series of three solutions of 2 % HzOz (and lO-‘M KNOs) at a rate of 2 l./min. After the solutions were allowed to stand overnight, 10-ml aliquots were taken from each and treated with Mn02, filtered, and the nitrate concentration was measured by both methods as described. The air samples were taken and tested to see whether there were any strong interferents present that had not been anticipated in the method development. Because the results of the two methods in each case agreed within 3% of each other, it may be inferred that no such interferences were present. The difference in the two concentrations of atmospheric NO, found-119 and 216 pg/m3-can be attributed to observed differences in traffic flow in the area since the samples were taken on two separate days. The Arizona State Department of Health in its Air Pollution Control Implementation Plan (11) used the Federal primary standard of 100 pg/m3 (annual average) as its ambient air quality standard for NOz. The values obtained for NO, (11) Arizona State Dept. of Health, “State of Arizona Air Pollution Control Implementation Plan,” January, 1972, pp 1-16.
in this study, expressed in terms of NOz, are somewhat high reflecting the presence of abnormally heavy truck traffic in the area (construction projects) during the test periods. CONCLUSIONS
A new potentiometric method for NO, determination has been developed. The importance of this to air pollution work is that this method is much simpler and faster than the spectrophotometric methods currently in use, and just as reliable. Additional advantages include the facts that the electrodes are small, portable, inexpensive, sturdy, and easily constructed, conditioned, and stored. Use of the coated-wire nitrate electrode with the absorption system described is more efficient than the flowing gas technique of DiMartini, and the system is certainly much less complex. Air sampling rates will have to be adjusted to accommodate individual situations ; the method could thus be an advantageous alternative to the existing ones. RECEIVED for review July 17, 1972. Accepted October 19, 1972. This work was carried out in part in the Atmospheric Analysis Laboratory supported by a grant from the Arizona Mining Association.
Theoretical and Experimental Evaluation of Staircase Volta mmetry J. J. Zipper and S. P . Perone Department of Chemistry, Purdue Unicersity, Lafayette, Ind. 47907 The electroanalytical technique of staircase voltammetry (SCV) was investigated as a computer-compatible approach to stationary electrode polarography (SEP). Theoretical relationships presented here show a marked dependence on the data sampling characteristics. Moreover, the severe restrictions upon correlating SCV and SEP data were established. Experimental studies were conducted to verify theoretical predictions for SCV. In addition, the analytical capabilities were assessed experimentally. A linear concentration dependence to 5 x lO-7M was observed, and optimum experimental parameters were defined. .A projected limit of detection of about 5 x 10-*M i s suggested.
THEELECTROANALYTICAL TECHNIQUE of staircase voltammetry was suggested by Barker ( I ) , and has been explored epperimentally by Mann ( 2 , 3) and by Nigmatullin and Vyaselev ( 4 ) . However, these earlier works were carried out prior to the development of an adequate theoretical description, presented later by Christie and Lingane (5). Moreover, the recent emergence of digital electronics and computerized instrumentation, with which the technique is inherently com(1) G. C. Barker, Adcan. Polarog., 1,144(1960). ( 2 ) C. K. Mann, ANAL.CHEM., 33,1484 (1961). (3) Ibid., 37,326 (1965). (4) R. S . Nigmatullin and M. R. Vyaselev, Zh. A n d . Khim., 19, 545 (1964). (5) J. H. Christie and P. J. Lingane, J. Electroanal. Chem., 10, 176 (1965).
