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Anal. Chem. 1980, 52, 1318-1322
Explosives", National Technical Information Service: Springfield, Va., 1978; p 597. (29) Fine, D. H.; Lieb, D.; Rufeh, F. J , Chromatogr. 1975, 107, 351. (30) Fine, D. H.; Rufeh, F.; Lieb, D.; Rounbehler, D. P. Anal. Chem. 1975, 4 7 , 1188. (31) Federoff, B. T.; Sheffield, 0. E., Eds., "Encyclopedia of Explosives and Related Items", Vol. 3; Picatinny Arsenal: Dover, N.J., 1966; p D99. (32) Ref. 31, p C484. (33) Ref. 31, p C613. (34) Ref. 31, p D1584.
(35) Parker, W. L. Proceedings, "New Concepts Symposium and Workshop on Detection and Identification of Explosives"; National Technical Information Service: Springfield, Va., 1978; p 441. (36) Urbanski, T. "Chemistry and Technology of Explosives", Vol. I; Pergamon Press Ltd.: Oxford, England, 1964; p 310.
RECEIVED for review September 17, 1979. Accepted March 26, 1980.
Comparison of Semi-Integral, Semi-Differential, Direct Current Linear Sweep, Direct Current Derivative Linear Sweep, Pulse, and Related Voltammetric Methods by Computerized Instrumentation A. M. Bond Division of Chemical and Physical Sciences, Deakin University, Waurn Ponds 32 17, Victoria, Australia
Computerized instrumentation is used to demonstrate the conslderable dependence of the semidifferential, semi-integral, and derivative techniques on the nature and data manipulation procedures undertaken on the dc current-voltage curve from which these measurements are derived. Provided that the dc linear sweep data are corrected for background current, differences in limits of detection in semi-differential, semi-integral, and derivative approaches are very small. However, altering the dc potential format from linear to staircase or pulsed ramps significantly improves the limit of detection. These techniques and those derived from them are therefore inherently superior to those derived from the linear potential-time ramp.
T h e technique of semi-integral electroanalysis or deconvolution voltammetry, which utilizes the semi-integral of the current time curve has been available for several years (see ref. 1-5 for example). More recently, semi-differential electroanalysis or convolution voltammetry has been developed (6-10) and applied to problems in analytical chemistry. Semi-differential and semi-integral electroanalysis are closely related techniques. Semi-differential electroanalysis, in fact, is simply the derivative of the semi-integral method. Linear sweep vGltammetry is a method intermediate between both of these techniques; however, experimentally it is the simplest to implement because the displayed and directly measured quantity is simply the current, i. T o obtain the semi-integral, m, or semi-differential, e, requires that the current, i, be first measured and then semi-differentiated or semi-integrated via either analog or digital methods. Clearly, these different methods operate on the same electrochemical time scale and in no sense of the word can they be envisaged as independent methods of electroanalytical chemistry. Derivative (first or second) linear sweep voltammetry (11-15) is also another closely related electroanalytical technique derived from the current-voltage curve in linear sweep voltammetry. This approach has been reported as being very successful in improving the analytical usefulness of linear sweep voltammetry. In view of this result, it is not surprising that Smith (16)has suggested that semi-differential techniques (Le., derivative of semi-integral) should prove advantageous 0003-2700/80/0352-1318$01 O O / O
to the semi-integral ones in analytical work. Linear sweep techniques, using a linear potential-time voltage ramp, have less favorable faradaic to charging current ratios than equivalent techniques using staircase or pulsed (17-21) potentials to generate the dc potential. Staircase techniques are therefore inherently more sensitive than their linear sweep counterparts. In principle, semi-derivatives, semi-integral, derivative, etc., methods derived from these staircase or pulse techniques could also be developed. However, when the dc ramp format is changed from linear to pulsed versions, the time scale of the measurement is altered and indeed new considerations apply. When analog instrumentation has been used to generate and process data, many of the above closely related techniques have been developed and discussed almost completely in isolation. While it is true that unique and technique dependent electronic developments were required in the analog work, it is also equally clear from the theory that very few of these techniques and/or concepts are independent ones. Indeed, for a given dc waveform and electrode process, all semi-integral, derivative, and semi-differential responses can be generated from exactly the same experimental data and, in principle, differences should therefore be confined to the method of data manipulation. With analog circuitry, experimental assessment of this hypothesis is difficult to implement. However, with the advent of computerized instrumentation and digital electronics, it becomes very easy to record and store the raw dc data in memory. Subsequently, it then becomes a simple matter to generate sequentially, semi-derivative, semi-integral, first derivative, second derivatives, etc., curves by applying the appropriate mathematical manipulation to the raw data. The requirement, or temptation to treat or report data from any of these methods in isolation or even the need to view them as anything other than closely related techniques therefore vanishes when using computerized versions of instrumentation. With a view to providing a systematic approach of all the above techniques and t o optimizing the performance of all approaches in analytical work, a computerized version of electrochemical instrumentation has been constructed which can collect the raw data and undertake all the required data manipulations and provide the required readout in the areas of semi-integral, semi-differential, and derivative electroanC 1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 5 2 , NO. 8, JULY 1980
