Article pubs.acs.org/ac
Quantitative Aspects of Ohmic Microscopy Charles A. Cartier, Doe Kumsa, Zhange Feng, Huanfeng Zhu, and Daniel A. Scherson* The Ernest B. Yeager Center for Electrochemical Sciences and Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106-7078, United States ABSTRACT: The potential difference between two microreference electrodes, Δφsol, immersed in an aqueous sulfuric acid solution was monitored while performing conventional cyclic voltammetric experiments with a Pt disk electrode embedded in an insulating surface in an axisymmetric cell configuration. The resulting Δφsol vs E curves, where E is the potential applied to the Pt disk electrode were remarkably similar to the voltammograms regardless of the position of the microreference probes. Most importantly, the actual values of Δφsol were in very good agreement with those predicted by the primary current distribution using Newman’s formalism (Newman, J. J. Electrochem. Soc. 1966, 113, 501−502). These findings afford a solid basis for the development of ohmic microscopy as a quantitative tool for obtaining spatially resolved images of electrodes displaying nonhomogenous surfaces.
water (UPW, 18.3 Ω cm, Barnstead UV pure system). A Pt disk electrode (1.5 mm in diameter) encased in a coplanar Teflon shroud (outer diameter 6 mm) was used as the working electrode faced upward. The distance from the surface of the disk electrode to the bottom of the cell was 0.95 cm and to the electrolyte-air interface 10.5 cm. The counter electrode was a gold wire (0.5 mm in diameter, Alfa Aesar, 99.9985% metal basis) made in the form of a ring (diameter ∼4 cm) placed 0.3 cm above the bottom of the cell and connected to the lead wires external to the cell via a glass insulated copper segment to preserve the axisymmetric character of the system. The reference electrode for the conventional voltammetric measurements was a Ag/AgCl (3 M KCl, World Precision Instruments, WPI) and was placed with its axis parallel and very close to the cell wall, with its tip near the bottom of the cell (see Figure 1). Microreference (μ-ref) Ag/AgCl electrodes were prepared by first striping off the surface oxides of a 5-cm-long Ag wire (200 μm diameter, Alfa Aesar 99.95%) with a dry polishing pad followed by immersion in a saturated KCl (Fisher Scientific, > 99%) solution for ∼2 h. Subsequently, the wire was thoroughly washed with UPW and then inserted into a pulled glass capillary made from a thin wall borosilicate glass capillary (o.d. 1 mm, i.d. 0.75 mm, WPI) using a commercial puller (PB-7, Narishige). The final pulled tip had a circular opening ∼50 μm diameter) as measured with an optical microscope. The assembled μ-ref electrodes were then placed in saturated KCl for more than 12 h and their stability tested against a commercial Ag/AgCl electrode (3 M KCl, WPI) in saturated KCl solution until the potential difference was found to be constant and smaller than 20 mV. Also measured was the difference in potential between the two μ-ref electrodes and
T
he ability of reference electrodes to measure local electrostatic potentials in electrolyte solutions has been known and indeed widely exploited for many decades. Particularly noteworthy in the area of physical electrochemistry are the contributions of Miller and Bellavance,1 for studies of the current distribution to a rotating disk electrode, Lillard et al.2 and Orazem, Vivier, and Tribollet3,4 for impedance spectroscopy, and those of Amatore et al.5−7 for mapping concentrations profiles of redox active species in solution. Efforts in our laboratory have focused on the implementation of this strategy for monitoring differences in the electrostatic potential, Δφsol, between any two points of a homogeneous electrolyte solution by using two microreference electrodes. As described in our previous communication,8 Δφsol values recorded while performing conventional cyclic voltammetric measurements of a Pt electrode using a potentiostat in a three electrode cell yielded curves which closely resembled those obtained by measuring the current through the external circuit. Evidence of the local character of Δφsol was obtained by employing a segmented Pt−Au electrode, whereby the response due to the Au or Pt could be isolated by placing the microreference electrodes next to each of the corresponding segments far away from the Pt−Au junction.8 This work seeks to provide a quantitative account of this methodology, we dubbed ohmic microscopy, by comparing the experimental results with those predicted by theory and may be regarded as a first step toward the development of a functional ohmic microscope capable of generating in situ spatially resolved images of interfacial reactivity of heterogeneous electrode surfaces.
