Analytical Applications of an On=Line Digital Computer in Fast-Sweep Derivative Polarography S. P. Perone,’ J. E. Harrar, F. B. Stephens, and Roger E. Anderson Chemistry Department, Lawrence Radiation Laboratory, Livermore, Calif. A small digital computer has been interfaced to electroanalytical instrumentation and has been utilized, on line, in conjunction with fast-sweep derivative polarographic experiments. The applicability of this arran ement for providing semiautomated electroanafysis was investigated. When the computer processing was preceded by an analog 2nd-derivative data reduction, it was possible to obtain reliable analytical data, automatically, over a concentration range of 3 to 5 orders of magnitude. Resolution of closelyspaced reduction waves was possible. The effects of background noise on computer processing were investigated. In addition, by using the computer to provide ensemble-avera ing, it was possible to extend the analytical sensitivity y at least an order of magnitude.
fl
SEVERAL recent publications have described the use of digital data acquisition techniques in electrochemical experiments (Z-3). The automatic digitizing of electrochemical data was shown to provide some distinct advantages over analog data acquisition techniques. For example, Booman (1)demonstrated that precise electrochemical data could be acquired with rapid time resolution (50 pseconds) and a large dynamic range (5 decades) within the same experiment. Brown, Smith, and DeFord (2) showed that digitizing and multiplexing could provide data from complex experiments in a format readily compatible with the large processing computer. The obvious extension of this earlier work is to include the digital computer directly in the experimental set-up. With the present availability of small digital computers, this becomes feasible. Lauer, Abel, and Anson (4) reported recently that they have successfully integrated a digital computer into their experimental instrumentation involving chronocoulometric adsorption studies. Lauer and Osteryoung (5) have reported also the successful interfacing of a digital computer to electrochemical apparatus, utilizing software to generate the necessary functions for a variety of standard electrochemical techniques. The basic objective of the work reported here was to provide a start toward the complete automation of certain types of electroanalytical procedures. The approach taken was to effect a hardwaresoftware link between a small digital computer and appropriate electroanalytical instrumentation; and to develop a program to provide automatic data acquisition and processing. It was desired to develop an overall system with sufficient reliability and applicability to be used routinely for analysis of diverse electroactive sample solutions. On the other hand, sufficient versatility was desired to allow 1 Present address, Department of Chemistry, Purdue University, Lafayette, Ind. 47907. Author to whom correspondence should be addressed.
(1) G. L. Booman, ANAL.CHEM., 38, 1141 (1966). (2) E. R. Brown, D. E. Smith, and D. DeFord, Zbid.,p 1130. (3) G. Lauer and R. A. Osteryoung, Zbid.,p 1137. (4) G . Lauer, R. Abel, and F. C. Anson, Zbid.,39,765 (1967). (5) G. Lauer and R. A. Osteryoung, 154th National Meeting ACS, Chicago, September 1967.
94550
the operator to cope with nonroutine problems and to conduct fundamental studies. It was expected that if the experiments with the small computer were successful, the methodology could then be utilized to connect the electrochemical instrumentation to an available remote time-shared computer system. The basic electroanalytical technique selected for these studies was fast-sweep derivative polarography with a controlled-drop-time dropping mercury electrode (DME). This technique was selected for several reasons. Because the time scale of the experiment is short and each cycle is automatically repetitive, digital data handling is inherently advantageous and the method is amenable to signal- or ensemble-averaging. Also, previous studies (6-8) have shown that improved resolution and sensitivity are obtainable with derivative voltammetry, and this technique has the further advantage that it minimizes the amount of data reduction required of the digital computer-i.e., differentiation minimizes base line effects (6), with the 2nd derivative being particularly effective. EXPERIMENTAL Electroanalytical Instrumentation and Apparatus. The fast-sweep derivative polarograph used was designed and constructed at the Lawrence Radiation Laboratory. The details of its design and performance are described elsewhere (9). The instrument circuitry is based on solid-state operational amplifiers, with 3-electrode potentiostatic and dative derivative circuitry similar to that used by Perone and Mueller (6). The polarograph provides for conventional, 1st-, or 2nd- derivative readout, with both single electrolysis cell and differential operation with matched cells. Output signals are conditioned by a 20-Hz, 3rd-order, active low pass filter. Current-voltage curves are displayed on a Hewlett-Packard (Palo Alto, Calif.) Model 141A variable persistence oscilloscope with a Model 1401A amplifier plug-in. Photographs of signal traces were taken with a Hewlett-Packard Model 197A oscilloscope camera using Polaroid 3000 speed, Type 107 film. The electrolysis cell assembly included DME working electrodes, spiral platinum wire counter electrodes and Beckman No. 39270 SCE reference electrodes. Salt bridge tubes for the reference and counter electrodes were asbestos fiber tip tubes available from Coleman Instruments (Maywood, Ill.) as their Cat. NO.3-702 reference electrode reservoirs. The DME was equipped with a mechanical drop dislodger controlled by the timing circuits of the polarograph. The timing and sequence of operations is the same as that of conventional cathode ray polarography (IO). When the polarograph is switched to operate, the initial potential is applied to the cell. With time zero referenced from the time of disS. P. Perone and T. R. Mueller, ANAL.CHEM.,37,2 (1965). S. P. Perone and J. R. Birk, Ibid.,37, p 9 (1965). C. V. Evins and S. P. Perone, Zbid.,39,309 (1967). F. B. Stephens, E. Behrin, and J. E. Harrar, U. S. At. Energy Comm. Rept. UCRL-50374 (1968). (10) H. M. Davis and J. E. Seaborn, “Advances in Polarography,” I. S. Longmuir, Ed., Vol. 1, Pergamon Press, New York, 1960, p 239.
(6) (7) (8) (9)
VOL 40, NO. 6, MAY 1960
a99
CPU
I/o
500Hz CLOCK
I 1
0 ~
ACTIVE
F.F.
0
-+ F L A G F.F.
: ENABLE F.F.
: INTERRURT
I1
:
-C
E ENABLE
Figure 1. Interface logic Experimental Sync Pulse coincides with start of voltammetric potential sweep. Enable flip-flop (F.F.) is set by a software Enable Command when the computer is ready to take data. When Enable F.F. is set, the Active F.F. can be set by the Experimental Sync. Pulse, and this initiates repetitive data acquisition steps at the rate of one every 2 msec. (interrupt request every 2 msec.) The 500-Hz clock train is enabled when the Active F.F. is set, so that the first interrupt pulse is seen exactly 2 msec later. The software initiated check and clear flag command verifies that the interrupt is coming from the experimental device, and an analog-to-digital conversion is initiated. A Disable Command is initiated by software after 512 data points are taken. This clears the Active F.F. and stops data acquisition. For successive runs an Enable Command is given immediately to re-initiate the whole cycle. If no further data acquisition cycles are required, no Enable Command is given, and the data processing cycle is initiated
lodgement of the previous mercury drop, the sweep is initiated after a "wait" time adjustable from 2 to 10 seconds. Sweep duration is adjustable from 1 to 3 seconds and sweep rates of 0.1 to 1.0 V/second are available from an internal function generator. A scope sync pulse is supplied at the start of the voltage sweep for synchronization with the readout oscilloscope sweep. This pulse was also used to initiate a cycle of data acquisition by the computer system. At the end of the voltage sweep, a pulse is applied to the DME drop dislodger to knock off the drop. At this time the control potential returns to the initial value and a new cycle begins. The electrolysis cell was partially submerged in a thermostated water bath maintained at 25.00" i 0.02' C. All solutions were deaerated for at least 15 minutes with high-purity nitrogen. All chemicals used were reagent grade. Solutions were prepared with deionized water. Digital Hardware. The digital computer used in this work was a Digital Equipment Corp. (D.E.C.) (Maynard, Mass.) Type PDP-8/S. This is a 12-bit, 4096-word core memory machine, with a nominal cycle time of 8.0 pseconds. Peripheral devices included a 12-bit analog-to-digital converter (A.D.C.) constructed from D.E.C. Flip-Chip logic modules, with a conversion time of 45 pseconds and a working input range of 0 to -10 volts; an ASR-33 Teletype; a D.E.C. Model 750, 300 characters/second paper tape reader; and a Tally Corp. (Seattle, Wash.) Model 424 paper tape punch. Interfacing between the computer and the electroanalytical instrumentation was accomplished by utilizing the D.E.C. Logic Laboratory and various D.E.C. logic modules. Peak-to-peak signals of 5-10 volts were required by the A.D.C. in order to take maximum advantage of its resolution of 1 part in 4096. Signal inversion was also required for those cases where the peaks of interest were not of the required polarity. Thus, inverter-amplifier circuits utilizing Philbrick