alysis. A summary of results obtained with the computerized instrumentation is presented in this paper in an endeavor to demonstrate that, provided the result from the primary dc experiment is known, the analytical chemist can immediately understand the extent and nature of improvements or losses in performance to be anticipated when using semi-integral, semi-differential, or derivative techniques, and, furthermore, decide whether implementation of such data manipulation procedures are warranted.
13'
EXPERIMENTAL All chemicals used were of reagent grade purity. All solutions were thoroughly degassed with nitrogen or argon prior to recording voltammetric curves. Ambient temperatures of (20 f 1)"C were used throughout. Most electrochemical measurements were undertaken with a PAR Model 174 Polarographic Analyzer interfaced to a PDP-11 Mini Computer. Details of this instrumentation and most of the data manipulation procedures are described elsewhere (22-24). A microprocessor controlled function generator (25) was used t o provide staircase waveforms. Other waveforms were generated with conventional analog circuitry. A three-electrode potentiostatic system was used for all measurements with a dropping mercury working electrode, a Ag/AgCl (1 M NaCl) reference electrode, and a platinum wire auxiliary electrode. The potential scan could be commenced at any given period after commencement of the mercury drop growth. RESULTS AND DISCUSSION T h e limit of detection in any analytical technique can be governed by the electronic noise level associated with the background measurement. The reality that each of the semi-integral, semi-differential and derivative voltammetric techniques are derived directly from the current-potential curve found in linear swep voltammetry is clearly revealed when examining the noise and background (nonfaradaic) levels associated with the various signals when derived solely by mathematical manipulation of the same raw data with a computerized system. When separate analog circuits are constructed to develop each technique, different RC network characteristics or different charging current correction approaches can produce apparent limits of detection which are an artifact of instrument design rather than intrinsic merit associated with each method. Figure 1 shows the i-E background or charging current data t h a t can be obtained in 1 M NaCl in the absence of an electroactive species. Figure l a is the single pass data collected with no deliberately applied filtering other than that inherent in playing back data a t slow speeds on an X-Y recorder. Figure l b demonstrates the average result obtained from 25 duplicate experiments, and Figure ICRC filtered data. The raw, nonaveraged data, contain considerable electronic noise which can be supressed by RC damping or minimized by ensemble averaging. T h e background current in the experiment described in Figure 1 arises from charging current associated with mercury area growth (dA/dt) and scan rate (duldt) terms associated with the experiment. This background current could be stored in memory and subsequently subtracted from data to improve the dc experiment. Alternatively, corrections can be made via computing the linear least-squares or quadratic leastsquares fit of data a t potentials removed from the faradaic current. Such computations enable predictions to be made concerning the background current a t potentials associated with the faradaic current (22-24). In certain instances, corrections for background levels made in this manner are preferable to the method of storing the blank in memory and using direct subtraction ( 2 4 ) . Figure 2 provides examples of dc linear sweep voltammetry curves of a 1 X 10-j M cadmium solution in 1 M NaC1. The background and electronic noise associated with data obtained
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Figure 1. Background current in linear sweep voltammetry in 1 M sodium chloride at a DME. Scan rate of 500 m V / s commenced 6 s after commencement of drop growth. (a) Raw data, 1 scan from 1 mercury drop. (b) Average of 25 scans from 25 mercury drops. (c)
Data
averaged by RC damping
in the absence of cadmium as presented in Figure 1 are clearly present along with the faradaic component due to reduction of cadmium. Choosing the data set produced by averaging 25 scans (Figure 3a) and assuming a linear extrapolation of background current as in Figure 3b leads to the background corrected curve in Figure 3c. In the absence of any significant background current component in Figure 3c and in view of the
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tegration. Consequently the signal-to-noise ratio associated with the derived semi-integral (Figure 3d) is superior to the parent curve in Figure 3a. Figure 3e demonstrates the application of a brute force least-squares fit of an assumed semi-integral wave shape to the data in Figure 3d.
