Efficiency of Plating and Anodic Stripping of Silver from Platinum Electrodes J. W. BIXLER’ and STANLEY BRUCKENSTEIN University of Minnesofa, Minneapolis, Minn. Published work on the plating of small amounts of silver on platinum electrodes has indicated that the anodic coulombs required to oxidize the plated silver are substantially less than the cathodic coulombs used to plate the silver. After properly pretreating a platinum electrode, this discrepancy vanishes. It is possible to plate less than two monolayers of silver on a platinum electrode and quantitatively account for the cathodic coulombs in terms of double layer charging effects and anodic coulombs. At oxidized platinum electrodes, apparent loss of plated silver occurs.
A
the application of anodic stripping analysis to the determination of silver has been known for some time, relatively few studies have been reported. Lord, O’Neill, and Rogers ( 5 ) report studies involving lo-@ to 5 X gram quantities of silver, using both stoichiometric plating on a platinum foil electrode and nonstoichiometric plating on a rotated platinum microelectrode (RPE) . In both cases, the electrode was completely stripped a t a constant applied potential. The application of constant current methodology to silver stripping has been mentioned by Shain ( 8 ) and Nisbet and Bard ( 7 ) . As a part of another investigation (3) it was necessary to make a detailed study of the plating and anodic stripping of small amounts of silver using a rotated platinum microelectrode (RPE). Our electrodeposition step was nonstoichiometric, since we wished to plate known small amounts of silver rapidly upon a R P E . Usually the electrode was plated a t constant potential and for such short times that Xg(1) depletion was negligible. The deposited silver was osidized by applying a constant anodic current and the time required to remove the plated silver completely determined from the recorded potential-time stripping curve. Sisljct and Bard ( 7 ) repoit ohserving an interesting phenoinenon during the constant current deposition and stripping of silver, using a stationary platinum electrode. They plated their elecLTHOUGH
Present address, Department of Chemistry, Lake Forest College, Lake Forest, Ill.
trode for less than the cathodic transition time, then reversed the current and stripped the electrode to a potential of 1.OO volt us. a Hg/Hg2S04 reference electrode. This plating and stripping process was repeated several times, keeping the plating time constant, and it was reported that the silver stripping time became shorter for each successive experiment. After making a series of these experiments, the stripped electrode was washed and transferred to a cell containing 1Jf HC104, where it was reduced a t constant current until a potential corresponding to the start of hydrogen evolution was reached. The current was then reversed and a new anodic transition time was found. Sisbet and Bard attribute this transition time to the dissolution of silver. They postulate that silver which deposits on oxidized platinum cannot be stripped until the platinum oside is reduced. We have performed numerous experiments attempting to reproduce the phenomenon reported by Nisbet and Bard ( 7 ) but have been able to reproduce only some of their results. Our evperiments indicate that the plating and stripping of silver from a clean platinum surface can be readily interpreted in terms of conventional electrochemical theory, provided corrections for double layer charging and overpotential effects a t partially plated surfaces are taken into account.
+
PLATING AND STRIPPING OF SILVER
The reduction of Xg(1) in 0.1M HCI04 begins at about +0.35 volt us. SCE, and a limiting current region proportional to the bulk concentration, CA%+,is reached a t about +0.05 volt us. SCE. With no external applied potential, a R P E in a Ag(1) solution has some ill-defined rest potential, E,. If a potential is applied to the electrode-e.g., &-which will produce a current limited by mass transfer, it is convenient to assume that, initially, current flow charges the double layer for t o seconds, consuming Qc coulombs, and then silver deposits on the RPE at a rate determined by the limiting current, ( i J A g + , corrected for residual current. .-it the end of t , seconds after the start of the experiment, the quantity of silver Wed, is (&)A%+ X ( t , - t o ) , because negligible depletion of CAE+
occurs under our experimental conditions. For a fixed cell geometry and constant values of El and Ez, both t o and QE are constant. If silver plated on the RPE is stripped electrically (anodically oxidized) a t a constant current li,’, the number of coulombs required to osidize the silver, ( Q a ) A g , is equal to li,l t , - Q c ’ , where t, is the anodic stripping time (seconds) and QE’is the number of coulombs required to charge the double layer because of potential variations during the stripping process. Equation 1 states the relationship between the quantities governing the plating and stripping of silver, Qt
-
Qc
=
( Q J A=~ x (t, - t o ) =
(iJAgf
li&
-
Qc’
(1)
where Q t is the esperimentally determined quantity of charge which has been consumed in t , seconds during the plating of silver on the R P E . Making the conventional assumptions, the steady-state electrode potential during the stripping cycle is given by Equation 2 a t 25’ C.