452
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
patible, allows a much more definitive theoretical and experimental evaluation of the method than possible previously. In our laboratory, we are particularly interested in the generation of a large computer-compatible data base for practical electroanalytical applications based on the measurement technique of stationary electrode polarography (SEP) (6). Because staircase voltammetry (SCV) is a computer-compatible approach which produces SEP-like results, it is the logical experimental choice for modern computerized electroanalytical systems ( 7 ) . Thus, an experimental evaluation of this technique under computer-controlled conditions appeared desirable, and this work is reported here. EXPERIMENTAL
Instrumentation. The potentiostat used in this work is shown in Figure 1. It uses a common three-electrode design. Current measurements are made across a load resistor, RL, placed in the controlling loop. A diode (H.P. 5082-2811) was placed parallel to RL and limited the voltage drop across RL to about 0.4 V. Thus, during large charging current pulses, nearly the total output voltage of the controlling amplifier can be applied to the cell, and a minimal charging time is required. Moreover, a booster amplifier can be added to provide additional current capacity if needed. (6) R. S . Nicholson and I. Shain, ANAL.CHEM., 36,706 (1964). (7) G. Lauer and R. A. Osteryoung, ibid., 40 (lo), 30A (1968).
.001pf
50K
90K
Figure 1. Potentiostat and computer interface schematic for SCV instrument A3 is Analog Devices P501-all others are Fairchild 741. RL can be a 2K, 5K, or 10K 1
The controlling potential is input through a 50-KHz low pass filter. This filter is required to eliminate high frequency noise spikes generated by the digital-to-analog converter (DAC). A lower pass filter (35 KHz) may be used. The stabilization loop around the controlling amplifier (Al) can be tuned to provide stability for a wide range of cell characteristics (8). The potential drop across R L is measured by a XlOO differential instrumentation amplifier; this can be followed by a non-inverting amplifier (X10) if necessary. The potential output can be taken from either amplifier. The band pass of the last two amplifiers is limited to 3 KHz by capacitors in the feedback loops. Because these amplifiers do not contribute to the control loop, their band pass can be considerably lower than for the control amplifiers. The only objective must be to provide adequate band pass to allow sampling data at a maximum rate without distortion. The laboratory computer system used for control, data acquisition, and data processing has been described previously (9). It includes a Hewlett-Packard 2115A computer with 8K core memory, a 10-bit, 30-psec analog-to-digital converter (ADC), and a 16-bit DAC. Digital control and interfacing are accomplished through a general-purpose interface panel described previously (10). It should be pointed out here that the primary limiting factor in the combined digital/analog instrumentation is the linearity and accuracy of the DAC. The main problem that arises is that, because of non-linearities in the DAC ladder network or because of non-uniform switching characteristics, the staircase sweep may be composed of steps of non-uniform size. Thus, some current pulses will be larger, and some smaller, than predicted-leading to a signal with a noisy envelope. A schematic diagram of the interface to the computer is included in Figure 1. A detailed diagram is available from the authors on request. Except for the programmable clock, all elements are DEC (Digital Equipment Corp.) R-series logic. The programmable clock (which provides the time
base for the DAC) is TTL logic followed by conversion to DEC R-series logic levels (10). Thus, the DAC clock is Programmable by software and provides the time base for the staircase sweep. The ADC clock rate is fixed and synchronized with the DAC clock; it provides a data acquisition frequency of 25 KHz. Because the ADC conversion time is 30 psec, this provides a data acquisition time close to the maximum available. Cell and Electrodes. The working electrode was a microburet type hanging mercury drop (HMDE) (Metrohm Ltd., Switzerland). For all experiments, the electrode surface area was 2.22 mm*. A Coleman 3-710 saturated calomel was used as reference electrode. An extension was added to the reservoir in order to properly fit the cell. The counter electrode was a platinum helix. The cell is a threaded 100-ml borosilicate glass bottle. A threaded lid for the cell was machined out of Teflon (DuPont) and all electrode and nitrogen holes drilled through the top. The cell was mounted using Plexiglas (Rohm & Haas) inside a metallic bread box (Sears, Model 11 H2816) that functioned as an electrical shield. Reagents. Ferric oxalate solutions were made by adding ferric ammonium sulfate to a 0.3M potassium oxalate, 0.1M oxalic acid buffer. All above were analytical reagent grade (Mallinckrodt Chemical Works, St. Louis, Mo.). The cadmium chloride and potassium chloride electrolyte were also analytical reagent grade (J. T. Baker Chemical Co., Phillipsburg, N.J.). Electrolytic purification of the electrolyte was tried with no noticeable improvement of background currents. Water used was distilled and passed through a mixed-bed ion exchange column. Solutions were deoxygenated with high purity nitrogen. Oxygen traces were removed by passing the nitrogen through two gas washing bottles containing chromous chloride and zinc amalgam (IZ). A following gas washing bottle contained distilled de-ionized water. All solutions were deaerated a minimum of 15 minutes and then blanketed by the same nitrogen stream.
