tion with positive feedback and doublepulse instrumentation. Of course, the use of better amplifiers will improve the effectiveness of all the methods for interpretation of the data taken a t short times. with advanced instrumentation, full advantage Of the potentiostatic technique will be realized only by application of correction methods. LITERATURE CITED
( 1 ) Booman, G. L., ANAL. CHEM.38, 1141 (1966). ( 2 ) Booman, G. L., I-Iolbrook, W. B., Ibid., 35, 1793 (1963). ( 3 ) Ibid., 37, 795 (1965). ( 4 ) Booman, G. L., Pence, D. T., Ibid., 37, 1366 (1965). ( 5 ) Brown, E. R., McCord, T. G., Smith, D. E., DeFord, D. D., Ibid., 38, 1119 (1966).
(6) De Vries, W. T., Van Dalen, E., J. Ezectroanal* “9 lS3 (1965). (7) Feldberg, S. W., Auerbach, C., ANAL. 36, 505 (1964). (8) Fischer, O., Dracka, O., Collection C‘zech. Chem. C‘ommun. 24, 3046 (1959). (9) Gerischer, H., Staubach, K. E., 2. Electrochem. 61,789 (1957). (10) Gerischer, H., Vielstich, W., 2. Physik. Chem. (Frankfurt)3, 16 (1955); 4, 10 (1955). (11) Imai, H., Bull. Chem. SOC.Japan 30, 873 (1957). (12) Koryta, J., Koutecky, J., Collection Czech. Chem. Commun. 20, 423 (1955). (13) Lauer, G., Osteryoung, R. A,, ANAL. CHEM.38, 1106 (1966). (14) Lingane, P. J., Christie, J. H., J. Electroanal. Chem. 10, 284 (1965). (15) Masters, B. J., Schwartz, L. L., J . Am. Chem. SOC.83, 2620 (1961). (16) Newton, T. W., Baker, F. B., Znorg. Chem. 4, 1166 (1965). (17) Nicholson, R. S., ANAL. CHEM.37, 667 (1965).
cHEM.
(18) Nicholson, R. S., Shain, I., Z b d , , 36, 706 (1964). (19) Okinaka, Y., Toshima, S., Okaniwa, H., Talanta 11, 203 (1964). (20) Oldham, K. B., J. Electroanal. Chem. 1 1 , 171 (1966). (21) Pouli, D., Huff, J. R., Pearson, J. C., ANAL.CHEM.38,382 (1966). (22) Reinmuth, W. H., Zbid., 36, 211R (1964). (23) Shain, I., “Treatise on Analytical Chemistry,” I. M. Koltoff and P. J. Elving, Eds., Part I, Vol. 4, p. 2560, Interscience, New York, 1963. (24) Shain, I., Harrar, J. E., Booman, G. L., Zbid., 37, 1768 (1965).
RECEIVEDfor review April 18, 1966. Accepted June 9, 1966. In part, Division of Analytical Chemistry, Winter Meeting, ACS, Phoenix, A r k , January 1966. Work supported by the U. S. Atomic Energy Commission under Contract No. AT(10-1)-205 through the Idaho Operations Office.
Some Investigations on Instrumental Compensation of Nonfaradaic Effects in Voltammetric Techniques ERIC R. BROWN, THOMAS G. McCORD, DONALD E. SMITH, and DONALD D. DeFORD Department o f Chemisfry, Northwestern University, Evanston, 111. The feasibility of achieving accurate, direct readout of the faradaic component in voltammetric techniques under conditions where nonfaradaic effects are substantial has been reinvestigated. compensation of ohmic potential loss was effected with the aid of the addition of a positive feedback loop to a conventional operational amplifier potentiostat. Double-layer charging current compensation was carried out b y direct subtraction of the current obtained with a solution of supporting electrolyte from the current obtained with a solution of supporting electrolyte and electroactive component. Application was made to cyclic voltammetry, fundamental harmonic a.c. polarography, and higher harmonic a.c. polarography. Readout of the faradaic component was possible with an apparent high degree of accuracy for at least moderately demanding conditions. All measurements were performed with the dropping mercury electrode. Successful application of the dropping mercury electrode was facilitated by a timing circuit which performed a number of functions including controlling and synchronizing mercury drop growth and fall in the two cells; controlling a sample-and-hold readout operation in a.c. polarographic measurements; controlling application of a triangular wave impulse in cyclic voltammetric measurements.
T
WIDELY recognized problems associated with the contributions of ohmic potential loss (iR drop) and double-layer charging current in voltammetric techniques remain a source of much concern in experimental electrochemistry (1-11, 16-20, 25-28, 31-34, 39-42, 46, 51, 52, 56, 57, 62, 64-67, HE
69-71).