E
=
EfAg+Ag
+ 0.0591 log (C..+ + -)/a,#
kAB+
(2)
where Ef.4a+,.4g is the forinal silver potential (tis. SCE) and kAg+is the 1)roI)ortionality constant between limiting cathodic silver current and bulk silver concentration on the limiting current jegion. It has been assumed that the surface activity of silver metal is unity in obtaining Equation 2, and it is recognized that this condition may not be exact at a platinum surface partially covered with silver. EXPERIMENTAL
Water. Triply distilled water was prepared. T h e second distillation was made from basic permanganate solution. A11 solutions were prepared using this mater. Perchloric Acid. 70y0 Mallinckrodt perchloric acid, used without further purification. Silver Nitrate. Dried analytical reagent silver nitrate was used to prepare all solutionc. Solutions were protected from light. Nitrogen. Linde prepurified nitrogen was used to deaerate all solutions. VOL. 37, NO. 7, JUNE 1965
791
16'
/-12.
-0
a
08
04
0
I
I
2
I
3
T I M E (mIn.1
Figure 1 . time
CA,+
Silver plating current vs.
= 1.00
X 10-%4 in 0.1M HClOa
Before use, the nitrogen was passed through an active copper column (6) a t 200" C. to remove traces of oxygen, then water - saturated by bubbling through triply distilled water. Apparatus. The electronic cons t a n t current source, the d.c. amplifier, and the recording potentiometer used have been described (4). All current-voltage curves were recorded with a Leeds & Northrup Electrochemograph Type E. The dual electrolysis cell used in this work consists of two identical cells. The main body of each cell is a 100-mm. piece of 50-mm.-diameter borosilicate glass tubing, with two chimney-like projections at the top to accommodate the R P E and a fritted gas bubbler. Two side arms contain fritted-glass disks and hold the auxiliary platinum electrode and the salt bridge leading- to the SCE. h transfer chamber was built which fitted over one of the chimneys from each cell, and permitted raising the R P E out of one cell and transferring it to the other cell under oxygen-free conditions. The transfer chamber was constructed from a BO-mm. length of 80-mm.-diameter glass tubing fitted with two 10-mm. thick Plexiglas caps a t the ends of the tubing. One cap, which served as the base of the chamber, had two holes which fitted snugly around a chimney from each cell. A slit was cut in the cap which served as the top of the chamber, and permitted horizontal movement of the R P E from one cell to the other. Nitrogen was flushed through the chamber with a gas dispersion tube. A Plexiglas plate covered the slit in the transfer chamber top when it was not in use. Lysing this apparatus, R P E plated with less than a monolayer of silver can be transferrrd from one cell to another with no appreciable air oxidation of silver. I
792 * ANALYTICAL
CHEMISTRY
Deposition of silver a t constant potential was accomplished by shorting the R P E to a large-area SCE. Conventional chronopotentiometric technique was used for both constant current oxidation of plated silver and constant current plating of silver. The RPE's were constructed from soft glass tubing and 27-gauge platinum wire and were of the form previously described (4). Two electrodes were used in this study. Both had platinum surface areas of about 0.15 sq. cm., estimated from physical dimensions. They were mounted in a 600-r.p.m. Sargent Synchronous Rotator. Electrical contact was made by means of a wire placed in the mercury-filled R P E . Three additional indicator electrodes were employed in studying the phenomenon described by Bard. One was a square of platinum foil hammer-welded to a platinum wire sealed in glass. The area of the foil electrode was about 2.9 sq. cm. Two platinum disk electrodes having areas of 0.2 and 0.4 sq. cm. were also used. Pretreatment of RPE. T o obtain reproducible results, we found it necessary to control the previous history of the R P E carefully. This is best accomplished by subjecting the R P E to a suitable pretreatment prior to each experiment. Two