E = E l j 2+ RT In nF
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Figure 2. Linear sweep voltammogram of M cadmium(I1)in 1 M NaCl at a DME. Raw data presented without any averaging. Scan rate of 500 mV/s commenced 10 s after commencement of drop growth
generally acceptable noise level it is no surprise that computing the semi-integral from these data provides the relatively high quality semi-integral curve shown in Figure 3d. Integration in electronics always reduces the noise level as does semi-in-
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( md m7 ) -
(md = limiting semi-integral, m = semi-integral.) This calculation demonstrates that high quality semi-integral data corrected for charging current data can be obtained at the 10” M level for cadmium and that improving the quality of the dc linear sweep data provides far superior performance than that usually associated with the technique. The least-squares fit of the data provides a smoothed curve from which md and Eliz can be computed statistically. A value of E l j zof (-0.6320 f 0.0002) V vs. Ag/AgCl was obtained in this manner. This compares with a polarographic E l j z value of (4.632 f 0.001) V vs. Ag/AgCl obtained a t the M concentration level. Taking the derivative of the least-squares smoothed semiintegral in Figure 3e provides the semi-differential curve presented in Figure 3f. The peak potential of the semi-differential curve is (0.633 f 0.001) V vs. Ag/AgCl, in close agreement with Eli2. Directly computing the semi-differential
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Figure 3. Linear sweep semi-integral and semi-differential curves of M cadmium(I1)in 1 M NaCl at a DME. Average of 25 scans. Scan rate of 500 mV/s commenced 10 s after commencement of drop growth. (a) Linear sweep curve. (b) Linear extrapolation of background current. (c) Background corrected linear sweep curve. (d) Semi-integral curve. (e) Least-squares fitted semi-integral curve. (f) Semi-differential curve
ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
response from data presented in Figure 3c or the derivative of data in Figure 3e provides a much noisier response than shown in Figure 3f. Direct computation of the semi-differential curve from RC damped data provided in Figure 3a leads to a low noise level response being obtained but is accompanied by slight distortion of the i-E curve, the distortion having its origins in the applied RC filtering. Direct computation of the semi-integral from data in Figure 2 confirms that electronic noise is lowered by the mathematical manipulation, but background to faradaic current values are relatively poor. Indeed, if using this direct approach traditionally employed with semi-integral analog instrumentation, M solutions become difficult to use in the analytical sense and on this basis one could conclude that semi-integral analysis is a rather inferior method. Conversely, with the semi-differential, the faradaic to background current values are improved at the expense of increased electronic noise in using the algorithm directly on data contained in Figure 2. Relative advantages obtained with analog circuitry could therefore be solely a function of the filtering rather than reflecting intrinsic merit. Examination of concentrations of cadmium in the lo4 to M concentration range in 1 M NaCl not unexpectedly confirms that unless an adequate dc linear sweep response corrected for background current can be obtained, semi-integration in the analytical context provides data considerably inferior to the dc linear sweep curve. Conversely, advantages in the semi-differential mode compared with the dc linear sweep method were marginal; the completely symmetrical peak shaped response and slightly more favorable faradaic to background current ratios offering slight improvement in readout format (26). It is well known that the most favorable faradaic to charging current ratio is obtained a t slow rates in linear sweep voltammetry. Figure 4 demonstrates the improved response at lower scan rates for determining lo* M cadmium in 1M NaC1. The need to measure lower faradaic current leads to increased electronic noise. However, the more favorable faradaic to charging current ratio makes the cadmium response readily seen a t the lower scan rate. Semi-integrals and semi-differential of the slower scan rate data are correspondingly improved under these conditions. The