Article pubs.acs.org/JPCC
Thin-Film Modified Rotating Disk Electrodes: Models of ElectronTransfer Kinetics for Passive and Electroactive Films Christopher Batchelor-McAuley* and Richard G. Compton* Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom ABSTRACT: This work explores the influence of both passive and electroactive thin films upon the steady-state voltammetric response of a rotating disk electrode, proposing simple physical and algebraic models. In both cases, it is clearly evidenced how the alteration of the mass-transport regime adjacent to the electrochemical interface leads to an apparent change in the electron-transfer kinetics. These results are of great significance because of the wide adoption of the rotating disk electrode technique for studying new electrocatalytic materials.
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where Ef0 is the formal potential for the electrochemical reaction, R is the gas constant (8.314 J K−1 mol−1), T is the temperature (kelvin), α is the transfer coefficient as defined by IUPAC,8,9 F is the Faraday constant (96485 C mol−1), r0 is the radius of the microhemisphereical electrode (meters), k0 is the standard electrochemical rate constant (meters per second), and D is the diffusion coefficient of the electroactive species (square meters per second). Hence, enhancement of the mass transport to the electrochemical interface (by decreasing the size of the electrode for instance) results in a corresponding shift in the voltammetric wave to larger overpotentials. Conversely, diminishing the efficiency of mass transport to a surface, i.e., by a reduction in the diffusion coefficient or an increase in the electrode radius, leads to a reduction in the required overpotential for a given electrochemical reaction. To put this succinctly, the overpotential for a given heterogeneous electron transfer is a kinetic parameter that depends upon both the rate of electron transfer and the local mass-transport regime. A more complex experimental example of this dependency of the mass-transport regime is found with the use of porous electrodes,10,11 where the thin-layer masstransport regime serves to minimize the overpotential required for the redox process to occur. Consequently, referring to the “reversibility” of a process in the absence of defining the masstransport regime is, arguably, an empty statement. Of the possible dynamic electrochemical methods available12 for analyzing the magnitude of a standard electrochemical rate constant (k0) one of the most prevalently used, both fundamentally and in application, is the rotating disk
INTRODUCTION Electrode modification is, and has been since the pioneering work of Murray in the 1980s, a prevalent and now very welldeveloped strategy for the tailoring of the electron-transfer properties of an electrochemical interface.1,2 Through the utilization of a relatively inert or “passive” electrochemical substrate, such as glassy carbon, the electrocatalytic properties of “state-of-the-art” materials may be apparently readily assessed,3−5 the underlying rationale often being that any differences in the electrochemical response of a “modified” and “unmodified” electrode (i.e., in terms of the voltammetric onset potential or another characteristic parameter) may be attributed directly to the altered rate of electron transfer associated with the novel modifying material. When, as is increasingly common, the surface modification is larger or much larger than simple monolayers of molecular thickness, the presented analyses of such electrode modification studies regularly belie the true complexities associated in making a quantitative comparison between the experimental and control results. It is well-established that, as a heterogeneous process, the concept of electrochemical “reversibility” is inherently associated with both the electrochemical rate constant of a reaction [k0 (meters per second)] and the local mass-transport regime [as parametrized by the mass-transport coefficient kc (meters per second)].6 This fact is perhaps most easily recognized via consideration of the voltammetric response of an irreversible redox species at a hemispherical microelectrode where the halfwave potential (E1/2) for a one-electron, kinetically first-order process varies as7 E1/2 = Ef 0 +
0 RT ⎛ r0k ⎞ ⎟ ln⎜ αF ⎝ D ⎠ © 2014 American Chemical Society
Received: October 17, 2014 Revised: November 18, 2014 Published: November 23, 2014 30034
