“Elementary Quanti1ative Analysis,” 2nd ed., p. 484, Harpw and Row, New York, 1963. (5) Blaedel, R J., Strohl, J. H., ANAL. CHEM36,445 (1964). ( 6 ) Bricker, C E., Sweetser, P. B., Ibad., 2 5 , 764 (1953). ( 7 ) Ewing, D. T., Eldridge, E . F., J . Am. P h ~ mSac 44, 1484 (1922).
(8) Furman, X. H., Bricker, C. E . , Dilts, R. v., ANAL. CHEM.25,482 (1953). ( 9 ) Lingane, J. J., “Electroanalytical Chemistry,” 2nd ed., pp. 316-22, Interscience, New York, 1958. (10) Molnar, J., M a g y . Kem. Folyozrat 68(11), 504 (1962). (11) Ramaley, L., Brubaker, R. L., Enke, C. G., ANAL.CHEM.35, 1088 (1963). (12) Smith, G. F., “Cerate Oxidimetry,”
F. Smith Chemical Co., Columbus. 1942. Someva, K.. Z . Anora. dllaem. Chem.
10,
RECEIVED for review January 6, 1964. Accepted March 3, 1964. Financial support through Grant No. hT(11-1)-1082 from the U. S. Atomic Energy Commission is gratefully acknowledged.
Resistance Cornpensatio n in Polarography Application to High-Resistance Nonaqueous Systems and to High Current-Density Aqueous Systems WARD B. SCHAAP and PETER S. McKINNEY’ Department o f Chemistry, lndiana University, Bloomington, Ind.
b The technique of derivative polarography was used to detect resistance TWO losses in polarographic cells. limiting cases were investigated-nonaqueous solutions with high specific resistances and low cell currents and aqueous solutions with high cell currents. In the nonaqueous solutions, the solution resistances evaluated at various distances from the D.M.E. were found to agree well with values calculated for a model assuming concentric spherical electrodes. This iR drop, present on all sides of the D.M.E., is not compensated for b y potentiostat action using typical three-electrode cells and can b e appreciable if either the specific resistance or the cell current is abnormally high. Resistance-free halfwave potentials can still b e obtained by extrapolation procedures, however. With concentrated aqueous solutions, an appreciable iR drop was detected when the concentration of the electroactive species exceeded 1 O-* M, though values of id/(: remained constant from to 10-’M.
T
HE DEVELOPMEKT of threeelectrode, resistance-compensating polarographic potentiostats ( 1 , 2 ,13-15) makes it possible to attempt precise polarographic studies in nonaqueous solutions utilizing tolvents of low dielectric constant and high specific resistance. The exper,iments of Arthur (1, 2) and of Kelley, Jones, and Fisher ( 1 4 , 15) show that such polarographic studies are feasible uqing their potentiostats, hut thorough studies in nonaqueous systems were not made. *%ttempts to use these techniques in the nonaqueous electrochemical studies in
Present address, Department of ChemCambridge,
istry, Harvard University, ;\lass.