In one way or another these nonfaradaic influences limit the scope of voltammetrio methods in kinetic and mechanistic studies of electrode reactions as well as in analytical applications. Particularly profound are their effects in modern electrochemical relaxation methods such as cyclic voltammetry (16, 20, 25, 42), a.c. polarography (55, 57, 64, 70, 7 l ) , and high-speed potentiostatic measurements (10, 11, 37, 55). The contributions of iR drop and double-layer charging current in these latter techniques can be made minimal in measurements involving time scales (the period of the alternating potential in a s . polarography and cyclic voltammetry, the measurement time in chrono-amperometry, etc.) which are large. However, with a small time scale their contributions to instrument readout frequently are sufficiently large that even the most simple-minded mechanistic conclusions are impossible until correction for these effects has been accomplished. The complexity associated with the corrections vanes, depending
on the nonfaradaic effect and experimental technique in question, but the tedium associated with these operations is seldom insignificant. Numerical correction for the doublelayer charging current often is accomplished by performing two experiments: one on a solution containing supporting electrolyte and electroactive component (the sample solution) and one on a solution containing only supporting electrolyte (the reference solution) (17). The current observed with the reference solution is subtracted from that observed with the sample solution. The subtraction operation may involve simple scalar subtraction, as in cyclic voltammetry, or the mathematically more cumbersome vectorial subtraction, as in a x . polarography. Due recognition must be given to the effects of iR drop before this subtraction can be effected accurately. In cases where the electroactive species significantly alter the double-layer capacity, a more sophisticated correction scheme must be employed (21, 60). To correct for the effects of iR drop, one must perform the additional experiment of measuring the effective ohmic resistance (10, 11, 17). Once this is accomplished, the data may be corrected for iR drop in some cases by simply considering its effect on the magnitude of the applied potential, as in d.c. and a s . polarography (17, 62, 67). In other techniques, the iR drop may VOL. 38, NO. 9, AUGUST 1966
0
1 1 19
manifest itself in a more insidious manner by altering another important kinetic parameter. An example of the latter effect arises in linear scan or cyclic voltammetry where the ohmic resistance influences the scan rate, and thereby alters the mass transfer rate (16, 20, 25, 62). In such cases, rigorous correction for iR drop normally requires explicit incorporation of its contribution into the theory for the current-potential curve, a nontrivial operation as recent literature on cyclic voltammetry attests (25,4@* These inconveniences and limitation s imposed by nonfaradaic effects have led to much expenditure of effort in attempts to reduce the magnitude of their contributions to instrument readout. Reduction of the effects of charging current has been accomplished by a variety of compensation techniques essentially involving electronic simulation of the charging current signal and subtraction of the simulated signal from the cell current (30, 33-35) (the simulation methods). Compensation also has been tried by subtraction of current signals obtained simultaneously from sample and reference solutions (14, 32, 52, 59, 72) (the direct method). Xeither of these approaches has been widely employed, especially in applications of the electrochemical relaxation methods. The simulation methods are not particularly compatible with the demands of versatility and accuracy associated with quantitative kinetic applications of the relaxation techniques. For example, precision electronic simulation of the charging current-d.c. potential profile observed in cyclic voltammetry, ax. polarography, etc. in the vicinity of the “water hump” (47) could be achieved only a t a cost significantly greater than that of the additional polarizing unit required in the direct method. Electronic simulation methods are also a t a disadvantage in techniques involving a.c. signals. Among possible objections to the direct method of compensation are the requirement of an additional polarizing circuit and the fact that the method is invalidated whenever the electroactive compounds significantly influence the double-layer capacity. However, these disadvantages are not of sufficient consequence to dictate against widespread application of the approach. The cost of an additional polarizing unit would soon be offset by the convenience and savings in time associated with accurate compensation for charging current. Error caused by influence of electroactive species on the double-layer capacity will be negligible with a significant fraction of the systems one may encounter. The most serious problem associated with the direct method, which may be primarily responsible for its infrequent 1120
ANALYTICAL CHEMISTRY
application, is the fact that accurate compensation for charging current cannot be realized unless contributions of iR drop are negligible (5.2). Significant ohmic resistances normally lead to differences in ohmic potential losses in the sample and reference cells, a t least where the cell currents differ, as in the vicinity of the faradaic wave. A corresponding difference in the effective potential applied to the two cells is the result. In such situations, a significant dependence of charging current on applied potential will cause the charging current magnitude obtained from the reference cell to differ from that in the sample cell leading to error in the subtraction operation. In a.c. polarography, iR drop-induced differences in the phase relations associated with charging currents in the sample and reference cells will lead to an additional source of error. Error in the direct compensation method arising from iR drop will become most noticeable in measurements involving small time scalesprecisely the situation when accurate compensation for charging current would prove most helpful. Numerous schemes to reduce the sources of ohmic potential loss have been reported. Among the most recent and successful has been the application of the three-electrode potentiostat, a device which is frequently constructed from operational amplifiers (10, 11, 28, 34, 56, 62, 64, 70, 71). The threeelectrode potentiostat removes many of the sources of iR drop operative in normal voltammetric procedures. However, it has been made abundantly clear in the literature that not all sources of iR drop are removed in the conventional three-electrode potentiostat (10, 11, 28, 41, 51, 56, 64). These devices do not compensate for iR drop in the working electrode and in the solution between the tip of the reference electrode probe and the working electrode. The electrode resistance is significant when a conventional dropping mercury electrode (DME) or a semiconductor electrode is employed. The solution resistance will be significant in low-conductance solvents and in high speed work in high conductance solvents. Hayes and Reilley (28)presented an ingenious method which should successfully compensate in most cases for these last remnants of ohmic potential loss in phase-selective ax. polarography. Using an electronic multiplier as the phase-sensitive detector, they incorporated the correction for iR drop in the electronic multiplication operation. Unfortunately, their approach appears somewhat limited in scope, not being rigorously applicable to techniques such as linear scan and cyclic voltammetry.
