except in cells with this specific geometry, it provides a very useful general correlation between the experimental parameters. Thus, the influence of a and s on the potential distribution is defined, and as with all experiments in which the working electrode is completely polarized, the potential gradient is directly proportional to the current density and solution resistance. On the basis of these considerations, the proper location for the reference electrode is obvious, qrovided the exact potential distribution is known. I n the general case when the potential distribution is known only approximately, the best approach is to use the same procedure as described with wire mesh electrodes-i.e., the reference electrode should be placed on the line of minimum separation between the counter and working electrodes. ACKNOWLEDGMENT
The authors express their appreciation t o Ervin Behrin for the design of portions of the instrumentation, to Ralph G. Gutmacher and Donald McCoy for the x-ray fluorescence analysis, and to Roman Bystroff for assistance in the spectrophotometric determinations. The helpful comments on this work by Dale J. Fisher of the Oak Ridge National Laboratory are gratefully acknowledged. LITERATURE CITED
(1) Agar, J. N., Hoar, T. P., Discussions Faraday SOC.1 , 158, 162 (1947). (2) Aletti, R., et al., Proc. Intern. Comm.
Electrochem. Thermodyn. Kinet., 3rd 30 (1952 ). ( 3 j Bard, A. J., Mayell, J. S., J . Phys. Chem. 66,2173 (1962). (4) Bard, A. J., Solon, E., Zbid., 67, 2326 (1963). (5) Barnartt, S., J . Electrochem. SOC.108. 102 (1961): . (6) Booman, G. L., Holbrook, W. B., ANAL.CHEM.35, 1793 (1963). (7) Breiter, M., Guggenberger, T., Z. Elektrochem. 60, 594 (1956). (8) delevie, R., J . Electroanal. Chem. 9, 311 (1965). (9) Drossbach, P., 2. Elektrochem. 56, 599 (1952). (10) Fleck, R. N., Hanson, D. N., Tobias,
Meeting, Manfredi, Milan, p.
C. W., U. S. Atomic Energy Comm.
Tech. SOC.17, 83 (1942). (25) Kronsbein, J., Plating 37,851 (1950). (26) Zbid., 39, 165 (1952). (27) Lingane:, J. J., “Electroanalytical Chemistry, 2nd ed., p. 174, Interscience, Xew York, 1958. (28) Zbid., pp. 351-3. (29) Zbid., p. 357. (30) Zbid., pp. 365-6. (31) Macaire, M., Guillou, M., Buvet, R., J . Chim. Phys. 60, 775 (1963). (32) Moulton, H. F., Proc. London Math. SOC.(Ser. 2) 3, 104 (1905). (33) Mueller, T. R., U. S. Atomic Energy Comm. Rept. ORNL-3750, 5 (1965). (34) Newman, J., Zbid., UCRL-16665, UCRL-16747 (1966). (35) Om, C. H., Wirth, H. E., J . Phys. Chem. 63, 1150 (1959). (36) Page, J. A., Talanta 9, 365 (1962). (37) Rousselot. R. H.. Metal Finishinu ‘ p. 56, October 1959. ’ (38) Rousselot, R. H., “Repartition du
Rept. UCRL-11612 (1964). (11) Gelb, R. I., Meites. L., J. Phvs. Chem. 68, 630 (i964). (12) Geske, D. H., Bard, A. J., Zbid., 63. 1057 (1959). -, (13) ‘GuGlou, M., Bull. SOC. France Electriciens 5, 439 (1964); C.A. 61, 1 5 6 6 2 ~(1964). (14) Haring, H. E., Blum, W., Trans. Electrochem. SOC.44, 313 (1923). (15) Harrar. J. E.. ANAL. CHEM. 35. 893 (i963j. (16) Harrar, J. E., Lawerence Radiation
1959. (39) Schaap, W. B., hIcKinney, P. S., ANAL.CHEM.36, 29, 1251 (1964). (40) Schwarz, W. M., Sham, I., Zbid., 35. 1770 (1963). (41) ’Scott, F. A.,’ Stouffer, J. C., Richardson, R. L., Doc. X o . €IN80365, Han-
troplaters SOC.26, 753 (1939). (18) Jacobs, W. D., ANAL.CHEM.33,1279 (1961). (19) Kardos, O., Foulke, D. G., in
(1964). (43) Wagner, C., in “Advances in Elec-
I
,
\ - -
~
Laboratory, Livermore, Calif., unpublished research, 1963. (17) Hull, R. O., Monthly Rev. Am. Elec-
“Advances in Electrochemistry and Electrochemical Engineering,” Vol. 2, 145-233, C. W. Tobias, ed., Interscience, New York, 1962. (20) Kasper, C., Trans. Electrochem. SOC.