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electrode.13 For a flat rotating electrode under laminar conditions, the electrochemical interface is uniformly accessible, and when the electrode is under steady-state mass-transport conditions (i.e., at sufficiently high overpotentials), the magnitude of the limiting current is given by the Levich equation.14 For nonlimiting current conditions, the electrochemical response may be described via the well-known Koutecky−Levich equation.15 Under the mixed diffusionkinetic regime, analysis of the electron-transfer kinetics may be undertaken by measuring the inverse of the electrochemical flux as a function of the square root of the electrode rotation rate. Modified forms of the Koutecky−Levich equation accounting for the presence of a membrane film upon the electrode have been previously derived.16 The simplicity of the Koutecky−Levich equation has, in part, encouraged the application of the rotating disk electrode technique for the analysis of a variety of electrochemical systems. This technique has particular ubiquity in application in the study of the catalysis of the oxygen reduction reaction but has also been applied in the “hot” areas of carbon nanotube and graphene electrochemistry, and to ionic liquid-based components.3−5,17−19 Recent research has sought to clearly highlight the influence of mass transport upon the recorded electrochemical responses of modified electrode surfaces. First, within the literature, the influence of a passive modifying film upon both the voltammetric20 and impedance spectroscopic21 response has been considered at stationary electrodes. Here, the passive film serves to simply alter the diffusion coefficients and solubilities of the electroactive species adjacent to the interface. This model clearly demonstrates how the apparent electron-transfer kinetics may be readily altered by the presence of the modifying layer. Second, work has demonstrated how the modification of a stationary electrode with a porous and electroactive film leads to an apparent enhancement of the electron-transfer kinetics due to the formation of a thin-layer regime upon the electrode surface.10 Third, the influence of the geometric roughness of an electrode surface, as may be associated with modification of a surface with nanoparticles, has been considered for both stationary22,23 and hydrodynamic systems.24 This article serves to propose simple physical and algebraic models for describing the influence of both passive and electroactive (porous) films upon the apparent electron-transfer kinetics of an electrochemical process when studied via the hydrodynamic rotating disk electrode system under laminar flow conditions. First, the simple case of a passive film is approached highlighting how the properties of the film with respect to solute solubility and diffusion rates may lead to either apparent “catalysis” or “inhibition” of the electron-transfer rate. Second, it has recently been highlighted by Zhang et al. that the use of a rotating disk electrode for the study of electron-transfer kinetics at porous and electroactive modifying layers “benefits” from a relative minimization of the contribution from the thinlayer response, as compared to comparable experiments performed under stationary conditions.17 Although obviously correct, this work does not seek to account for the influence of the electrode porosity on the apparent electron-transfer kinetics. Demonstration of the importance of this latter point is shown in the experimental work of Erlebacher et al.,19 who evidence the influence of the porous surface “architecture” upon the apparent electron-transfer kinetics of the oxygen reduction reaction. Consequently, the latter part of this text
examines the electrochemical response of an electroactive porous rotating disk electrode under steady-state conditions.
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RESULTS AND DISCUSSION The steady-state voltammetric responses of a rotating disk electrode modified with, first, passive and, second, electroactive porous layers are considered theoretically. In both cases, the apparent electrochemical rate constant may differ dramatically from the true underlying value solely because of the altered mass-transport regime adjacent to the electrochemical interface. Passive Films. In considering the effects of the passive nonelectroactive film, the layer is taken to alter only the solubilites and diffusion coefficients of the electroactive species adjacent to the electrochemical interface within the film as shown schematically in Figure 1.
Figure 1. Schematic of the model used in this article, where X is the distance perpendicular to the electrode surface (X = 0). The film thickness is Xf, and the hydrodynamic boundary layer is XD.