(8) J. E. Davis, Clinical Laboratory, Barnes Hospital, St. Louis, Mo. 63110, private communication, 1972. (9) S. P. Perone, D. 0. Jones, and W. F. Gutknecht, ANAL.CHEM., 41,1154 (1969). (IO) S. P. Perone and J. F. Eagleston, J. Chem. Educ., 48, 317 (1971).
RESULTS AND DISCUSSION The technique of staircase voltarnmetry involves the imposition at a stationary electrode of a controlled potential (11) L. Meites, A n d . Chim. Acta, 18,364 (1958).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
453
Table I. Theoretical $ p and Epas a Function of LY and AE nF n - = - mv-1
RT
nF
cy
0.00 0.05
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0.55 0.60 0.65 0.70 0.75 0.80
-(AI?) RT
-1.0
-0.8
-0.6
-0.4
-0.2
-0.117
-0.08
-0.04
0.57208 2.0 0.57988 2.0 0.58813 2.0 0.59687 2.0 0.60618 2.0 0.61612 2.0 0,62679 2.0 0.63832 2.0 0.65086 2.0 0,66459 2.0 0.67979 2.0 0.69680 2.0 0.71765 1.0 0,74788 1.0 0.78443 1.0 0.83022 1.0 0,89058
0.52866 1.8 0.53540 1.8 0.54252 1.8 0.55006 1.8 0,55808 1.8 0.56664 1.8 0.57581 1.8 0.58571 1.8 0,59645 1.8 0.60821 1.8 0.62121 1.8 0,63574 1.8 0.65224 1.8 0.67464 1.0 0.70413
0.47238 2.0 0.47724 2.0 0.48318 1.4 0.48964 1.4 0.49650 1.4 0.50383 1.4 0.51170 1.4 0.52019 1.4 0.52942 1.4 0.53953 1.4 0.55072 1.4 0.56324 1.4 0.57748 1.4 0.59399 1.4 0.61363 1.4 0.63781 1.4 0.66914 1.4 0,72107 0.8 0.80740 0.8 0.99626 0.8
0.40438 1.8 0.40810 1.4 0.41233 1.4 0.41680 1.4 0.42152 1.4 0.42654 1.4 0.43191 1.4 0.43767 1.4 0,44391 1.4 0.45071 1.4 0.45820 1.4 0.46653 1.4 0.47596 1.4 0.48684 1.4 0.49979 1.o 0.51807 1 .o 0.54179 1.o 0.57504 1.0 0,62484 1.o 0.75260 0.6
0.30425 1.4 0.30634 1.4 0.30854 1.4 0.31085 1.4 0.31328 1.4 0.31585 1.4 0.31859 1.4 0.32151 1.4 0,32466 1.4 0.32807 1.4 0.33207 1.2 0.33656 1.2 0,34163 1.2 0,34745 1.2 0.35431 1.2 0.36270 1.2 0,37431 1 .o 0.39058 1.o 0.41701 0.8 0.47734 0.8
0.24095 1.424 0.24219 1.424 0.24351 1.307 0.24492 1.307 0.24642 1.307 0.24799 1.307 0,24966 1.307 0.25145 1,307 0.25337 1.307 0,25544 1.307 0.25779 1.19 0.26043 1.19 0,26341 1.19 0.26681 1.19 0.27082 1.073 0.27595 1.073 0,28253 1.073 0.29187 0.956 0.30714 0,956 0.34175 0.722
0.20324 1.32 0.20412 1.32 0.20505 1.32 0.20602 1.32 0.20704 1.32 0,20812 1.32 0,20928 1.24 0.21054 1.24 0.21190 1.24 0.21336 1.24 0.21496 1.24 0.21675 1.16 0.21880 1.16 0.22116 1.16 0.22392 1.16 0.22740 1.08 0.23186 1.08 0.23822 1.o 0.24858 0.92 0.27180 0.76
0.14777 1.28 0.14822 1.28 0.14870 1.24 0.14921 1.24 0.14973 1.24 0.15029 1.24 0.15089 1.24 0.15153 1.20 0.15222 1.20 0.15297 1.20 0.15378 1.20 0.15459 1.16 0.15572 1.16 0.15690 1.12 0.15830 1.12 0.16002 1.08 0.16224 1.08 0.16537 1.04 0.17045 0.96 0.18176 0.84
1.0
0.85 0.90
0.95
25.6
0.97665 1.o 1.1172 1.o 1.4268 1.o
1.0
0.74089 1.o 0.78911 1.0 0.85753 1 .o
0.96874 1.0 1.2125 1.0