77, 353, 365 (1940); 82, 153 (1942). (21) Zbid., 78, 131 (1940). (22) Zbid., p. 147. (23) Klingert, J. A., Lynn, S., Tobias, C. W., Electrochim. Acta 9, 297 (1964). (24) Kronsbein, J., J. Electrodepositors
Potentiel et du Courant dans les Electrolytes,” pp. 22-3, Dunod, Paris,
ford Atomic Products Operation, Richland, Wash., 1964. (42) Stelzner. R. W.. Kellev. hl. T.. Fisher, D.’ J., U. S. Ato& Energy Comm. Rept. ORNL-3537, pp. 9-12
tSochemistry and Electrochemical Engineering,” Vol. 2, 8-14, C. W. Tobias, ed., Interscience, New York, 1962. (44) Wagner, C., J . Electrochem. SOC.98, 116 (1951).
RECEIVEDfor review April 28, 1966. Accepted June 17, 1966. Work supported by U. s. Atomic Energy Commission Contract Nos. AT(ll-1)-1083 and W-7405-eng-48.
Evaluation of Stationary Electrode Polarography and Cyclic Voltammetry for the Study of Rapid Electrode Processes S. P. PERONE Department of Chemistry, Purdue University, Lafayette, Ind. The application of stationary electrode polarography and cyclic voltammetry to the study of very rapid electrode processes has been evaluated using a solid-state operational amplifier potentiostat. Several different redox systems, representing reversible, irreversible, and quasi-reversible behavior, were investigated. Potential scan rates varying from 1 .O to 50,000 volts/second were employed. In addition, to test further the time-response characteristics of the potentiostat and electrolysis cell, potentiostatic currenttime experiments were performed under diffusion-limited conditions with measurements made in the 5- to 200pec. region, It is concluded that
1 158
ANALYTICAL CHEMISTRY
scan rates as fast as 2000 volts/ second may be employed with confidence in fast sweep experiments where the response characteristics of the potentiostat and electrolysis cell have been optimized. Scan rates as fast as 20,000 volts/second or greater appear possible under these conditions, but the interpretation of data in some cases may be difficult due to sweep distortion by potentiostat response or uwompensated ohmic losses. The results of these experiments indicate that chemical rate processes coupled to the charge transfer step may be studied with time resolution of the order of 1-100 psec., using linear sweep techniques.
T
techniques of stationary electrode polarography and cyclic voltammetry offer a distinct advantage for the investigation of complicated electrode processes. Variation of the scan rate parameter results in peak current and/or peak potential changes characteristic of the mechanism of the particular electrode process. I n addition, kinetic data for coupled homogeneous chemical reactions may be evaluated quantitatively from rigorously derived expressions relating the rate parameters to the characteristics of current-voltage curves obtained (9). Furthermore, in theory, the time scale of a n experiment in stationary electrode polarography or HE ELECTROCHEMICAL
cyclic voltammetry may be adjusted to match the kinetics of the process being studied by increasing or decreasing the scan rate to the appropriate range. Although successful applications of these stationary electrode techniques for studies of slow to moderately fast processes (using scan rates up to about 200 volts/second) have been reported (8, 16), their extension to the study of very rapid processes (scan rates greater than 200 volts/second) have not been reported. Two primary reasons for the lack of application to rapid electrode processes can be pointed out: First, charging currents become large compared to faradaic signals, even for millimolar solutions, when scan rates greater than 100 volts/second are employed. Moreover, because charging current depends on the first power of scan rate and faradaic current depends on the square-root power, further increases in scan rate result eventually in the complete obliteration of the faradaic signal. The second and most important problem involved in the study of rapid electrode processes is that concerning instrumental and cell response. The essential characteristics of this problem have been discussed extensively recently (2, 3, 14); although these treatments have been oriented toward response to a step-function input signal, the conclusions can be applied in principle to the linear sweep case considered here. The important experimental factors involved are the rise-time, stability, and current capacity of the potentiostat; the total cell resistance; the uncompensated resistance; and the doublelayer capacity. The primary objective of the work reported here was to optimize these experimental factors such that the investigation of electrode processes with microsecond time resolution might be possible utilizing linear sweep techniques. EXPERIMENTAL
