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Real-Time Computer Optimization of Stationary Electrode Polarographic Measurements S. P. Perone, D. 0. Jones, and W. F. Gutknecht Department of Chemistry, Purdue University, Lafayette, Ind. 47907

A small digital computer has been employed on-line in stationary electrode polarographic experiments to automatically optimize experimental measurements. This was accomplished by allowing the computer to interact with the experiment in real time. That is, the computer was able to modify the course of the experiment-during the experiment-based on the nature of the continuously monitored output. The nature of the experimental modifications was simply to cause a temporary interruption of the linear voltage sweep after each reduction step, in order to dissipate the reducible species in the diffusion layer and minimize interference with succeeding reduction steps. The interrupt potential and length of the delay are computed in real time from the characteristics of the preceding reduction step. Thus, the applied experiment is uniquely tailored to each different sample composition. The result of applying this “sample-oriented” type of experiment has been to improve significantly the quantitative resolution for stationary electrode polarographic measurements of mixtures where Eliz’s differ by greater then 150 mV. STATIONARY ELECTRODE POLAROGRAPHY (SEP) has been widely adopted as a versatile and sensitive electroanalytical technique. A useful variation of this technique is fast-sweep derivative polarography, the characteristics of which have been described previously (I, 2). A recent publication (3) has described the incorporation of an on-line computer in an electroanalytical system providing stationary electrode polarographic and derivative measurements with the objective of providing semi-automated electroanalysis. That publication enumerates several reasons for choosing the fast-sweep derivative measurement for automated electroanalysis. These include the fact that the experiments are rapid and repetiticre, thereby being inherently advantageous for digital data acquisition, processing, and control; the measurements provide sensitivity and resolution; and the derivative read-out provides data in a format from which the computer can readily extract important information. In addition, the instrumentation is relatively simple and reliable, and the experiment can be compatible with a dropping mercury electrode-both very important considerations for automated electroanalysis. The work presented here has resulted from a further evaluation of the limitations of stationary electrode polarograohy (and the derivative read-out approach) for automated electroanalysis, and from a consideration of how the on-line digital computer can best be used to minimize those limitations. Moreover, the work reported here reflects an attempt to devise experiments which take advantage of on-line computer operations to provide optimization of stationary electrode polarographic measurements. The approach involves realtime interaction between the computer and the experiment, and the generation of an electroanalytical measurement technique unattainable without the aid of an on-line computer. (1) S. P. Perone and T. R. Mueller, ANAL.CHEM., 37, 2 (1965). (2) C. V. Evins and S. P. Perone, ibid., 39, 309 (1967). (3) S. P. Perone, J. E. Harrar, F. B. Stephens, and Roger E. Anderson, ibid., 40, 899 (1968). 1154

ANALYTICAL CHEMISTRY

EXPERIMENTAL

Cell and Electrodes. The cell used in this work was constructed from a 100-ml borosilicate glass centrifuge bottle (No. 8422, E. H. Sargent Co.) with a threaded mouth. A threaded lid, through which the electrode assemblies and nitrogen dispenser fit, was machined from Teflon (Du Pont). The lid and electrode assemblies were mounted in a stationary configuration while the cell could be removed or replaced readily. The working electrode was a microburet-type hanging drop mercury electrode (No. E410, Brinkmann Instruments, Des Plaines, Ill.) modified as described earlier (4).

The capillary of the microburet-type electrode apparently becomes contaminated quite easily. This contamination manifests itself through withdrawal of the mercury column several millimeters into the capillary after drop dislodgment. This problem can be overcome by cleaning the electrode before each use. The cleaning process is accomplished by drawing various solvents through the capillary by means of a vacuum. For normal cleaning, the process consists of drawing 100 ml of distilled-deionized water through the capillary followed by 5 ml of ethyl ether and 20 minutes of drying (simply drawing air through the capillary). The capillary is treated originally with a silicone antiwetting agent by the manufacturer. After several weeks of constant use, this coating is apparently lost and normal cleaning will not prevent withdrawal of the mercury column. Thus it is necessary to resiliconize the inside of the capillary. As suggested by the manufacturer, General Electric “DriFilm” SC-87 was used for this purpose. First, the capillary is cleaned by drawing approximately 50 ml of 1 % “ 0 3 through it. Next water and ethyl ether are used as described above. Then 2-5 ml portions of 5 % “Dri-Film” SC-87 in n-hexane are drawn through the capillary with 0.5 hr of drying following each portion. Finally the treated capillary is again washed with water and ether. By following this procedure, satisfactory electrode reliability and reproducibility were obtained for this work. The counter electrode was a 14-cm2 cylinder of platinum screen, mounted for symmetrical placement around the working electrode. The reference electrode was a Coleman NO. 3-510 saturated calomel electrode (Coleman Instruments, Maywood, Ill.). No attempt was made to minimize uncompensated ZR drop by placement of the reference electrode, because maximum ZR drops encountered were less than a few millivolts. Solutions. All chemicals used were reagent grade, and the water used was purified by distillation and passage through a mixed-bed cation-anion exchange resin. Cell temperature was ambient, and all solutions were deaerated with high purity nitrogen. The concentrations of electroactive species varied from 2 X 10-6 to 4 X 10-4M. Specific concentration ratios are given in the text. Potentiostat, Interface, and Computer Hardware. A block diagram of the experimental apparatus is presented in Figure 1. The cell potential is controlled and sweeps are initiated by the computer through the interface logic to the potentiostat (4) Robert H. Wopschall and Irving Shain, ANAL. CHEM., 39, 1527 (1967).