sweep with a staircase function (2, 5). A series of current pulses are obtained. If the current value near the end of each step is plotted ES. potential, a peak-shaped polarogram is obtained, analogous to SEP, except that-like pulse polarography (12)-the measured currents are primarily faradaic and free from charging current. Thus, the important controlled variables include the step height ( A E ) and the step width (T); the step width is obviously related to the step frequency (f = l / r ) . The “sweep rate” can be equated t o A E / r . This sweep rate is discontinuous, however, except in the limit as AE + 0, and therefore should not automatically be equated with the linear sweep rate variable used in SEP ( 6 ) . The theoretical treatment of staircase voltammetry with reversible systems was presented by Christie and Lingane (5). An inherent assumption in their theory is that the current is measured only at the end of each step. They show, as expected, that the polarogram obtained is identically equal to that predicted from SEP theory (6) when AE + 0 at constant sweep rate, A E / r . In addition, they discussed the effect of sweep rate on peak currents. This consideration is com(12) H. Schmidt and M. von Stackelburg, “Modern Polarographic Techniques,”Academic Press, New York, N.Y., 1963, pp 63-70. 454
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
z/;ip nF
s(E,
- Ew)
plicated by the fact that, for this method, the sweep rate can be varied experimentally in two ways. It was predicted that peak currents should vary linearly with (l/r)1/2and approximately linearly with AE1‘2. An experimental factor not considered by Christie and Lingane is the sampling of data. This is particularly important with computer-controlled measurements. For example, it is possible to sample the current during each step at a time shorter than r. Also, as a noise rejection technique, multiple samplings might be averaged during each step. Because these possibilities were not considered previously, we have provided here a theoretical and experimental foundation to assess their effects. Theory. The theoretical equations of Christie and Lingane ( 5 ) lead to tabulated values of the current function, +s, dependent on E - Eli2 and on AE. The current, i, for the j t h step is given by :
i = nFACO*D01~2+,(j,AE,t) (1) where n is the number of electrons transferred, F is the Faraday, A is the electrode area, C,* is the bulk concentration of reducible species, 0, and Dois the diffusion coefficient of 0. Christie and Lingane (5) derive a general expression for +s given in Equation 2 .
+*
=
.I
1 1 x{[l -1
+
1
d Z 7
+
Q
0.3
’
4
where t is time measured from the beginning of the sweep,
and Et is the initial potential at which the sweep begins. Note that different subscripting is used here than that of Christie and Lingane (5) to clarify the fact that the first c value appearing in the solution refers to the potential reached on the first step. Christie and Lingane made the substitution of t = j T in Equation 2, assuming that sampling would always be at the end of each step. They obtained the expression for +s given in Equation 4 after factoring out (f/T)1’2.