progress in this laboratory met with only partial success. These preliminary studies indicated t,hat, complete resist’ance compensation was not always attained in such systems, and this sit’uation prompted a more careful investigation of the factors affecting resistance compensat,ion. It was mentioned in the previous paper of this series (26) that it is necessary to distinguish t,wo types of highresistance syst’ems when considering resistance compensation. The first of t.hese includes systems in which the specific resistance of the solution and the cell current are both small or moderate, and the high resistance is primarily a result of cell or electrode design--.Le., a long or restricted current path exists between the D . M . E . and the auxiliary counter electrode. In this first case the ohmic pot’ential difference (iR drop) in the immediate vicinity of the D.M.E. is relatively small, though measurable (19). If care is taken to position the reference electrode on the side of the D.M.E. opposite the counter electrode, the potentiostat will compensate for essentially all the cell resistance effect and undistorted polarograms can be recorded. The potential difference between the D.M.E. and the reference electrode is not influenced by the large iR drop caused by the flow of cell current through the high resistance located between the D.M.E. and the counter electrode. The second type of system includes those in which the specific resistance of solution is very high, so that even a nominal current density in the vicinity of tjhe D.M.E. gives rise to an appreciable ohmic potential drop in this region. In this case a large iR drop can exist even though the cell is designed to minimize overall cell resistanceLe., with a short current path of large
cross-sectional area. Because the D.M.E. is a very small diameter electrode, all points on its surface are essentially equidistant from t,he counter electrode. Thus, current will flow equally from its entire equipotential surface and t’he current path will a t first proceed radially from the D.1I.E. before turning in the direction of the counter electrode. The ohmic potential gradient will be significant on all sides of the D.M.E. if the specific resistance of the solution is very high and will approach spherical symmetry near the drop surface. T i t h this situation, the usual placement of the three electrodesLe., with the D.M.E. betvieen the reference and counter electrode.; and at, appreciable distances ( 2 0.5 em.) from both- will not accomplish complete compensation for resistance losses in the cell and the recorded polarograms will show a distortion, due to iR losses, of a magnit’ude proportional to the cell current and the specific resistance. I t is the iR drop existing in the solution between the D.M.E. surface and the tip of the reference electrode salt bridge that is not compensated for by the action of the potentiostat. I t is then obvious that the effectiveness of resistance compensation depends not only on the specific resistancp of the solution used, but also on the current density and the placement of the controlling reference electrode with respect to the D.1I.E. and counter electrode. In the experiments reported below, the actual magnitude of the uncompensated resistance is measured as a function of D.M.E. to reference-electrode probe distance using anhydrous nbutylamine (dielectric constant = 5.3) ( 2 7 ) as solvent. % . special threeelectrode cell was designed which allowed the position of the reference electrode to be varied and its distance VOL. 36, NO. 7 , JUNE 1964
1251
from the D.M.E. to be measured. The theory and techniques for evaluating uncompensated rwi-tance from dcrivative po1arogral)hic measurements are d e s c r i h l in a previous paper (f8). Also repoi,ted bc,low are the reslrlts of resistance componsation studies on systems in which the ohmic potential drop around the D.M.E. is the result of a very high current density in a solution of low specific resistance. For this purpose aqueous solutions were employed which contained the electroactive species a t concentrations in the range of 0.01 to 0.1M. EXPERIMENTAL
Cell Design. T h e cell used for the evaluation of uncompensated resistance is shown schematically in Figure 1. T h e volume of each of the three compartments was approximately 25 ml. The anode compart,ment was separated from the D.M.E. compartment, by a fine porosity glass disk approximately 1 em. in diameter. The reference electrode probe was a 4-mm. glass tube, 6 cm. long, pulled down to a tip diameter (0.d.) of about 0.5 mm. The probe was inserted into a 6-mm. glass tube fused into the side of the D.M.E. compartment, which served as a guide for the probe. A piece of Tygon tubing served as a gasket between the probe and the out'er guide tube so that the probe could be positioned a t various distances from the polarized electrode. The distance between the probe tip and t'he D.M.E. was measured either directly with a cathetometer or indirectly by comparing the difference in distance between the upper portions of t,he D.M.E. and reference compart,ments with the distance between them when the probe was posit'ioned so that it just t'ouched the mercury drop a t its maximum diameter. Sitrogen bubbling tubes were provided in each compartment for the eliminat,ion of dissolved oxygen. Selection and Preparation of the Electrolytic Solution. The solution employed for the nonaqueous studies was selected so that' it would have a high specific resistance, would allow the reducible species to be present a t a concentration large enough to provide substantial faradaic current. and would provide a reversible electrode reaction. Fulfilling these criteria should provide an uncompensated resistance of sufficient magnitude to be easily measurable and should allow t,he theoretical derivative equations, derived for reversible systems, to be applied. Previous work in this laborat'ory (do) indicated t,hat, the reduction of thallium(1) in anhydrous n-butylamine with SaCIOl as the supporting electrolyte proceeds reversibly. When pure, n-butylamine is a clear liquid with a strong ammoniacal odor. It' is hygroscol)ic and strongly basic. Its boiling point is 77.8" C. a t 760 mm. pressure. Ikcausc its dielectric constant is only 5.3 a t 21' C., dissolved salts exist essentially as ion pairs in
1252
ANALYTICAL CHEMISTRY
COUNTER ELECTRODE
M.E.