900 *
ANALYTICAL CHEMISTRY
Researches Inc. (Dedham, Mass.) Model P65AU operational amplifiers were used to feed the instrument output to the A.D.C. In addition, the resultant output signal was biased by -5.000 volts so that the A.D.C. would see both positiveand negative-going peaks. The bias voltage was obtained from a mercury battery circuit. Auxiliary Equipment. A Quantek Laboratories (Whippany, N. J.) Model 420 noise generator was used to supply broadband noise for the synthesis of artificially noisy signals. A Tektronix, Inc. (Beaverton, Ore.) Type 1A7 oscilloscope plug-in was used as a bandpass filter to define the noise bandwidth. Signal levels were measured with a John Fluke (Seattle, Wash.) Model 910A ac rms voltmeter. A HewlettPackard Model 3300A function generator was also used to generate synthetic waveforms and to provide superimposed noise of known frequency. Signals and noise were mixed with a Philbrick P65AU operational amplifier adder circuit. RESULTS AND DISCUSSION
The primary reason here for including a small digital computer on-line in electroanalytical experiments was to provide semiautomated analyses of appropriate electroactive solutions. Therefore, several experiments designed to evaluate the capabilities and limitations of the software and hardware involved were carried out. Because the program was written for a smoothed signal, one primary concern was what effect noise would have on the data processing. Another question was how well could the various reduction waves in a complex mixture be resolved. Also, the reliability, utility, and precision of the overall system for automatic analysis of diverse sample solutions had to be evaluated. Finally, the question remained as to what extensions or improvements upon exist-
INSTRUMENT FUNCTIONS
11
COMPUTER FUNCTIONS
I
SAMPLE& INSTRUMENT PREPARATION INSTR OF VOLTAMMETRIC BEHAVIOR EXPT'L SYNC
V'LE
SYNCHR,ONIZE PULSE FOR EACH SWEEP
4
1-512
PULSES
Figure 2. Timing and logic for two successive data acquisition cycles ing analytical Capabilities might be made as a result of having the digital computer available on-line. Software Characteristics. The working program at its present stage of development, occupies slightly less than 1.4K of core memory. In addition, 1024 core locations are required for storing 512 data points in double-precision (24-bit) words. Thus, about 1.6Kof core memory locations are still available for further programming modifications, expansion of data storage facilities, and certain operating programs such as tape loading routines. Because of paging requirements (11) in the D.E.C. 12-bit computer, the amount of core space used is not presently occupied with maximum efficiency. Rearranging the existing program to occupy core with maximum efficiency could increase available core space by about 400 locations. The present program includes the capabilities of: taking and storing data at a rate determined by the interface logic; performing double-precision addition of data points in the ensemble-averaging mode; carrying out ensemble averaging (2 to 2048 averaging cycles) and normalizing final results; processing the final data; locating and measuring uni-directional peaks in the current-voltage curve ; providing diagnostics indicating noise level and the presence of broad peaks; printing out the final results, including the diagnostics; printing out, if desired, all 512 data points for a given run or averaged runs (the data dump); obtaining any specified number of replicates and, finally, allowing itself to be altered on line by the operator, using the teletype keyboard for communication with the computer. This last-mentioned capability, allowing on-line program changes, is restricted to some 12 program parameters. These include specification of the number of replicates to be taken, the number of signal-averaging cycles for each replicate, current- and potential-thresholds below which the computer is instructed to ignore any peaks which occur, and several of the criteria used in processing the current-voltage curve. In addition, the operator can issue several commands via the teletype. These include start; repeat; reset; program change; and data-dump commands. (11) "Small Computer Handbook," Digital Equipment Corp., Maynard, Mass., 1967.
