 2013 American Chemical Society

Received: July 30, 2013 Accepted: October 14, 2013 Published: October 14, 2013 10920

dx.doi.org/10.1021/ac402378n | Anal. Chem. 2013, 85, 10920−10926

Analytical Chemistry

Article

Figure 1. Schematic representation of electron transfer: (a) between redox centers in an electrolytic environment at bare Au electrodes (unimpeded electron transfer) and (b) between redox centers tethered to an underlying electrode through an intervening self-assembled monolayer dielectric (impeded electron transfer).

Figure 2. Electron-transfer rate analysis using Nicholson’s and/or Laviron’s methodologies, both based on quantifying the displacement of redox peak potential (Vpa and Vpc for anodic and cathodic peaks respectively; yellow circles) with sweep rate as shown here schematically. (a, b) Cyclic voltammetric changes in cathodic and anodic peak potential for C4-passivated electrode surface. (c, d) Analogous representations with C6-passivated surface. The electron-transfer rate at both interfaces was analyzed for 1.00 mmol·L−1 redox probe solution concentration. Extracted quantitative values were compared with those derived from the ECS methodology outlined below (Figure 5 and Tables 1 and 2).

an Autolab potentiostat PGSTAT30 (Ecochemie NL) equipped with an ADC750 and a FRA (frequency response analyses) module and FRA software. The CVs were acquired only for the purpose of comparisons between the two methodologies. Single CV sweeps were also performed to predefine faradaic windows prior to electrochemical impedance spectroscopy (EIS) analysis. Alternating current (ac) frequencies for impedance experiments ranged from 0.1 MHz to 10 mHz, with an (root mean square, rms) amplitude of 10 mV. All obtained impedance data were checked regarding compliance with the constraints of linear systems theory by Kramers− Kronig by use of the appropriate routine of the FRA Autolab software. The complex Z*(ω) (impedance) function was converted into C*(ω) (capacitance) through the physical definition Z*(ω) = 1/iωC*(ω), in which ω is the angular

cell, previously deoxygenated by bubbling with nitrogen for 20 min; deaerated conditions were maintained by flushing with nitrogen throughout data acquisition. Passivated surfaces were prepared on freshly polished electrode surfaces (prepared as above) by overnight incubation at room temperature in 1 mmol·L−1 solutions of 1-butanethiol (C4) and 1-hexanethiol (C6) in anhydrous ethanol. 1Octanethiol (C8) passivated surfaces and 6-ferrocenylhexanethiol (FcC6) modified surfaces were similarly generated for the purpose of verifying tunneling decay patterns and comparative capacitative responses. Note that standard cyclic voltammetry (CV) methodologies were not suitable in calculating electrontransfer rate at C8 passivation levels (Figure 3b). Instrumentation and Procedure. Cyclic voltammetry (CV) and impedance measurements were carried out by use of 10921



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Figure 3. (a) Trumpet plot evaluation of electron-transfer rate between [Fe(CN)6]3−/4− and Au electron metallic states where the latter are C4modified. Such analyses obviously require data acquisition across a broad range of voltammetric scan rates (for instance, Figure 2). The method is, thus, both laborious and associated with significant fitting error (fitting error/accuracy is largely dependent on the number of data points acquired and thus time invested in acquisition and processing; the slope at high scan rates in panel a, for example, is clearly tremendously sensitive to the number of data points in this regime). In contrast, kr can be directly evaluated in a single-step measurement by ECS (from the frequency of the peak of a C″/C′ plot) shown in Figure 5d (red star curve). See also Table 1 for cross comparison. va and vc are the anodic and cathodic limiting rates of electron transfer (emphasized by yellow circles), respectively. (b) Capacitance-derived electron-transfer rates kr, plotted as a function of the underlying SAM chain length for both ECS and CV methodologies. Note that, for 1-octanethiol (C8), used to confirm a resolved sensible tunneling decay regime, resolution of kr is achievable only by ECS, as definable redox peaks are not detectable by CV. Finally note that, in panel b, a zero methylene number corresponds to bare gold with SAM designations as follows: 1-butanethiol (C4, n = 3), 1-hexanethiol (C6, n = 5), and 1octanethiol (C8, n = 7).

frequency. From this operation, note that C″ = φZ′ and C′ = φZ″, where φ = (ω|Z|2)−1 and |Z| is the modulus of Z*. CVs and EIS scans were measured in a 5 mL, one-compartment cell, containing the GDE, an Ag/AgCl, KCl (3M) counter electrode and a platinum gauze counter electrode. As a supporting electrolyte, 1 mol·L−1 M KNO3 (pH = 6.5) was used, containing [Fe(CN)6]3−/4− at specific concentrations. All solutions used were deoxygenated by bubbling with ultrapure nitrogen and purging the surface for the experiment duration. Impedance data were acquired at half-wave potential of the redox probe, with modulation frequencies varied in 200 steps from 1 mHz to 1 MHz.