concentration range 5 X to 2 X M cadmium in 1 M NaCl encompassed the limit of detection of all of the methods of dc linear sweep, semi-integral, semi-differential, and first derivative dc linear sweep when used under optimized conditions with computerized instrumentation and a t a scan rate of 50 mV/s. The origin of the above conclusion is of course that all techniques so far considered are very closely related because they use the same dc waveform. Provided high quality data of low noise level and corrected for charging current can be obtained with computerized instrumentation in any of the modes, then it logically follows that the data can be transposed to an alternative form to provide analytically closely related performance. In contrast to the above sub-set of techniques derived from the dc linear sweep method, when altering the applied waveform to, for example, a pulse technique, then a new and possibly a fundamentally more favorable faradaic to charging current ratio will be observed from this procedure. Figure 5 shows a fast sweep normal pulse voltammogram for reduction of M cadmium in 1 M NaC1. Even without any data manipulation strategies, high quality data equal to or better than the semi-integral method obtained under optimum conditions are obtained as shown in Figure 5a. Background correction (Figures 5b and 5c), least-squares smoothing (Figure 5d), and differential readout (Figure 5c) provide for a highly successful data manipulation routine as used previously on
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Figure 4. Linear sweep voltammograms of lo-' M cadrniurn(I1)in 1 M NaCl at a DME. Scan commenced 6 s after commencement of drop growth. Average of 25 scans. (a) Scan rate = 500 mV/s. (b) Scan rate = 50 mVls
the semi-integral, semi-differential series of curves. A detection limit of 8 X to l X M is obtained with this approach for cadmium in 1 M NaCl using the computerized instrumentation. Using a staircase waveform, an alternative series of closely related techniques with essentially the same detection limit range is obtained. However, using fast sweep differential pulse voltammetry, which has an even more favorable faradaic to charging current ratio than the pulse method, leads directly to the result presented in Figure 6 at the M level. Clearly, superior results are obtained directly and without any complex mathematical manipulation with this approach than with any of the others considered. The detection limit of approximately M for cadmium with this technique (24) confirms the analytical superiority of the differential pulse voltammetric method. Studies with computerized instrumentation on a range of other techniques such as anodic stripping voltammetry a t hanging mercury drop and thin film electrodes, and in studies on irreversible electrode processes confirm the generality of the above conclusions. That is, optimizing the raw data with the dc linear sweep or stripping leads to optimum performance in the semi-integral, semi-differential, or derivative approaches and that under instrumentally equivalent conditions where the dc experiment has been optimized with respect to electronic noise and background correction, limits of detection are not markedly different within the sub-set of related ap-
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
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4 6 5
Figure 6. Differential pulse voltammogram of lo-’ M cadmium(I1) in 1 M NaCl at a DME. Duration between pulses = 80 ms. Pulse width = 40 ms. Scan rate = 50 ms. Pulse amplitude = -50 mV. Scan commenced 5 s after commencement of drop growth. No averaging
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faradaic to charging current ratio. This added feature is not inherently present in the dc linear sweep method, and thus, for most classes of electrode process and electrodes, the dc techniques or their mathematically related variations will be analytically inferior to the pulsed or staircase approaches. In summary, it logically follows that any mathematical “trick” improving the dc based sub-set can be applied t o the pulse versions. Therefore, the conclusion that usually eventuates from this logical sequence is that the method with the analytically most advantageous raw data will remain superior after having had the raw mathematical manipulation applied to it. This has been seen to be so when using computerized instrumentation.