Potentinstot ond Romp Generotor

Cell

TI

Currenl Meosulrement ond Differenhotor

Instrumentotion

I

,-

10

Digitol

logic and analog-to-digital converter were performed using DEC W601 and W510 logic cards. The potentiostat and ramp generator circuits are presented in more detail as part of Figure 2. All resistors in Figure 2 are 1 % metal film and wirewound types. Resistances are given in ohms, and capacitances are given in microfarads. All amplifiers and logic packages were connected to their respective power supplies using 0.01- or 0.1-pF ceramic capacitors, respectively, shunted to ground to help compensate for power supply lead inductances. The + 5 V and +8 V power supplies required for the logic and analog switches were constructed from National Semiconductor Model LM300 monolithic integrated circuit voltage regulators connected to a Philbrick Model 300 =t 15 V power supply (6). The potentiostat was of conventional operational amplifier design (7). A National Semiconductor Model LM302 monolithic integrated circuit voltage follower was used as a high impedance buffer from the calomel reference electrode in the cell. It is presented as amplifier A9 in Figure 2. It was isolated from the reference electrode with a 1 Kohm resistor, and a driven guard was provided to the electrode to maintain the input impedance of the amplifier and aid in noise reduction. The controlling amplifier in the potentiostat, amplifier A10, is a Fairchild Model 741 monolithic integrated circuit operational amplifier used in an adder configuration. The ramp generator input allowed the cell potential to be driven at the 1 volt per second sweep rates used in this work. The ramp generator consists of amplifier A8, an Analog Devices Model 501C field-effect-transitor-input operational amplifier, used as an integrator. The sweep rate was set at exactly 1 volt per second with R1. The integrator voltage reference source, RS1, was constructed using a National Semiconductor LM300 voltage regulator powered from the general supply. The ramp generator was controlled using a Fairchild Model SH3001 integrated circuit metal oxide silicon

+, Computer

Converter

t

I

Clock

SEP-I

Figure 1. System block diagram

and ramp generator. Cell current is measured from the working electrode and operated on by the current measurement and differentiator instrumentation. These signals are digitized by the analog-to-digital converter and passed to the computer. Precise timing is achieved using a crystal clock. A Hewlett-Packard Model 21 15A computer, equipped with an 8192-word core memory, an extended hardware arithmetic unit, a teleprinter, a high-speed paper-tape reader, and a high-speed paper-tape punch, was used for data acquisition, processing, and control operations. Conversion of the analog voltages resulting from the cell current and its derivatives to digital values for computer processing was done with a Digital Equipment Corporation (DEC, Maynard, Mass.) Model COO2 10-bit 33-psec conversion time analogto-digital converter. Precise timing for data acquisition was achieved with a DEC Model B405 10-MHz crystal clock counted down to 1 KHz using DEC Model B200 and R202 flip-flop logic cards (5). All interface logic was constructed using DEC logic cards. Input and output voltage level conversion to and from the computer and the DEC interface ( 5 ) “Logic Handbook,” Digital Equipment Corp., Maynard,

Mass., 1967.

(6) “Application Note AN-1,” National Semiconductor Corp., Santa Clara, Calif., 1967. (7) W. M. Schwarz and Irving Shain, ANAL.CHEM.,35, 1770 (1963).

I I

I I

L

- - - - - - -Diftcrcntiotor -------

1,

- - - - -Ovfpvl - - -Amplifier ---

I, - d l

I

I --I

Figure 2. Schematic diagram of interface logic and electroanalytical instrumentation VOL. 41, NO. 10,AUGUST 1969