A method of potentially more general applicability has been suggested by Booman and Holbrook (10). This approach involves a minor modification of the three-electrode potentiostat in which an additional feedback (positive) loop is employed to add a signal equal to the iR drop to the input voltage. Hayes and Reilley (28) reported an attempt to implement this method in which they were unable to prevent oscillation of the control loop. Recently, Lauer and Osteryoung (37) and Pouli and coworkers (51) have reported successful applications of this technique, Xeither the numerical method nor the instrumental procedures mentioned above can completely eliminate all manifestations of iR drop when a large ohmic resistance (in the electrode or solution) is combined with large differences in current density across the electrode surface. In such situations a spacial distribution of iR loss across the electrode-solution interface exists, rather than a fixed value of iR drop (1, 19, 22), resulting in an uneven potential distribution on the solution side for large solution resistances and an uneven distribution on the electrode side for large electrode resistances. This effect has been proposed as a possible source of polarographic maxima (22, 45). The methods described above can, a t best, effect correction for an average iR drop in such systems. Fortunately, a significant spacial dependence of the iR drop is likely to occur only in extreme cases (very large ohmic resistances and/or large variations in current density across the electrode surface) which arise infrequently in electrochemical investigations. This is particularly true in the electrochemical relaxation techniques where measurements are confined to short times and the geometry effects giving rise to uneven current distributions normally have insufficient time to become significant (1). The possibility of achieving negligible influence of ohmic potential loss in electrochemical relaxation techniques performed under conditions where the ohmic resistance is significant is appealing in itself. This appeal is enhanced by the fact that such elimination of ohmic influences makes more realistic the possibilities of highly accurate implementation of the direct method of charging current compensation. These considerations led us to undertake a study of the feasibility of achieving direct readout of the faradaic current component in electrochemical relaxation techniques using the three-electrode potentiostat with the modification of Booman and Holbroolc in combination with the direct method of charging current compensation. The results reported here illustrate the degree of success we have realized to date.
Fundamental harmonic a x . polarography, higher harmonic a x . polarography, and cyclic voltammetry, a group of relaxation techniques which are notably sensitive to nonfaradaic influences, were employed in this study.
AUXILIARY /ELECTRODE
EXPERIMENTAL
The electrochemical instrument employed in this work was constructed entirely from solid-state operational amplifiers. A variety of amplifier models was employed, none of which required noise-producing 60-Hz. power to drive electromechanical or photoconductive choppers. Whenever appropriate, specific amplifier models utilized in construction of various units will be indicated below. The notably improved instrument performance obtained with solid-state operational amplifiers relative to that observed with their vacuum tube counterparts more than justifies the additional expense. In comparison with a vacuum tube instrument described previously (62), the qolid-state instrument employed in this work is definitely superior in characteristics such as noise level, long-term stability, and overall reliability. For example, in either normal or phase-selective a x . polarographic measurements, drift in instrument response observed with a dummy cell seldom exceeded +O.lyoin a period of 2 to 3 hours (after a short warm-up). Potentiostats and Compensation for iR Drop. Figure 1illustrates a slightly modified version of a potentiostat in the voltage follower mode (ignore dashed line) originally given by 1300nian and Holbrook ( l o ) , which wm employed in most of the work reported here. The positive feedback path provided by connecting the center-tap of the potentiometer R, to one of the potential inputs permits, through proper adjustment of R,, complete compensation of the ohmic losses in the cell and resistor RL ( I O ) . Obviously, the same approach is applicable to many other potentiostat configurations such as the commonly used current-follower (11, 15, 58).
The current-follower version is obtained from Figure 1 as indicated in the caption. In this case, R, is adjusted t o compensate only for the cell resistance. The voltage follower configuration exhibited a noticeably wider stability margin under most operating conditions, which is the reason its application was favored. Stable operation was achieved through the use of feedback capacitors across the control and current amplifiers (11, 13, 68). The capacitors employed were of sufficient magnitude to ensure stability, but not so large that they influenced the performance of the control loop a t the frequency of interest. More sophisticated stabilization networks (11) which might have negated the observed difference in stability obtainable with the current and voltage follower configurations were not employed in the present work. The stability problem is discussed further below.
WORKING
ry CURRENT OUTPUT
L
r
Figure 1.