Instrumentation. The potentiostat used in this work was constructed from a P35A solid-state differential operational amplifier and a P66A solid-state current booster amplifier obtained from G. A. Philbrick Researches, Inc., Dedham, Mass. The P66A was wired with external ballast resistors, allowing currents of =t100 ma. to be drawn (11). The power supply was a Philbrick PR-300, h 1 5 volts, h300-ma. supply. The circuit for the controlled potential experiments performed here is shown in Figure 4b of Schwarz and Shain ( 1 3 ) . The working electrode was grounded directly; the reference electrode potential was sampled directly at the inverting input of the P35A. The noninverting input of the P35A was driven by the ground-referenced potential function to be imposed across the working and reference electrodes; the
output of the P35A was followed by the P66A booster and was applied to the counter electrode. A floating load resistor was placed in the feedback loop, and currents were measured by sampling the iR drop with the differential input of a Type D plug-in unit in a Model 536 Tektronix oscilloscope. For cyclic scan experiments, the horizontal deflection of the scope was driven by the reference electrode potential, using a Type G plug-in. For single cathodic sweep experiments, the Type T timebase plug-in was used to generate a horizontal sweep. Oscilloscope traces were recorded with a Duhlont No. 2620 Polaroid camera. Square-wave and triangular-wave signals were generated by a HewlettPackard Model No. 3300A function generator with a No. 33028 plug-in trigger unit. Single or continuous scans could be generated from frequencies of 0.008 to 100,000 C.P.S. Sawtooth signals were generated by taking the sawtooth output of a Tetronix Type T plug-in unit and dividing it down to an appropriate level. For all cyclic experiments, the triangular-wave amplitude was 0.50 volt; for all single cathodic sweep experiments, the amplitude was 1.00 volt. The characteristics of the operational amplifiers used in the potentiostat circuit have been published (11, 12). The selection of the P35A as the control amplifier was a compromise choice based on its bandpass (4Mc.) and input impedance (1.5 megohms). A higher bandpass differential amplifier would be preferable, but none was available with sufficiently high input impedance. The choice of the P66A as booster amplifier was arbitrary. Other booster amplifiers are available (particularly vacuum tube type) which can deliver significantly more power. One of these should be used for maximum performance with potential-step type experiments or with large area electrodes ( 2 ) . However, for linear sweep experiments with microelectrodes a t scan rates less than 100,000 volts/second, the current capacity of the P66A was considered adequate. No significant improvement in frequency response, and considerable loss of stability, resulted when a Krohn-Hite DCA-10 10-watt booster amplifier replaced the P66A. For slow scan experiments, to minimize high-frequency noise, a variable capacitance was connected from the output of the P35A to its inverting input. Very small capacitance values were required (0.0001 to 0.01 mf.), and no alteration of response characteristics for slow scans was observed. For scan rates greater than about 200 volts/ second, no feedback capacitance was required. No attempts to add stabilizing circuits, such as those discussed by Booman and Holbrook (S), were made, because the potentiostat remained stable and responsive under the most extreme conditions imposed in this work. Evaluation of Optimum Response and Uncompensated Resistance. The most critical experimental maneuver in this work was the adjustment of the
reference electrode probe-working electrode separation for optimum response. A Luggin capillary probe was used and placement of the mercury drop electrode was as close as possible to the probe without loss of stability in the potentiostat. As pointed out by Booman and Holbrook (3), potentiostat stability and control are lost when the uncompensated resistance is reduced to zero. On the other hand, it was observed in this work that the electrode separation could be reduced in most cases to less than 0.1 mm. without loss of stability or control. Thus, for each system investigated, the cell response was optimized, a t the fastest scan rate to be used with that system, by gradually bringing the working electrode closer to the reference probe until loss of control was indicated by large oscillations in the voltammetric curves. The working electrode was backed off from this point until the circuit had just re-achieved stability, and just tolerable oscillations were obtained. This position was considered optimum and was readily reproducible. For relatively low conductivity solutions, this situation was achieved just a t the point of light contact between the Luggin capillary and the mercury drop. In very