The diffusion-mediated redox characteristics associated with bare gold (Au) were analyzed by Nicholson’s approach18 since this format presents largely unimpeded surfaces to solution (meaning electron transfer is diffusion-limited).19 The electrontransfer rate at sterically impeded films such as those presented by C4 (1-butanethiol) and C6 (1-hexanethiol) modifications was calculated by Laviron’s methodology and associated Trumpet plots (see Figures 2 and 3).20−23 The resolved tunneling decay lies within the expected regime, consistent with steric/distance effects being dominant in kr versus thickness trends as shown in Figure 3b. As expected, the Au bare surface does not follow the same trend due to the strong (diffusionmediated) coupling and associated different kinetic regime. It is clear that, unlike CV, ECS can be used in a consistent manner wholly independent of kinetic regime. In previous work we have shown that charge injection into surface-confined redox sites manifests itself, very cleanly, as a capacitive storage term (redox capacitance).16,24 This is most conveniently resolved through a simple mathematical manipulation of standard impedance data, such that capacitance components are highlighted.16 We have subsequently demonstrated that this resolved capacitive storage can be usefully applied in a biosensing format.24 However, when redox probes are free in solution and exchanging electrons with a solid metallic interface, this term is not present (only an associated charge-transfer resistance, Rct; that is, a loss energetic term exists). Though resolved Rct can be used in the derivation of an electron-transfer rate, this also requires rather laborious fitting.1,3 The central idea of the methodology proposed here is, first, that redox-related energy loss is maximal at an applied ac frequency equivalent to the heterogeneous electron-transfer rate, and second, that this energy loss is reported through C″/ C′. In Figure 4, comparative impedimetric and capacitive Bode diagram responses of electroactive monolayer and redox centers free in solution are shown. Before we address the proposed methodology in detail, first note the differences existing between electron transfer occurring in free redox centers and

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RESULTS AND DISCUSSION The most common means of determining interfacial electrontransfer rate is through application of the phenomenological Butler−Volmer model (including its related Tafel’s plot analysis)1 or through the fitting of voltammetric or polarographic data to microscopic Marcus theory.14 We have recently introduced electrochemical capacitance spectroscopy (ECS)15−17 as a means of mapping out the faradaic and dielectric features of molecular films when electroactive redox entities are bound to an electrode. Herein we extend this methodology to demonstrate an ability of standard impedance/ capacitance methodologies to detect capacitive changes associated with the charging (and with subsequent electron transfer) of solution-phase redox molecules within the double layer region, that is, regions close to the electrode. The spectrally resolved frequency of this charging conveniently and directly reports on the rate of electron transfer in a facile singlestep method that requires neither curve fitting nor equivalent circuit. We specifically herein demonstrate the application of this new form of ECS to the resolution of electron-transfer rate between [Fe(CN)6]3−/4− and bare Au or SAM dielectric passivated electrode surfaces where heterogeneous electrontransfer rate is tuned through either concentration gradient (diffusion) or steric effects. 10922



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Figure 4. (a, b) Experimental Nyquist impedimetric plots of electron transfer between [Fe(CN)6]3−/4− free in solution and Au electron metallic states for unimpeded (bare gold, in red) and impeded surfaces (C4, in green). Panel b is a magnified region of high frequency. In both unimpeded and impeded surfaces, impedimetric Randles-like patterns are obtained where a diffusive regime is clearly observable at low frequencies as indicated in panel b. (c, d) Bode diagrams of diffusive regime and SAM blocking effects and associated capacitance plateau for unimpeded (bare gold, in red) and impeded surfaces (C4, in green). Also shown is the response of a FcC6 film (yellow) where a clear capacitive plateau corresponding to faradaic charging is evident.16,24 Obviously, there is no redox-related capacitance during electron transfer between [Fe(CN)6]3−/4− free in solution and Au electron metallic states for either unimpeded and impeded surfaces. The original electroactive monolayer capacitance spectroscopy (EMCS) approach16 cannot, then, be applied in calculating electron-transfer rate for redox free states, that is, in the absence of redox energy storage.

