ANALYTICAL CHEMISTRY, VOL. 51, NO. 3, MARCH 1 9 7 9 G. Horlick, Anal. Chem., 44, 943 (1972). T. R . Brunner, R. C. Williams. C . L. Wilkins. and P. J. McCombie, Anal. Chem., 46, 1798 (1974). P. C. Jurs, Anal. Chem., 43, 1812 (1971). P. F. Seelig and H. N. Blount, Anal. Chem., 48, 252 (1976). J. F. Evans, Ph.D. Dissertation, University of Delaware, Newark, Del., 1977. D. T. Shang and H. N. Blount, J . Electroanal. Chem., 54, 305 (1974). G. C. Whitnack and R. Sasselli, Anal. Chim. Acta, 47, 267 (1969). Princeton Applied Research Corporation Application Note, AN-108. L. Meites, "Polarographic Techniques", John Wiley and Sons, New York, 1965, p 89. W. W. Cooley and P. R. Lohnes, "Multivariate Data Analysis", John Wiley and Sons, New York, 1971. 8. Carnahan, H. A. Luther, and J. 0. Wilkes, "Applied Numerical Methods", John Wiley and Sons, New York, 1969. M. Abrahmowitz and I . A. Stegun, Ed., "Handbook of Mathematicai Functions", National Bureau of Standards Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1964. W. H. Reinmuth, J . Am. Chem. Soc., 79, 6358 (1957). W. H. Reinmuth. Anal. Chem., 33, 185 (1961).
(40) (41) (42) (43) (44) (45) (46) (47) (48) t49)
(50) (51) (52)
337
T. M. Florence, J . Electroanal. Chem., 27, 273 (1970). R . G. Clem, G. Litton, and L. D. Ornelas, Anal. Chem., 45, 1306 (1973). W. R . Matson, D. K. R o e , and D. E. Carritt, Anal. Chem.. 37, 1594 (1965). S. P. Perone and K. K . Davenport, J . Nectroanal. Chem., 12, 269 (1966). W. R . Matson, Ph.D. Dissertation, Massachusetts Institue of Technology, Cambridge, Mass., 1968. W. T. DeVries, J . Electroanal. Chem., 9, 448 (1965). M. J. Pinchin and J. Newharn, Anal. Chim. Acta, 90, 91 (1977) W. T. DeVries and E. van Dalen, J . Electroanal. Chem., 12, 9 (1966). R . K. Mehra, I€€€ Trans. Auto. Control, 15, 175 (1970). R. A. Hofstader, 0. I. Milner, and J. H. Runnels, Ed., "Analysis of Petroleum for Trace Metals", Adv. Chem. Ser., No. 156, 1976. 2 . Stojek and 2. Kublick, J . Hectroanal. Chem., 77, 205 (1977). K. R . Betty and G. Horlick, Anal. Chem., 49, 351 (1977). K. Steiglitz "An Introduction to Discrete Systems", John Wiley and Sons, New York, 1974, p 50.
RECEIVED for review August 2, 1978. Accepted November 3, 19i8.
Correction for Background Current in Differential Pulse, Alternating Current, and Related Polarographic Techniques in the Determination of Low Concentrations with Computerized Instrumentation A. M. Bond"' and B. S. Grabaric2 Department of Inorganic Chemistry, University of Melbourne, Parkville, 3052, Victoria, Australia
despite the improved sensitivity offered by these more modern polarographic methods, the fact remains that it is still the background or residual current, rather than an unfavorable signal to noise ratio, which ultimately determines the limit of detection available with these techniques. With direct current polarography, the charging current or background current in general is approximately a linear function of potential. This approximation is certainly an excellent one over the small potential range occupied by a sigmoidal shaped direct current wate. Indeed, many commercially available polarographs provide an analog circuit, using the linear approximation, to compensate for the charging or background current and accurate measurement of limiting current is facilitated by this method. More recently, the advent of instrumentation using laboratory computers has become common (5,6). With data obtained in digital format, correction for the background current can be made by storing the data obtained on a blank, if available, and mathematically subtracting the result from the test solution made up in the bame matrix. Alternatively, a mathematical algorithm to represent the background currents may be constructed from data obtained a t potentials removed from the faradaic current. An extrapolation to the potentials of interest where the faradaic current is present and subtraction of calculated values thereby enables the purely faradaic current t o be calculated. This latter procedure has been exploited in direct current and normal pulse polarography with considerable success (7) and with alternating current techniques assuming the background current is purely capacitive (8). T h e former approach is, in fact, equivalent to the dual cell or subtractive method of polarography available in analog instrumentation ( I ) and the second is akin to the linear compensating analog electronic circuit available with direct current polarographic instrumentation. However, both methods are implemented far more successfully with computerized instrumentation than with purely conventional instrumentation.