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EXPERIMENTAL SECTION Measurements were performed in a Teflon cell (2 cm high, 4 cm inner diameter) filled with a nondeareated 0.1 M H2SO4 (Fisher Scientific, 98%) aqueous solution made with ultrapure © 2012 American Chemical Society
Received: May 19, 2012 Accepted: July 28, 2012 Published: July 28, 2012 7080
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The two μ-ref Ag/AgCl electrodes labeled as R1, R2 in Figure 1 were solidly mounted on individual holders (Warner Instruments) and, in turn, to individual micromanipulators, (460A Series, Newport Corp.) with their main axes forming an angle of ∼60° with respect to the normal to the electrode surface (z axis). As found by experience, the potential difference between any two μ-ref electrodes, although not zero, was very small, on the order of a few millivolts and constant over the time required to collect all the measurements. These differences were subtracted from the observed Δφsol values. For the experiments presented in this work, the tip of one of the μ-ref electrodes was placed along the z axis normal to the center of the disk, i.e., r = 0, and the tip of the other along or parallel to that axis. Once the tips were set at the desired coordinate values, a series of cyclic voltammetric curves were recorded using a potentiostat (Autolab, PGSTAT302N, AUT84413, Nova 1.6, Metrohm), while Δφsol vs t data were acquired with a digital multimeter (Keithley 3706 System Switch/Multimeter) at rates as high as 14 000 points/s using the Labview platform.
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THEORETICAL FORMALISM It will be assumed in what follows that the electrochemical processes of relevance are capacitive and/or kinetically unhindered pseudocapacitive, as is the case with Pt and Au in solutions devoid of species which can undergo sustained redox reactions. Because of the minute changes in the concentration of species in solution induced by surface limited processes, the electrolyte itself may be regarded at all times as being of virtually uniform composition. It thus follows that the system,
Figure 1. Schematic diagram of the cell in which the ohmic microscopy data were acquired: WE, working electrode; CE, counter electrode; RE, reference electrode; R1 and R2, μ-ref electrodes. The vertical red line represents a glass insulated Cu wire that connects the Au ring electrode to the outside (see the text for details).
found to yield stable values no larger than 10 mV. Only μ-ref electrodes displaying these attributes were used in the experiments.
Figure 2. Cyclic voltammetry (thin blue solid lines, right ordinates) and Δφsol vs E curves (open circles, left ordinates) recorded simultaneously in experiments where the tips of the μ-ref electrodes were placed along the axis normal to the center of the Pt disk electrode keeping the center of the tip of R1 fixed at 0.225 mm above the center of the disk for four different positions of the center of the tip of R2. The values in the inserts represent the distance in mm between the center of the two tips, i.e., 1 (Panel A); 1.5 (B); 2 (C) and 2.5 mm (D). The solid black lines are the results of the theoretical simulations based on Newman’s formalism. See text for details. 7081
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was repeated under precisely the same conditions (data not shown). Shown in Figure 3 in solid black circles is the average Δφexp sol extracted from these two experiments and Δφth sol calculated
as described, will generate what is known as a primary current distribution. Analytical solutions to this problem for a disk electrode embedded in an insulating surface have been given by Newman in his pivotal contribution9 under conditions in which the counter electrode is assumed to be far enough from the working electrode so that its physical shape and position can be effectively neglected. Within this framework, the electrostatic potential, ϕ, in a media of constant conductivity, κ, induced by the passage of a current, I, through a disk of radius a embedded in an insulating surface is given by ϕ 2 = 1 − tan−1 ξ ϕo π
(1)
where ξ is a rotational elliptical coordinate, related to the rotational cylindrical coordinates, r and z, by the expressions z = aξη r = a (1 + ξ 2) + (1 − η2)
(2)
where η is the other rotational elliptical coordinate and ϕo =
I 4κa
(3)
Figure 3. Plots of the average Δφexp sol vs z, where z is the vertical distance between the center of R2 and the center of the disk (solid black circles) extracted from Figure 2, and a completely independent experiment and Δφth sol vs z calculated from eq 4 (solid red circles) for a current I = 0.7 mA. The open symbols in this figure were calculated based on numerical simulations of the actual cell (see insert) using Cell-Design (open circles) for the same current flowing through the disk. The solid squares were determined from Newman’s model for different positions of R1 (see text).
is the potential on the disk. For the conditions under which the experiments were performed, κ = 0.047 S cm−1 10 and a = 0.75 mm. The potential at any point within the solution, i.e., fixed r and z, or equivalently, ξ and η, was obtained by first calculating ϕo from eq 3 for a given value of the experimental current I observed in the cyclic voltammogram and then using eq 1 to determine ϕ at that point. On this basis, the difference in electrostatic potential between the points where the probes are placed, say 1 and 2, Δφth sol would be given by th Δφsol = ϕ2 − ϕ1 =
2 ϕ (tan−1 ξ1 − tan−1 ξ2) π o
from eq 4 (solid red circles), as a function of the distance between the center of the tip of R2 and the surface of the disk, (0,0), for a current I = 0.7 mA. As indicated, the differences between theory and experiment were found to be no larger than ∼2 mV. Simulations of the actual cell performed in CellDesign (see insert in Figure 3, where the yellow circle represents the ring counter electrode) yielded very similar results (see open circles in this figure), which serve to validate the analytical solution under the conditions in which the measurements were performed. Also shown in this figure are Δφth sol based on Newman’s formalism assuming R1 was placed 25 μm closer (solid black squares) and 25 μm farther away (solid blue squares) from the surface of the electrode to illustrate the extent to which uncertainties in the actual position of R1 would affect the predicted potential differences. A similar set of measurements was carried out by placing the tip of R1 along the axis normal to the center of the Pt disk electrode, (0,1.525), and that of R2 along an axis normal to the surface at r = 1. The experimental and theoretical results based on Newman’s formalism for (r,z) = (1,1.525); (1, 2.025); (1, 2.525); and (1, 3.025) are provided in panels A−D, respectively, in Figure 4. Shown in Figure 5 is a comparison th between Δφexp sol and Δφsol values extracted from the data in Figure 4 in experiments for I = 0.16 mA, where the symbols have the meaning as those in Figure 3. The agreement between theory and experiment based on these data is of about 1−2 mV.