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ACKNOWLEDGMENT The computer programs used in this work were written by B. S. Grabaric, and grateful acknowledgment of this contribution is given.
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LITERATURE CITED
-6 5c
Figure 5. Normal pulse voltammograms of M cadmium(I1) in 1 M NaCl at a DME. Duration between pulses = 80 ms. Pulse width = 40 ms. Scan rate = 50 mV/s. Scan commenced 0.2 s after commencement of drop growth. No averaging. (a) Normal pulse voltammogram. (b) Linear extrapolation of background current. (c) Background corrected nwmal pulse voltammogram. (d) Least-squares fitted normal pulse voltammogram. (e) Pseudoderivative normal pulse voltammogram
proaches. Of course, resolution and ease of use of a method providing a peak-type readout (semi-differential) are superior to those with sigmoidal shaped readout (semi-integral). Methods of electroanalysis having their origins in staircase, normal pulse, or differential ramps employ a procedure to discriminate against charging current or provide improved
L. Nadjo, J. M. SavBant, and D. Tessier, J . Nectroanal. Chem., 52, 403 (1974), and references cited therein. K. B. Oldham, Anal. Chem., 44, 196 (1972), and references cited therein. H. W. Van den Born and D. H. Evans, Anal. Chem., 46, 643 (1974), and references cited therein. M. Goto and K. B. Oldham, Anal. Chem., 48, 1671 (1976), and references cited therein. A. M. Bond, “Modern Polarographic Techniques in Analytical Chemistry”, Marcel Dekker, New York, 1980. M. Goto and D. Ishii, J . Elecboanal. Chem., 61, 361 (1975). P. DalwmDle-Alford, M. Goto. and K. B. Oldham, J . Electroanal. Chem.. 85, 1 (1977). P. Dalrymple-Alford, M. Goto, and K. B. Oldham, Anal. Chem., 49, 1390 11977) M. Goto, K . Ikenoya, M. Kajihara, and D. Ishii, Anal. Chlm. Acta, 101, 131 (1978). M. Goto, K. Ikenoya, and D. Ishii. Anal. Chem., 51, 110 (1979). F. B. Stephens and J. E. Harrar, Chem. Instrum., 1, 169 (1968). S.P. Perone, J. E. Harrar, F. B. Stephens, and R. E. Anderson, Anal. Chem., 40, 899 (1968). T. R. Mueller, Chem. Instrum.. 1. 113 (1968). W. F. Gutknecht and S. P. Perone, Anal. Chem., 42, 906 (1970). L. 8. Sybrandt and S. P. Perone, Anal. Chem., 43, 382 (1971). D. E. Smith, Anal. Chem., 48, 221A (1976). C. K. Mann, Anal. Chem., 33, 1484 (1961); 36, 2424 (1964): 37, 326 (1965). J. H. Christie and P. J. Lingane, J . Electroanal. Chem., I O , 176 (1965). D. R. Ferrier and R . R. Schroeder, J . Electroanal. Chem.. 45, 343 (1973). D. R. Ferrier, D. H. Chidester, and R. R. Schroeder, J . Electroanal. Chem., 45, 361 (1973). J. J. Zipper and S. P. Perone, Anal. Chem., 45, 452 (1973). A. M. Bond and B. S. Grabaric, Anal. Chlm. Acta, 101, 309 (1978). A. M. Bond and B. S. Grabaric, Anal. Chem., 51, 126 (1979). A. M. Bond and B. S . Grabaric, Anal. Chem. 51, 337 (1979). A. M. Bond and A. Norris. Anal. Chem., 52, 367 (1980). R. F. Lane, A. T. Hubbard, and C. D. Blaha. J. Nectroanal. Chem., 95, 117 (1979).
RECEIVED for review November 26, 1979. Accepted April 1, 1980. Financial assistance from the Australian Research Grants Committee in the support of this work is appreciated.