high conductivity solutions, the optimum separation of Luggin capillary probe and working electrode was the order of 0.1 mm. The uncompensated resistance, R,, could be estimated in one of two ways. The electrolyte conductivity and reference probe placement could be combined to calculate R, as described by Booman and Holbrook ( 2 ) . This approach requires an accurate measure of the working electrode-reference probe separation for best results. Another approach applied in this work was to use a system which behaved reversibly up to very fast scan rates where relatively large currents would flow. At a scan rate where the first definite measurable shift in E, occurred, an estimate was made of the uncompensated resistance which would completely account for the shift. This set an upper limit to R, under the conditions obtained in the electrolysis cell. This value of R, could be used for correcting peak shifts in the investigation of systems with similar conductivity and reference probe placement. In any event, the lowest estimated upper limit of R, was used. For example, an estimated value of R, of 1.0 ohm was obtained in the investigation of Cd(I1) in 1 . O M KK08 from the initial sKift of E, at 2000 volts/second. [The procedure of Booman and Holbrook (2) predicts an upper limit of 3 to 4 ohms for R,.] This lower value of R, was used in correcting data obtained in l.0iM NazSOa solution, because very similar conductivity was obtained, and placement of the Luggin capillary was identical. For the high conductivity solutions, such as 3.i’hf H2S04 used in this work. R, was estimated to be 0.6 ohm by the procedure of Booman and Holbrook (2)* VOL. 38,
NO. 9,
AUGUST 1966
1159
Figure 1. input
Response to square-wave
Plot of working vs. reference electrode potential. Vertical scale, 0.050 volt/div.; horizontal scale, 2 psec./div. Sample solution 1 X 10-aM Cd(ll), 1 .OM KNOa; hanging mercury drop electrode; load resistor, 5 ohms
Cells and Electrodes. The cell and electrode assembly has been described previously (IO). The only changes for this work were that the counter electrode was a 6-cm., 22gauge platinum wire coiled in a 2-cm. diameter circle around the working electrode and that a Luggin capillary salt bridge (4)was used to isolate the reference electrode from the sample solution. The large saturated calomel reference electrode was separated from the Luggin salt bridge, which contained the same inert electrolyte as the sample solution, by a fine porosity sintered glass disk. The end of the Luggin probe was bent into a U-shape with the tip pointed up and positioned directly below the working electrode. This arrangement allowed easy and reproducible manual adjustment of the reference-working electrode separation. The radii of the hanging drop electrodes used in this work were the order of 0.05 cm. All experiments were performed a t ambient temperatures between 23" and 25" C. Reagents. All chemicals used in this work were reagent grade. The water used in preparing all solutions was purified either by triple-distillation or by passage of single-distilled water over a mixed-bed cation-anion exchange resin. KO significant difference in electrochemical behavior was observed for the different sources of purified water. High purity nitrogen was used for deaeration. RESULTS AND DISCUSSION
The most important question in this work is that of evaluating the response characteristics of the instrumentlation and electrolysis cell. One approach to this problem is to evaluate the transfer functions of the potentiostat electrolysis cell and predict the response limitations 1 160
ANALYTICAL CHEMISTRY
imposed by various combinations of cell resistance, uncompensated resistance, and double-layer capacitance (2, 3, 14). This approach is strictly applicable only for the case where faradaic currents are negligible (S), although the general principles involved are useful guidelines. [The combined effects of faradaic and capacitive currents in the potentialstep approach have been discussed by Booman and Holbrook (S)]. An alternate approach to evaluating response characteristics would be to monitor the potential difference between the working and reference electrodes in the actual electrolysis cell and compare this with the input signal. This method would give an estimate of the fastest rise-time obtainable; that is, the response would reflect the characteristics of the potentiostat upon driving a capacitive load through the experimentally attainable uncompensated resistance. However, the actual timedependence of the working electrode potential might be distorted due to uncompensated ohmic losses (6, 7). Perhaps the best way to evaluate combined instrumental and cell response is to investigate an electrode process whose behavior could be predicted accurately for very rapid scan rates.