Modern electroanalytical techniques, such as differential pulse and atternating current polarography, can be used to accurately determine concentrations of electroactive species at I O - ' M concentration levels, or below, provided the background current can be corrected for. Using computerized instrumentation, a quadratic least squares fit of data removed from the faradaic peak current of interest is shown to provide a general method of predicting the base line over all of the required potential range. Since no theoretical assumptions are involved in the calculation, contributions from residual oxygen levels or other trace impurities are included in the background prediction and correction procedure, and the method is applicable to a wide range of techniques and conditions. Results are presented for the determination of cadmium in the io-' to lo-* M concentration range in 1 M NaCI, and data at these very low concentration levels are generally found to be superior to those obtained by storing a polarogram of the blank in memory and subsequently subtracting the result from test solutions.
As an analytical technique. direct current polarography suffers from the disadvantage of having a relatively unfavorable faradaic to charging current ratio (1-3). Consequently, modern polarographic techniques such as differential pulse polarography, phase-selective alternating current polarography (fundamental and second harmonic), linear sweep voltammetry, and other techniques which substantially discriminate against the charging current are becoming widely used as alternatives to the direct current method ( 4 , 5). However, P r e s e n t address, D e a k i n U n i v e r s i t y , D i v i s i o n of C h e m i c a l a n d Ph sical Sciences, W a u r n P o n d s , V i c t o r i a , 3217. A u s t r a l i a . 'On leave from t h e D e p a r t m e n t of I n o r g a n i c C h e m i s t r y , F a c u l t y of Technology, U n i v e r s i t y of Zagreb. Zagreb. Yugoslavia, 1975-1977.
0003-2700/79/0351-0337$01.00/0
C
1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 3, MARCH 1979
Of particular relevance to the present study is the work of Perone et al. (9, 10) who have described in detail the use of on-line interactive data processing procedures and presented examples in the area of linear sweep and cyclic voltammetry a t a dropping mercury electrode (10). Even a t the relatively M high (compared to our Rork) concentration level of these authors report considerable difficulty in correcting for the blank using the analog dual cell or subtractive method because of problems in adequately matching the dual cells. The computerized subtractive method of recording the blank in an initial experiment and subtracting the result from subsequent experiments could, however, be carried out conveniently and accurately. At the concentration levels well below lo4 M that we wished to examine, this result indicates computerized approaches will almost be mandatory and indeed this is our experience as subsequent results will demonstrate. b'ith differential pulse, alternating current, and other modern polarographic techniques, the background current cannot be approximated by a linear function of potential as is the case with direct current polarography, so that mathematical correction for charging current is not straightforward. Furthermore, because the techniques are so sensitive, with concentrations of many species in the lo-' to lo-' M range producing measurable responses. the apparent background current in the real analytical situation is unlikely to be void of a faradaic component from an "impurity". For example, oxygen a t variable, but trace, levels can represent a significant component of the background when trying to determine concentration of other species below 10 M. Thus, the obvious approach of recording the polarogram a t a blank and storing the data in memory for subsequent subtraction from test solutions is not as reproducible and reliable as it may appear to be in principle, when determining species near the limit of detection with modern polarographic methods. Other terms such as electrode area growth during the course of current measurement may also contribute to the background current ( 1 1 ) . T h e correction for background current, which is a prerequisite for accurate analysis a t trace levels via polarographic methods, therefore represents a non-trivial problem which needs to be solved to take full advantage of the capabilities of modern instrumentation. In view of the fact that correction for background current is a problem always confronted when working near the limit of detection with the extremely sensitive modern polarographic techniques, we thought it might be useful to describe a general approach to the problem of correction for background current t h a t we have developed for use with on-line computerized polarographic instrumentation. This is the purpose of the present communication. T h e technique uses a quadratic least-squares fit of the data a t potentials removed from the faradaic current and, unlike most previous methods, it is applied directly to the solution being measured without making any assumptions about the nature or theory pertaining t o the background current. Numerical background fitting techniques have been successfully employed in other areas of analytical chemistry, for example, mass spectrometry (9) and chromatography (9, 12-14). Thus, despite the fact that such techniques do not appear to have been employed in the polarographic area, available data from these other studies imply that such a n approach will be successful. Measurement on the reduction of cadmium in chloride media in the lo4 to lo-* M concentration range are presented t o demonstrate the fidelity of the method. This reduction process has been considered because it represents a difficult situation for the following two reasons. Firstly, the reduction process occurs near the electrocapillary maximum where the shape of the double-layer capacitance changes rapidly as a
'
function of potential and is, therefore, not as easily defined as a t more negative or more positive potentials. Secondly, oxygen is reduced over the same potential range making the shape and magnitude of the residual current critically dependent on the oxygen concentration present in solution.