The influence of the passive film upon the apparent electrode kinetics of a simple one-electron transfer has been previously described,20 assuming a linear concentration profile across the passive film and a semi-infinite diffusion regime of A and B in solution. For the electrochemical reaction A + e− ⇌ B
(1)
and using the Butler−Volmer formalism the flux (j) may be described by the following equation ⎛ ∂[A]s ⎞ j = DA,s⎜ = kRed,App[A]0 − k Ox,App[B]0 ⎟ ⎝ ∂x ⎠x = xf
(2)
where k0KA e−∝ θ
kRed,App = 1 + k 0xf
1 + k 0xf
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1 −∝ θ e DA,f
+
)
(3)
)
(4)
1 βθ e DB,f
k0KBe βθ
k Ox,App =
θ=
(
(
1 −∝ θ e DA,f
+
1 βθ e DB,f
F (E − E f 0 ) RT dx.doi.org/10.1021/jp5104593 | J. Phys. Chem. C 2014, 118, 30034−30038
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where k0 is the electrochemical rate constant (meters per second), Di,s and Di,f are the diffusion coefficients (square meters per second) of the ith species in the solution and film, respectively, and Ki is the associated partition ratio across the film−solution interface, at a distance xf from the electrochemical interface, and is defined as follows. Ki =
characterized hydrodynamic system in which the electrochemical interface is uniformly accessible and the convective and diffusive fluxes can be considered one-dimensional. Under steady-state conditions, the limiting cathodic (ilim,c) current to a bare RDE is given by7 ilim,c = −1.554FADA 2/3W1/2ν−1/6[A]bulk
[i]xf,f
(5) −1
where F is the Faraday constant (96485 C mol ), A is the area of the electrode (square meters), DA is the diffusion coefficient of species A (square meters per second), W is the rotation rate (hertz), ν is the viscosity of the solution (square meters per second), and [A]bulk is the concentration of species A in bulk solution. Accordingly, the corresponding diffusion-layer thickness (xD) is given by
[i]xf,s
Figure 2 depicts how the apparent reductive and oxidative rates vary as a function of overpotential. For the values of the
x D = 0.643W −1/2ν1/6D1/3
(6)
When the diffusion layer is significantly further from the electrode than the film thickness such that xD ≫ xf, then, at steady state, the flux to the film−solution interface is j=
DA ([A]bulk − [A]xf,s ) x D,A
=
−DB([B]bulk − [B]xf,s ) x D,B
= kRed,App[A]xf,s − k Ox,App[B]xf,s (7)
Consequently, if the concentration of B in bulk solution is taken to be zero, the diffusion-limited flux of species i to the surface is given by
Figure 2. Variation of kRed,App (solid red line) and kOx,App (solid blue line) as a function of the overpotential (E − Ef/V) with values of xf = 100 nm, DA,f = DB,f = 1 × 10−10 m2 s−1, α = β = 0.5, k0 = 1 × 10−6 m s−1, and KA = KB = 1. Dashed lines represent the Butler−Volmer responses in the absence of the passive film.
jlim,i =
Di,s[i]bulk x D,i
(8)
Then the inverse of the electrochemical flux is given by film thickness and the in-film diffusion coefficients used, at low overpotentials the rates closely approximate that obtained from the Butler−Volmer equation (dashed lines). However, importantly, at high overpotentials, the apparent rate of electron transfer becomes limited by the rate of diffusion across the passive layer, leading to the apparent electrontransfer rate becoming independent of the applied potential. In the presence of a passive modifying film, the electrochemical response of a rotating disk electrode may be significantly altered. The rotating disk electrode is a well-
1 1 1 = + j kRed,App[A]bulk jlim,A
(9)
Hence, analysis of the steady-state response of an RDE with a passive film will follow Koutecky−Levich behavior. In the mixed diffusion-kinetic regime, the slope of a plot of the inverse of the electrochemical flux versus the inverse of the square root of the rotation rate (for a set potential) will yield information relating to the diffusion coefficient of the electroactive species in solution.