Figure 3. curves
Potentiostatic current-time
1 X IO-aM Cd(ll), 1.OM KNO3; hanging drop electrode; vertical scale, 2 ma./div.; horizontal scale, 5 psec./div. Upper trace: potentiostatic reduction of Cd(ll) lower trace: blank, in 1 .OM KNOa
Figure 2. Response to wave input
triangular-
10,000 volts/second; vertical scale, 0.050 volt/div.; horizontal scale, 10 psec./div. lower trace: output of function generator Upper trace; plot of working VI. reference electrode potential with triangular wove input at 10,000 volts/second. l o a d resistor, 5 ohms; sample solution same as for Figure 1; hanging mercury drop electrode
For example, a process which exhibited reversible cyclic-voltammetric behavior from slow scans through megacycle frequencies would be ideal. However, no such system has been reported. Thus, one is limited a t best to investigating quasi-reversible processes. On the other hand, the voltammetric behavior of these processes may be predicted theoretically as a function of scan rate (8), and the study of these processes proved useful in this work. Potentiostat Response Characteristics. The combined response of the solid-state potentiostat and the electrolysis cell to both square-wave and triangular-wave input signals is illustrated in Figures l and 2. For a step function, the rise-time appears to be the order of 2 to 3 psec. Furthermore, for the triangular-wave signal no significant distortion appears a t scan rates below about 50,000 volts/second. To further characterize the rise-time of the potentiostat a potential-step experiment was performed with 1.0 x 10-3M Cd(1I) in 1.0M KNOI. The potential was stepped from -0.47 to -0.77 volt us. S.C.E., where El/1 is -0.60 volt. Thus, diffusion-controlled currents were expected, and a linear plot of a us. t - l l 2 should have been obtained (6). Figure 3 shows the shapes of the electrolysis current-time curve
( I/t 112 ' Figure 4. Plot of i vs. t - ' / 2 for potentiostatic reduction of Cd(ll) at the hanging drop electrode
and the blank obtained in the first 50 psec. Figure 4 shows a plot of data obtained from 3 different current-time curves covering the range from a few psec. to 200 psec. The currents are corrected for blanks, and a linear plot of i us. t - I ' * is indeed obtained with ,measurements a t times as short as 6 psec. Scatter in the data a t short times is due to random errors in subtracting comparable numbers. Blankcorrected currents a t shorter times were consistently low, perhaps indicating that the uncompensated ohmic loss a t short times was so large that the working electrode could not attain a sufficiently cathodic potential for diffusion control. il 6-psec. potentiostatic rise-time does not necessarily define the limiting response for linear sweep experiments. With linear sweep techniques charging current flows continuously a t a relatively constant level, whereas in controlled potential-step experiments extremely large current surges are required to charge the double layer in a few microseconds ( 2 ) . The responselimiting step for linear sweep experiments is the attainment of a charging current level sufficient to maintain the imposed scan rate. -1lthough this accomplishment may not be instantaneous, if the potentiostat catches up with the input signal before the foot of the voltammetric wave, no scan rate error occurs. (Of course, some sweep distortion may occur during the faradaic peak due to Uncompensated ohmic losses.) Observations of the shapes of charging current curves, with the reference electrode probe located for minimum unconipenss ted resistance, indicated that the initial induction period required before the imposed voltage coincided with the input signal varied with the value of uncompensated resistance obtained. Thus, in 1.0X K X 0 3 the induction period was the order of 10 to 15 hsec.; in 3.7M HzSO( the induction period lasted only 2 to 4 psec. No data were reported in this work for cases where this induction period appeared to extend beyond the foot of the voltammetric wave.