REFERENCE ELECTRODE
Figure 1. Diagram of three-electrode polarographic cell used to evaluate uncompensated resistance as function of distance between D.M.E. and tip of reference electrode salt bridge
butylamine. The resistance of solutions containing even rather large amounts of dissolved salts is therefore quite large. Typical D.iL1.E.-to-anode resistances were in the range of 0.5 to 1.0 megohms. Resistances between the D.M.E. and the reference electrode, including the drawn-out probe, were ordinarily on the order of 10 megohms. The amine, Fisher reagent grade (99.6%), was purified further by allowing the solvent to stand over solid sodium hydroxide for several days and then distilling in a nitrogen atmosphere from sodium metal and collecting in a container with an outlet tube so that the distilled solvent could be transferred directly into a volumetric flask containing the dried salts. The salts were dried in a vacuum oven a t 80" C. for 8 hours. The solutions were prepared by weighing the desired amounts of the supporting electrolyte and reducible material into dry, nitrogen-filled flasks. The distilled solvent was then added directly from the collection flask. The solutions were stored in a desiccator over Drierite until used. For studies of resistance compensation at very large current densities in solutions of lou specific resistance, aqueous solutions were prepared containing cadmium ion at concentrations ranging from 10-3 to O . l M > each containing 551 Kal;Oa as the supporting electrolyte. Instrumentation. A resistance compensating, three-electrode polarograph of the Kelley, Jones, and Fisher design ( 1 4 , . 15) was constructed and then modified slightly for use in these experiments. The modification was necessary for successful application of the instrument to studies in systems of very high specific resistance, 2 lo4 ohm em., and will be described briefly. In the original design of the polaro-
graph, a 1.0-pf. capacitor is placed in a feedback configuration in the controlledpotential amplifier circuit ( 1 4 ) . The purpose of this capacitance is to limit the frequency response of the amplifier so that it does not follow the current spike which exists momentarily a t drop detachment. However, in order for this large capacitor to become charged it is necessary that a small amount of current be drawn through the reference electrode (9). This presents no problem if the reference electrode resistance is not large. I n fact, the resistance in series with the auxiliary counter electrode may be as high as 20 megohms and yet cause no appreciable distortion of the polarogram just so long as the reference electrode resistance remains low. If the reference e!ectrode resistance is large, an iR drop can develop across it due to the flow of current needed to charge the large feedback capacitor. This appears as an uncompensated potential distorting the resulting wave. The problem becomes particularly acute if the resistance in series with the counter electrode is also large, since in this case the large feedback capacitor must charge to a high voltage (because of the large iR drop in series with the counter electrode) and the current necessary to establish this voltage is drawn, a t least partially, through the large reference electrode resistance. This latter situation obtains in solutions of very high specific resistance. h study of this problem in a simulated system using aqueous solutions and external repistors indicated that distortion of the wave becomes noticeable when the resistance in series with both the reference and counter electrodes reaches approximately 0.20 megohm. The distortion becomes very severe when both resistances are several megohms and useful polarograms can no longer be recorded using unmodified circuitry. If the resistance in series with the counter electrode is reduced to a small value, the resistance of the reference electrode can be increased to about a megohm before distortion becomes evident. For the work reported here, the instrument was modified by inserting a rotary switch to which were connected six capacitors ranging in size from 1.0 to pf. Any one of these could be selected as the feedback capacitor of the controlled-potential amplifier. By selecting an appropriate capacitance value it was possible to eliminate the distortion a t resistances as large as 5 megohms in series with both electrodes. The effect of decreasing the size of the capacitor on derivative waves is illustrated in Figure 2 . Because the noise level tends to increase as the capacitance value is decreased, the largest possible capacitor size commensurate with an undistorted wave should be selected. Table I indicates the approximate maximum allowable capacitance when R1 (in series with the reference electrode) and Rz (in series with the counter electrode) have the values indicated. Since the completion of the studies reported here, another approach to the
4 Figure 2. Derivative polarograms showing effect of sire of feedback capacitor on shapes of derivative waves recorded in presence of large inter-electrode resistances Curve 1 (solid line): no resistance added; 1-pf. feedback. Curve 1 (dashed line): 4 . 7 megohms in series with counter and with reference electrode; 220-ppf. feedback. Curve 2: 4.7 megohms in each cell arm and 0.1 -pf. feedback. Curve 3: 4.7 megohms in each cell arm and 1-pf. feedback. (Solution contained 5 X 1 O-4M C d + 2 in 0.1M KCI; scan rate = 50 mv./minute and sensitivity = 1 5 pa. full scale.)