Figure 3. Variation of RDE voltammetry as a function of the passive-film properties (DA,s = DB,s = 1 × 10−9 m2 s−1, DA,f = DB,f = 1 × 10−10 m2 s−1, k0 = 1 × 10−6 m s−1, [A]bulk = 1 mM, α = β = 0.5, and W = 10 Hz]: (a) influence of film thickness (0−10 μm), with KA = 1.0, and (b) influence of partition ratio (0.01−100), with a film thickness of 100 nm. 30036
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Figure 4. (a) Schematic of a porous electrode surface and (b) the predicted voltammetric peak current for a porous electrode surface under nonhydrodynamic conditions, demonstrating that the thin-layer contribution is only significant at higher scan rates. Calculation based upon an electrode geometric area (A) of 3.14 × 10−6 m2, a film thickness (z) of 10 μm, a porosity factor (Θ) of 0.95 (used to calculate V for the thin-layer model), an electroactive species concentration ([A]) of 1 mM, and a diffusion coefficient (D) of 1 × 10−9 m2 s−1.
Utilizing eq 9, the influence of the passive film upon the voltammetric response of an RDE is considered, the results of which are depicted in Figure 3. Figure 3a demonstrates how as the film thickness increases the limiting current at high overpotentials becomes limited not by the mass transport in solution but because of the hindered mass transport across the passive film. This arises due to the apparent rate of electron transfer becoming independent of the applied potential (cf. Figure 2). Figure 3b highlights how the partition ratio of the electroactive species in the film and solution influences the apparent electron-transfer kinetics. Increasing the solubility of the electroactive species adjacent to the electrochemical interface (as reflected by the partition ratio) leads to an apparent increase in the electron-transfer rate. This behavior is easily understood from eq 3, which demonstrates that the apparent electron-transfer kinetics for reduction varies linearly with the partition ratio. Consequently, analysis of the electrode kinetics for an electrochemical process at an RDE modified with a film is determined not only by the electron-transfer kinetics but also by the properties of the film adjacent to the interface. Situations in which the solubility of the redox species is increased next to the electrochemical interface will lead to effects that would be easily mis-ascribed as being due to electrocatalysis. Finally, we mention that because of the widespread use of organic capping agents for the stabilization of nanoparticulate materials,25 the presence of a passive film upon an electrode may arise adventitiously. Consequently, the model developed above has applications for understanding a wide variety of systems. Porous Electroactive Films. Having looked at the situation in which an electrode is modified with a passive film, we will next consider the voltammetric response of a porous electroactive surface. In accordance with previous simulation studies, the surface is considered to be approximated by a solid block that is penetrated by a regular distributed array of cylindrical pores. Using the diffusion domain approximation,26 this surface may be parametrized as schematically shown in Figure 4a. The porosity factor (Θ) is given by
Θ=
re 2 rd 2
where re and rd are as defined in Figure 4a. Under non-hydrodynamic conditions, the contribution, to the current, of the material contained within the film can be considered through comparison of the Randles−Sevcik equation to the predicted current for a thin-layer cell. Figure 4b plots the relative contributions of these two processes to the predicted peak current as a function of scan rate for a 10 μm thick film (porosity factor Θ = 0.95). It should be noted that not dissimilar results for the dependency of the voltammetric peak height are obtained upon consideration of rough electrodes, where the surface is idealized by a fractal model.27,28 Importantly for Figure 4b, for scan rates below 1 V s−1 the thin-layer contribution to the current is relatively negligible. For a rotating disk electrode, the contribution of the in-film material to the total current is even smaller because of the