Anal. Chem. 1996,67,694-700
Use of Multiple Electrodes To Provide Uniform Potential Distribution during Controlled Potential Electrolysis A. Scott Hinman* and Peter Wlebe Department of Chemistry, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
In practice, the size of a single working electrode in controlled potential electrolysis cells can be extended in only two dimensionswhile maintaining uniform potential distribution. A previously published theoretical model predicted that working electrode dimensions in controlled potential electrolysis cells could be effectively extended in three directions while maintaining uniform potential distribution by utilizing several working electrodes interconnected with appropriately chosen extemal resistors. A controlled potential electrolysis cell utilizing three working electrodes placed at successively increasing distances along the current path from the counter electrode has been designed and tested. The electrodeswere connected in either series or parallel with extemal compensating resistors calculated accordingto theory. Nearly identical interfacial potentials were observed for all three electrodes, with dramatic reduction of the potential errors observed without the use of the extemal resistors. It was further demonstrated that if optimum placement of the reference electrode did not pertain, then the multiple electrode/&mal resistance network behaved as a single electrode operatingwith a single uncompensated solution resistance. This should facilitate the use of conventional positive feedback techniquesto "izepotential control errors. Because changes in cell geometry or solution require different sets of compensating resistors, two operational amplifier-based circuits which eliminate this inconvenience were designed and tested. The circuits employ comparison of either individual electrode currents or potentials and feedback control to maintain these at identical values. One of the principles of good design for controlled potential electrolysis cells is that all points on the surface of the working electrode be kept equidistant from the counter electrode. Cell designs which do not meet this criterion suffer from nonuniform potential distribution across the working electrode/solution interface.' This results from varying ohmic potential losses between the counter electrode and different points on the working electrode surface. For maximizing electrode area with a single working electrode, these considerations generally require that the dimensions of the working electrode be varied in only two directions, both normal to the current path between the counter and working electrodes. In practice, this frequently limits the (1) Harrar,J. E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1975; Vol. 8, pp 1-167.
694 Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
maximum useful working electrode area that can be attained for a given cell. In a previous publication? we discussed the possibility of circumventing this problem by utilizing several working electrodes placed at successively increasing distances from the counter electrode, with each individual electrode adhering to the requirements noted above. Based on a simple transmission line model, it was shown that, in principle, the interfacial potentials of all electrodes could be maintained at identical values through the use of appropriately chosen external compensating resistors to interconnect the electrodes. The external resistors could be connected either in series, with a resistor between each pair of adjacent electrodes, or in parallel, with a resistor between electrode 1 (i.e., the electrode placed farthest from the counter electrode) and each additional electrode. For the series case, appropriate external resistances for a cell with n electrodes could be calculated according to eq 1. In eq 1, i
n
Rcj is
the value of the external compensating resistance required to maintain uniform potential distribution between electrodes j and j 1, where j = 1 denotes the electrode farthest from the counter electrode. Rs is the solution resistance between electrodes 1 and 2. As discussed previously,2the constants u and b allow for various geometries to be considered. The constant uj represents the ratio of the interfacial impedance of the fi electrode to that of electrode 1,while bj is the ratio of the solution resistance between electrodes j and j + 1 to that between electrodes 1 and 2. For the parallel case, eq 2 pertains. In eq 2, Rcj is the external
+
i
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compensating resistance to be placed between electrode j and electrode 1. Other parameters have the same significance as in eq 1. One of the objectives of the work described in this manuscript was to verify the predictions of the extemal resistance model. In a practical sense, however, selection of appropriate external compensating resistors requires knowledge of the solution resistance between adjacent electrodes as well as the ratios of the (2) Hinman, A. S.; Tang, C.Electrochim. Acta 1991,36, 841.