pretreatments were devised. PRETREATMENT A. Step Al. The R P E was oxidized anodically for minute a t 500 Ma. in a 150-ml. beaker containing 0.1Ji HC104. Ster, A2. The oxidized R P E was rotatid for 1 minute in a beaker of freshly prepared cold aqua regia to dissolve the platinum oxide coating partially and was then washed thoroughly with distilled water. Step A3. The R P E was reduced cathodically for 2 minutes a t 500 pa. in a 150-mi. beaker containing nitrogenbubbled 0.1M HC1O4. Hydrogen gas is evolved a t the R P E surface duringthe reduction. Step A4, The R P E was held at 0 volt us. S C E in nitrogen-bubbled 0 . l M HC104 for 5 minute; to oxidize any hydrogen on the electrode surface. PRETREAThlENT B. Step B1. The R P E was oxidized anodically for 1 minute a t 500 pa. in 0.1Jf HC104. Step B2. The R P E was reduced cathodically for 3 minutes a t 500 pa. in nitrogen-bubbled 0.1JI HC104. Step B3. 0 volt us. SCE was applied to the R P E for 5 minutes in nitrogenbubbled 0.1-11 HCIO,. Either pretreatment gave satisfactory results; Pretreatment B has the advantage of eliminating the use of aqua regia. Experimental Technique. All experiments were performed a t 25" + 0.2O C. Plating and anodic stripping of the R P E were carried out in one of the dual cells described above. Fifty milliliters of silver solution of the desired concentration were pipetted into the cell and deaerated for 20 minutes with nitrogen. Enough 0.1M HClO4 was introduced into the cell side arms to make electrical contact with the salt
bridge and auxiliary electrode. A N a N 0 3 salt bridge was interposed between the SCE and the cell to prevent chloride contamination of the silver solution. After pretreatment, the R P E was d a t e d with silver from the dilute silver solution. The plating was carried out at 0 volt us. SCE, which is in the limiting current region for the reduction of Ag(1). Relatively larger amounts of silver were deposited upon the R P E from a 5.00 X 10-sM Ag(1) solution for times ranging from to 5 minutes. Smaller amounts of plated silver were deposited on the R P E by plating from a 1.00 X 10-6M dg(1) solution for times ranging from a few seconds to 5 minutes. The limiting current of a 5.00 X 10-5.M Ag(1) solution was 6.93 pa. a t 0 volt us. SCE, corrected for the residual current. The plated R P E was stripped, usually in the plating cell, by applying a constant anodic current across the R P E and an auxiliary platinum electrode. The stripping process was followed by recording the voltage-time curve. The stripping current was selected to give stripping time of 5 to 15 seconds. In the experiments attempting to repeat the Nisbet and Bard experiments (Y), the experimental procedure was taken from data supplied by Bard (1).
Procedure. Step 1. Pretreat the electrode by making a series of several chronopotentiograms. Carry the plating through the transition time, then reverse the current and strip the electrode to +1.35 volts US. SCE. Step 2. Stir the solution and wait 1 minute. Plate a t constant current for 15 seconds, reverse the current, and strip to f1.35 volts us. SCE. This step is repeated two times. Step 3. Stir the solution and wait 10 seconds. Again strip the electrode to f1.35 volts us. SCE two times. Step 4. Stir the solution and wait 1 minute. Repeat Step 1 once. Step 5. Stir the solution and wait 1 minute. Plate a t constant current for 22.5 seconds, reverse the current, and strip to 1.35 volts us. SCE. Step 6. Repeat Step 2 four times. Step 7. Wash the electrode thoroughly with deaerated water and transfer it under air-free conditions to a cell containing deaerated, silver-free lAVfHClOr. Step 8. Reduce the electrode at constant current to the point where hydrogen evolution begins. Step 9. Reverse the current and strip a t constant current until the electrode potential reaches 1.35 volts us. SCE. Except for Steps 7 through 9, the experiments were carried out in deaerated 5.00 X lO-3Jf Ag(1) solution in lAkf HC104 supporting electrolyte, using a current density of 339 pa. per sq. cm.