1155

field effect transistor (MOSFET) switch for MS1 and a similar, though normally closed, Fairchild Model SH3002 switch for MS2. These MOSFET switches were driven by the computer through the interface and internal control logic. By appropriate manipulation of switches MSl and MS2, the ramp-and-hold functions used in this work could be generated. The switching characteristics of MS1 and MS2 were more than adequate. Switching times were less than 1 psec. Off impedances were such that capacitor leakage in the “Hold” situation was less than 0.2 mV/sec. MSI, the MOSFET switch labeled “Hold” in Figure 2, was used to start and stop the sweep. It was driven through G3, a positive NAND gate. All gates in the internal control logic section of Figure 2 were portions of Motorola Model MC846P integrated circuit quad two-input diode transistor logic positive NAND gates. Gate G3 allows control of MS1 to be performed by either the computer or the operator. When S3 is connected to ground, (a logical 0), MS1 is closed and a ramp will result if MS2 is open. When S3 is connected to +5 V, (a logical l), MS1 is open if the 0 output of the flip-flop FF1 in the interface logic section is at logical 1. MSl can thus be manually operated. Also, when S3 is at a logical 1, FFl can control the operation of MS1. FF1 is controlled by the computer through gates G1 and G2 which are negative OR gates. When either output bits 14 or 12 go to a logical 0, the Q output of FF1 will go to a logical 0. MS1 will then close, generating a ramp. To stop the ramp, eithe: output bits 15 or 13 must go to a logical zero setting the Q output of FF1 to a logical 1 and opening MSl. This will result in either a “Hold” or “Clear” depending on whether bit 13 or 15 is output. The fact that both start and restart as well as clear and stop bits come from a computer output word allows MS1 to be operated on either alone or with MS2, the ramp MOSFET Switch. Gate G4 and flip-flop FF2 perform an analogous operation to that above with MOSFET Switch MS2, with the difference that MS2 is normally closed rather than normally open. When open, MS2 allows the integrator A8 to be controlled by MS1. When MS2 is closed, capacitor C1 is shorted through R2 and the “On” resistance of MS2. This provides a means of resetting the ramp generator to zero when output bit 15 from the computer is a logical zero. In addition, MS2 provides for a safety reset of A8 when for any reason the integrator output reaches a threshold value. The integrator output is amplified by A10 the output of which is connected through diodes D1 and D2 to one input of G5 which is being used as a simple inverter. When the output of A10 reaches about +2.8 V, the output of G5 goes to a logical 0 setting the flip-flop constructed from G6 and G7. The output of G7 then goes to a logical zero closing MS2 and limiting the voltage across MS2-and the electrochemical cell-to a safe value. MS2 remains closed until momentary switch S5 is pressed resetting the flip-flop and returning control of the ramp generator to MS1. This system provides four things. First, it allows for a computer-controlled reset of the ramp generator through FF2 and G4. Second, it provides a safety shut-down of the ramp generator should the computer fail to reset it or should noise trigger it into operation. Third, it provides for a safety shutdown should the electrodes be disturbed in a manner that would cause the output of A10 to go too high. This sometimes happens when removing or replacing a solution. Fourth, it provides manual operation by pressing S5 when both S3 and S4 are at a logical 1. In this mode of operation, the ramp generator automatically goes to 2.8 V and resets to zero. A front panel indicator lamp is used to monitor the output of G7. The current measurement and differentiator instrumentation presented in Figure l is also presented in more detail as a part of Figure 2. The cell current is measured from the hanging mercury drop working electrode with the current-tovoltage converter made up of amplifiers A1 and A2. Amplifier A1 is an Analog Devices Model 501C while amplifier 1156

ANALYTICAL CHEMISTRY

A2 is a National Semiconductor Model NH0002C hybrid integrated circuit current booster. Transistors Q1 and 4 2 provide input voltage protection for A1 (8). A fractional feedback circuit (9) is used in the converter to keep the impedance to ground of the summing point of A1 as low as possible to help reduce noise pickup. The current booster A2 is enclosed in the feedback loop to allow the size of the divider resistors R3 through R5 to be smaller than they could be using the small output current capabilities of Al. This allows the feedback resistors R6 and R7 to be smaller making the impedance to ground of the summing point of A1 even less. This feedback arrangement provides current sensito 3 X lo-’ amps/volt output in a tivities from 1 x 1-3 switching sequence. Amplifiers A3 and A4 are connected as third-order Butterworth low pass filter sections (IO) with cutoff frequencies of 20 Hz. The amplifiers used for A3 through 17 are Fairchild Model 741C. Amplifiers A5 and A6 are differentiators providing both the first- and second-derivatives (9). Amplifier A7 is a simple gain of ten inverter used to give the proper signal polarity and signal level to take advantage of the dynamic range and resolution of the analog-to-digital converter. DISCUSSION

Analytical techniques generally are applied under nonideal conditions because of one or more of a variety of practical problems. For example, spectrophotometric measurements, ideally, ought to be made with a zero slit width. But such conditions would prohibit the making of a measurement, because of a lack of signal. Thus, a compromise is reached with a finite, but small, slit width. In electroanalytical techniques one of the foremost practical problems is that mixtures of electroactive species are difficult to analyze because the reduction signal of one component may distort seriously or conceal the reduction signal of another. The degree of seriousness of this problem varies with the particular technique applied, with ac and pulse polarographic techniques being less susceptible. Stationary electrode polarography, (SEP), despite its many desirable characteristics for automated analysis, is limited seriously for application to mixtures. Because of the continuous nature of the experiment, currents from easily-reducible species continue to flow and contribute to, distort, or mask currents measured for more-difficultly-reducible species. The nonideal aspect of the technique is the fact that a continuous linearly varying potential is applied to the electrolysis cell, regardless of the composition of the sample. If the linear sweep were discontinuous, stopping briefly after each reduction step to allow the more complete dissipation of the easily-reducible species in the diffusion layer around the electrode, the interference with reduction steps for more difficultlyreducible species would be considerably diminished. However, such a discontinuous or “interrupted-sweep” experiment would require some foreknowledge as to the composition of the mixture-and this is not a likely situation in real analytical situations. Thus, the SEP technique, as ordinarily applied, is not “sample-oriented.” (In fact, this is a practical shortcoming of most analytical techniques.)