0
Figure 2. Dependence of SCV polarogram shape on
01.
E A E = -0.117 RT Equation 5 describes the sampled current, i, at time, 7 ’ , of thejth step. Equation 6 was evaluated, and Table I contains at the peak, as well as peak pothe tabulated values of tentials, as a function of a and AE. In evaluating Equation 6 , any term involving the square root of a non-positive argument was ignored. (The column of values for nF/RT AE = 0.117 corresponds to AE = 3.00 mV which is a step size used for most experimental work here.) It is important to note that the tabulated values are very much dependent on a. The peak potential shifts anodic and the values for + D increase with increasing a . Other more subtle trends occur, and these are noted below. Also, it should be pointed out that for a = 0, the tabulated results are identical to those of Christie and Lingane (5). Experimental Studies. The experimental data discussed below were obtained with the objectives of defining optimum conditions for analytical measurements and evaluating experimental correlations with theory. The variables considered included AE, T , and sampling conditions. Sampling approaches included: varying the sampling time, T ’ , such that T’ 5 T , varying the number of samples, N , averaged on each step; and utilizing ensemble averaging (13) with multiple runs for each of the sampling methods mentioned. In addition, least squares digital smoothing (14) was applied to the raw data for cases where noise levels precluded meaningful data processing. Theoretical Correlations. The very first observation which should be made is that experimental data obtained with SCV can be correlated validly with SEP theory only in the limiting case where AE and a both approach zero. Because it may not often be desirable or possible to impose these conditions on an SCV experiment, the experimental studies reported here have been correlated to SCV theory, focusing attention particularly on the effects of data sampling conditions.
d&*
L[-1 1
+
El-1
d j- ( j - 1)
-
1-
d j- ( j - 2)
It is possible to evaluate the series solution for +s (5) at a sampling time, T ’ , which is less than T . The parameter, a , will be introduced here to describe the variation in sampling time, where a = 1 - T ‘ / T . Thus, t = ( j - &)T was substituted into Equation 2. This substitution and rearrangement yields (5)
where ,-
1
(13) D. J. Fisher, Chem. Instrum., 2,3 (1969). 36, 1627 (1964). (14) A. Savitzky and M. J. R. Golay, ANAL.CHEM., ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
455
Table 11. Experimental Dependence of i, and E , on a and T (lO-4M Fe(II1) in oxalate buffer; AE = 3 mV) A . Vary T' to keep CY 'v 0 B . Vary T, r' constant c. Vary r', r constant -Ep DS. r,psec a SCE, mV QP"
1000 2000 loo00 2 m
0.16 0.08 0.032 0.016 0.008
1.623 1.612 1.572 1.537 1.563
225 228 225 225 222
1000 2000 5000 loo00 2 m
0.16 0.58 0.83 0.916 0.958
1.620 1.615 1.604 1 ,597 1.615
219 213 213 210 210
2000 2000 2000 2000 2000 2000 2000 2000
0.78* 0.68 0.58 0.48 0.38 0.28 0.18 0.08
1.688b 1.639 1.620 1.614 1.598 1.596 I ,592 1.600
210 219 219 222 219 222 225 225
5000
:7
--
(E-E,,,)
Figure 3. Comparison of experimental SCV polarogram
nF
to theoretical shape. - AE RT 2000 psec, N = 1
-0.117;
=
CY
=
0.58, T =
i ,112
1 X 10-4MFe(III)in O.1Moxalic zcid, 0.3Moxalate. Lfne = theoretical: circles = experimental
a Q
'Pi _ -_ where T is in seconds and i, in @A(X 50).
B -
G$,
For the conditions of this experiment, the charging current is non-zero at time, 7'.