Potentiostat
Amplifier C-Philbrick P - 2 operational amplifier with P-5 booster Amplifiers FI and FrPhilbrick P-2 operational amplifiers Amplifier I-Burr-Brown 1 5 0 6 operational amplifier Input resistors of Amplifier C-l OOK, z t O . l % Resistor RI-0 to 1.2 megohm ESI Model D S l 4 6 4 Dekastot Decade Resistor Resistor R,-l Kohm Bourns Model 3 7 0 0 s - 1 - 1 0 2 , 1 0-turn potentiometer Resistor R8-l Kohm, *O.l% in most cases Resistor R ~ - 5 0 0Kohm, iO.lY0 in most cases Resistor R r l Kohm, &O.I% in most cases Voltage-Follower Mode: delete dashed line Current-Follower M o d e connect points a and b (dashed line) and delete R1, RL and amplifier FZ
The positive feedback approach in principle provides for complete compensation of a constant ohmic resistance. There is no provision for handling a varying ohmic resistance which one encounters with the dropping mercury electrode (8, 36). This problem was solved in this work by confinement of measurements to a short period in the life of a mercury drop during which the ohmic resistance is essentially invariant. The methods employed to effect this mode of measurement are described below. Charging Current Compensation. Compensation for charging current was achieved with the aid of two potentiostats of the type shown in Figure 1; one controls a sample cell and one controls a reference cell. The potentiostats were driven by common signal sources. The output signals from the two potentiostats were subtracted with an electronic subtractor. For these operations to have any meaning, a number of conditions must be met: (a) the concentrations of supporting electrolyte must be identical in the sample and reference cells; (b) the electroactive materials must not significantly influence the double-layer capacity; (c) the surface characteristics of both working electrodes must be identical; (d) the charging current signals generated in the sample and reference cells must correspond to the same electrode area. Item a is almost trivial and items b and c represented no problem in the present work. All of the work de-
scribed here employed the dropping mercury electrode (DME) and the condition represented by item d was met as follows. Synchronization of mercury drop growth and fall in the two cells was achieved with the aid of mechanical drop-dislodgers which were activated by a timing circuit described below. Mercury flow rates were adjusted carefully to ensure that mercury drop areas were identical a t the time of measurement. The final stage in this adjustment was usually performed by observing the output of the subtractor at d.c. potentials where only charging current was flowing in each cell and adjusting mercury column height until a negligible signal was observed. Mode of Measurement. Signal conditioning in addition to the subtracting operation was unnecessary in cyclic voltammetry. Cyclic voltammograms were obtained in the normal manner by applying the output of the subtractor to the Y-axis of an oscilloscope while driving the X-axis with the triangular wave voltage source. All cyclic voltammetric investigations involved single-cycle experiments run a t a slowly growing DME. Moderately fast scan rates were employed (2 volts per second to 200 volts per second) so that drop growth w m negligible during the period of the triangular wave impulse. The triangular wave impulse was applied automatically to both cells late in the life of the DME's with the aid of the same timing circuit used t o synchronize drop fall. VOL 38, NO. 9, AUGUST 1 9 6 6
1121
In a x . polarographic measurements, the output of the electronic subtractor was subjected to tuned amplification (62) followed by conventional fullwave rectification or phase-sensitive rectification. All a x . components of the rectified signal were eliminated with the aid of a low-pass filter of the Butterworth type (49). The resulting d.c. signal was applied t o a sampleand-hold circuit (sampling circuit), permitting precise measurement of the a x . polarographic signal at a point late in the life of the mercury drop (essentially at the end of drop life). Each measurement was held by the sampling circuit until the corresponding point in the life of the succeeding drop when a new sample was taken, etc. The output of the sampling circuit was recorded. This readout technique was originally employed by Barker and coworkers in square-wave, radio-frequency, and pulse polarography (3, 4, 6). It was utilized in this work to avoid the problem of the varying ohmic resistance associated with the DME (8, 36). -411 a.c. polarographic phase angles were calculated from the information provided by total and phaseselective current measurements. Signal Conditioning Devices. The electronic subtractor was constructed from a Philbrick P-2 operational amplifier utilizing the standard subtractor circuit (1.9, 50) and precision ( i 0 . 1 7 0 ) wire-wound 10 kohm resistors. A previously described circuit (62) employing a twin-T network in the feed-back of an operational amplifier served as tuned amplifiers. A Philbrick P-5 booster amplifier in combination with a Philbrick P-2 operational amplifier comprised the amplifier section. The twin-T network was constructed from i l C j & Mylar capacitors and a three-gang Model A Beckman helipot (ten-turn) as the source of resistors in the twin-T network. The full-wave rectifier used to obtain a.c. polarograms of the total current was based on a well known precision absolute-value circuit which has been described in various sources (13, 29). Philbrick P-35 operational amplifiers were employed together with i.O.170 mire-wound resistors. The performance of this circuit was outstanding. Linearity in response was within approximately = t O . l % for signal levels ranging from a few millivolts to the voltage limit of the amplifiers (-11 volts). Such performance was observed for frequencies up to 10 kHz. The phase-sensitive rectifier utilized in this work was constructed from operational amplifiers employing a circuit (12) which apparently has not been published. Its performance with regard to linearity and frequency response was similar to that of the absolute value circuit mentioned above. Further details of this circuit will be given elsewhere, as they contain no featyes essential to the present discussion. Low-pass filters employed to filter the output of the rectifiers were characterized by a second-order Butterworth response with a cut-off frequency of 1122
ANALYTICAL CHEMISTRY