0003-2700/95/0367-0694$9.00/0 Q 1995 American Chemical Society
Ag wire reference electrodes 1Luggin Capillaries
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interfacial impedances of electrode pairs. Hence, different cells or different combinations of solvent supporting electrolyte require different sets of external compensating resistors. This is inconvenient. We have therefore designed and tested two operational amplifier-basedcircuits to circumvent this difficulty. The circuits utilize comparison of either the interfacial potentials or currents of individual electrodes. An appropriate feedback network is employed to control these to identical values for each electrode. EXPERIMENTAL SECTION Chemicals and Solutions. Acetonitrile @DH) was used as solvent in all experiments employing external compensating resistances. This was refluxed over CaHz and distilled prior to use. Anhydrous LiC104, used as received from Alfa Inorganic Chemicals, was employed as supporting electrolyte. 9,lO-Diphenylanthracene @PA) was used as received from Aldrich. AgC104was used as received from Alfa. AU solutions contained 0.1 M LiClOd and 0.01 M AgC104. 1,2-Dichloroethane @CE, Caledon) containing 0.1 M tetra-n-butylperchlorate (") was utilized as solvent in experiments employing electronic feedback networks. DCE was filtered through alumina, refluxed over CaHz, and distilled prior to use. TBAP was recrystallized from 2-propanol/water and dried in vacuo at 100 "C. Cell Design. Figure 1 illustrates the electrochemical cell utilized for all experiments. This is a conventional glass Hcell fitted with three planar Pt gauze working electrodes, 14 mm x 14 mm, separated by a distance of 1cm. The Pt gauze electrodes were welded to bare Pt wires which extended upward through a Teflon cell cap. Each wire was held in place by a small screw through the side of the cell cap. These screws also served to provide electrical connectionsto the working electrodes. ATefloncoated magnetic stirring bar was placed in the working electrode compartment to facilitate stirring. The stirring rate was held constant for all experiments. Three bare Ag wires placed in melting point capillary tubes served as reference electrodes. Capillary tips were positioned immediately adjacent to the counter electrode side of each working electrode. Bulk electrolyte was drawn into contact with the Ag wires by capillary action.
Agt (as AgClOJ dissolved in the bulk electrolyte provided the oxidized form of the reference redox couple for experiments in acetonitrile. Because AgC104proved insoluble in DCE, when this solvent was employed, the silver wires were rinsed first with concentrated NH3 and then with distilled water. After air-drying, they were soaked overnight in DCE containing 0.1 M TBAP to which a crystal of AgC104had been added. When this procedure was used, all electrodes were found to have identical potentials. No drift in the potentials of the Ag wire quasireference electrodes (QREs)was observed throughout the course of the experiments. Throughout this paper, the working electrode placed farthest from the counter electrode will be designated as working electrode 1,while working electrodes 2 and 3 are placed successivelycloser to the counter electrode. A similar designation is utilized for the reference electrodes. Instrumentation and Measurements. Figure 2 illustrates the experimental setup utilized for measurements involving external compensating resistances. A PAR Model 173 potentiosat was used to afford primary potential control. Except where noted otherwise, the working and reference electrode leads of the potentiostat were connected to working electrode 1and reference electrode 1,respectively. Resistive connections between working electrodes were accomplished with decade resistance boxes ORBS)having a resolution of 1Q. For the series case discussed in the introduction, one DRB was placed between working electrodes 1 and 2, and a second was placed between electrodes 2 and 3, as illustrated in Figure 2. For the parallel case, one DRB was placed between electrodes 1and 2, and a second was placed between electrodes 1 and 3. The interfacial potentials of working electrodes 2 and 3, as measured against their respective reference electrodes, were determined with the aid of two high input impedance difference amplifiers. These were constructed in our laboratory using TL 081 bifet input operational amplitiers according to ref 3 and provided an input impedance of r1012 a. The outputs of the difference amplitiers were monitored with a Macintosh I1 computer fitted with a G.W. Instruments MacAdios I1 analog-digital (3) Horowitz, P.; Hill, W. The A e of Electronics, 2nd ed.; Cambridge University Press: Cambridge, U.K, 1989 p 428.
Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
695
interface. The computer also monitored the electrometer and current follower outputs of the potentiostat. Modifications to this basic experimental setup when feedback-based automatic compensation is employed are indicated in the text. Programming of the applied potential in all experiments was afforded by a digital to analog converter output taken from the computer to the summing input of the potentiostat. The potential vs time program was in the form of a staircase, with potential increments of 30 mV. After each potential step, a 2 s delay was invoked. Following the delay, the cell current and each of the working electrode potentials were measured in succession at 10 p s intervals. This sequence of measurements was repeated 200 times, and the results were averaged prior to application of the next potential increment. COMPENSATIONWITH EXTERNAL RESISTANCES Experimental Testing of the Series and Parallel Models. In acetonitrile containing 0.1 M LiC101, DPA undergoes a reversible oneelectron oxidation with a half-wave potential of 0.875 V vs Ag/Agt (0.01 M). In order to determine the b values in eqs 1 and 2, a current-potential scan was run on a stirred solution containing 1.0 mM DPA, with only working electrode 1connected to the potentiostat. Working electrodes 2 and 3 were open circuited. During this scan, reference electrode 1provided the control potential sensed by the potentiostat, and the potentials E2 and E3 of reference electrodes 2 and 3, placed immediately adjacent to working electrodes 2 and 3, were monitored by the computer. The solution resistance between electrodes 1 and 2 was calculated as the ratio of the potential difference, EZ - El, to the total cell current. The resistance between electrodes 2 and 3 was similarly determined from the difference E3 - EZ and the cell current. Resistances of 12 and 15 Q were found between electrodes 1and 2 and between electrodes 2 and 3, respectively, for 0.1 M LiC104 solutions. From these, the values bl = 1.00 and bz = 1.25 were determined. The a values in eqs 1 and 2 were determined from separate current-potential scans measured for each individual electrode. The ratio of the limiting current observed at electrode 2 to that at electrode 1 gave a2 = 0.99, and the ratio of the limiting current observed at electrode 3 to that at electrode 1 gave a3 = 0.89. Figure 3 illustrates total cell current vs applied potential in a stirred solution containing 0.1 mM DPA with all three working electrodes shorted together (R,J = R,,z = 0 Q). The differences in interfacial potentials of electrodes 2 and 3 and that applied by the potentiostat at electrode 1during this current-potential scan are illustrated in Figure 4. In regions of zero current, no significant potential errors are observed, since no ohmic losses are present in solution. In the limiting current region, the interfacial potential of electrode 2 exceeds the control potential by approximately 50 mV. This potential error results from smaller solution resistance and smaller ohmic loss between the counter electrode and electrode 2 as compared to that between the counter electrode and electrode 1. The interfacial potential of electrode 3, which lies still closer to the counter electrode, exceeds the control potential by 150 mV in the limiting current region. Figure 5 illustrates potential errors associated with electrodes 2 and 3 using external compensating resistances of R,J = 6 Q and Rc,2 = 27 Q connected in series, as indicated in Figure 2. Values of Rc,l and Rc,2 of 5.6 and 26.7 Q, respectively, were calculated from eq 1using the experimentally determined a and b values indicated previously. In the figure, no significant errors 696 Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
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in the interfacial potentials of electrodes 2 and 3 are apparent at applied potentials below about 0.90 V. In the limiting current region, maximum potential errors of -10 and -25 mV are observed for electrodes 2 and 3, respectively. While this repre sents a considerable improvement with respect to the errors observed with the electrodes short circuited, the negative values suggest a small degree of overcompensation. In a subsequent experiment, the compensating resistances were each reduced by 1 9 to values of Rc,l = 5 Q and RC,z= 26 9. In this case, the maximum potential error for electrode 3 in the limiting current region was reduced in magnitude to -13 mV. No measurable potential error was observed for electrode 2. Thus, small changes in the values of the external compensating resistances can have a significant influence on the degree of potential control afforded. This effect is anticipated to be amplified at higher cell currents. Figure 6 illustrates the errors in interfacial potentials of electrodes 2 and 3 for external compensating resistances placed in parallel. Rc,land Rc,2values of 12 and 37 Q, respectively, were utilized in accordance with values of 11.9 and 37.4 Q calculated from eq 2. The same solution and identical conditions as in
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Figures 3-5 were employed. The results are essentially indistinguishable from those presented in Figure 5 for series compensating resistors. Maximum potential errors for electrodes 2 and 3 of -10 and -25 mV, respectively, were observed in the limiting current region. Again, the negative errors obtained indicate a slight degree of overcompensation. While perfect agreement between theory and experimental observations was not attained, the results clearly indicate that the external resistance/multiple electrode approach can be used to improve significantly the potential distribution in controlled potential electrolysiscells and substantiate to a considerable extent the utility of the model from which eqs 1 and 2 were derived. It should be pointed out that the theoretical model ignores the possible existence of current paths around the edges of the electrodes. Because the present cell design does not eliminate the possible existence of such current paths, it is possible that gradients in interfacial potential exist along each working
electrode surface in directions parallel to the electrode planes. Other cell geometries, for instance cylindrical working electrodes arranged concentrically around a cylindrical counter electrode, would be more effective at " i i g such effects. Such cell designs, however, would of necessity lack the simplicity of design and ease of construction afforded by the planar geometry. Influence of Reference Electrode Placement. In the experimental results presented so far, reference electrode 1, immediately adjacent to working electrode 1,provided the control potential sensed by the potentiostat. This represents an optimum placement of the reference electrode with respect to minimizing error between actual and control potentials due to uncompensated resistance between the tip of the Luggin capillary and the working electrode surface. In certain cell designs-thin-layer cells, for instance-optimum reference electrode placement may be diflicult to achieve in practice. A prediction of the model presented in ref 2 was that if other than optimum placement of the reference electrode pertained, but appropriately chosen external compensating resistors were employed, then the multiple electrode/external resistor network would behave as a single working electrode operating in conjunction with a single uncompensated resistance. In this case, conventional positive feedback techniques could be employed to minimize the potential error. To test this prediction, an experiment was run with the reference electrode lead of the potentiostat connected to reference electrode 3. The potentiostat's working electrode lead remained connected to working electrode 1. The actual interfacial potentials of each working electrode, with respect to their immediately adjacent reference electrodes, were then determined with the aid of high impedance Merence amplifiers as before. Results from this arrangement are presented in Figure 7. This illustrates the difference between the interfacial potential of each working electrode and the applied potential sensed by the potentiostat as a function of the applied potential during a potential scan in a stirred 0.1 M LiClOd/CH$N solution containing approximately 0.5 mM DPA. Series external compensating resistances of RC,l = 5 R and RC,z= 26 SZ were employed. Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
697
turn raises the potential of the inverting input of OA10, connected
Working and Reference Electrodes RE3
Figure 8. Schematic of the circuit utilizing interfacial potential comparison for control of potential distribution in the multiple electrode cell. R1 = 100 kQ, R2 = 470 Q, C1 = 50 pF, and C2 = 0.1 p F ; OAl, OAl 0, and OAl 1 = TL081; OA8,OA9 = 'hMC1458; all other OAs = 'IzTL082.