EXPERIMENTAL All chemicals used were of analytical grade purity. Solutions were thermostated at 22 k 1 "C and degassed with argon or nitrogen prior to recording a polarogram. A11 polarograms were obtained using a conventional threeelectrode configuration. The reference electrode was Ag/AgCl (1 M NaC1) and the auxiliary electrode was platinum wire. The electrochemical instrumentation consisted of a PAR Model 174 Polarographic Analyzer (Princeton Applied Research Corporation, Princeton, N.J.) interfaced t o a PDP 11/10 minicomputer (Digital Equipment Corporation, Marlborough, Mass.) used in conjunction with a CAPS-11 operating system. The computer was equipped with a DR-11 general purpose interface which could be used to provide the logic and buffer register necessary for program controlled parallel transfers of 16-bit data between the PDP-11 system and the Polarographic Analyzer. This interface also includes status and control bits that could be controlled by either the program or the external device for command, monitoring, and interrupt functions. A TA-11 Cassette System Interface was used t o load programs and for the input/output of data. Sampling of the current output from the Polarographic Analyzer was performed using an AR-11 real time analog sub-system which included a 16-channel, 10-bit A/D converter with sample and hold. a programmable real time clock with one external input and a display control with two 10-bit D/A converters. Sampled data as well as any transformed data were displayed on either a Tektronix D13 Storage Oscilloscope or on an X-Y recorder. A program operating the Polarographic Analyzer, acquiring data, evaluating data, and displaying data was written in BASIC language using system sub-routines written in PAL-11 assembly language. The program for background correction was written in BASIC language and is a quadratic least-squares fit of an equation of the type I = A ( E - E*)2+ B where A , E* and E are constants, I is the current, and E the applied potential. The computer controlled system, background correction, and data reduction form an interactive system. Thus the operator can specify which data points the quadratic least-squares fit is applied to. Having defined the background from a least squares fit of chosen data points, prediction of the background current, I , for all values of ( E E*) can be made. This result is stored in memory and the result subtracted from subsequent experiments. Replicate scans can be made for averaging of data; however, all data presented in this paper was based on a single scan of the potential. Peak heights and peak positions are calculated via a quadratic least-squares fit of data located near the peak. Listings of all programs are available on request to the authors. Pulse polarographic measurements were performed with the aid of modifications t o the commercially available instrument described elsewhere ( I 5 , 1 6 ) . A PAR Model 129 two-phase/vector lock-in-amplifier using an Optimation Inc. Model RCD-10 sinewave oscillator to provide the input and reference signals was used to obtain phase-selective and total alternating current polarographic measurements. The ac circuitry and polarograph were interfaced with PAR accessory Model l74/50. ~
RESULTS AND DISCUSSION In recording a polarogram of a species t o be determined by differential pulse or an alternating current technique, a potential range sufficient to cover the peak shaped faradaic current response plus the background base-line current on either side of the peak is required. From the profile of the base-line current a t potentials removed from the faradaic current, it is necessary to predict what the base line would have been a t the peak position and possibly other potentials on the wave. Subtraction of the predicted base-line current should lead to the purely faradaic current response required for analytical or theoretical purposes.