0.5
0.6 -E,pp
VS.
0.7 S.C.E. (Volts)
problem of eliminating this distortion was suggested t o us by Fisher and Stelzner (9). A stabilized voltagefollower amplifier, of a design proposed by DeFord ( 7 ) ,was inserted between the reference electrode and the potentialcontrol amplifier. This high-impedance follower is able to prcwide the necessary charging current, so that no current is drawn through the reference electrode. This approach allows the feedback capacitor t o be maintained a t 1 pf. even when cell resistances as large as 10 megohms in both cell arms are encountered. I n actual experiment, the derivative polarogram recorded with very little resistance in series with both electrodes was virtually superirnposable with the derivative wave recorded with 4.7 megohms in series with both the reference and counter electrodes and with the follower amalifier inserted into the circuit. Filtered conventional and derivative polarograms were recorded using all sections of the parallel-T, RC filter network, which allows the time-average current to be recorded with no D.M.E. oscillations visible. Measurements of inter-electrode resistances were made with a Serfass conductivity bridge, Model RCM 15, a t 1000 c.p.s. Specific resistance measurements were made with a dipping-type conductivity cell (cell constant = 0.0565 cm.-l) and the Serfass bridge. -Accurate potential measurements were made using a Rubicon Portable Pointerlight Potentiometer, Model 2730, or with a NonLinear Systems, Inc. digital voltmeter, Model 481. Scan Rate. I n our experience, derivative waves recorded in non-
0.8
aqueous solvents tend to be “noisier” t h a n polarograms recorded a t similar sensitivities in aqueous solutions. This appears t o be due, in large part, to a n increase in “capillary noise”-i.e., irregularities in the growth pattern of the mercury drops and the droptime (3, 6). For this reason it is desirable to record derivative waves in nonaqueous solvents a t scan rates which are as fast as permissible in order to enhance the signal-to-noise ratio. (The value of d i / d t is directly proportional to the rate of potential scanning.) There is, however, a limitation on the scanning rate if derivative polarograms of theoretical shape are desired. The filter network, which must be employed to record derivative waves, imposes a lag on the recorded signal and, as a result, the maximum height of the derivative tends to be less than its theoretical value and the half-peak width (V1/J tends to be greater. It is usually possible to make the lag negligible by employing sufficiently slow scan rates. I n the absence of uncompensated resistance, the maximum allowable scan rate is approximately 40 n/mv./minute. I n the presence of uncompensated resistance the true scan rate is always less than the applied scan rate by a n amount equal to the product of R and dZi/dt--i.e., the uncompensated resistance times the instantaneous derivative of the total average cell current. Therefore, the applied scan rate can be larger when uncompensated resistance is present without introducing appreciable distortion in the recorded derivative polarograms. It was found experimentally, using aqueous solutions containing l O - 3 M cadmium and known amounts of un-
compensated common-path resistance ( I @ , that the derivative waves of cadmium (n= 2) were negligibly distorted due to instrument lag a t scan rates of 100 mv./minute when the uncompensated resistance exceeded lo4 ohms. Thus, it was concluded that derivative waves of thallium ( n= I) could be recorded at this scan rate in the high-resistance butylamine solutions with no appreciable distortion. For the aqueous studies reported below, a scan rate of 40 mv./minute was employed throughout. General Procedures. T h e reference electrode compartment of the cell shown in Figure 1 contained mercury in contact with n-butylamine contairiing NaC104 as supporting electrolyte. Though this is not a particularly reproducible or well poised reference electrode, it was considered adequate for these studies since absolute halfwave potentials were not of interest and because