about 1.5 Ha. (49). Philbrick P-35 amplifiers and a circuit given in the literature (49) served as the basis for this unit. By utilizing the Butterworth response, it was possible to reduce the a x . ripple on the rectified signal to less than O.l%, even at the lowest frequencies employed (10 Hz.), without attenuating significantly (>O.l%) the response of the instrument to current oscillations associated with mercury drop growth and fall. To obtain a measurement of the instantaneous alternating current magnitude a t low frequencies with a normal RC low-pass response, a time constant must be employed which is insufficient to reduce the effects of ripple to a negligible level. Thus, the low frequency performance of the instrument mas notably enhanced by application of the Butterworth filter. The sample-and-hold operation was accomplished with the aid of a Philbrick P-2 amplifier in the follower configuration, a high quality 1- to 2-pf. Mylar capacitor connected between the follower input and ground, and a normally open mercury-wetted contact relay (C.P. Clare Model HGSS1002 single-side stable relay) in series with the signal source. The circuit has been described in the literature (53, 64). Usually a resistor was placed between the signal source and sampling circuit to prevent short-term overloading of the signal source. The time constant thus introduced normally was of the order of 0.03 second. Signal Sources. The d.c. voltage sources were comprised of a precision (*0.1%) initial voltage source and a voltage ramp generator, both constructed from conventional operational amplifier circuits (15, 34, 58). A Hewlett-Packard Model 241.4 sine wave oscillator was employed as the source of sinusoidal voltages in a.c. polarographic measurements. The frequency stability of this oscillator is more than compatible with the demands imposed by the use of tuned amplifiers (62). For cyclic voltammetric measurements, a triangular-wave oscillator was constructed from a published circuit ($8) which employs an operational amplifier integrator and a trigger (voltage comparator) with hysteresis ( I S , 60) in a loop configuration. A Philbrick P-35 operational amplifier was employed in the integrator stage. The trigger utilized a Philbrick P-45 amplifier. Single-cycle operation was effected with the aid of a C. E.’ Clare Rlodel HGSRllO16 bistable mercurywetted contact relay with a doublewound coil. The relay was placed across the feedback capacitor in the integrator stage. In a closed position, the relay prevents charging of the condensor and, thus, suppresses the oscillation. A voltage step from an external timing circuit which is capacitively coupled to one coil winding serves to open the relay and initiate a cycle. The oscillation is terminated at the end of one cycle by capacitively coupling the output of the trigger to the second coil winding. The voltage step at the
trigger output, which is associated with the end of the cycle, is of the right polarity to effect relay closure suppressing further oscillation. A new cycle does not ensue until a voltage step from the timing circuit reopens the relay, etc. Because of the finite response time of the mercury-wetted relay (-2 msec.) , single-cycle experiments a t scan rates in excess of 200 volts second-’ were not possible. Readout Devices. Cyclic voltammograms were obtained with the aid of a Tektronix Model 502A oscilloscope and a Tektronix Model C-13 oscilloscope camera. The oscilloscope was also employed to measure amplitudes of applied potentials in a.c. polarographic measurements and as a general purpose monitor of various aspects of instrument performance. An Electro Instruments Model 480 X-YY’ recorder with Model 468 (Xaxis) and Model 420 (Y-axis) plug-in modules was employed to record a x . polarograms. The dual Y-axes feature of this recorder permitted simultaneous readout of conventional a.c. polarograms (total alternating current) and phaseselective 8.c. polarograms (the resistive current component). The phase relations were then immediately caIculable from these recordings. A Hewlett-Packard Model 5243L electronic counter served to measure frequency of applied alternating potential. With a Hewlett-Packard Model 5265A plug-in, this counter was converted to a digital voltmeter which provided for precise, high resolution measurement of d.c. signal levels. A Hewlett-Packard Model 5262.2 plug-in permitted the use of this counter in timeinterval measurements for assessment of the performance of the timing circuitry. Timing Circuits. Figure 2 illustrates the multiwroose timine: circuit which was emiloykd to contrd mercury drop life, the sample-andhold operation in ax. polarography, and the application of the triangular wave impulse in cyclic voltammetry. A voltage ramp generator composed of an electronic integrator with a fixed input voltage serves as the clock for this unit. A scan rate of +1.000 volt per second is realized with the component values indicated in Figure 2. The output of the ramp generator is applied at the input of two trigger (voltage comparator) circuits ( I S , 50, 62). The triggers are set t o switch from a state of zero volts to -10 volts when the scan generator output reaches a predetermined value. This switching point is controlled by a second input network comprising a voltage divider and a 50 Kohm potentiometer. The switching points are adjusted so that trigger 1 is the first to change state to -10 volts. It remains in this state until the ramp generator output reaches the level where trigger 2 changes state. The voltage step at the output of trigger 2 closes relay R1, discharging the capacitor of the ramp generator. This drives the output levels of the ramp generator and the trigger circuits
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Ampliflers 1 and 2-Philbrick P-45 operational ampliflers Amplifier 3-Philbrick P-35 operational amplifier All flxed resirtors-fO.l% wire-wound Variable resistors (5OK)-Bourns Model 35005-2, 1 0-turn potentiometers 1 -pF. capacitor-Southern Electronics Model M C l 0 6 G 1APL, f1 % Diodes-Hughes type 1 N483B Ri-C.P. Clare Model HGSSlOO2 mercury-wetted contact relay &-single pole 3-position switch with position 1 -operate (scon) position 2-standby (hold) position 3-off (reset)
back to zero volt, permitting relay R1 to reopen, a new cycle to ensue, etc. Thus, the timing circuit basically is a low frequency oscillator with three available waveforms. The ramp generator furnishes a sawtooth waveform. Trigger 2 furnishes a pulse train composed of narrow (-2 msec.) pulses coinciding with the end of each cycle of the ramp generator output. Trigger 1 furnishes a train of pulses whose width can be controlled from a minimum of zero (no pulse) to a maximum corresponding to the period of the sawtooth oscillation. The outputs of triggers 1 and 2 are employed to control external circuitry as indicated in Figure 2 . The output pulse of trigger 2 is employed to activate drop-dislodger circuitry making the mercury drop life equal to the period of the oscillation of the timing circuit. In cyclic voltammetry, the change in state of trigger 1 to - 10 volts is used to
initiate the triangular wave voltage sweep. Trigger 2 is set to change state, ending the drop life, etc., shortly after completion of the triangular wave cycle. I n experiments in which the sampleand-hold readout procedure is employed (a.c. and d.c. polarography), the change in state of trigger 1 to -10 volts serves to close relays in the sampling circuits, commencing the sampling operation. Trigger 1 is permitted to remain in the - 10-volts state for a time significantly longer (0.1 to 0.2 seconds) than the above-mentioned input time constant of the sampling circuits. Under these conditions, the sampling circuits will hold a voltage corresponding to the input signal level a t the end of the sampling operation (not an average of the signal over the sampling period). When trigger 1 returns to the zero volt state, the sampling circuit relays reopen, ending the sampling operation.