+
+
Bard (1) reports making equivalent ,If hg(1) in experiments in 1.00 X 1M HC104, using a current density of 600 pa. per sq. cm. Several of our ex-
ping, double layer charging required 4 pc. Thus 229 pc. of silver were recovered, compared to 231 pc. of silver plated. Introducing Qc’ = 4 pc. and Equation 3 into Equation 1, we obtain
BB A
120
80
40
4,o
80
I
I
400
0
(i,)Ap+ t, Figure 2. A. Slope = 1.00 1 3 vcoulombs.
I20
1200
80 0
I
A.
Imicrocoulombr)
Anodic stripping of silver
B . Slope = 1.00, intercept on x axis =
periments were also made under these conditions. The dual cell with transfer chamber described above was used to perform the Kisbet and Bard experiments, since it was necessary to transfer the RPE from one cell to another under oxygen-free conditions. RESULTS AND DISCUSSION
Constant Potential Plating and Constant Current Stripping of Silver. Experiments were performed to test the conformance of the R P E to the theory described above. -4value of Qc was determined in silverfree 0 , l M HC104 by passing a constant current and recording a potential-time curve between the equilibrium potential (E1 = 0.440 volt us. SCE) and Et = 0.00 volt us. SCE. Fifteen microcoulombs of charge were required for this potential span. A value of QE’ can also be estimated from this experiment. I n our stripping experiments, on applying the constant anodic current the potential shift going from the open circriit condition to the voltage plateau at the beginning of the stripping process is about 0.1 volt. Thus, Qc’ is about ‘I4 Q c , or 4 pc. The current-time curve illustrated in Figure 1 was recorded during a 3minute plating at 0 volt us. SCE in 1.00 x M Ag(1) in 0.1M HC104. After the initial double-layer charging pulse, the current drops and slowly rises to a steady value. The area under the curve in Figure 1 was integrated and a value of 231 pc. of plated silver was obtained. This number is corrected for 2 pc, of residual and charging effects, determined by recording and integrating
a similar curve in silver-free 0 . M HC104. A value of 15 pc. for Q . cannot be used to correct the data in Figure 1. This choice of Qc would be an overcorrection, since the full charging effect is not observed in Figure 1 because of slow recorder response. The constant current technique used for determining the charging coulombs does not suffer from the recorder response disadvantage, since the times involved are within the recorder capabilities. It is secii in Figure 1 that the current reached a steady-state value of 1.38 pa. after about 65 pc. of silver have plated. This quantity of charge corresponds to about two monolayers of silver, assuming the electrode surface is smooth. Ipparently, 0 volt us. SCE does not produce a limiting current of silver on a platinum surface-Le., the overvoltage for the deposition of silver on platinum is sufficient to reduce the silver reduction current below its limiting value. -4fter some silver deposits on the R P E (less than two layers), a limiting current region is reached. Assuming that the cathodic limiting current is constant at 1.38 pa. throughout the entire plating experiment, we calculate 248 pc. of silver plate, 17 pc. more than obtained by integration. Thus, for the RPE used in the experiments described in this paper ( Q p ) A g (microcoulombs) may be expressed in terms of the experimental quantities by the empirical relationship ( Q p ) ~ p
= ( i i ) ~ g +
X
tp
- 17 MQ (3)
T o oxidize the silver deposited in the experiment illustrated in Figure 1, 233 pc. were required. During this strip-
Equation 4 is valid only for the R P E used in these studies, since the constant term is a function of the area and surface condition of the R P E . Equation 4 predicts that a plot of iotaus. (illAg+t, is a straight line intersecting the ( i J A g t+, axis a t 13 pc. and has a slope of unity. Equation 4 is not valid if less than 65 pc. of silver are plated. I n this case, a constant limiting current value is not reached during the experiment. The data obtained from a number of anodic stripping determinations are plotted in Figure 2 , A . The points lie on a straight line with a slope of unity. The lower points from curve d are plotted on an expanded scale in curve B , together with the theoretical line defined by Equation 4. The lower points, which are less than 65 pc,, lie slightly to the left of the theoretical line, as one would predict. The agreement between theory and experiment is excellent. Anodic Stripping Potentials. I t is possible t o calculate the theoretical potential during the anodic stripping process using Equation 2. T h e formal potential of silver in 0.1M HCIOl was determined by making potentiometric measurements with a silver wire electrode and by plotting E us. log CAB+(2). The slope of this line was 0.059 and the formal potential of silver in 0.1M HC10, was determined to be +0.556 volt us. SCE. Substituting the formal potential and kAg+ from limiting current data into Equation 2 yields :