(8) “Product Notes, Vol. 2-1,” Keithley Instruments, Inc., Cleve-

land, Ohio. (9) Charles F. Morrison, Jr., “Generalized Instrumentation for Research and Teaching,” Washington State University, Pullman, Wash. 1964, pp 35, 46. (10) Leonce J . Sevin, Jr., “Field Effect Transistors,” McGrawHill Book Co., New York, 1965, p 103.

x ’@)P

X(ar)P

Table I. Values of Current-Function Ratios, __ X(aOE’ x ’ ( a t ) E ’ ~

and n(E - El/?), mV

-as Functions of ( E - E I I Z ) ~

x”(at)P X”(a?)E

x(at)p

x ’(arb

x “(ath

X(Ut)E

x’(at)E

X“(Ut)E

- 150

6.044 1.813 7.983 1.991 2.153 10.18 2.299 12.54 2.436 15.02 - 250 2.563 17.63 - 275 2.671 20.22 - 300 - 325 2.788 22.99 26.16 - 350 2.896 3.096 32.28 - 400 3.304 38.90 - 450 See Refs. ( 2 , 12) for definition of symbols.

15.01 24.08 35.03 50. 26

- 175 - 200 - 225

IC

a

68.00

88.90 115.6 144.5 172.6 241 .O 330.0

Figure 3. Comparison of normal and interrupted-sweep stationary electrode polarography Stationary electrode polarogram (WjO interrupt) Stationary electrode polarogram (With interrupt) C. Applied cell potential (W/O interrupt) D. Applied cell potential (With interrupt) A. B.

One important objective of the work reported here was to take advantage of the on-line digital computer to overcome the resolution problems associated with the usual necessity for applying stationary electrode polarography under nonideal conditions. Two approaches seemed appropriate: (1) Run the experiment as usual, but allow the computer to extract analytical information from overlapping reduction steps by de-convoluting techniques. (2) Allow the computer to interact with the experiment in real-time to generate an interrupted-sweep experiment which was effectively “sampleoriented.” Each of the two approaches mentioned above has advantages not present in the other. The second approach, involving real-time computer interaction, will be described here. The other approach will be described in a later publication (1 I>. A second objective of the work reported here was to demonstrate how real-time computer processing can improve the quality of analytical data. For example, the computer can be used to compute the n-value of a particular reduction step, during the reduction step, and this information can be used to improve the interrupted-sweep experiment by allowing a more reasonable choice of interrupt potential. Also, realtime integration of voltammetric data is accomplished readily by the on-line computer, even for high-speed experiments. Integrated data is less susceptible to high-frequency noise problems, and can provide more precise analytical information. In this work high-frequency noise was not a problem. However, integral data were used to provide diagnostic information and to contribute to n-value calculations. Sample-Oriented Analysis-Interrupted Sweep Approach. RESOLUTION LIMITS. The theories of conventional stationary electrode polarography (12) and stationary electrode polarography with derivative read-out ( I , 2) allow the accurate prediction of resolution limits. This can be done by calcu(11) William F. Gutknecht and S. P. Perone, unpublished data, 1969. (12) Richard S. Nicholson and Irving Shain, ANAL.CHEM.,36, 706 ( I 964).

lating the theoretical ratio of the current functions at the peak and at some potential beyond the peak. Using the mathematical approaches outlined previously ( I , 2, 12), and considering only reversible systems, this has been done for 0-, 1st-, and 2nd-derivative measurements (13). The results are shown jn Table I. [The peaks chosen for the 1st- and 2nd-derivative current functions are the largest ones in each case-at n(E - El,*)= 18.8 and - 14.4 mV, respectively.] Several observations can be made based on the theoretical data of Table I: the interference with a succeeding reduction diminishes considerably with derivative measurements and with increased potential separation of reduction steps ; resolution increases with the order of the derivative; however, even with the derivative measurement, the resolution is not particularly good when reduction steps are closer together than about 300/n mV. Thus, considering arbitrarily a separation of 300/n mV and equal n- and D-values, it would be possible to resolve, with 5 contribution of the first reduction step to the second, concentration ratios of 1:7, 1:1, and 5.8:l for the 0-, 1st-, and 2nd-derivative measurements, respectively. These calculations are exclusive of any other background contributions, with the assumption that they are negligible or can be measured independently for correction. It would, of course, be possible to correct mathematically for the interference caused by overlapping reduction steps. However, a limit is reached with this approach when the interference is so great as to preclude even the recognition of a succeeding reduction step. In any event, this approach has been considered in our laboratory and will be discussed elsewhere (11). For the work reported here, however, we attempted to improve the inherent resolution of the technique by real-time modification of the experiment by the on-line digital computer, as discussed above. DETAILS OF INTERRUPTED-SWEEP EXPERIMENT. The interrupted-sweep experiment involves the computer-controlled potentiostat, (described in the Experimental section), and realtime analysis of fast-sweep derivative polarographic data. The computer continuously monitors the experimental output, is instantaneously aware of the occurrence of reduction steps, and can interrupt the linear potential sweep at an appropriate (13) Paul E. Reinbold, Master’s Thesis, Department of Chemistry, Purdue University, Lafayette, Ind., 1968. VOL. 41, NO. 10,AUGUST 1969

1157

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Computations r-- _ _ _ _

Stort Sweep

1

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Integration:

Computation of fi Value. I

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Figure 5. Analytical measurements from first- and secondderivative voltammetric data.