The accompanying output pulse from trigger 2 ends the drop-life. Obviously, it is essential that the sampling operation is terminated before the mercury drop is dislodged. To ensure this, the output of trigger 2 is connected to the input of trigger 1. When trigger 2 changes state to -10 volts it forces trigger 1 to zero volt at a time shortly before the similar effect associated with the discharge of the scan generator becomes operative. Thus, the return of trigger 1 to zero volt and the accompanying opening of the sampling circuit relays are not retarded by the time constant associated with discharge of the ramp generator. The proper sequence of events is further guaranteed by a relatively long time constant in the drop-dislodger circuitry. Timing measurements indicate that the electromechanical drop dislodgers are activated approximately 2 msec. after completion of the sampling operation, VOL. 38, NO. 9, AUGUST 1966
1123
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The electromechanical hammers serving as drop-dislodgers (Guardian Type 4-24 volt solenoids) were activated by a relay closure which discharges a 750-~f. capacitor. through their coils. h separate hammer was employed for each cell. The high currents associated with this operation demanded a relatively heavy duty relay (Potter and Brumfield Type LM52500 ohm SPDT relay) whose closure could not be affected by direct application of the low power pulse from the P-45 operational amplifier of trigger 2. Thus, the mechanical termination of drop life was accomplished with a two-stage circuit as shown in Figure 3. Trigger 2 activates a mercury-wetted contact relay, applying a voltage to the heavy duty relay which is sufficient for closure. The timing and drop-dislodger circuitry just described has been in use in these laboratories for over one year with excellent results. The only maintenance required in that period has been one battery replacement. Perusal of data obtained with this equipment indicates that erratic operation, such as failure to properly dislodge a drop, is a rare event. The probability of an obviously poor reading on a given mercury drop is no more than 0.001. The reproducibility of the timing operatione.g., the reproducibility of the controlled drop life-is of the order of *1 nisec. (average deviation). Miscellaneous Supporting Equipment. Except where they did not contribute significantly to the response of the instrument, passive components of high quality were employed with resistors (wire-wound or metal-film) normally characterized by & O . l % tolerance and capacitors (Mylar or polystyrene) of 1% tolerance. The dummy cells normally were comprised of an ESI Model DS1464 decade resistor and *l.% Mylar capacitors (Southern Electronics Corp.). When more precise dummy cell measurements were desired , an ESI Model DC-57 Decade capacitor originally calibrated at the factory to 0.1% was employed in place of the & 1% capacitors. Sargent Model 5-29390 polarographic cells thermostated by an Aminco Model 4-8600 constant temperature bath were employed. Most measurements were
1124 *
ANALYTICAL CHEMISTRY
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performed at 25' C. Sargent Model S-29417 polarographic capillary was utilized for the DME. Saturated calomel reference electrodes with Luggin probes and platinum auxiliary electrodes served as the other electrodes Reagent grade chemicals were utilized in solution preparation. Most solutions were prepared from distilled water which had been treated with activated charcoal or the solutions themselves were subjected to charcoal treatment. Determination of Series Resistance. To employ the above-described positive feedback scheme for eliminating contributions of ohmic resistance, one must know the effective uncompensated ohmic resistance which is normally operative in the threeelectrode potentiostat-Le. , the ohmic, resistance contribution observed in absence of the positive feedback loop. A number of methods have been suggested for measuring this resistance (8, 10, 11). Convenience dictated our choice of method which was based on the phaseselective a x . polarographic readout. The method involved adjusting the instrument to measure the resistive (inphase) alternating current component and selecting a d.c. potential at which only charging current is observed. The iR compensation control (potentiometer R, in Figure 1) was then adjusted until zero signal was observed. Under these conditions, negligible resistive component is an indication that contributions of iR drop are negligible. This procedure simultaneously achieves proper adjustment of the instrument to negate effects of ohmic potential loss and determination of the magnitude of the effective ohmic resistance which is calculable from the setting of R,. Care must be taken to ensure that only charging current is present when the adjustment of R, is made. Otherwise, the method was satisfactory. Its validity was verified by dummy cell experiments. With the aqueous systems employed in this work, the predominate source of ohmic resistance was the DME capillary resistance which ranged from 60 to 90 ohms. The appropriate setting of R,, determined in the manner just described, agreed closely with the setting required to compensate only for the capillary resistance. For this reason, compensa-