Figure 3. Flowchart of computer and instrmnental functions
Interface Characteristics. The interface logic and timing characteristics are shown in Figures 1 and 2. In initial work a D.E.C. Type R-405 2-MHz crystal clock provided the time base. This was scaled down to a count rate of 500 Hz for the data acquisition process. The scaling logic was automatically initialized for each run so that the first data point was taken at 2 mseconds after the start of the sweep with an absolute uncertainty of f25 pseconds. Later work was performed with a gated D.E.C. Type 401 variable clock adjusted to 500 Hz; pulse-to-pulse jitter of this module is specified as less than 0.2 %. (Copies of the complete program listing and interface schematic diagram are available upon request.) Complete System for Semiautomated Electroanalysis. The flowchart in Figure 3 shows the roles of the digital computer and the electrochemical instrumentation in providing semiautomated electroanalysis with the present experimental design. The flowchart emphasizes the fact that the electrochemical instrumentation and computer are each free-running and independent, except that the data acquisition cycle in the computer is synchronized with the voltammetric sweep. This arrangement is perfectly adequate in this case because the total experimental cycle time is as short as the D.M.E. drop-life (3 to 6 seconds), and therefore no more than a few seconds delay are ever encountered because of the computer and electrochemical instrumentation being out of phase. For more lengthy experiments, it would be desirable to have the computer initiate the experiment by output command. Figure 4 shows a typical sequence of input/output statements and the resultant computer print-outs for the analysis of a sample solution. The computer statements have been underlined in the dialogue between operator and computer. All input statements are in octal, 2's complement notation (11) as it is most convenient to communicate with the comVOL 40, NO. 6, MAY 1960
901
TYPE R B T S I R B T N S I T A B U ~ T A Y D I 7 A B B K l f A B S T . t A B U S T s T ~ ~ D S T ~
AVGTBrP2AVGiITRSLDsETRSLDt 0400J 0400J 7775) 77751 7650) 7650) 7775) 7775) 0001 J 0000 J 04001 2700)('=TJ?
G /MXI= 1945 IMX3= a000 I M X S 0000 ENIT= 1408 NOISY=0000
E M X I = 1674 EMX3r 0000 EMXSr 0000 EEND= 1980 TRBLSs0000
I M X O ~ 0e00 JMX4= 00B0 IMX6r 0000
EMX2r 0 0 0 a EMX4. 000Q EMX6m 0 0 0 0
RPT? Figure 4. Typical input/output statements for sample analysis puter in this way. By virtue of a program subroutine for conversion, the numerical results in the output statements and the data dump are presented in decimal form. In the output statements (underlined), IMXl refers to the value of the peak height and EMXl to its location. Up to 6 peaks can be indicated in a scan. ENIT and EEND designate the first and last locations in memory of the voltammetric wave data. Diagnostic indications of excessive noise and broad peaks appear in NOISY and TRBLS as numbers other than zero. Quantitative Results. PROCESSING CAPABILITIES AND LIMITATIONS. Evaluation of the processing capabilities and limitations of the software involved a determination of the effects of noise and signal levels, as well as the ability to resolve closely spaced reduction peaks. The processing routine used for locating a peak involved scanning the stored data points until a sharply decreasing slope indicated a peak had been passed. At that point the scan is reversed until a sharply decreasing slope is indicated again. The mid-point between those two points is identified as the peak. The peak-location processing criteria over which the operator has control are specification of a minimum decreasing slope which must be exceeded and the number of consecutive data points over which that slope must be established. These criteria were varied in studies which provided the following evaluations of the software. Voltammetric data were processed under various conditions of noise level and bandwidth by superimposing noise from an electronic noise generator on the voltammetric signals. It was found that the degree of sensitivity to low-level noise could be diminished within limits by varying the peak-location processing criteria discussed above. However, at some point, lowered noise sensitivity resulted also in insensitivity to the voltammetric peaks. The degree of freedom available depended on the signal-to-noise ratio and, to some extent, on the noise bandwidth. An example of a test system is given in Figure 5 , which shows the derivative voltammetric signal alone and with superimposed 100-kHz bandwidth noise. For this system, with the noise greater than 0.4 V rms, it was necessary to employ ensemble averaging to resolve the main peaks from the noise. One hundred and twenty-eight averaging cycles were required when the noise level reached 0.86 V rms. Moreover, as might be expected, resolution becomes more difficult 902
ANALYTICAL CHEMISTRY