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I I I

A. First derivative B. Second derivative Compute

I

I I

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ond Delay Time

I Interrupt Sweep for Colc'd Deloy

4 Continue Sweep

Figure 4. Flowchart for real-time computer-optimized SEP potential cathodic of each peak. The interrupt potential is held for a length of time computed to allow sufficient depletion of the electroactive species in the diffusion layer, and then the sweep is restarted. The interrupt delay time, 7,is calculated in proportion to the magnitude of the reduction step, with the restriction that T not be so long as to cause convection processes to occur or to allow significant electrolysis of the next electroactive species. Thus, the controlling potential function-which is basically a series of ramp-and-hold stepswill be different for each experiment, depending on the sample mixture and composition. The experiment is custom-tailored to the sample-Le., sample-oriented. A simplified comparison of the continuous- and interrupted-sweep experiments is shown in Figure 3. A flow-chart of the computer-controlled experiment is given in Figure 4. (A listing of the assemblylanguage computer program is available upon request.) The information taken in by the computer is extracted from either the 1st- or 2nd-derivative signal. Only the negative region of the derivative signal is seen by the analog-todigital converter, and the measuring circuit is arranged so that only the largest peak in each case is the correct polarity. The result is shown in Figure 5 . The computer is programmed to look for sharp peaks-above an arbitrary threshold-and to measure and store peak heights, peak areas, and peak locations in real-time. The programming and machine speed are such that data acquisition rates slightly greater than 1 KHz can be tolerated and still allow the computer to complete all required data processing and decision-making between data points. A maximum data acquisition rate of l KHz was used in this work. When a complete peak is observed-Le., one which goes above threshold, goes through a sharp maximum, and then comes back down below threshold-the computer calculates the n-value, the potential at which the sweep should be inter1158

ANALYTICAL CHEMISTRY

rupted, ED,and the delay time, 7. Then the computer allows the sweep to continue (if necessary) until the desired interrupt potential (ED)is reached; the sweep is interrupted at this point for time, 7 ; the sweep is then re-initiated with the computer looking for the next reduction step, ready to reexecute a similar interrupted-sweep. (The delay time, 7, is computed in proportion to the peak height, with the restriction that T be between 100 and 1000 ms.) It was hoped that the combination of the interrupted-sweep experiment and derivative measurements would provide substantially enhanced resolution. The practical objective was to develop a technique which would be useful for automated electroanalysis for samples where concentrations ranged from to 10-6M. Thus, the experimental data reported below represent an attempt to evaluate how closely this practical objective is reached, and to specify what the limitations are. Advantages of Real-Time Calculations. USESOF INTEGRAL DATA. It was possible to integrate the derivative peaks seen by the computer in real-time and to use these integral data for analytical purposes, for calculating appropriate interrupt potentials, and to provide diagnostic information. At first glance it might appear unlikely that analog differentiation followed by digital integration could provide any useful information. However, this is not the case. Analog differentiation performs the useful function of reducing the raw data to a format which is easily assimilated and processed by the digital computer for peak location. In effect, differentiation causes all peak information to be referred to a virtual zero base line. Thus, the dynamic range limitations of the analog-to-digital converter becomes less important. Digital integration of those peaks in the derivative curves seen by the computer (refer to Figure 5 ) provides several useful functions. First of all, the area under a peak is directly proportional to the peak height and, therefore, to the concentration of electroactive species. Thus, the peak integral, Q p ,is a concentration-dependent output. Moreover, should the peak location routine in the program fail because the derivative peaks are too noisy, broad, or small, the peak integrals will still be taken and provide a useful, reliable, source of analytical information. In addition, a peak area threshold is incorporated into the program, whereby the area of a given peak must exceed some arbitrary value before the computer will recognize a signal excursion as a bonafide reduction peak. This is a very useful processing parameter. In the case of 1st-derivative read-out, the value of the integral of the observed peak is equivalent to the peak height of the conventional stationary electrode polarogram. It has been shown previously that, for a reversible system, the ratio of the

(ED- Eid CO/CR

Table 11. Interrupt Potential Required for Specified Surface Ratio, Co/CR 0 - 28. 5/17 -59.1ln - 100/n - 118/n 111

113

1st-derivative peak height, I,’, to the conventional peak height, i,, is related to n (2), as given by Equation 1.