tion for ohmic resistance was effected in many of the experiments described here by simply adjusting R, to compensate for the known capillary resistance. Methods of Instrument Evaluation. The assessment of the success of the foregoing instrumental concepts in compensating for nonfaradaic influences was based on measurements with dummy cells and with electrochemical systems which previously had been subjected to careful experimental study. Dummy cell measurements permitted evaluation of the scope and accuracy of experimental procedures with the aid of passive components of accurately known value. Dummy sample and reference cells were constructed, simulating ohmic resistances, charging currents, and faradaic currents of values consistent with those found in electrochemical systems. In experiments with actual electrochemical systems, the direct readout of the instrument was taken as the faradaic component and compared with theory and/or previously reported experimental data. The ferric-ferrous redox couple in 0.5M potassium oxalate (the iron system) and the cadmium ioncadmium amalgam redox system in 0.5.V hydrochloric acid (the cadmium system) were employed as systems representing diffusion-controlled or reversible systems (8, 54, 64, 67, 70) under the experimental conditions utilized. Results obtained with these systems were compared to theory for the reversible case (64). The chromicyanide - chromocyanide system in 1.0M potassium cyanide (the chromium system) and the titanyltitanous couple in 0.2.U oxalic acid (the titanium system) were employed as representative of systems in which both heterogeneous charge transfer and diffusion play a significant kinetic role (quasireversible systems) (54, 61). Charge transfer rates obtained from data on these systems were compared to previously reported rate parameters. The voltammetric waves of the iron and titanium systems occur in the region of the water hump (47) of the double-layer charging current-potential profile. The associated large variations of charging current with potential enhance the demands on the charging current compensation operation. RESULTS AND DISCUSSION
Fundamental Harmonic A.C. Polarography. Figure 4 illustrates the efficiency with which compensation for charging current can be effected in a.c. polarography. Both polarograms shown in Figure 4 were recorded with compensation for the iR drop in effect. The effective ohmic resistance in this and in all other experimental data presented below was approximately 80 ohms. Conditions were such that the charging current was substantial, although not overwhelming. As Figure 4 indicates, subtraction of charging current yielded negligible back-
Figure 4. Fundamental harmonic a.c. polarograms of the iron system with and without subtraction of charging current System: 0.80 X 10-3M Fe(lll) in 0.50M KzCzOa Applied: 160 Hz., 10 mv. peak-to-peak sine wave; d.c. scan rote 50 mv. per minute Measured: 1 6 0 Hz., current component at the end of drop life with compenration for iR drop; ordinate uncalibrated
ground current. More significant is the fact that the polarogram obtained with alleged compensation of charging current and i R drop (lower polarogram in Figure 4) is of the shape predicted by theory for a reversible one-electron process which the iron system represents. For example, the half width of the wave is precisely the predicted 90 mv. These facts indicate that compensation for nonfaradaic influences was achieved quantitatively for the case in question. The a x . polarographic theory based on the planar diffusion model predicts that a plot of
(Zp is the peak alternating current and Z is the current a t any point along the wave) us. d.c. potential should yield a straight line of f(118/n)-mv. slope at 25" C. with reversible processes (64). The plus sign applies to the slope on the positive side of the a.c. wave and the minus sign to the negative side. Calculations (24) indicate that this plot is relatively insensitive to the recently discussed effects of spherical diffusion
(23). Figure 5 illustrates such a plot obtained from the cadmium system. The agreement between theory for the reversible wave and experiment again indicates a negligible nonfaradaic contribution. Similar agreement between theory and experiment was observed with the iron system. Although these log plots are not so sensitive to nonfaradaic effects as certain other forms of data presentation, they are nevertheless responsive to such influences. For example, failure to compensate for ohmic resistance under conditions of the experiment shown in Figure 5 yielded straight lines of 66-mv. slope, indicating a 12y0 contribution of iR drop to this characteristic. For the same conditions, a 20% decrease in peak height of the conventional a x . polarogram resulted from failure to compensate for the ohmic resistance. An a x . polarographic observable which is extremely sensitive to nonfaradaic contributions is the phase angle. Results obtained with the iron and cadmium system fell close to the 45' phase angle (cot @ = 1.00; 9 = phase angle) expected for a reversible system
when compensation for nonfaradaic contributions was in effect. For example, one set of a.c. polarographic data on the iron system a t 40 Hz. yielded cot 9 = 1.01 0.04 ( A relative average deviation) over a 225-mv. portion of the a.c. wave. The deviations of cot 0 from the expected value of unity became smaller if measurements were confined to d.c. potentials nearer the peak of the wave. Cot 9 = 1.01 =t 0.02 for d.c. potentials within 50 mv. of the peak. Equally good agreement with expectations was found with the cadmium system which was studied a t frequencies between 20 and 80 Ha. As suggested above, phase angle results were particularly sensitive to effects of ohmic resistance. Failure to compensate for the 80-ohms capillary resistance with the cadmium system a t 40 Hz, yielded an apparent phase angle of 29" (cot = 1.80) a t the peak of the wave. Phase angle data also were obtained on the chromium system a t frequencies of 10, 20, 40, and 80 Hz, Plots of cot @ us. u ~yielded / ~ a straight line characteristic of a quasireversible system. The apparent k , value ( k , = standard rate constant for heterogeneous charge transfer at E o ) obtained from the slope of the straight line using a previously reported diffusion coefficient (63) was 0.21 =t 0.02 cm. second-'. This result is in good agreement with previously reported values of 0.22 cm. second-' (63) and 0.25 cm. second-1 (54)