Figure 5. Synthetically noisy voltammetric data for software evaluation 30.6 pg/ml CU(II), 49.8 p g / d P b o in 1.OM HCI; 1st-derivative read-out; scan rate 1.0 V/sec; initial potential +0.10 V us. SCE; horizontal scale, 0.1 V/div; vertical scale, 2.0 pA/sec/div, 1.0 V/div A . (Upper trace) Without superimposed noise B. (Lower trace) With superimposed 0.86 V rms, 100-kHz bandwidth noise
as the noise bandwidth approaches the frequency of the sample waveform, at constant noise power. In evaluating the software capabilities of resolving reduction waves in mixtures of electroactive components, several factors concerning the limitations of this system should be considered. First, only a finite number of data points can be taken in a run-512 in this system. With the basic 4K core memory computer, some voltage axis resolution was sacrificed to provide additional core space for double-precision computations and to allow for program modifications. Thus with the sweep rates and sweep durations usually employed, the resolution ranged between 4 mV/data point and 0.2 mV/data point. In the work reported here, the resolution was 2 mV/data point for a 1.O Vlsecond sweep and 1 mV/data point for a 0.5 V/second sweep; for the analytical investigations this resolution appeared to be quite adequate. The overall resolving power of the system involved not only the density of data points, but also the software characteristics-Le., how many data points were required to allow the computer to locate a peak? Obviously, the two criteria for resolution are interrelated. For a higher density of data points, more are required to locate a peak with reliability. The converse is also true. However, with lower data density the inherent accuracy goes down. This problem of resolution was investigated experimentally by taking advantage of the ability to vary the processing criteria in the program with the computer on-line. Thus it was found that, for smooth data, and at 2 mV/data point, the processing criteria could be adjusted such that a minimum of 7 data points were required to locate a peak with acceptable
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Figure 6. 2nd Derivative voltammetric curves for 2.1 X IO-' Cd(1I) in 1.OM KCl Scan rate, 1.0 V/sec differential mode. Initial potential, -0.20 V us. SCE A . Oscilloscope trace, single scan Vertical scale 1.0 V/div
B. Computer average of 64 scans Total analysis time, 3 min
Horizontal scale 0.1 sec/div
*
precision (within 1 data point) and reliability. Moreover, as long as the peaks of interest were 1 to 5 V in size (and not grossly distorted), the number of data points required was always within 10 to 15. As indicated earlier, for the case where non-smooth, or noisy, signals are to be analyzed, the processing criteria can be adjusted, within limits, to provide relative insensitivity to the noise, while still locating the main peaks. However, the resolution is considerably diminished, and 15 to 30 data points may be required to locate a peak for a reversible, 2-electron process. Moreover, the accuracy and reliability can be seriously diminished. Experimentally, the resolving power of the program was tested for the reduction of a mixture of Cd(I1) and In(II1). The voltammetric peaks are separated by less than 50 mV,
and even the 2nd-derivative read-out does not completely resolve the two reduction processes. However, the computer had no difficulty in locating and measuring the closely spaced peaks. Thus, with further program modifications, it might be possible to correct overlapping peaks for mutual distortions. ANALYTICAL DATA.As a critical test of the complete system, two electrochemical processes were studied over a concentration range of several orders of magnitude. The systems examined were Cd(I1) and Pb(I1) in 1.OMKC1. An overall objective of the study was to determine the general utility and precision of the digital data acquisition and computer processing as applied to fast sweep polarography. A specific objective was to determine whether extensions of analytical precision and sensitivity could be attained by using
Table I. Computer-Processed Derivative Voltammetric Data Cd(II) in 1.OM KCI, differential 2nd-derivative mode, scan rate 1.0 V/sec Ip" = negative-going peak height, no base line correction 5 Ensembles
10 Single scans
16 Scans each Ip", mean
Ip", mean
Concn. (c)M 1.0 x 10-3
pA/sec2 25930 2614 257.5 25.78 5.745
1 . 0 x 10-4 1.0 x 10-6 1.0 x 10-6 2 . 1 x 10-7 Ip"/Ccalcd. from largest ensemble.
s
%
0.11 0.21 0.42 3.6 10.0
pA/sec2 25910 2617
s
Z
32 Scans each Ip", mean
pA/sec2
s
64 Scans Each
IPOIC
Zp",mean pA/sec2
s
%
0.09 0.13 256.0 25.88
0.50 2.1
26.02 5.592
0.5 1.3
CtA/seczl P M
25.91 26.17 25.60 26.02 26.63
Table 11. Computer-Processed Derivative Voltammetric Data Pb(I1) in 1.OM KCI, differential 2nd-derivative mode, scan rate 1.0 V/sec Ip" = negative-going peak height, no base line correction 5 Ensembles 10 Single Scans 16 scans Each 32 Scans Each 64 Scans Each IP"/C Ip", mean I p K ,mean Ip", mean Ipw,mean crAIsec2I Concn. ( C ) M pA/secZ s % pA/sec2 8 % pA/secZ s % clA/sec2 s % WM 1 . 2 x 10-3 43440 0.25 4091 0.22 1 . 2 x 10-4 1 . 2 x 10-6 407.7 0.44 1 . 2 x 10-6 40.12 4.3 1 . 2 x 10-7 3.757 17 Ip*/Ccalcd. from largest ensemble.