_ -- 13.2 nu I” i, where L; is the scan rate in volts/sec. Thus, a determination of the ratio of the derivative peak height to the peak integral can lead to an evaluation of n, and the computer is programmed to d o this in real-time so that the information is available for interrupted-sweep decisions. This information is also useful for qualitative identification of species or for providing an error diagnostic if wrong n-values are obtained for known systems. A similar relationship exists between the n-value and the ratio of the 2nd-derivative peak height to the peak integral. The measured integral is equivalent to the difference between the positive- and negative-going 1st-derivative peaks. The relationship can be calculated from previous theoretical data (1) and is given in Equation 2.

Thus, the n-value can be obtained from either the 1st- or 2ndderivative measurements. For reversible processes, the computed n-value is accurate. For irreversible processes, the n-value a t least reflects the broadness of the peak, and this is useful for the interrupt potential calculations discussed below. SELECTION OF INTERRUPT POTENTIAL. In the interruptedsweep experiment, the potential, ED, selected to be held during the delay period, T , is very critical. The objective is to select a potential which is cathodic enough to deplete adequately the electroactive species in the diffusion layer. That is, the potential should be chosen such that the concentration ratio C,jC,, approaches zero at the electrode surface. The obvious problem is that selecting a value of EDcathodic enough to truly deplete the electroactive species at the electrode would eliminate the possibility of observing a succeeding closely-spaced reduction. Thus, a compromise must be reached, and a knowledge of the n-value for the reduction step on which the delay is made is very critical in selecting the appropriate interrupt potential. In this work, interrupted-sweep experiments were run with the interrupt potential (ED)selected by the computer after it has observed a complete derivative peak-ie., when the derivative signal is going through zero. ED is selected relative to the potential, E,, at which the derivative signal goes through zero. The computer uses information provided initially by the operator in order to calculate ED - E,. That is, the operator initially specifies n(ED - E z ) ; the computer determines n and E,, and then selects ED. Experiments are reported below where the operator-selected value of n(ED - E,) was varied for a series of runs to observe the effect of ED on quantitative resolution. The influence of ED on the surface concentrations of species in the redox couple, 0 and R, is shown in Table 11. The calculations for Table I1 are based on the Nernst equation and

1/50

1/10

- 177/n l/lOOo

l/lW

Table 111. Characteristics of Standards a. [ 2 e - ] - [ 2 e - ] system En us. SCE (volts) Electroactive First Second species derivative derivative nobs -0.514 -0.542 1.88 Pb(I1) -0.666 -0,694 2.05 Cd(I1) b.

TU) Pb(I1)

[ l e - ] - [ 2 e - ] system

-0.464 -0.748

-0.498 -0.778

1.10 1.70

reversible behavior. Also, it should be noted that E, - Eli2 is -28.5/n mV for the 1st-derivative measurement, and -66.5In mV for the 2nd-derivative measurement. RESULTS

Two different two-component systems were studied in this work. One system consisted of a one-electron reduction process followed by a two-electron reduction process; the other consisted of a two-electron reduction process followed by a second two-electron reduction process. The first system consisted of Tl(1) and Pb(I1) in 1.OM NaOH electrolyte. The half-wave potentials for these two species are separated by approximately 280 mV. A [le-]-[2e-] reduction system having such an EliPseparation was selected so that the Faradaic interference could be significant, while interference due to the charging spike for sweep re-start would be at a minimum. The second system studied was that of Pb(I1) and Cd(I1) in a 2 M ammonium acetate-acetic acid electrolyte. The separation for this case was approximately 150 mV. This system was selected to establish the limitations of the interrupted-sweep experiment for closely-spaced reduction steps. The four reduction processes studied are described as reversible in the literature (14). All runs were made at a scan rate of 1.00 V/sec. Data points were taken at 1- or 2-mV intervals, and both the firstand second-derivatives of the reduction currents were observed for each system. The peak potentials and n-values measured for the various signals observed with standard solutions of each component are shown in Table 111. The nabs values are the n-values computed by the program, and differ slightly from the reversible values suggested from polarographic experiments (14). Various experiments were applied to the two systems. These included normal SEP and interrupted-sweep SEP with computer-selected interrupt potential. The values of ED - Ez)employed varied from O/n mV to values which resulted in noticeable charging spike interference. The delay time, 7, for the first peak in each example was always near to or equal to 1000 msec., since the first peaks were always quite large. The results of these tests are shown in Tables IV-IX. (14) “Handbook of Analytical Chemistry,” Louis Meites, Ed., 1st ed., McGraw-Hill Book Co., Inc., New York, 1963, pp 5-23 et seq. VOL. 41, NO. 10, AUGUST 1969

1159

Table IV. First-Derivative Data for Pb(I1) in 30: 1 ~ l ( I ) ] : ~ b ( I IMixture )] Condition (I, ’lconcn)= Z Std. ( Qp’/concn)a Standard 7.40 100.0 1.55 W/O interrupt 3.76 50.8 0.477 (ED- Ez)= O/n mV 6.65 89.9 1.25 (ED- Ez)= -5/n mV 6.69 90.4 1.28 (ED- Ez) = - 1O/n mV 6.82 92.1 1.32 (ED- Ez) = -20/n mV 6.87 92.8 1.35 (ED- Ez)= -4O/n mV 7.04 95.1 1.42 (ED- Ez)= - l00jn mV 7.25 97.9 1.40 Predicted error in Ip’/concn = -48.4%, W/O interrupt. Re1 std dev = &1.6x for I p ’ , &1.42 for e,’. Arbitrary units.