E
=
0.556
+ 0.0591 log (CAg+ + 0.15 ”)
(5)
Using Equation 5, the theoretical anodic stripping potentials have been calculated for a number of the points plotted in Figure 2. These values are tabulated in Table I. The experimental anodic stripping curves resemble Figure 3 when large amounts of silver were plated and high stripping currents were used. When small amounts of plated silver and Ion currents were used, the stripping potential was not constant, but became more positive as the stripping progressed. This phenomenon is probably due to a decrease in the activity of metallic silver JX hen less than a monolayer remains on the R P E surface. The values of the potential both a t the beginning and near VOL. 37, NO. 7, JUNE 1965
793
9 is due to plating silver onto oxidized platinum, increasing the amount of oxide on the surface should enhance the effect. The R P E and large disk electrode were oxidized in 0.1M HClO4 for 1 or 2 minutes a t current densities of 600 and 6000 pa. per sq. cm., and were then carried through Steps 6 through 9 in 1 x lo-* JI‘ &(I), using a current density of 600 pa. per sq. cm. The anomalous effect was not observed in Step 9 with either electrode. Experiments were performed with the R P E in which the reduction in Step 8 was allowed to proceed for 3 minutes a t a current density of 6000 pa. per sq. cm. A long wave was observed in Step 9 arising from the oxidation of hydrogen. This wave could be almost completely eliminated by rotating the RPE during Step 8, and no “retained” silver was observed in Step 9. The R P E was used to verify that no “retained” silver was oxidized or washed away during Step 7 . Following Pretreatment 13, the R P E was plated and stripped as in Step 2. I t was again pretreated, replated for 15 seconds, transferred, and stripped in deaerated 1-21 HC104. This was repeated, washing the R P E as in Step 7 during the transfer. KO loss of plated silver was observed in either the transfer or washing operation. The large disk electrode was plated for 3 minutes a t 0 volt us. SCE in 1 X 10-4 Jf -\g(I), rotating the disk electrode during the plating. This was followed by stripping a t 600 pa. per sq. cm. After three of these plate-strip cycles, the electrode was carried through Steps 7 through 9, no silver wave being observed in Step 9. I n none of our experiments have we found evidence of the recovery of “retained” silver in Step 9. Nisbet and Hard ( 7 ) report the recovery of 60 layers of retained silver, assuming the electrode is smooth. If their explanation is correct, the entire platinum electrode surface cannot be completely covered with PtO, and their estimation of 60 layers of silver would correspond to many more layers of silver on the oxidized surface. On the basis of their proposed explanation, one would expect only a few layers of retained
TIM E Figure 3. Chronopotentiornetric anodic stripping curve
the completion of the stripping are listed in Table I. Agreement between calculated and measured potentials is fairly good. In many cases, the calculated value lies between the two measured values. “Silver Retention” Effect. Numerous experiments were performed in a n a t t e m p t to reproduce the phenomenon described by Nisbet and Bard (1,Y). On repeating Step 2 we obtained results in good agreement with those previously reported. Figure 4,A , illustrates the shape of the curves obtained in Steps 2 and 6. When this experiment was repeated several times in succession, the anodic stripping time became progressively shorter, which agrees with Bard’s observations. The type of curve we obtained in Steps 8 and 9 is shown in Figure 4,B. The cathodic portion from Step 8 agrees with the data reported by Bard. However, in Step 9, Bard reports observing the type of anodic wave illustrated by a dashed line in Figure 4,C. According to Hard’s data, in some cases the anodic wave from Step 9 was u p to four times as long as the cathodic wave in Step 8. Using the laige disk or foil electrode, we observed no wave in Step 9. Using the small disk electrode cvhich had a rough surface, an anodic wave was observed in as large as Step 9 which was ahout the cathodic wave in Step 8. However. it was shown that’ this electrode had a faulty seal. If the effect reported by Bard in Step
Table I.