enhanced mass transport to the surface, and because the experimental voltammograms are regularly recorded at low scan rates (cf. 10 mV s−1) to ensure the system is at or near the steady state, this conclusion is in agreement with the results reported by Zhang et al.17 Although under steady-state conditions the magnitude of the limiting current is not significantly influenced by the presence of the film, the apparent electron-transfer kinetics may be significantly altered. For an electrochemical process exhibiting irreversible electron-transfer kinetics, the apparent electrontransfer kinetics are given by22 0 kApp ∼ Ψk0
where Ψ ∼ 1 + 2Θ
Ze re
The parameters Ze and re are as defined in Figure 4. Consequently, for porous and electroactive films, the apparent electrochemical rate constant (k0App) measured from simple 30037
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Figure 5. Schematic showing how for “thick” modifying layers the upper surface of the modifying layer should be considered within the proposed model. (10) Henstridge, M. C.; Dickinson, E. J. F.; Aslanoglu, M.; BatchelorMcAuley, C.; Compton, R. G. Sens. Actuators, B 2010, 145, 417−427. (11) Sims, M. J.; Rees, N. V.; Dickinson, E. J. F.; Compton, R. G. Sens. Actuators, B 2010, 144, 153−158. (12) Alden, J. A.; Compton, R. G. Anal. Chem. 2000, 72, 198A− 203A. (13) Opekar, F.; Beran, P. J. Electroanal. Chem. Interfacial Electrochem. 1976, 69, 1−105. (14) Levich, V. G. Physicochemical hydrodynamics; Prentice-Hall: Upper Saddle River, NJ, 1962 (translated by scripta technica, inc.). (15) Koutecky, J.; Levich, V. G. Zh. Fiz. Khim. 1956, 32, 1565−1575. (16) Leddy, J.; Bard, A. J.; Maloy, J. T.; Savéant, J. M. J. Electroanal. Chem. 1985, 187, 205−227. (17) Guo, S. X.; Zhao, S. F.; Bond, A. M.; Zhang, J. Langmuir 2012, 28, 5275−5285. (18) Liang, Y.; Li, Y.; Wang, H.; Zhou, J.; Wang, J.; Regier, T.; Dai, H. Nat. Mater. 2011, 10, 780−786. (19) Snyder, J.; Fujita, T.; Chen, M. W.; Erlebacher, J. Nat. Mater. 2010, 9, 904−907. (20) Hepburn, W. G.; Batchelor-Mcauley, C.; Tschulik, K.; Barnes, E. O.; Kachoosangi, R. T.; Compton, R. G. Phys. Chem. Chem. Phys. 2014, 16, 18034−18041. (21) Eloul, S.; Batchelor-McAuley, C.; Compton, R. G. J. Solid State Electrochem. 2014, DOI: 10.1007/s10008-014-2662-1, in press. (22) Ward, K. R.; Compton, R. G. J. Electroanal. Chem. 2014, 724, 43−47. (23) Gara, M.; Ward, K. R.; Compton, R. G. Nanoscale 2013, 5, 7304−7311. (24) Masa, J.; Batchelor-McAuley, C.; Schuhmann, W.; Compton, R. G. Nano Res. 2014, 7, 71−78. (25) Kainz, Q. M.; Reiser, O. Acc. Chem. Res. 2014, 47, 667−677. (26) Amatore, C.; Savéant, J. M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39−51. (27) Parveen; Kant, R. J. Phys. Chem. C 2014, 118, 26599−26612. (28) Kant, P. R. Electrochim. Acta 2013, 111, 223−233.
application of the Koutecky−Levich equation may differ dramatically from the true standard electrochemical rate constant. Here the change in the apparent alteration in the kinetics is a result of only the changed geometry and hence altered mass transport at the electrochemical interface. A final caveat to this result is that for thick porous electroactive layers (where the condition Ze ≪ xD does not hold) the values of Ze and re should be interpreted as representing the top of the electroactive porous layer at the layer−solution interface. This situation is schematically shown in Figure 5.
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CONCLUSION This article has explored the influence of both passive and electroactive modifying films upon the recorded voltammetric responses of rotating disk electrodes. In both situations, it has been clearly demonstrated how the apparent electron-transfer kinetics can differ greatly solely because of the altered mass transport adjacent to the electrochemical interface. Consequently, the simple application of the Koutecky−Levich equation, or even qualitative comparisons of the electrochemical responses of “modified” and “unmodified” rotating disk electrodes, is cautioned.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 320403.
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