Rapid Linear Sweep Experiments with Various Electrode Processes. REVERSIBLE AND IRREVERSIBLE SYSTEMS. Three systems were selected for study as typical reversible and irreversible processes. These were Fe(II1) in 0.3M oxalate-0.1M oxalic acid solution, Cd(I1) in 1.OM KN03, and Ni(I1) in 0.2.V K?1T03. The first two are ordinarily considered to be among the fastest electrode processes, whereas the last system is Figure 5. Linear-sweep current-voltcompletely irreversible. None of the age curves for Fe(lll) at the hanging three systems studied with single-sweep drop electrode experiments was found completely 1 X 10-3M Fe(lll), 0.3M oxalate, 0.1M oxalic satisfactory for characterizing the overacid. Single-sweep experiments all instrumental response. Si(I1) bevertical Upper trace: 1000 volts/second; haved as predicted (9); the reduction horizontal scale, 0.1 00 scale, 200 Ha./div.; peak shifted cathodic with increasing volt/ d iv. Lower trace: 1.O volt/second; vertical scale, scan rate, but became obscured by 1.4 pa./div.; horizontal scale, 0.1 00 volt/div. solvent reduction for scan rates greater than 100 volts/second. Both Fe(II1) and Cd(I1) remained reversible up to defined variable, 4. k, is the standard scan rates of about 1000 volts/second, heterogeneous rate constant; is the (as indicated by constant values of transfer coefficient; and $ is defined as E, and iP/vl/2). However, for faster yak,/(mzDo)1'2,where a is nFv/RT, u scan rates, deviation from reversibility is the scan rate, y is (DO/DR)l/z, and the was observed, which could not be acother symbols have their usual counted for by uncompensated ohmic significance. The separation of cathodic losses alone. On the other hand, no and anodic peaks is dependent on $. deviation occurred a t scan rates lower Experimentally, the peak separation than 1000 volts/second. Thus, conwith a particular scan rate is compared fidence in the overall instrumental reto a working curve of (nAE,) vs. $. sponse for scan rates up to this range With $ evaluated, a value of k , may be was established. Figure 5 compares obtained as long as the constant terms linear sweep current-voltage curves for are known. .is Sicholson points out (8), Fe(II1) a t a slow scan rate and at 1000 the value of a has relatively little effect volts/second. on the working curve, and theoretical QUASI-REVERSIBLE SYsTEhfs. The incurves with CY = 0.5 may be used with vestigation of typical quasi-reversible reasonable accuracy for $ > 0.1. systems proved satisfactory for the In the work reported here, values of $ evaluation of instrumental response, less than 0.1 were encountered. Thus, because deviations from reversibility an accurate evaluation of cy had to be occurred a t slower scan rates, where made for each system to compare heterogeneous kinetic parameters could experimental to theoretical data, The be measured with confidence. Correlatechnique used to evaluate CY involved tion with values obtained at faster scan a determination of the symmetry of the rates then provided a reliable check on cyclic voltammetric curve under condiinstrumental limitations. tions where large peak shifts had ocNicholson (8) has described the curred. The observed symmetry was theoretical cyclic voltammetric behavior then compared with the predicted expected with quasi-reversible systems. symmetry for various values of a. The behavior depends on the fundaTheoretical computations were made mental parameters, IC, and cy, and on a using the IBM 7094 computer and (Y
VOL. 38, NO. 9, AUGUST 1966
0
1161
Effhct of a on Symmetry
Table 1.
-
n(E,, Ei/z),
n(E,, Ei'z),
mv .
CY
mv.
- 182
0.25 0.40 0.50
82 94 103 116
- 133 - 114 - 101
0.60
For all data in Table,
+ = 0.10,
Nicholson's numerical solution (8). A switching potential of 350/n mv. past Elizwas used arbitrarily for all calculations. The cathodic peak shifts, anodic peak shifts, and total peak separations were computed for a-values of 0.25, 0.4, 0.5, and 0.6 with $- values from 0.030 to 0.75. At the uppermost $value insignificant differences between computations for each a-value were obtained . To illustrate the relationship between symmetry and a,Table I gives cathodic and anodic peak shifts a t $ = 0.10 for the various values of a. For an accurate evaluation of CY, it was necessary to obtain data for $ less than 0.20. The two quasi-reversible systems selected for study here were Cd(I1) in 1.02' Na2S04and in 3.7M H2S04. The first system was selected for comparison to kinetic data obtained by Kicholson (8) who used scan rates varying from 48 to 120 volts/second and obtained a
Table II.
Cyclic Voltammetric Data for Cd(ll) in 1.OM N a 2 S 0 4at the Hanging Drop Electrode
Scan Rate, v, volts/second
nAE,, mv.
50 100 200 500 1000 2000
86 98 117 140 160 188 244
5000
+values based on peak separations.
Table 111.
'CL
=
* 0.91 0.61
0.38 0.26 0.20 0.14 0.074
k,, cm./second
0.33 i 0.06 0.31 f 0.04 0.28 i 0.04 0.31 f 0.05 0.33 f 0.06 0.32 f 0.05 0.27 i 0.05
Uncertainties in k , reflect uncertainty in measuring
0.53.
Cyclic Voltammetric Data for Cd(ll) in 3.7M H&O4 at the Hanging Drop Electrode
Scan rate, v, volts/second
nAE,, mv.
IC.