Anodic Stripping Potentials
T
=
25’ i 0.2” C .
E,,,tl
I %aI
CAS’
pa.
I 00
x
10-5
50 20 5
5 00
x
10-5
250 100
794
e
10
ANALYTICAL CHEMISTRY
Eealcd
+o +O +O +0 +0 +O
354 329 298 313 390 369
Beginning
+o
+0 +0 +O +O +O
354 321 262 288 418 385
Conclusion +0 +0 +0 +0 +O +0
364 345 309 327 418 395
1.4
C
0.6 CYII..t
0.2 (
30Sec.
-0.2
’
e n 2 .rdution
TIME Figure
4.
Silver retention effect
A. Step 2 or 6 (see t e x t ) B . Steps 8 and 9 C. Reported silver retention effect ( 7 )
silver, a t the most, since silver deposited on oxide would be stripped until the electrical contact between silver on platinum and silver on oxide is broken. Therefore, unless their electrode has a large roughness factor, their explanation appears to be inconsistent with the experimental data they present. I n addition, we have performed experiments in 0.1M Sax03 as the supporting electrolyte. Before plating, the electrode was heavily oxidized for 1 minute a t an anodic current of 60 pa. in 0.1M NaN08. In this medium, an oxidized platinum surface is reduced a t +0.25 volt us. SCE, which is substantially more negative than the reduction of silver (about f0.48 volt us. SCE). Thus, when silver is deposited on the electrode it deposits on a surface that is almost 100% oxidized; 80% of the silver plated on this oxidized surface is recovered by anodic stripping. CONCLUSION
By properly pretreating a platinum electrode, it is possible to deposit and quantitatively recover quantities of silver corresponding to a few monolayers. Classical voltammetric theory gives results in good agreement with observed steady-state potentials during constant-current stripping of silver. As was observed by Nisbet and Bard ( 7 ) , we find that the total number of cathodic coulombs apparently used in depositing silver on an oxidized platinum surface substantially exceeds the anodic coulombs required to remove silver from the electrode. Under our experimental conditions, a contributing factor toward this discrepancy is that partial reduction of the oxidized platinum surface occurs simultaneously with silver deposition. In addition, mechanical loss of silver from an oxidized platinum surface may be occurring. We do not find any evidence for retained silver on an oxidized platinum surface.
ACKNOWLEDGMENT
This work was supported in part by the National Science Foundation. J. W. Bixler is also indebted to the Ethyl Corp., E. I. du Pont de Nemours & Co., and the Procter and Gamble Co. for financial aid during the course of the studies.
LITERATURE CITED
(1) Bard, A. J., private communications, 1963. (2) Ph.D. thesis. IJniversitv ~, Bixler. J. W.. of Minnesota (1963). (3) Bruckenstein, s., Bixler, J. W., ANAL. CHEM.37, 786 (1965). (4) Bruckenstein, S.. Naeai. T.. Ibid.. 33, 1201 (i96ij. ’ (5) Lord, S. S., Jr., O’Neill, R. C., Rogers, L. B., Ibid., 24, 209 (1952). I
I
(6) Meyer, F. R., Ronge, G., 2. Angew. Chem. 52, 637 (1939). (7)Xisbet, A. R..Bard. A. J.. J . Electroanal. Chem. 6. 332 i1963). (8) Shain, I., ‘“Treatise ’on Analytical Chemistry,” I. M. Kolthoff and P. J. Elving, eds., Part I, Chap. 50, Interscience, New York, 1963. .