Because this instrumentation significantly reduces the influence of charging current, the minimum concentration at which quantitative a.c. polarographic measurements can be performed is reduced correspondingly. Studies on the iron system indicated that data of nearly the quality indicated above could be obtained to concentrations a t least as low as 5 x lO-5M. At much lower concentrations, data quality was degraded significantly, particularly for measurements of total alternating current where suppression of charging current is not promoted by phasesensitive detection. Because faradaic currents of the cadmium system exceed those of iron by more than a factor of four under similar conditions, it should be possible to obtain reasonably good quantitative data down to concentrations of about 1 X 10-6M in the case of cadmium. However, this has not been attempted to date. Higher Harmonic A.C. Polarography. The measurement of higher harmonic a.c. polarographic currents contributes little to the assessment of the ability of the instrumentation to compensate for charging currents because of the small contribution of the latter (39, 64, 67). However, higher harmonic a.c. polarograms represent a sensitive index of the degree of VOL. 38, NO. 9, AUGUST 1966
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from Figure 6. Second harmonic 0.c. polarograms of the iron with and without iR
a fundamental harmonic a.c. polarogram of the cadmium system
System: 1.O X 10-8M Cd(ll) in 0.50M KCI Applied: 40.0 Hz., 10 mv. peak-to-peak sine wave; d.c, scan rate 25 mv. per minute Measured: 40.0 Hz. faradaic current component at end of drop life with cornpensation for nonfaradaic effects
success in eliminating contributions of iR drop because of the dependence of these polarograms on higher powers of the applied alternating potential. For small iR drops, the second harmonic alternating current, which depends on the square of the applied alternating potential (64), will be influenced by an iR drop roughly twice as much as the fundamental harmonic polarogram. Under similar conditions, the influence on the third harmonic currents will be roughly three times as large. The origin and nature of the effects of ohmic resistance on higher harmonic currents have been discussed a t length elsewhere (&), where it was pointed out that, among other things, the peak separation is a good indicator of the contribution of iR drop. In general, second and third harmonic a x . polarographic results obtained with compensation for nonfaradaic effects indicated a negligible influence of iR drop. Figure 6 illustrates t'wo second harmonic polarograms obtained with 1126
ANALYTICAL CHEMISTRY
System: 2.0 X
lO-%i Fe(lll) in 0.50M KzCz04 peak-to-peak sine wave; d*c* Ican rate 25 Applied: 42.0 mv. per minute except between two peaks where it was reduced to 12.5 mv* per minute Measured: 84.0 Hr. faradaic current component at end of drop life; ordinate uncalibrated Polarogram A: With compensation for nonfaradaic effects Polarogram 6: Without iR compensation
the iron system. The polarogram obtained with iR compensation is characterized by equal peak heights and a 69-mv. peak separation as expected for a reversible process (64). As illustrated, failure to compensate for ohmic resistance yields a smaller, second harmonic wave (peak heights are 22% smaller) with an overly large peak separation of 75 millivolts. As one would expect (48),the effects of iR drop on the second harmonic a.c. polarogram of the cadmium system are considerably larger. With iR drop compensation, the expected 34-mv. peak separation was observed, while a 45-mv. peak separation was obtained without compensation. Peak second harmonic currents observed with and without iR compensation differed by 38%. Figure 7 illustrates a third harmonic a.c. polarogram observed with the cadmium system. The peak separations are precisely as predicted by planar diffusion theory (48)-e.g., 29 mv. separate
the central and outer peaks-indicating little influence of ohmic resistance. The predicted peak height ratio of 1:3 : 1 also is approximately obeyed, although the most positive peak is slightly low and the more negative peak noticeably high relative to the height of the central peak. It is difficult to attribute this disparity to an influence of iR drop in light of the nearly ideal peak separations and the excellent symmetry observed in the fundamental harmonic ax. polarogram, which primarily determines the characteristics of the iR distortion (48). The disparity may manifest a slight kinetic effect of charge transfer or coupled chemical reaction. However, a contribution of spherical diffusion which has been predicted to be significant with amalgam-forming systems (23) appears to be the most likely source of this disparity in peak heights (66). The spherical correction appears to have little influence on peak separation (65).
5 W
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evices, Cambridge, +x., 1965. (69) Takahashi, T., hiki, E., Tulanta 1, 245 (1958). (70) Underkofler, W‘. L., Shain, I., ANAL. CHEM.37. 218 (1965). (71) Walker, I).E., ildams, R. N., Alden, J . R . , Ibid., 33, 308 (1961). (72) Yasumori, Y., J . Electrochem. SOC., J a p a n ( J a p a n E d . ) 24, 309 (1956). RECEIVEDfor review April 7, 1966. Accepted June 2, 1966. Presented in part a t the Division of Analytical Chemistry, 150th Meeting, American Chemical Society, Phoenix, Ariz., January 1966. This work was supported in part by a National Science Foundation cooperative fellowship (E. R. B., 1964-65), an Electrochemical Society summer fellowship (T. G. RI., 1965) and by National Science Foundation grant GP-3484. ~
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