89 104 122 141
0.80 0.54 0.38 0.26
200
500
1,000
2,000 5,000
10,000
$-values based on a: = 0.58. separations.
1 162
k,-value of 0.24 cm./second. The second system was selected because the high acid electrolyte provided nearly the highest conducting medium available. Thus, uncompensated resistance problems were minimized in the sulfuric acid solution, and the most rapid measurements were made in that medium. Cyclic voltammetric curves were obtained from both single- and multisweep experiments. Although slight differences in the peak heights were observed, differences in peak separations were negligible. These observations were consistent with those of Nicholson (8). Thus, multi-sweep data were used for all correlations reported here, because oscilloscopic observations could be made more conveniently under steady-state conditions. Tables I1 and I11 summarize the cyclic voltammetric data obtained with each system at the hanging mercury drop electrode. Figure 6 shows typical curves obtained near the upper limit of scan rates employed. The values of k, given in Table I1 for 1.OM il'a&04 are in good agreement with Nicholson's results. Confidence in the values of k, evaluated in both Sa2S04and H2S04 is justified by the consistency observed with scan rates varied from 50 to 5000 or 10,000 volts/second. The value of CY obtained in 1.0.M Sa2S04 (0.53) does not agree well with that obtained by Nicholson (8). However, for his work an accurate value of a was not required, and his reported value of 0.25 was
160 200
0.19
0.12
k,, cm./sec. 0.59 f 0.11 0.63 i 0.08 0.61 f 0.08 0.61 i 0.10 0.69 i 0.09 0.63 i 0.07
Uncertainties in k, reflect uncertainty in measuring peak
ANALYTICAL CHEMISTRY
Figure 6. Cyclic voltammetric curves for Cd(ll) at the hanging drop electrode 1.0 X 10-3M Cd(ll), 1.OM NazSOa; 1000 volts/second; vertical scale, 0.5 Upper trace:
ma./div.; horizontal scale, 0.052 volt/div. lower trace: 1 X 1 O - W Cd(ll), 3.7M Hzso4; 5000 volts/recond; vertical scale, 1.25 ma./ div.; horizontal scale, 0.052 volt/div.
admittedly a rough estimate. Moreover, a value of 0.37 has been obtained by Bauer and Elving (1) with a.c. polarographic measurements in 1.OM Na2SOe. The peak shifts reported in Tables I1 and I11 were corrected for uncompensated ohmic contribution in the conventional manner ( 7 ) . The uncompensated resistance in each case was estimated as described in the Experimental section. In the worst case for 3.7M (10,000 volts/second), the correction amounted t o 12 mv. out of a total 112-mv. peak separation. The worst case for 1.O.M Na2S04(5000 volts/ second) involved 8 mv. out of a total 130-mv. peak separation. This type of correction, of course, does not account for any distortion of the sweep rate around the peak. For large ohmic losses this could cause considerable error because the peak location is theoretically scan rate dependent. For this reason, reported data for scan rates beyond about 2000 volts/second with these systems at the hanging drop electrode may be in error. Cyclic Voltammetric Data with a Smaller Working Electrode. To make measurements where uncompensated ohmic losses were negligible a t the
fastest scan rates investigated, cyclic voltammetric data were obtained using as a working electrode only the mercury-plated platinum wire tip (16) from which mercury drops were ordinarily hung. The area of the working electrode formed this way, and hence the corresponding voltammetric currents, were about an order of magnitude smaller than for the hanging mercury drop electrode. The surface was replenished for each run by hanging two drops in sequence and knocking them off. The area reproducibility was poor and depended upon how much mercury adhered when a drop was knocked off. However, if only a measure of the peak separation was required, the approach was satisfactory. Table IV summarizes the cyclic voltammetric data obtained with this small area working electrode for 1 X 10-3?11 Cd(I1) in 3.7-11 H2S04. Figure 7 shows typical current-voltage curves obtained. With the small area electrode uncompensated ohmic losses appeared negligible up to a scan rate of 20,000
Figure 7. Cyclic voltammetric curves for Cd(ll) at a reduced-size mercury electrode 1 X 1O%I Cd(ll), 3.7M H2504 Upper trace: 5000 volts/second; vertical horizontal scale, 0.052 scale, 65 pa./div.; volt/div. vertical Lower trace: 20,000 volts/recond; horizontal scale, 0.052 scale, 250 po./div.; volt/div.