Z Std 100.0 30.8 80.6 82.6 85.2 87.1 91.6 90.3

Table V. Second-Derivative Data for Pb(I1) in 30:l rl(I)]: [pb(II)] Mixture Condition (I,’’/concn)a Standard 3.78 3.50 W/O ir terrupt 3.81 (ED- Ez) = O/n mV 3.78 (ED- Ez)= -5/n mV 3.84 (ED- Ez) = - l0jn mV 3.81 (ED- Ez) = -20/n mV 3.75 (ED- Ez)= -40/n mV Predicted error in Z,“/concn = -5.20%, W/O interrupt. Re1 std dev = 4~1.5%for I,”, 3Z2.5Z for Q,“, Arbitrary units.

Z Std 100.0 92.6 100. 8 100.0 101.6 100.8 99.2

(Q,”/~oncn)~ 5.66 4.88 5.73 5.71 5.70 5.66 5.60

Table VI, First-Derivative Data for Cd(I1) in 1O:l [pb(II)]:[Cd(II)] Mixture Condition (I, ’/concn)a Z Std ( Q,’/concn)“ Standard 1.137 5.25 100.0 0.265 2.38 WjO interrupt 45.3 1.01 5.48 104.4 (ED- E z ) = O/n mV (ED- E z ) = -2.5112 mV 0.995 5.50 104.8 0.995 5.50 (ED- Ez) = -5/n mV 104.8 0.963 (ED- Ez)= -10/n mV 5.57 106.1 0.963 (ED- E z ) = -2O/n mV 5.50 104.8 0.933 5.37 102.3 (ED- E z ) = -3O/n mV Predicted error in I,’/concn = -45.6%, W/O interrupt. Re1 std dev = 2 ~ 2 . 1 Zfor I,‘, 3~2.8%for Q,’. a Arbitrary units.

Table VII. Second-Derivative Data for Cd(I1) in 1O:l [Pb(II)]:[Cd(II)] Mixture ( Q,”/concn)a Condition (I,”/concn)n Z Std 2.60 100.0 3.79 Standard 2.39 91.9 3.48 W/O interrupt (ED- Ez) = O j n mV delay 2.60 100.0 3.53 (ED- Ez) = -2.5/n mV delay 2.61 100.2 3.57 (ED- Ez)= -5jn mV delay 2.60 100.0 3.52 (ED- Ez) = - l O / n mV delay 2.57 98.8 3.49 (ED- Ez)= -20/n mV delay 2.26 86.9 3.32 (ED- Ez)= -40jn mV delay 2.06 79.2 3.96 Predicted error in Ip”/concn = -8.20z, W/O interrupt. Re1 std dev = 3~1.6% for Ip”,=t2.0% for Q,”. Arbitrary units.

Also included in these tables are the theoretical estimates of overlap error based on the data from Table I. The 1st-derivative data for the [Tl(I)]-[Pb(II)] system (Table IV) show continued improvement with increasing (ED - Ez). Note, however, that at (ED- Ez) = 1OO/n mV, the Qp’/concn value decreases, while Ip’/concn increases. This distortion apparently is caused by the charging spike of the re-started sweep overlapping slightly with the Pb(I1) signal. 1160

ANALYTICAL CHEMISTRY

Z Std 100.0 86.2 101.2 100.9 100.7 100.0 98.9

2 Std 100.0 23.3 89.1 87.5 87.5 84.7 84.7 82.1

Z Std 100.0 91.8 93.1 94.2 92.9 92.1 87.6 104.5

The error due to overlapping reduction signals shown in the 2nd-derivative data for the [Tl(I)]-[Pb(II)] system (Table V) is small even without the interrupted-sweep. (This is predicted, of course, from Table I.) The improvement with the interrupted-sweep is significant, however. The experimental effects of the interrupted-sweep for both the first- and secondderivatives can be visualized in Figures 6 and 7. The first-derivative data for the [Pb(II)]-[Cd(II)] system

Figure 7. Second-derivative curves for 30: 1 Fl(I)][Pb(II)] system 3.21 X lO-4M TI(I), 1.05 X 10-5M PqII), 1.OM NaOH Upper trace: W/O interrupt Lower trace: With interrupt; ED - EZ = 10/n mV Figure 6. First-derivative curves for 30: 1 [Tl(I)][Pb(II)] system 3.21 X 10-4MTI(I),1.05 X 10-6MPb(II), 1.OMNaOH Upper trace: W/O interrupt Middle trace: With interrupt;ED - EZ = loin mV Lower trace: With interrupt; ED - EZ = 40/n mV The signals observed are: ( A ) Tl(1) signal; ( C ) Pb(I1) signal; ( B ) and (D)charging spikes; and ( E ) and (F) current decay occurring during interrupt