I
I
0.2
0.4
I
,
0.6
0.8
a =O
nF
RT ( A E ) nF
Figure 4, Dependence of Z/&,/AE1I2 on - AE and 01 RT Effects of 01. Table I demonstrates a marked dependence of the polarographic results on the value selected for a. Experimental data were obtained to verify the predicted behavior. These data correspond t o a single sampling ( N = l) during each voltage step. The shape of the polarogram obtained with SCV depends on the value of a , This is shown in Figure 2 for a specific value of AE. Not only does the peak become sharper and 456
larger with increasing a , but the peak potential also shifts anodic. The same general trends are observed, regardless of AE, but the relative changes vary somewhat, as can be seen from Table I. A direct comparison of the shape of a n experimental polarogram with that predicted by theory is shown in Figure 3. It should be pointed out that cy can be varied in a series of experiments in two ways. The sampling time, T ' , can be kept constant while the step duration, T , is varied. Alternatively, T' can be varied while keeping T constant. Theoretically, the effect of cy on the shape does not depend on how cy is varied. When the sweep rate is varied by changing T , the product, i , ~ l / ~should , be constant as long as ct is kept constant. If cy is allowed to vary, the value of $, will change, but the term i,T1/2/$p should remain constant. This prediction is verified by the data of Table I1 which correspond to three series of runs-one where T was varied while keeping cy as close to zero as possible, one where both T and cy were varied simultaneously, and one where T was held constant and cy was varied. Also given in Table I1 are the observed peak potentials for these series of runs. The experimental results of Table I1 show excellent agreement with theory. The fluctuations in Q, are entirely within experimental error. However, it should be noted that the experimental resolution of Ep is limited by the finite AE values used; also, the tabulated values of (E, - El,2)are similarly limited in resolution (Table I). When the sweep rate is varied by changing AE, the dependence of the peak current is not as straightforward as when T is varied. Christie and Lingane (5) pointed out that the term i,/AE112 was "nearly" constant. However, they
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
Table 111. Experimental Dependence of i, and E, on AEfor CY = 0.12 (10-4M Fe(II1) in oxalate buffer; 7 = 1000 psec.) AE , mV
in, P N X 50)
1 2 3 4
75.76 102.12 130.77 146.84 160.33 173.66 185.50 195.74 207.75 218.38
5
6 7 8 9 10 Figure 5. Experimental SCV polarogram for 1 X 10+~M Cd(II), 0.2MKCl N = 15, 1E
=
4 mV,
7 =
5 msec,
T’ =
1040 Fsec, 4 ensembles.
Upper trace, raw data; lower trace, smoothed data considered only the case where CY = 0. When CY is not zero, the term i,iAE’/* may vary considerably with AE. Moreover, the nature of the dependence on AEis markedly different for various CY values. This is shown in Figure 4 where it is seen that negative deviations occur for small a’s, and positive deviations for large a’s. For CY ‘v 0.75, the value of i,/AE1’2 remains approximately constant. Table I11 shows the experimentally observed dependence of i, on AE for CY = 0.12. The correlation reported is ip/$pwhich should be a constant as AE varies. Also reported are the values of the peak potential. As predicted, E2,shifts cathodic with increasing AE. Effect of N . The primary reason for making multiple current samplings (integration) on each voltage step is to achieve some noise filtering. If the sampled signal were constant over N samples, the signal-to-noise ratio should increase with “12. Because the signal is not constant, and because the time dependence is not described by a simple expression, the theoretical improvement factor cannot be generally stated. Experimental data were obtained, however, to show the dependence of signal-to-noise ratio on N . These experiments involved varying N from 1 to 25 for AE = 3 mV, = 2000 psec, r’ = 560 psec, where T’ corresponds to the sampling time of the first point. The solution used was 1 x 10-4M ferrioxalate in oxalate buffer. The signal-to-noise ratio was obtained by determining the standard deviation, s, of integrated currents for 10 base-line steps and calculating the ratio i,/s. All integrated points were normalized by dividing by N . The signal-to-noise ratio improved by a factor of about 3 for a 25-fold increase in N . It should be pointed out that when N > 1, it is not possible to have cr = 0. Moreover, the specific effective value of CY to be used for theoretical correlations is difficult to assess. Not only is the time-dependence of each current step not expressible in a closed form, but the time-dependence varies so that the effective value for CY would be different on each step. Thus, although current integration can be very useful for reducing the noise level, theoretical correlations are not feasible. Nevertheless, if only analytical information is desired, integration can be used as long as N , AE, r , and r’ are kept constant. Effect of Ensemble Averaging. The technique of ensemble averaging is well established as a signal enhancement approach (13). It is applicable to repeatable signals. Thus, it should be useful for SCV.