Table IV.
Cyclic Voltammetric Data for Cd(l1) in 3.7M H2SOa at a Mercury Electrode of Reduced Size
Scan rate, v, volts/second 200 500 1,000 2,000 5,000
nAE,, mv.
10,000
20,000 50,000 +values based on peak separations.
a =
$ k,, cm./second 0.80 90 0.58 f 0.11 0.40 114 0.60 f 0.08 126 0.35 0.57 f 0.08 0.24 148 0.55 f 0.10 0.16 176 0.59 f 0.09 0.11 204 0.58 f 0.07 240 0.077 0.58 f 0.07 290 0.048 0.55 f 0.08 0.58. Uncertainties in k. reflect uncertainty in measuring
volts/second. However, because of the increased proportion of charging current a t the higher scan rates it is very difficult to locate peak potentials with good accuracy for scan rates greater than 10,000 volts/second. One approach used satisfactorily in this work was to increase sensitivity and look a t only one branch of the cyclic curve a t a time. Good agreement exists between d3ta obtained with the hanging mercury drop electrode, with correction for ohmic losses, and the data with the smaller electrode where no significant uncompensated ohmic loss was involved. This correlation indicates that the method of evaluation of and correction for uncompensated resistance used in experiments with the hanging drop were reasonably accurate. On the other hand, attempts to use the smaller electrode with less highly conducting solutions were only moderately successful, because placement of the working electrode for minimum uncompensated resistance was more critical. The small size of the working electrode and the design of the Luggin capillary made it quite difficult to find and reproduce optimum placement. Further work in the design of an electrolysis cell utilizing the smaller working electrode is in progress. From the data in Table IV one might conclude that scan rates as fast as 50,000 volts/second may be employed in the study of rapid electrode processes. However, one must recognize that the experimental conditions obtained for data reported in Table IV may not always be realizable. Working with typical nonacid electrolyte media of 0.1 to l . O M , the fastest scan rate attainable with confidence is probably about 1000 to 5000 volts/second. However, considering the major portion of a typical stationary electrode polarogram to encompass about 100 mv., a scan rate of 1000 volts/second enables one to observe a complete polarographic experiment in the order of 100 microseconds.
Moreover, a scan rate of 50,000 volts/ second corresponds to a complete polarographic experiment in about 2 psec. Thus, the study of chemical rate processes coupled to charge transfer with first-order rate constants as large as lo* to IOe second-‘ ought to be possible. ACKNOWLEDGMENT
The author acknowledges the stimulating conversations of Irving S h a h and Richard Nicholson regarding this work. The author also acknowledges the assistance of C. V. Evins who carried out the numerical calculations. LITERATURE CITED
(1) Bauer, H. H., Elving, P. J., ANALCHEM.30, 341 (1958). (2) Booman, G. L., Holbrook, W. B., Ibzd., 35, 1793 (1963). (3) Booman, G. L., Holbrook, W. B., Ibid., 37, 795 (1965). (4) Delahay,. Paul, “New Instrumental Methods in Electrochemistry,” 2nd ed., p. 393, Interscience, New York, 1954. (5) Ibid., p. 51. (6) Ibid., p. 132. (7) Nicholson, R. S.,ANAL. CHEM.37, 667 (1965). (8) Ibid., p. 1351. (9) Nicholson, R. S., Shain, I., Ibid., 36, 706 (1964). . (10) Perone, S. P., Mueller, T. R., Ibid., 37. 2 (1965). (11) ‘Phdbrick Researches, Inc., Bull. P66A/lBl, Rev. June 1, 1965. (12) Philbrick Researches, Inc., Bull. P35A/1B1, Rev. April 1, .1965. (13) Schwarz, W. M.,Shain. I., ANAL. ‘ ’ CHEM.35, i770 (1968). (14) Shain, I., Harrar, J. E., Booman, G. L., Zbid., 37, 1768 (1965). (15) Shuman, M. S., Shain, I., Great Lakes Regional ACS Meeting, Chicago, Ill., June 1966. (16) Underkofler, W. L., Shain, I., ANAL. CHEM.33, 1966 (1961). RECEIVEDfor review April 6, 1966. Accepted May 31, 1966. Great Lakes Regional Meeting, ACS, Chicago, Ill., June 1966. Work supported by Public Health Service Research Grant No. CA-07773-02 from the National Cancer Institute.
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