IX. As seen from these data, there is a considerable improvement in quantitative resolution when the interrupted-sweep experiment is employed. For the 1OO:l mixture, the second peak is undetectable with a 1st-derivative read-out (see Figure 9). With the interrupted-sweep, however, not only is the second peak detectable, but the measured value comes up to

Table VIII. Data for Pb(I1) in 1OO:l [Tl(I)]:pb(II)] (Table VI), using the interrupted-sweep experiment, shows considerable contribution to the Cd(I1) peak from the charging spike, even with small values of (ED - Ez). This interference is illustrated in Figure 8, and results in a positive error for the second peak. The width of the charging current spike for both the firstand second-derivative is observed to be approximately 100 mV. Thus, if ED is to be set cathodic of Ez,the end of the first signal peak and the start of the second signal peak must be at least 100 mV apart. This is a significant limitation on the interrupted-sweep experiment. The second-derivative data for the [Pb[II)]-[Cd(II)] system (Table VII) show better overall results than the first-derivative data. This was to be expected, on the basis of earlier studies (I, 3), and the data of Table I. It is observed that for both systems the peak integral data, Q,' and Q,",show greater error than the peak height data. This is not unexpected, because the area from the peak base is missed when peak overlap occurs. Thus, peak areas should not be the primary source of analytical data. [Tl(I)]-[Pb[II)] 1OO:l and 1OOO:l mixtures in 1.OM NaOH were also studied. The results are shown in Tables VI11 and

Mixture A.

1st-derivative Data

Condition Standard W/O interrupt (bo - Ez) = -40/n mV

(ED - Ez)

-lOO/n mV Predicted error in I,'/concn = Re1 std dev = A6.2z for I,'. a Arbitrary units. =

(I,f/concn)a Z Std 7.40 100.0 No peak *.. detected 5.24 70.8 6.18 83.5 - 160%, W/O interrupt.

B. 2nd-derivative Deta Condition (I,"/concn)a 4.09 Standard 3.63 W/O Interrupt ( E D - Ez) = -4O/n mV 4.13 (ED - Ez)= -100/n mV 4.21

?z Std 100.0

88.7 101.o 102.9

Predicted error in I,"/concn = 17z,W/O interrupt. Re1 std dev = A4.6% for I,". a

Arbitrary units.

VOL. 41, NO. 10,AUGUST 1969

1161

Figure 8. First-derivative curves for 10 :1 [Pb(II)][Cd(II)I system 1.05 X 10-4M Pb(II), 1.11 X 10-6M Cd(II), 2M NH40Ac, 2M HOAc

Upper trace: W/O interrupt Lower trace: With interrupt; ED

- EZ = O/n mV

84% of the correct value, for 1st-derivative read-out, and

Figure 9. First-derivative curves for 100: 1 [Tl(I)][Pb(II)] system

100% for 2nd-derivative read-out. For the 1OOO:l mixture the second peak is undetectable, even with a 2nd-derivative measurement. Employing the interrupted-sweep experiment with 2nd-derivative read-out, however, reliable and quantitative detection could be obtained, as shown in Table IX.

2.68 X 10-4M Tl(I), 2.63 X 10-6MPb(II), 1.OM NaOH (Arrow shows Pb(I1) peak) Upper trace: W/O interrupt Middle trace: W/O interrupt; sensitivity increased 5X Lower trace: With interrupt, ED - EZ = 40/nmV; sensi-

tivity same as middle trace

CONCLUSIONS The work presented here was intended to demonstrate that an on-line digital computer could be used to optimize an experimental measurement technique by real-time interaction with the experiment. This principle was applied to the technique of stationary electrode polarography, and an interrupted-sweep experiment was developed with real-time computer-optimization of the analytical measurements. The

Table IX. Second-Derivative Data for Pb(I1) in 1000: 1 [Tl(I)]: [Pb(II)] Mixture Condition Standard W/O interrupt ( E D - Ez) = -40 n mV (ED- Ez) = -100 n mV

Predicted error in I,"/concn = Re1 std dev = &4% for IP". a Arbitrary units.

(ZP"concnp 4.09 No peak

detected

% Std 100

...

3.2 78 4.0 98 - 5 2 z , W/O interrupt.

results clearly show a dramatic improvement in quantitative resolution of overlapping reduction signals, provided a minimum E,/*separation of about 150 mV is present. Thus, the optimized measurement is subject to at least this one severe limitation, but, nevertheless, appears quite useful. The authors do not intend to represent thecomputer-oriented technique described here as the answer to resolution problems in electroanalysis. Certainly, one can do much better using pulse polarography or related techniques (15). However, it can be stated that, for applications involving stationary electrode polarography, the on-line computer-optimized measurements are a considerable improvement. Most importantly, the principle of real-time computer-optimized measurements in analytical chemistry has been demonstrated here by application to a real system. RECEIVED for review April 14, 1969. Accepted May 19, 1969. Work supported by Grant No. GP-8677 from the National Science Foundation. (15) Helmut Schmidt and Mark von Stackelburg, "Modern Polaro-

graphic Techniques," Academic Press, New York, 1963, pp 63-70. 1162

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