iPId&
-ED US. SCE, mV
514.5 502.6 535.4 528.8 523,5 524.0 524.0 522.8 528.4 531.5
212 214 216 220 220 222 217 224 225 230
Table IV. Analytical Data for Cd(I1) in 0.2M KCI [Cd(II)I, (W 1 x 10-4 1 x 10-6 1 x 10-6 5 x 10-7 a 2K Load resistor. 10K Load resistor.
i,, ( 4 ) 6.46 =tO.OIOa 0.641 0.010” 0.0635 0.0015* 0.0330 i 0.002P
*
With random super-imposed noise, the signal-to-noise ratio should improve with the square root of the number of averaging runs. This expectation was realized in the work reported here, as ensemble averaging was utilized in the analytical studies described below. Multiple runs were obtained by manually dialing new electrode droplets, but an automated DME set-up (15) could be used-if large numbers of averaging cycles were required and sweep times could be kept under one second. Analytical Results. In Mann’s early work ( 2 ) a non-linear concentration dependence was noted over the range 2 x 10-6 to 2 X 10-3M for Cd(II), Zn(II), and Mn(I1). This was attributed to uncompensated iR drop in the cell. A study of the concentration dependence of SCV measurements was carried out here for two purposes. First, it was desired to confirm the predicted linear concentration dependence. Also, an experimental assessment of the limit of sensitivity was desired. The major limits on sensitivity are two-fold: systematic noise and background currents. If only charging current background is considered, it is obvious that this can be minimized by letting r’ be large compared to the cell time constant--i.e., compared to double-layer charging time. However, as r‘ increases, the current level decreases relative to the noise. Thus, the optimum value of r’ is as short as possible consistent with the level of background charging current that can be tolerated. For example, in the analytical study reported here, a value of r’ of about 1000 psec was considered optimum. The minimum r’ used in this work was 440 psec (roughly 4 x the worst cell time constant encountered). With regard to systematic noise problems, the major sources and methods of handling have been discussed above. The magnitude of the problem depends on the specific instrumental set-up and environment. Conclusions drawn here must necessarily pertain only to our system. (15) S. P. Perone, J. E. Harrar, F. B. Stephens, and R. E. Anderson, ANAL.CHEM., 40,899 (1968).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
457
In our work, analytical measurements were made on Cd(I1) to in 0.2M KC1 over the concentration range of 1 x 5 x lO-7M. The measurement conditions were: N = 15 (the time of the f i s t sampling, T’, is 1040 psec), AE = 4 mV, T = 5 msec, and 4 ensemble averaging cycles per run. As shown in Table IV, the peak currents obtained were linearly dependent on concentration within experimental error over the entire range studied. All peak values were corrected for background currents. Figure 5 shows traces of raw and smoothed data for 1 X 10-6M Cd(I1). At this concentration, the signal-to-background ratio was about 1.5:l. A 7-point cubic-quartic smoothing function was used (14). It should be obvious that the analytical sensitivity can be extended below lOPM if larger N-values and ensemble averaging are used. Considering a practical limit of about 100
averaging cycles (15), the detection limit for our system appears to be about 5 x 10-*M. In order to minimize background current contributions at the lower concentrations, a larger value of 7 ’ could be used. But the signal-to-noise factor would suffer, and a larger number of averaging cycles would be required to achieve the same sensitivity. ACKNOWLEDGMENT.