practically no current is drawn through the reference electrode as i t functions in the controlled-potential polarograp h. The three cell compartments were filled with nitrogen prior to the addition of the amine solution. Mathrson prepurified nitrogen, presaturated with pure n-butylamine t o minimize evaporation, was used to eliminate oxygen from the solution in each cell compartment. Deaeration was allowed t o proceed for 30 minutes. -1polyethylene bag was then placed around the cell and closed in such a way that, a slight positivp pressure of nitrogen could be maintained in the bag to minimize the diffusion of water vapor and oxygen into
Table I. Maximum Allowable Size of Feedback Capacitor in Control Amplifier Circuit as Function of Resistance
R1 = resistance in series with reference electrode and Rz = resistance in series with counter electrode. Maximum RI, RP capacitor size, (megohms) ILf. 10,lO 4.7,4.7 2.7,2.7 1. 0 , l . 0 0,56,0.56 0.10.0.10 1o;o.0 0.0,lO
0.0001 0.00022 0,001 0.01 0.1
1.0 0.1
1.0
VOL. 36, NO. 7, JUNE 1 9 6 4
1253
the cell during the polarographic measurements. I t was found, in general, that the first polarogram recorded wit,h a new solution had a more or less pronounced maximum. Thus, asast,andard practice, the solution was cathodically preelectrolyzed for several minutes before the first polarogram was recorded. ;Ifter this procedure was well defined, reversible polarograms were obtained. A series of polarograms was recorded with each solution. The first and last waves of each series were filtered, average-current polarograms recorded a t the smallest possible DA1.E.-toreference electrode probe distance. Derivative polarograms were recorded at a series of measured D.il1.E.-to-probe distances. The solution resistance between the three electrodes was noted and, finally, the specific resistance of the solution was determined. Two difficult experimental problems encountered in working with this solvent are the absorption of impurities from the atmosphere, especially oxygen and water vapor, and the evaporation of the solvent during deaeration. Though extreme care was taken to avoid these difficuhies, a number of solutions had to be discarded because of poor reproducibility of the recorded polarograms. For the high current density studies carried out in aqueous solutions, the cell utilized was identical to that shown in Figure 1 except that it' was water jacketed so that the temperature could be maintained at 25" f 0.05' C. The reference electrode was a saturated calomel electrode. Fikered, unfiltered, and derivative polarograms were recorded wit'h the reference electrode probe positioned approximately 2 cm. from the D.M.E., on the side opposite the counter electrode, and with the probe placed very close to the D.M.E. surface-i.e., at about 0.02 em. from the surface of the drop a t its maximum size. Calculations The deviat'ion from theory of the maximum (peak) height' of the derivative of a polarographic wave is a convenient' and sensitive measure of uncompensated solution resistance. I n this study, the derivative peak heights were measured as a funct,ion of the distance of the reference electrode probe from t h e D . M . E . surface. The equation which relates the maximum height, of the derivative of total average cell current, with respect to time, t,o the uncompensated, average resistance has been derived in a p r t \ i )us paper (18) and may be wittell 1
and where Z i (total) = ifnrhdslc f irosldual. "SC.W" refers to the scan rate applied by the instrument-i.e. dE, d t ; S is the derivative of the residual current with respect to the true electrode potential a t the D.M.E. surface (no iR loss)-Le., di,/dEd,; K = RTtF and R is the uncompensated solution resistance. Equation 1 can be used to evaluate uncompensated resistance because all factors other than R are experimentally and Independently measurable (18). The diffusion current, which is independent of R, can be obtained from the filtered (average current) polarograms even though resistance losses occur and distort the wave. d z i l d t can be evaluated by directly recording the derivative