In Figure 7, no difference between the actual applied potential and the individual interfacial electrode potentials is apparent in regions of no current flow, since there is no ohmic loss between reference electrode 3 and working electrode 1. In the limiting current region, a potential error of -70 mV is apparent for each electrode. In contrast to the situation portrayed in Figure 4, however, where a different potential error is observed for each electrode, it is apparent that all working electrodes have the same interfacial potential, albeit subject to an uncompensated resistance error. This clearly substantiates the predictions of ref 2, that if other than optimum placement of the reference electrode pertains, the multiple electrode/external resistance network will behave as a single electrode operating with a single uncompensated resistance. AUTOMATIC ELECTRONIC FEEDBACK COMPENSATION
Circuit Employing Comparison of Interfacial Potentials. Figure 8 presents a schematic of the potential comparison circuit utilized. The circuit common in the figure is connected directly to the circuit common of the potentiostat The reference electrode lead of the potentiostat is connected to reference electrode 1.The counter electrode lead of the potentiostat is connected directly to the counter electrode (not shown in the figure) as with conventional cells. The working electrode lead of the potentiostat is not utilized. The operation of the circuit can be understood by considering that the interfacial potential of working electrode 1 is controlled with respect to reference electrode 1by the potentiostat. Operational amplifiers OM,OM,and OA4 constitute a high impedance difference amplifier which measures the interfacial potential of working electrode 2 with respect to reference electrode 2. This is compared by OA8 to the interfacial potential of electrode 1, as sensed by OAl. If the interfacial potential of working electrode 2 is, for instance, more positive than that of electrode 1, a positive voltage is generated at the noninverting input of OA10. This in 698 Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
directly to working electrode 2. The interfacial potential of working electrode 2 is thereby reduced to a value equal to that of electrode 1. The interfacial potential of electrode 3 is similarly controlled to an equal value by identical circuitry. The operating principle is similar to that commonly used in bipotentiostats for rotating ring-disk electrodes: except that dynamic rather than static control is afforded. The circuit of Figure 8 is designed to function with potentiostats in which the working electrode lead is held at ground, or virtual ground. Operational amplifiers OAl, -2, -3, -5, and -6 should be a high input impedance type. The maximum current which can flow through electrodes 2 and 3 is limited to the current capability of operational amplifiers OAlO and OAll. These can be boosted using conventional techniques. Higher current capability may also require smaller resistance values for the feedback resistors R2. Total cell current may readily be determined as the potential drop across a resistor placed between the potentiostat and the counter electrode. Alternatively, the individual currents through working electrodes 2 and 3 may be determined as the potential drops across the feedback resistors R2. Working electrode 1may be connected to the virtual ground input of a conventional operational amplifier-based current follower, as opposed to a direct connection to the circuit common, to facilitate measurement of its current. The interfacial potentials of working electrodes 1,2, and 3 are readily available as the outputs of operational amplifiers OAl, -4, and -7, respectively. Inclusion of the filter networks composed of capacitors C1 and C2 and resistors R1 was found to si@cantly reduce the noise associated with measurement of the interfacial electrode potentials. Cicuit Employing Comparison of Individual Electrode Currents. Control based on comparison of electrode potentials requires a separate reference electrode for each working electrode. The requirement for multiple reference electrodes can be obviated by basing control on comparison of individual working electrode currents. Figure 9 illustrates the circuitry used to accomplish this. In Figure 9, operational amplifier OAl generates a voltage proportional to the current through working electrode 1. Operational amplifiers OA2, -3, and -4 detect the current through working electrode 2 as the voltage drop across the feedback resistor R2 of OA10. OAS compares the currents through electrodes 1 and 2 and applies any voltage to the noninverting input of OAlO required to maintain these at equal values. The current through electrode 3 is similarly controlled at a value equal to that of electrode 1. In this work, we have employed identical resistances in the feedback loops of operational amplifiers OAl, -10, and -11. This assumes that identical current vs voltage behavior pertains for each electrode. Where this assumption is not valid, as for instance, where working electrodes of different area are employed, appropriate corrections to the values of these feedback resistances may be made in order to achieve uniform potential distribution. Experiments Employing Automatic Feedback Compensation. In DCE containing 0.1 M TBAF', DPA undergoes a reversible oneelectron oxidation with a half-wave potential of 0.47 V versus the Ag wire QRE. Cyclic voltammetry at 100 mV/s (4) Roberts, D.T.; Roberts, J. L.,Jr. Experimental Electrochemistryfor Chemists; Wiley: New York, 1974; p 259.