The authors would like to thank J. E. Davis for his helpful suggestions in potentiostat design.
RECEIVED for review October 11, 1972. Accepted November 27, 1972. This work was supported by the National Science Foundation, Grant GP-21111.
Pulse Polarography in Process Analysis Determination of Ferric, Ferrous, and Cupric Ions E. P. Parry and D. P. Anderson1 North American Rockwell Science Center, Thousand Oaks, Cd$. 91360 A form of pulse polarography is described which can be used for automated analysis of process streams. The technique is rapid, has good sensitivity, and is not severely affected by small amounts of oxygen. Only one 50-millisecond pulse to the diffusion plateau for each species to be analyzed is all that is required for the analysis after suitable calibration. The choice of supporting electrolyte(s) is of great importance in the successful application of the technique. For determination of two different oxidation states of the same species (or where both oxidation states can be present), it is necessary thst the pulse polarographic wave be irreversible. The kinetic parameters are discussed. Pyrophosphate solution is shown to be a suitable medium for the simultaneous determination of ferric and ferrous ions and the pulse polarographic behavior of these ions, as well as cupric ion in this medium, is described in detail.
THERECENT GROWING NEED for process analysis and process control has aroused interest in the application of new instrumentation and techniques for this purpose. The use of colorimetric analyzers and selective ion electrodes is well-known. Potentiometric and potentiometric titration analyzers as well as conductometric analyzers have also been used in monitoring process streams, but the possibility of using polarographic techniques has not received much attention. Pulse polarography, a polarographic technique described in some detail in previous publications ( I , 2), has several attractive features. It has good sensitivity, is not severely affected by small amounts of oxygen, and a reading can be made quickly as will be subsequently described. It also should be quite suitable for use with various solid electrodes, although the present application is with the dropping mercury electrode. Present address, Cutter Laboratories,Berkeley, Calif. (1) E. P. Parry and R. A. Osteryoung, ANAL. CHEM.,37, 1634 (1 965). (2) Zbid.,36, 1366 (1964). 458
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
We have combined a sample handling system with a custom designed pulse polarograph and have successfully applied this system to the on-line analysis of the ferric, ferrous, and cupric ions in a copper etching bath used in microelectronics manufacture. The sample handling system and instrumentation will be described in future publications. It is the purpose of this paper to describe the principles which are required for application of pulse polarography to process analysis and to elucidate the details of the chemistry which underlie the pulse polarographic determination of ferric, ferrous, and cupric ions. It is shown that ferric and ferrous ions can be determined in a pyrophosphate supporting electrolyte a t pH of 8 containing Triton X-100. Although copper ion gives a wave in this medium, mutual interferences dictate that copper be determined in an acidified potassium sulfate solution. THEORY
Pulse Polarography in Process Analysis. Normal and derivative pulse polarography have deen described (1). The normal mode has been used exclusively in this application and will be the only one described here. In the usual normal pulse polarographic application, potential pulses of gradually increasing amplitude are applied to a n electrode starting from a “rest” potential which is anodic of the electrode process of interest. The potential pulses applied t o the electrode are approximately 50 milliseconds duration, but the potential between pulses always returns to the “rest” potential. If the area of the electrode is changing ( e . g . , dropping mercury electrode), the pulses are always applied a t a fixed time in the life of the drop, so a constant electrode area can be maintained. Current values are measured before each pulse and toward the end of each pulse application, and the current difference is read out as a function of pulse amplitude. The curve obtained is very similar to a normal polarogram with the limiting current being proportional to the concentration of electroactive species in the solution. For process application, it is found most convenient to apply, from a potential well anodic