wave, measuring the height of the peak from the zero line and then multiplying by a previously evaluated calibration factor to convert i t to the time-derivative value. The residual current slope i3 expressed in terms of the true electrode potential, Edc, so that S is unaffected by uncompensated resistance. S can be considered to be a constant over the narrow potential range encompassed by the derivative wave, since the residual current is nearly a linear function of potential except a t the electrocapillary maximum. The value of S can be obtained by measurement of the interpolated residual current a t potentiali corresponding to the apparent onequarter and three-quarter points on the filtered polarographic nave. For a oneelectron reversible reduction, the theoretical potential difference between these two points is 56.4 mv. arid thus, even in the presence of uncompensated resiqtance, the true electrode potential difference measured a t the D.M.E. surface must also be equal to this value. Division of the quantity (i7)l -
A
0
Figure 3.
I. 0.3mm.
0.1 0.2 0.3 - k P p v s . Hq Pool (volts)
1
0.4
Derivative polarograms of
1.3 X lop4thallium (I)in n-butylamine
(z)
where is the maximum value or max peak height of the derivative of the average total cell current with respect to time 1254
ANALYTICAL CHEMISTRY
recorded at D.M.E.-to-reference probe distances of ( 7 ) 0.3 mm., ( 2 ) 1 .O mm., and (3) 2.0 mm. (Solution contained 7.5 X 10-*M NaC104 as supporting electrolyte; specific resistance = 2.5 X l o 4 ohm cm.; scan rate = 100 mv./minute
4 , by 56.4 mv. gives a good estimate of the value of S . The scan rate was determined by accurately measuring the applied potential before and after each recorded wave. The value of S C A W in the above equation was taken to be the average of the closely agreeing individual scan rates of each series of polarograms.
RESULTS
Nonaqueous Studies. h typical series of derivative polarograms recorded for t'hallium in n-butylamine is shown in Figure 3. The amine cont'ained 1.3 X 10-4M thallous nitrate and 7.5 X 10-2JI sodium perchlorate as supporting electrolyte. The derivatives were run successively using t,he same solution and the same applied scan rate, varying only the distance of the tip of the reference electrode probe from the surface of the D.11.E. (The distances listed are with respect to the D.1I.E. surface at maximum drop size and are measured along a line perpendicular to the equator of the drop 011 the side of the D.M.E. opposite the auxiliary counter electrode.) the distance of the tip of the probe from the D.1I.E. surface increases. the peak height decreases, the half-peak width increases, and the peak potential, which corresponds t'o the apparent shifts to a more negative value. This behavior is exact,ly that expected when increasing amount,s of solution resistance are not being compensated for by the potentiostat. Equation 1 allows a quantit.ative calculation of the average uncompensated resistance to be made using data obtained from conventional and derivative polarograms. The results obtained from measurements made on amine solutions containing several different concentrations of supporting electrolyte, in order to provide several different values of the specific resistance of t>he solution, p , are shown in Figure 4. The value of the average uncompensated resist'ance, R, is plot'ted as a function of the distance of the reference electrode probe from the D.M.E. surface. The average uncompensated resistance is observed to change very rapidly with distance in the immediate vicinity of the D.M.E. and to attain a reasonably constant limiting value at a distance greater t'han about 5 or 6 mm., which corresponds to a distance roughly 10 times the maximum radius of the mercury drop. This behavior is that expected for a spherically symmetrical, radial flow of current from a spherical electrode and arises because of the increasing size of the volume element a s the distance from the surface of the sphere increases. The resistance of the solution between the surface of an inner
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