(4)
The values predicted by this model were compared to those obtained by simulating the real electrochemical system using the boundary element option in Cell-Design (L-Chem, Cleveland, OH) ignoring effects associated with the physical presence of the reference and μ-ref electrodes.
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RESULTS AND DISCUSSION Shown in Figure 2 are a series of voltammetric curves (I vs E, thin blue line, right ordinate) for the Pt disk electrode recorded by the potentiostat at a scan rate of 30 V/s and of Δφexp sol vs E data (open circles, left ordinate) acquired simultaneously by the multimeter. For these experiments, the two μ-ref electrode tips were placed along the z axis, r = 0, i.e., normal to the disk surface at its center. Specifically, the center of the tip of R1 was set at about 0.225 mm away from the surface of the Pt disk electrode, i.e., (0,0.225), and that of R2 at (0,1.225) (panel A), (0,1.725 (B), (0,2.225) (C), and (0,2.725) mm (D). The distances in the inserts in these panels are those between the tips of the two microference electrodes. As clearly evident from these results, the shapes of both the voltammogram and Δφexp sol vs E curves were found to be very similar regardless of the height at which R2 was placed. In other words, Δφexp sol tracks rather accurately the cyclic voltammetric curve. Also given in black solid lines in this figure are values of Δφth sol obtained using eq 4. The Pt electrode was then polished, and this experiment 7082
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Figure 4. Cyclic voltammetry (thin blue solid lines, right ordinate) and Δφsol vs E curves (open circles, left ordinate) recorded simultaneously in experiments where the center of the tip of R1 was placed at a fixed distance of 1.525 mm along the axis normal to the center of the Pt disk electrode, whereas the center of the tip of R2 was placed along an axis normal to and 1 mm away from the center line. The numbers (in mm) in the inserts represent the differences in the axial coordinates of the centers of the tips of R1 and R2, i.e., 0 (Panel A); 0.5 (B); 1 (C) and 1.5 (D). The solid black lines are the results of theoretical simulations based on Newman’s formalism. See text for details.
and thus determine local heterogeneities such as those associated with different facets of the same metal or different metals exposed to the electrolyte. Efficient algorithms to solve this inverse problem are currently being developed and will be reported in due course.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Funding for this research was provided by NSF (Grant CHE0911621). Figure 5. Same as Figure 3 based on data shown in Figure 4.
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REFERENCES
(1) Miller, B.; Bellavance, M. I. J. Electrochem. Soc. 1973, 120, 42−53. (2) Lillard, R. S.; Moran, P. J.; Isaacs, H. S. J. Electrochem. Soc. 1992, 139, 1007−1012. (3) Frateur, I.; Bayet, E.; Keddam, M.; Tribollet, B. Electrochem. Commun. 1999, 1, 336−340. (4) Frateur, I.; Huang, V. M.; Orazem, M. E.; Tribollet, B.; Vivier, V. J. Electrochem. Soc. 2007, 154, C719−C727. (5) Amatore, C.; Pebay, C.; Scialdone, O.; Szunerits, S.; Thouin, L. Chem.Eur. J. 2001, 7, 2933−2939. (6) Amatore, C.; Szunerits, S.; Thouin, L. Electrochem. Commun. 2000, 2, 248−253. (7) Amatore, C.; Szunerits, S.; Thouin, L.; Warkocz, J. S. Electroanalysis 2001, 13, 646−652. (8) Chen, Y. J.; Belianinov, A.; Scherson, D. J. Phys. Chem. C 2008, 112, 8754−8758.
CONCLUSIONS The results of this investigation have shown that provided the currents flowing through the working electrode are capacitive and/or pseudocapacitive in nature, the potential difference between two microreference electrodes immersed in the solution, Δφsol, is determined by the primary current distribution as prescribed by solving Laplace’s equation subject to the appropriate boundary conditions. Since such solutions are expected to be unique once the system is fully specified, it seems conceivable one could determine from a map of the potential distribution in solution measured experimentally the local current densities across the electrode−electrolyte interface 7083
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(9) Newman, J. J. Electrochem. Soc. 1966, 113, 501−502. (10) Darling, H. E. J. Chem. Eng. Data 1964, 9, 421−426.
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