absent even for impeded diffusion controlled kinetics (the high frequency plateau observed here corresponds to a modified double layer charging, non faradaic process as introduced in previous works).16,17 In the absence of any redox-related capacitive storage, the previously introduced EMCS methodology cannot be applied to any resolution of electron-transfer kinetics. However, we show herein that a modification of the EMCS methodology equally well reports on the redox charging/ discharging associated with solution-phase entities transiently diffusing into the double layer region if a C″/C′ functionthat is, the ratio between imaginary and real capacitive componentsis analyzed instead of C″ alone.16,24 This ratio function ultimately represents the energy loss during the electrontransfer rate process, and the associated frequency where this is maximized directly reports the electron-transfer rate (Figure 5). In extending these analyses (Figure 6) across a range of tuned redox kinetic regimes (achieved by tuning the passivating film thickness or redox probe concentration), we show that resolved

that in redox centers trapped at the electrode surface (Figure 4). From Figure 4a,b it is possible to observe the Nyquist impedimetric plot of electron transfer occurring between [Fe(CN)6]3−/4− free in solution and Au electron metallic states for unimpeded (bare gold, in red) and impeded surfaces (C4, in green). At both surfaces, the impedimetric Randles pattern is observable as a diffusive regime; the characteristic linear line running 45° between real and imaginary components in the low-frequency regime is known as a Warburg circuit element.3 A comparison to the resolved purely capacitive response with a surface-confined (trapped or tethered) redox moiety, here 6ferrocenylhexanethiol (FcC6), is shown in yellow. As expected, no diffusive response is observable for such interfaces.16,24 In Figure 4a,b, diffusive and impeded diffusion regimes are shown for bare gold (in red) and C4-modified surfaces (in green). For the FcC6 film, there is no diffusive element but a clearly resolved energy storage (plateau regime) at a frequency corresponding to the rate of electron exchange.16,24 For diffusively mobile [Fe(CN)6]3−/4− this feature is completely 10923



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Figure 5. Bode plots of the ratio between imaginary and real capacitive terms, C″/C′, obtained for different [Fe(CN)6]3−/4− redox probe concentrations for (a) bare Au and two different (impeded) SAM surfaces, (b) C4 and (c) C6, as a function of redox probe concentration. In all cases, the peak frequency reports directly on kr. The inset in panel c illustrates this and the progression to higher frequency/kinetics as redox probe concentration is increased. (d) Effect on electron-transfer rate of surface passivation through SAM thickness. All the curves shown are mean average curves of measurements conducted across three different electrodes. Note also the existence of minima in these plots that corresponds to the nonfaradaic interfacial charging.16,17 For bare Au in panel a, there is no clear observed peak. This is a graphical limitation of the ECS proposed methodology that can be overcome by looking for the maximum directly in the experimental data sheet. The error can be compared with CV analysis in Table 1 (note that in CV analysis at least 10 points were obtained in the linear regime in order to minimize error).

jc + jd = σE + iωC*E

kinetics are both conveniently reported and map well onto those obtained by conventional cyclic voltammetry under the same conditions (see Tables 1 and 2 for numerical detail). It is important to observe in Figure 5 that the acquisition of a maximum is graphically not sensitive at low concentrations of redox probe in solution. This is an apparent limitation of the proposed analysis that can be overcome by finding a maximum value directly in the data sheet (errors in electron-transfer rate comparatively obtained for CV carefully acquired with enough data points match very well, as can be numerically observed in Tables 1 and 2). The origins of the C″/C′ function to be correlated with electron-transfer rate can be understood by analogy to dielectric loss phenomenology25 and the resonance of maximal energy loss in a varying electric field.26 If one imposes an oscillatory electrochemical potential perturbation on an electrochemical interface describable by E = ΔẼ eiωt, where i = √−1, ω is the oscillatory frequency, and ΔẼ is the amplitude of the perturbation, then the electrochemical current density response (defined according to Maxwell equations27) can be divisible into conducting (jc) or loss and the displacement (jd) current densities;27

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Note that all variables of the equations are given per unit of area, where jc = σE and jd = iωC*. σ is the conductance and C* is the complex capacitance dissolvable into real and imaginary components:16,24

C* = C′ − iC″

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where i = √−1, so that that eq 1 can be rewritten as jc + jd = σE + iω(C′ + iC″)E = (σ + ωC″ + iωC′)E = (σ ′ + iωC′)E

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where it can be noted that σ′ = σ + ωC″, jc = σ′E, and jd=iωC′E. Accordingly, the ratio (σ + ωC″)/ωC′ represents the loss tangent (tan δ) of the electrochemical process (i.e., the ratio between jc and jd, observing the analogy with dielectric theory)26 and can be defined as the ratio (or angle, δ, in a complex plane) of electrochemical energy loss (σ + ωC″)26 during the field-driven electron transfer and the lossless (or storage) energetic term (ωC′). The ratio (σ + ωC″)/ωC′ approximates C″/C′ if σ is zeroed, that is, if it is assumed there 10924