ANALYTICAL CHEMISTRY, VOL. 51, NO. 3, MARCH 1979
339
M Solution of Table I. Comparison of Two Different Methods of Background Correction for a 1 X Cadmium in 1 M NaCla data corrected by subtraction of data corrected by quadratic least-squares fit or backgroundb background
run no.
peak height, nA
1 2 3 4 5 6
81.6 82.3 80.6 81.2 83.0 81.6 82.5 83.1 80.8 83.0
7 8 9 10
peak position, V vs. Ag/AgCl peak height, nA -0.6344 -0.6350 -0.6352 -0.6349 -0.6340 -0.6342 -0.6346 -0.6355 -0.6360 -0.6347
80.9 82.0 83.2 81.6 82.0 82.0 81.6 80.8 83.4 80.2
peak position, V
VS.
AgIAgCl
-0.6345 -0.6348 -0.6358 -0.6342 -0.6351 -0.6342 -0.6358 -0.6341 -0.6349 -0.6342
average 82.0 i 0.8 -0.6349 5 0.0005 81.8 t 0.8 -0.6348 2 0.0005 Solutions Differential pulse polarography. Drop time = 5.0 s. Pulse amplitude = - 2 5 mV, Temperature = 22 "C. degassed with argon for 3 0 min prior t o recording a polarogram. a
_I; / _I_/ T
lOnA
I
(b'
-0 8
-0 7
Volt
-0 6
vs
-0 5
Ag/A,Cl
Figure 1. Differential pulse polarogram of 1 M NaCI. Pulse amplitude = -25 mV, drop time = 1.0 s. (a)and (b) linear extrapolations from data obtained at potentials removed from where cadmium electrode process would occur Figure 1 shows the background current recorded by differential pulse polarography on a 1 M NaCl solution at a drop time of 1.0 s over the potential range required for the determination of cadmium. The magnitude of the currents being measured is small, and some noise is present in the response. However, it is clear t h a t the background current cannot successfully be approximated by a straight line. Furthermore, as shown in Figure 1, a linear extrapolation from either extremity of the d a t a range, as required in the real situation, would lead to a poor prediction of the base line in the middle of the data range where the peak due to reduction of cadmium would be observed. In Figure 2, a computer plot of a quadratic least-squares fit to all of the data presented in Figure 1is given. Obviously, the computer implemented approximation of the background current to a parabola is far superior t o the linear one usually employed in manual graphical interpolations. Figure 3 shows t h e determination of lo4 M cadmium in 1 M NaCl using the quadratic least-squares fit to correct for the charging current. In Figure 3a, the raw data are shown with a drop time of 1.0 s and pulse amplitude of -25 mV. A quadratic least-squares fit made from data obtained a t both extremities of the data range provides the curve shown in Figure 3b. Subtraction of curve 3b from raw data in Figure 3a produces t h e corrected differential pulse curve shown in
-0.8
-0.7
-06
-05
V o l t vs Ag/AgCl
Figure 2. Differential pulse polarogram of 1 M NaCl and a computerized quadratic least-squares fit of data. Pulse amplitude = -25 mV, drop time = 1.0 s Figure 3c. In the corrected curve, current values near the foot of both sides of the peak are close to zero and shape analysis and peak position of the observed wave is essentially identical to that obtained a t higher concentrations when the base-line problem is unimportant. From the corrected curve, a quadratic least-squares fit of data enables peak location to be made with a reproducibility of fl mV a t the lo4 M level under the conditions presented in Figure 3. The peak height is reproducible to k2% under the same conditions and both peak position and height agree within the limit of experimental error to values obtained via subtraction of background current obtained from a blank obtained as in Figure 1, providing care is taken to completely remove oxygen from both test and blank solutions when using the latter approach (see later). Representative data a t the I O + M concentration level are presented in Table I. Some options available in the computer program enabling the final data shown in Figure 3c to be obtained should be mentioned. Importantly, in establishing which data to employ in constructing the quadratic least-squares fit, complete flexibility is available and any number of data points may be used as specified by the operator. In Figure 3, the initial points on the most positive potential side of the peak, where the scan is commenced, were not included in the calculation because
340
ANALYTICAL CHEMISTRY, VOL. 51, NO. 3, MARCH 1979
- 0.'8
,
- 0.7
- 0.6 volt
- 0.5 vs
AS/A~CI
Figure 3. Differential pulse polarogram of 1 X M cadmium in 1 M NaCI. Pulse amplitude = -25 rnV, drop time = 1.0 s. (a) Raw data. (b) Background current calculated by quadratic least-squares fit. (c) Final data from which peak height and position are calculated.
