electrode system, only a mixture of the two products, or the pure triptycene could be obtained. ACKNOWLEDGMENT The authors are grateful to M. Ariel for the encouragement and interest shown during the development of the instruments. LITERATURE C I T E D (1) E. R. Brown, T. G. McCord, D. E. Smith and D. D. DeFord, Anal. Chem., 38. 1119 (1966). (2) S.Barnartt, J. Nectfochem. Soc.,108, 102 (1961). (3) G. Lauer and R. A. Osteryoung, Anal. Chem., 38, 1106 (1966). (4) E. R. Brown and D. E. Smith, And. Chem., 40, 1411 (1968).
(5) A. Bewick, Electrochim. Acta, 13,825 (1968). (6) W. W. Goldsworthy and R. G. Clem, Anal. Chem., 44, 1360 (1972). (7) R. Bezman, Anal. Chem., 44, 1781 (1972). (8)J. Devay, B. Lehgyei, and L. Mezaros, Acta Chim. Acad. Sci. Hung., 66, 269 (19701. (9) J. G.’ Graeme, G. E. Tobey, and L. 0. Huelsman, “Operational Amplifiers,” McGraw-Hill, New York, N.Y. 1971, p 273. (10) Ch. Yarnitzky, US.Patent Application, Allowed Oct. 1971. (11) Ch. Yarnitzky, Continuation in parts, U S . Patent Application, Allowed Feb. 1974. (12) H. Bohm, J. Kaio, Ch. Yarnitzky, and D. Ginsburg, Tetrahedron, 30, 217 (1974).
RECEIVED for review August 22, 1974. Accepted December 27, 1974.
Dynamic Compensation of the “Over All” and “Uncompensated” Cell Resistance in a Two- or ThreeElectrode System-Transient Techniques Chaim Yarnitzky and Naphtali Klein Department of Chemistry, Technion-lsrael Institute of Technology, Haifa, lsrael
The dynamic compensation of the current-resistance potential drop is discussed. The compensation is achieved by applying a common positive feedback, pre-adjusted in less than 1 msec. The over-all response rate for a rapld change in potential after the adjustment is a few microseconds. The instrument is useful for fast electrochemical technlques such as cyclic voltammetry and pulse polarography. Complete diagrams and experimental results are given.
In a previous paper ( I ) , it has been shown that automatic
iR compensation can be achieved in slow electrochemical techniques such as regular polarography. The response rate of the electronic circuit is in the range of 100 msec. Naturally, fast techniques need an over-all response rate in the range of a few microseconds to milliseconds (2).The necessity of another approach is quite obvious. In the new electronic system suggested, regular positive feedback is still used, controlled, however, by a digital method; the actual resistor closing the loop of the feedback is a parallel combination of several binary coded resistors, connected in series to electronic gates. The gates are closed or left open according to orders given by a unit which measures the cell resistance. Two prototypes have been constructed. One is described here, the second is under inspection and will be described later. Digital Positive Feedback. Consider the basic circuit shown in Figure 1. With the main gate closed, this constitutes a simple positive feedback loop. It can easily be 880
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
proved that in this condition complete compensation of the cell resistance is achieved when:
If the main gate is open, the open loop gain (K,) of the circuit from point A to point B is given by
Thus a short pulse of amplitude Vi# applied a t point A, would cause a pulse of amplitude VBP to appear a t B, where
(3) provided the potential drop across the double layer is negligible. For example, 0.1 volt applied to a cell (Rcell= 1 kR) for 10 mec will give rise to a change of 1 millivolt on a 1 WF capacitor; clearly if the circuit is adjusted for complete compensation of Rcell (Equation I), we have:
V,. = -Vi nP
(4)
This provides a simple solution for setting up the circuit, using a variable resistor for R , and a voltage comparator (operational amplifier 5) between points A and B to sense the null point. Automatic adjustment is achieved by the use of digital logic circuitry for timing, sensing, and switching opera-
VI:
setting its gate to the “ON” position, and then applying a pulse to input A (see Figure 1).If the output of the voltage comparator is negative (1 Vinq > I V B 1,~R , is high enough and so the gate is left “ON.” If the output is positive, R , is too low, the gate is switched off again. After the last resistor has been set, the main gate is closed, leaving the circuit ready for use. This sequence of operations is frequently used in common Analog to Digital converters and is known as the “successive approximation” technique (3). Since R , is set to a value which is a digital approximation of the one required, a finite error in that value will exist; the magnitude will be equal to or less than the conductance of the last (highest) resistor in the sequence. If the error resistance Re, is considered to be parallel with R,, then:
( FULSEDI
JzgR: GATE
COMPENSATION NULL OUTPUT
Figure 1. A common positive feedback set-up, supplied with a null amplifier for feedback adjustment
and it can be shown that the effective (i.e., uncompensated) resistance of the cell will be
h
DROP FALL DETECTOR
where Rg is the ninth resistor in the series (e.g., if R = R , = R1 = 10 kR,Rg = 256 X R1 2: 2.6 MQ SO Reff = 40 R). With a nine-resistor combination, the maximum error will be 0.2% of the highest resistance with which the system can cope. The second prototype designed for the sake of simplicity is based on a commercial analog to digital converter (ADC). A short current pulse is applied to the cell (W.E. gate is open) causing a voltage pulse whose height is proportional to cell resistance (Figure 3). Again, the charge injected (10 pA at 100 psec = 1 nanocoulomb) does not significantly change the potential difference across the double layer (1 mV a t a 1 pF). The resulting pulse is then applied via a sample-and-hold circuit to a 8-bit ADC. The outputs of the ADC are connected to 8 electronic gates which are connected in series to 8 binary coded resistors by means of 8 drivers. All the resistors and their gates are connected in parallel and they create the proper positive feedback. Once the gates are all set, the working electrode is again connected in the usual mode by the W.E. gate and the main gate closed. As mentioned above, complete details and schemes for this system will be published ( 4 ) .