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considered that the time scale of electron transfer is τr, the maximum electrochemical energy loss occurs for a frequency equal to that of electron-transfer rate frequency, that is, 1/τr (the inverse of the time scale of the redox process), which is correlated to loss tangent through tan δ =

Table 1. Comparative kr Values for Different [Fe(CN)6]3−/4− Redox Probe Concentrations at Bare Au Surfacesa kr on bare Au (±SD), s−1 CV

0.10 0.25 0.75 1.00

101.5 218.7 445.6 464.9

ECS

(±14) (±18) (±27) (±21)

115.0 219.6 419.9 460.6

(±13) (±15) (±28) (±24)

a

kr values were obtained from traditional electrochemical CV and introduced ECS approaches. Standard deviations (SD) represent the experimental variance. Note the values of kr for bare Au are consistent with those previously reported.27

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CONCLUSION Impedance derived capacitance analyses reported herein and previously are equally applicable to any redox kinetic analysis, surface-confined or diffusion-mediated. An underpinning complete theoretical analysis will be the subject of future work. In conclusion, we have introduced a single-step practical experimental way of calculating kr, based on plotting the C″/C′ ratio as a function of AC frequency and noting the plot maximum.

Table 2. Comparative kr Values Obtained for Different [Fe(CN)6]3−/4− Redox Probe Concentrations at C4 and C6 Thiol Passivated Interfacesa kr (±SD), s−1 C4 thiol layer redox probe concn, mmol· L−1 0.10 0.25 0.75 1.00 a

CV 35.2 43.8 84.6 101.4

(±3.6) (±4.3) (±8.0) (±8.4)

C6 thiol layer

ECS 31.4 41.5 87.0 112.4

(±4.3) (±2.1) (±4.8) (±9.7)

CV 0.71 0.78 1.20 2.13

(±0.13) (±0.13) (±0.2) (±0.4)

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ECS 0.64 0.78 1.23 2.35

(±0.09) (±0.11) (±0.09) (±0.15)

*Phone +55 16 3301 9642; fax +55 16 3322 2308; e-mail [email protected]. *E-mail [email protected]. Notes

is no other parallel conductivity (or energy loss) besides that related to electron transfer itself given by ωC″, so that σ + ωC″ C″ = ωC′ C′

AUTHOR INFORMATION

Corresponding Authors

Standard deviations (SD) represent the experimental variance.

tan δ =

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Consequently, the resonance or maximum of C″/C′ occurs for frequencies (Figure 5) where kr = 1/τr; that is, the energy loss associated with electron transfer from electrode sites to redox species free in solution (or vice versa) is directly related to electrochemical charge-transfer resistance (and obviously its reciprocal, the electrochemical conductance). In an ac-driven field, the pathway conductance is maximal when electrochemical currents are in phase (associated with δ) with the applied voltage and hence cause maximum electrochemical loss; note that, because of the manner in which data are acquired by ECS, this loss is wholly faradaic in nature. Now, in applying this developed concept we first acknowledge that an increase in redox probe concentration leads to an increasing effective electron-transfer rate,1 while an increase in SAM thickness leads to a predictable suppression of this. Both effects are equally resolved by Nicholson, CV, and ECS (crosscompared in Figure 6 and Tables 1 and 2).1,18,20−23 It is notable that kr values obtained from ECS trends lie within 5% of those acquired by traditional CV for any electrode surface modification or redox probe concentration (see Figure 5 and Tables 1 and 2 where numerically reported). CV scanrate analyses are tedious, complicated by peak broadening and loss of definition at high sweep rates, and associated with significant fitting error. The approach outlined herein reports kinetics in a single spectroscopic step, over a few minutes, without any additional data fitting; data are spectrally acquired and plotted, and the maximum is identified as the electrontransfer rate.

Figure 6. Comparative analysis of electron-transfer kinetics as resolved by ECS and cyclic voltammetry (Nicholson or Laviron) across different electrode interfaces and as a function of redox probe solutionphase concentration. Note that the relative independence of kinetics at C6 interfaces with concentration is better visualized by the numerical values shown in Tables 1 and 2.

redox probe concn, mmol·L−1

C″ 1 = C′ ωτr

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This work was supported by the São Paulo State research funding agency (FAPESP) and São Paulo State University (UNESP) grants. T.A.B. acknowledges CAPES for his scholarship.

In other words, it is assumed that electron-transfer exchange between electrode and solution redox probe centers is the process fully responsible for energetic loss. Finally, if it is now 10925



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A Facile Measurement of Heterogeneous Electron Transfer Kinetics

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