I
znA
I
-0.8
- 0.7
I'
\
/
\
- 0.5 1
-0.6
Volt
vs
- 0.8
- 0.7
i
-0.6
- 0.5
Ag/AgCI
NaCI. Pulse amplitude = -25 rnV, drop time = 5.0 s. (a) Raw data. (b) Background current calculated by quadratic least-squares fit. (c) Final data from which peak height and position are calculated.
Figure 4. Differential pulse polarogram of 1 X lo-' M cadmium in 1 M
they are clearly not relevant to defining the base line a t the peak. This is shown on Figure 3a. T h e first few data points obtained commonly had to be rejected with differential pulse measurements because of instrumental distortion associated with them. Data points resulting from a bad drop could also be rejected from the quadratic least-squares fit to obtain the background. The problem of the background current obviously becomes more severe a t lower concentrations and, a t least with differential pulse polarography, it is critically governed by the drop time, with the most favorable faradaic to charging current
ratio being obtained a t longer drop times. Thus, to determine concentrations in the lo-' t o lo-* M concentration range by differential pulse polarography, a drop time of 5 to 10 s needs to be employed, rather than the 1.0 s shown in Figure 3. Shorter drop times are more suitable for higher concentrations, with the trade-off, of course, being the concomitant increase in scan time required to obtain the data when using long drop times, vs. sensitivity. Figure 4 shows the determination of lo-? M cadmium in 1 M NaCl using a drop time of 5.0 s and a pulse amplitude of -25 mV. While the background current is of considerable
ANALYTICAL CHEMISTRY, VOL. 51, NO. 3, MARCH 1979
Table 11. Comparison of Two Different Methods of Background Correction for a 1 x lo-' M Solution of Cadmium in 1 M NaCl with Variable Degassing Time' data corrected by quadratic leastdata corrected by squares fit of subtraction of background backgroundC degasspeak peak position, peak position, ing peak time,b height, V vs. height, v vs. min AgiAgCl nA nA Ag/AgCl 5 8.0 -0,6352 12.3 -0.6382 5 8.2 6.4 -0.6322 -0,6371 5 8.4 -0,6364 5.8 -0.6341 15 8.0 -0,6368 6.8 -0.6362 15 8.2 -0,6340 10.2 -0,6384 15 8.2 -0.6351 10.0 -0,6396 30 8.3 -0,6346 10.6 -0.6384 30 8.2 -0,6359 9.8 -0.6384 30 8.2 -0,6356 8.2 -0.6362 ' Differential Pulse Polarography. Drop time = 5.0 s, pulse amplitude = -25 mV, temperature = 22 " C . b Argon. Background recorded after same time as test solution. magnitude, the final curve after correction is eminently suitable for analytical work. A reproducibility of peak position of f 2 mV and peak height of f 3 % was obtained with the above conditions. A limit of detection of M is obtained with the present computerized instrumentation, a t long drop time with differential pulse polarography, and plots of peak height vs. concentration are linear within the limit of experimental error over the concentration range of lo4 to M as predicted theoretically. We therefore conclude that the quadratic least-squares fit to obtain the base line is extremely successful in differential pulse polarography. When working a t t h e lo-' to M concentration range, t h e base line is critically dependent on the presence of trace amounts of oxygen. In our hands, approximately half an hour's degassing with argon on both t h e blank and test solution was necessary to provide reproducible data when using the background correction method of recording a blank and subtracting the result from subsequent solutions containing trace amounts of cadmium in the same media. Furthermore, because long drop times and slow scan rates are required to determine low concentration, the problem of maintaining oxygen-free conditions while recording a polarogram is a non-trivial problem and, a t the lo-' level, results with a reproducibility of better than f 5 % are very difficult to obtain with this correction method. Additionally, such a process inherently contributes noise to t h e measured response and it is very time consuming. By contrast, when the base line is calculated from a quadratic least-squares fit, variable oxygen levels and the presence of other trace impurities are essentially accounted for in the calculations and, provided products of the oxygen electrode process do not cause interference with the electrode species being determined, extreme care to