43430 4099 407.1 39.72
0.04 0.00 0.08 2.2
406.9 39.63 3.078
0.09 0.83 8.3
40.31 3.181
0.68 6.9
36.19 34.16 33.91 33.59 26.51 ~
VOL. 40, NO. 6, MAY 1968
903
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the ensemble averaging capabilities of the on-line computer. An additional objective was to ascertain the concentration range over which it was possible to obtain quantitative analytical data without modification of the simple analog and digital data reduction schemes to account for non-zero base line. In order to minimize base line effects, both 2nd derivative and dual-cell differential, or subtractive (IO), polarography were employed. Tables I and I1 present the results of the concentration study using standard Cd(I1) and Pb(I1) solutions. The entries in the table were obtained by taking the values of 10 single scans and 5 ensembles from the Teletype printout and averaging these values manually to obtain an estimate of the mean and standard deviation. No corrections of the raw data for base line were made. The precision of the measurements at the higher concentrations was excellent even without ensemble-averaging and little advantage was gained with it. At the lower concentrations considerable improvement was evident with averaging; the statistical expectation that the precision should improve as the square root of the number of scans per ensemble was in general borne out. At the lO-7M concentration level for both Cd(I1) and Pb(II), because of the high noise level relative to the voltammetric signal, the computer system did not indicate the voltammetric peaks reliably on single scans. The readout always contained many noise peaks in addition to the voltammetric peak, and occasionally only noise peaks were indicated. The ensemble-averaging resulted in sufficient smoothing of the data so that when it was searched by the computer program, the effects of the noise were significantly reduced. However, with the 1.2 X lO+M Pb(I1) solution, for which the peak-topeak noise level was nearly the same as that of the voltammetric signal, performance was still not very satisfactory even with 64 scans per ensemble. The advantage of ensemble-averaging is more clearly illustrated by the experiments with the 2.1 X lO-7M Cd(I1) solution. Figures 6A and B show the result of a single scan with this solution and a plot of the computer-averaged data from 64 scans. It is obvious that the signal-to-noise ratio of the data has been significantly increased by the averaging process. In this case the ensemble-averaging method of smoothing was 904
e
ANALYTICAL CHEMISTRY
B. Computer average of 128 scans Total analysis time, 6 min
more valuable than additional analog filtering because the frequency components of the noise were close to those of the signal. The data of Table I indicate that analyses of Cd(I1) solutions accurate within 1 to 2% would be possible over the entire concentration range without background corrections. This range is more restricted in the case of Pb(I1) (Table 11). Although not studied in detail here, it appeared that the 2nd derivative mode of operation, by itself, was sufficient to eliminate base line corrections down to about 10-6M. Below this level, differential operation was required, along with the ensembleaveraging for improved precision. Of course base line effects, principally due to the charging current, vary with the potential region where the voltammetric wave of interest occurs. It was noted that additional freedom from base line corrections could be obtained by measurement of the peak-to-peak magnitude of the 2nd derivative wave. However, with the present system this requires separate scans for measurements of both the positive-going and negative-going peaks. Figures 7 A and B show the signals obtained in the analysis of a sample of high-purity boron. Although the single scan signal-to-noise ratio was not as low as for the data of Figure 6, because of lower required instrumental sensitivity, the benefits of ensemble-averaging were still realized in the precision of the measurements. The sample solution was saturated in boric acid, and was obtained by dissolution of the boron in HN03-H2S04; thus only single-cell operation was possible. The analog derivative circuitry easily resolved the voltammetric waves of Cu and Cd; the species causing the apparent waves between those for Cu and Cd, and superimposed on the charging current, were not identified. The concentrations of Cu and Cd in the original boron, determined by standard addition measurement of both the positive-going and negative-going peaks, were 15 and 16 ppm, respectively, and about 10-6M in the polarographic cell. CONCLUSIONS
The system described here is obviously far from being complete. Many diverse extensions and modifications appear attractive. For example, blank solution curves might be obtained and stored in the computer memory for automatic
base line compensation. Software routines could also be included for further data smoothing, peak resolution, calibration of analytical data in concentration units, location of both positive and negative peaks, and several other processing routines to minimize operator data handling. In addition it would be desirable to provide more computer control functions, such as automatic instrumental sensitivity changes. On the other hand, the present system is capable of providing semiautomated electroanalysis on a routine basis within a broad concentration range with good precision. A useful system for digital data acquisition and on-line processing in voltammetry has been constructed and tested. In addition,
the value of ensemble-averaging as a means for sensitivity enhancement in electroanalysis has been demonstrated. ACKNOWLEDGMENT The authors thank Gordon Jones for his contributions to several hardware and software modifications. RECEIVED for review January 31, 1968. Accepted February 29, 1968. Presented at the 155th Meeting ACS, San Francisco, April 1968. Work performed under the auspices of the US.Atomic Energy Commission. Partial support was provided also for one of the authors (S.P.P.) by the National Science Foundation, Grant No. GP-6131.