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Working Electrodes
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indicates that this is followed by an irreversible oxidation with a peak potential of 0.92 V against the same reference electrode. Figure 10 illustrates the current through each individual working electrode observed in a stirred DCE/O.l M TBAP solution containing 1.0 mM DPA Each working electrode was connected to the virtual ground input of a separate operational amplifierbased current follower, effectively short-circuiting all electrodes together. A staircase potential-time program with potential increments of 30 mV and 1.0 s duration was employed. Currents were sampled at the end of each potential increment as discussed in the Experimental Section. During this experiment, high impedance difference ampljjiers were employed to simultaneouslymonitor the interfacial potentials
of working electrodes 2 and 3 with respect to their immediately adjacent reference electrodes, as indicated previously for measurements utilizing external compensating resistances. The interfacial potential of working electrode 1with respect to reference electrode 1was controlled by the potentiostat. In Figure 11,the difference in the interfacial potentials of working electrodes 2 and 3 and the potential applied by the potentiostat at electrode 1 are plotted against the applied potential. In Figures 10 and 11, it is evident that all interfacial potentials are equal in regions of no current flow. When current begins to flow, the interfacial potentials of electrodes 2 and 3 increase as compared to the applied potential owing to their closer proximity to the counter electrode. The potential error is most pronounced for electrode 3, which lies closest to the counter electrode. In fact, the potential of electrode 3 becomes sufficient to start removing a second electron from DPA when the applied potential just exceeds the half-wave potential for the first oxidation. This is clearly evidenced in the current vs applied voltage curve for this electrode in Figure 10. Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
699
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In a subsequent experiment employing a fresh but otherwise identical solution,the voltage comparison control circuit of Figure 8 was utilized. Figure 12 illustrates the difference in the interfacial potentials of working electrodes 2 and 3 and the applied potential of electrode 1 for this experiment. Krtually identical potentials for all three working electrodes are apparent throughout the run. Figure 13 illustrates the currents through each individual electrode during an experiment in which the current comparison control circuit of Figure 9 was employed. The conditions and potential-time program were identical to those of the previously described experiments. It is clear in Figure 13 that identical current versus applied voltage curves are imposed on each electrode by the control circuit. Figure 14 illustrates the error in the interfacial potentials of electrodes 2 and 3 with respect to the applied potential measured during the same experiment from which the data of Figure 13 were taken. The potential measurements were facilitated with the aid of high impedance difference amplifiers as before. Some error in the potentials of these electrodes is apparent. This can be attributed, in part, to the use of identical resistances in the feedback loops of operational amplifiers OAl, -10, and -11in Figure 9. As pointed out previously, the use of identical feedback resistors is based on the assumption that identical current voltage
700 Analytical Chemistry, Vol. 67, No. 4, February 15, 1995
curves pertain for each electrode. In practice, these conditions are dacult to meet precisely. Nonetheless, the potential errors are dramatically reduced in comparison to those evident in Figure 11, where no control circuitry was employed. In particular, the degree of potential control afforded by the current-comparison circuitry prevents removal of a second electron from DPA at applied potentials sufficient to facilitate one-electron oxidation at a mass transport limited rate. ACKNOWLEDGMENT
The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for hancial support of this work.
Received for review March 29, 1994. Accepted November 18, 1994.@ AC940296P
Abstract published in Advance ACS Abstracts, January 1, 1995.