341
completely eliminate oxygen is not required. Data obtained under various conditions a t the M level are provided in Table I1 and the superiority of the quadratic least-squares method is clearly obvious. We have therefore reached the conclusion t h a t , despite t h e inherently more complex mathematics involved in the use of the quadratic least-squares fit, results are substantially superior to a simple background subtraction procedure because of the complete generality of the method. While the above discussion is presented with respect to differential pulse polarography, the same approach has been tested with alternating current polarography (phase-selective fundamental and second harmonic), as well as with differential pulse and alternating current. anodic stripping and normal voltammetry a t the dropping mercury and stationary electrodes. Results are equally as impressive with these techniques as for differential pulse polarography, so the widespread applicability of the background correction problem can be appreciated. Overall, we therefore believe the approach to be both versatile and extremely useful. In particular, area growth terms which can cause difficulties when undertaking fast sweep alternating current or differential pulse voltammetric measurements a t a dropping mercury electrode are accounted for (16, 17) in situations where species t o be determined appear as shoulders on another faradaic wave; for example, with species reduced or oxidized near the solvent limit, the quadratic least-squares f i t is also successful in correcting the data for this kind of faradaic interference.
LITERATURE CITED (1) H. Schmidt and H. Von Stackelberg, "Modern Polarographic Methods", Academic Press, New YorkiLondon, 1963. (2) L. Meites, "Polarographic Techniques", 2nd ed.. Interscience, New York/London/Sydney, 1965. (3)J. Heyrovsky and J. Kuta, "Principles of Polarography", Academic Press, New York, 1966. (4) J. B. Flato, Anal. Cbem., 44 (ll),75A (1972). (5) A. M. Bond, "Modern Polarographic Methods in Analytical Chemistry", Marcel Dekker, New York, in press.
(6) "Computers in Chemistry and Instrumentation", J. S. Mattson, H. D. MacDonald, Jr., and H. B. Mark, Jr., Ed., M. Dekker, New York, 1972. (7) A. M. Bond and B. S. Grabaric, Anal. Chlm. Acta, 101, 309 (1978). (8) R. J. Schwall, A. M. Bond, R. J. Loyd, J. G. Larsen, and D. E. Smith, Anal. Chem., 49, 1797 (1977)and references cited therein. (9)J. W. Frazer, L. R. Carison, A. M. Kray, M. R. Bertoglio, and S. P. Perone, Anal. Cbem., 43, 1479 (1971). (10) S.P. Perone, J. W. Frazer, and A. Kray, Anal. Chem.. 43, 1485 (1971). (11) J. H. Christie and R. A. Osteryoung, J , €/ecfrcana/.Cbem., 49, 301 (1974). (12) F. Baurnann, E. Herlicksa, A. C. Brown, and J. Biesch, J . Cbrornatogr. Sci., 7,680 (1969). (13) F. Baurnann, A. C . Brown, and M. 8 . Mitchell, J . Cbromatogr. Sci., 8. 20 (1970). (14) H. A. Hancock, Jr., L. A. Dahm, and J. F. Muldoon, J . Cbromatogr. Sci., 8,57 (1970). (15) A. M. Bond and R. J. O'Halloran. J . €lectroanal. Cbem., 68,257 (1976). (16) H. Blutsein and A. M. Bond, Anal. Chem., 48, 242 (1976). (17) A. M. Bond and 8. S. Grabaric, Anal. Cbem., 51, 126 (1979).
RECEIVED for review March 9, 1978. Accepted December 4, 1978. T h e financial assistance of the Australian Research Grants Committee in support of this work is gratefully acknowledged. B.S.G. also wishes to express his appreciation to the University of Melbourne for providing a Post-Doctoral Research Grant.