I
RECEIVED for review September 3, 1964. Accepted March 12, 1965.
Optimum Stabilization Networks for Potentiostats with . Application to a Polarograph Using I ransistor Operational Amp1ifiers . r
GLENN L. BOOMAN and WAYNE B. HOLBROOK Phillips Petroleum Co., Atomic Energy Division, ldaho Falls, ldaho
b The selection of impedance values in the cell-current-measuring circuit to obtain maximum bandwidth with particular control amplifier characteristics, is discussed and application is made to a polarograph with transistor operational amplifiers. Methods are described for determining the circuit values for the best possible response time with a wide stability margin and tabulated data are given for the transistor polarograph circuit. These optimum values ensure measurements and control to the desired accuracy and simplify the electrochemical cell design for use in many experimental techniques.
I
vacuum tube equipq e n t , transistor amplifiers greatly increase the circuit reliability, useful operating time, and signal-to-noise ratio of many measurement circuits. The replacement of vacuum-tube operational amplifiers in polarographic potentiostat circuits by their transistor counterparts has been accomplished with no problems. Many circuits are used to obtain potential control of a 3-electrode cell ( 2 , 3, 5, 8 ) . The selection of the transistor circuit, described in this paper, was weighted towards use as a versatile research instrument rather than for a specific routine use (8). A follower amplifier with high-input impedance was selected to minimize the I R drop when used with high-resistance reference electrodes and to prevent the polarization of low-tesistance, micro reference electrodes. The necessary bandwidth shaping is then easily accomplished operationally in the highgain stage. Mixing of offset, sweep, and N CONTRAST T O
various function generator signals is readily obtained a t the high-gain amplifier input, with the external signals referred to ground level. The unity-inverter, compensating circuit for measuring the cell current was chosen because only one booster amplifier is required for fast pulse or controlled - potential coulometric applications. For measurements in which a 0.1- to 10-megohm load resistor is desired, or in cases where boosters are not required the circuit can be simply changed to the “current-follower” mode (5). The methods of obtaining stability in closed-loop systems containing an electrochemical cell have been discussed previously (2). However, the selection of optimum impedance values in the cell-current-measuring circuit, as influenced by the available control amplifier characteristics, has not been discussed explicitly in the literature. d basic understanding of how the cell geometry and electrical parameters affect the available range and accuracy of electrochemical measurements is needed by the worker making these measurements. These interactions are discussed from the servomechanism viewpoint, using a very simple, but extremely useful and practical approach, well substantiated experimentally. The chemist must have sufficient knowledge of what parameters under his control are important to the control system performance to be able to evaluate and communicate the special problems that occur in terms the electronic specialist can understand. Optimum is defined here as being the fastest possible risetime obtainable across a certain double layer capacity with a given total cell resistance, and
given control amplifier characteristics. This optimum performance is to be obtained by the addition of passive networks and through adjustment of the reference electrode position in the electrochemical cell. Because the presence of faradaic currents reduces the response time of the control system, this “optimumJ’ performance will occur when the faradaic contributions approach very small values. This condition exists out of necessity in many trace analysis applications. I n kinetic studies, working a t low concentration levels decreases the signal-to-noise ratio. Hence the “optimum” conditions described in this paper should be considered as a limiting case-Le., the best attainable response time as the faradaic current is reduced toward zero. The effect of faradaic current on the response time is included in this discussion. A detailed discussion of the design and construction of the polarograph using transistor operational amplifiers, lowvoltage power supplies, and a controlled-potential plug-in unit is given below. The calculation of the stabilizing network components for the potentiostat and the determination of the optimum value for the reference to measuring electrode resistance is discussed explicitly. Knowing this optimum value can simplify the cell design for many measurements. Placement of the Luggin capillary probe close to the measuring electrode may not be required or even be desirable. If the proper uncompensated resistance can be obtained with the reference probe located away from the measuring electrode, the location of the probe becomes less critical, more robust electrodes can be used, and special VOL. 37, NO. 7, JUNE 1965
795