On Determining Spectral Peak Positions from Composite Spectra with a Digital Computer J. R. Morrey Battelle-Northwest Laboratories, Battelle Memorial Institute Richland, Wash. When spectral transitions seriously overlap, it is difficult to determine visually their energies. This paper describes the limiting conditions for the detection of overlapping peaks and a method to quickly and automatically determine energies with statistical reliance. The method involves the fitting of equidistantly spaced data to a quartic equation and examination of the first, second, third, and fourth derivatives of the spectrum. This information is sufficient to accurately place peaks which appear only as shoulders on stronger peaks. Estimation of widths and intensities is also discussed. Use of this method is contingent upon the capability of obtaining spectra in digital form and using a digital computer.
LACKOF RESOLUTION is often a hindrance to the theoretical interpretation of spectra, particularly when accurate energies and intensities are required. This difficulty normally is attributable to the wide distribution of perturbational influences on the sample rather than instrumental inadequacies. When this happens we are faced with the problem of extracting information from a composite curve made up of overlapping distribution functions. Ideally one should be able to resolve the composite curve into its individual components, but this is often difficult because the forms of the distribution functions are not known and a given resolution is never mathematically unique. This problem is one of our current interests. Where appropriate in this paper we discuss Gaussian, Lorentzian, and Student T3 distributions. A paper is in preparation which will outline from a statistical point of view the reasoning behind the use of T3 distributions. In recent years it has become common practice in some laboratories to record spectra in digital form for direct coupling to digital computers. The advantage to this approach, aside from the fact that it provides a convenient storage system, is that efficient and objective interpretation of large quantities of data can be made. An example of such objective interpretation is given in this paper. The computer program resulting from the analysis described in this paper has recently been added to an ana-
logue-digital-magnetic tape conversion system which is described in detail elsewhere (1). However, it can be made compatible with other data acquisition systems with relatively little effort. MATHEMATICAL DEVELOPMENT Statistical Analysis. To make use of statistical analysis we first fit the digital data of a segment of a spectrum to a quartic equation. This can be done economically, provided the ordinate values are equidistantly spaced along the x axis (2, 3). Let
5
(3)
5
yj””
=
C
Cr(i - I) (i - 2) (i - 3) (i - 4)xji-s = 4!c5
i=l
(5)
Here x, is a position relative to a position x k spanned by the segment and the primes on the yj’s refer to derivativesi.e., y j ’ is the first derivative. At peak positions the following conditions exist as illustrated in Figure 1. (1) J. R. Morrey and H. S. Gile, Analogue-Digital-Magnetic Tape Conversion System, BNWL-343, May 1967. Clearinghouse for
Federal Scientific and Technical Information, National Bureau
of Standards, U. S. Department of Commerce, Springfield, Va. (2) C. A. Bennett and N. L. Franklin, “Statistical Analysis in Chemistry and the Chemical Industry,” John Wiley and Sons, N. Y.,1954. (3) A. Savitsky and M. J. R. Golay, ANAL.CHEM., 36, 1627 (1964). VOL. 40, NO. 6, MAY 1968
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