TO MAIN GATE CI R C U I T S COMPARATOR
Figure 2. Block diagram of a parallel combination of resistors, gates, and logic circuits for the automatic operation of the positive feedback
tions. The variable resistor R , is provided by nine binary coded resistors in parallel, each with a separate gate, as shown in Figure 2. The setting-up sequence is preceded by the opening of the feedback loop by means of the main gate. The resistors are then selected, one a t a time, starting with the lowest (most significant) value and ending with the highest (least significant). A resistor is selected by first
8
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Figure 3. A digital positive feedback controlled by an analog to digital converter ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
881
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Figure 4. Electronic circuit of the digital self adjusted positive feedback: successive approximation method
EXPERIMENTAL Fast linear scan polarograms were run on a Tektronix type 502A oscilloscope. The generators used were Chemtrix Type 800A and Phillips P M 516B. Differential pulse polarograms were carried out with a PAR Model 174 polarographic analyzer and Model 172 drop timer, and recorded on a Phillips Model P M 8100 recorder. The polarographic cell was a Metrohm type EA 880, equipped with DME and reference electrodes. Nitrogen used for oxygen removal was scrubbed with vanadous chloride solution. All experiments were carried out at 22 f 2 O C . 882
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
Triple distilled mercury and reagent grade chemicals were used without further purification.
RESULTS The instrument using a “digital self-adjusted positive feedback” (successive approximation method, Figure 4) was tested in several series of experiments in which rapid compensation was required. The voltammograms shown in Figure 5 were recorded in
i
- 30
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a
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=
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1
1
1
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15
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0
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Volts v s Aq / A g C i alcc
0
- 0.5
-I
Figure 5. Cyclic voltammetry of 1O-4MCdPf in 0.1 M KCI. R,.II = 3 kR (drop area 0.026 cm2); scan rate: 20 Vlsec. ( a ) Uncompensated. (b) Compensated. (c) Compensated, 10-kQ resistor connected in series with the cell. (@ Compensated, 100-kfl connected in series with the cell. (e) As (d), uncompensated
E
a
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- 20
c C
z a
v
o
C
20
a solution of 10-4M Cd2+ in 0.1M KC1 with an overall cell resistance of approximately 3 kR: ( a ) without compensation; ( b ) with compensation. The cell resistance was then increased by connecting 10- and 100-kR resistors in series with the cell. With compensation, no significant difference was noticed (Figures 5c and 5d respectively); without, peaks disappeared (Figure 5 e ) . Since the mercury drop area affects cell resistance, the use of a simple manual positive feedback system necessitates readjustment for any change in drop size. T o measure the relationship between peak height and drop area, in fast linear scan polarography, the delay time between the drop fall and the generator trigger is varied. However, each change requires a corresponding change in feedback. The automatic system eliminates the need for constant manual readjustment. Figure 6 shows the current-potential curves: (a) with and without compensation, ( b ) as a function of drop area, ( c ) as a function of sweep rate. At this point, it should be remembered that complete and constant compensation cannot be achieved when the over-all cell resistance is time-dependent. In this case, decreasing the compensation by means of the feedback resistor of the inverter shown in Figure 4 is suggested; the maximum compensation allowed can be easily calculated. Undoubtedly, the most important analytical use of the instrument is in the field of pulse polarography. When using the PAR Model 174 in the differential pulse mode, maximum cell resistance allowed is about 10 kR. For polarograms run on the model 174 in conjunction with the auto-
-0 3
-05
-0 7 Volt8 v s A g / A g C l eiec
Figure 6. Cyclic voltammograms ( a ) 4.5 X 10-4M CdC12 without supporting electrolyte with (high peaks) and without compensation, scan rate: 20 Vlsec; R,.II = 8 kR. (b) Compensated, 10-4M CdCI? without supporting electrolyte recorded at drop life of 0.7, 1. 1.5, 2 seconds. Reell 30 kR (minimum). (c)Compensated, 4.5 X 10-4M CdC12 without supporting electrolyte recorded with sweep rates of 2, 5, 10, 20 Vlsec
+pz==
PAR
MODEL
174
Figure 7. An automatic compensator connected to PAR Model 174
polarograph The voltage across the cell appears with opposite polarity. The delay of the instrument should be matched to (and shorter than) the delay of the PAR instrument within a few milliseconds
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
883
i
/
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0
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Figure 8. Pulse polarograms of TI+, Cd2+, Ni2+ in polyethylene glycol 400
UNCOMPENSATED
1
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t
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COMPENSATED
-
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-10
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2
3
4
5
6
7
M
8
9
1011 12
Anthroquinone x
IO6
Figure 10. Calibration curve for anthraquinone in polyethylene glycol
-13
V o l t s v s A g l A g C I elec
Figure 9. Pulse polarograms of anthraquinone (6 X 10-6M) in poly-
justment of the feedback. As a result, accurate currentpotential curves are obtained.
ethylene glycol 400
matic compensator (Figure 7), cell resistance as high as lh MQ is allowed. This is illustrated by the following experiments: the trace analysis of metal cations in polyethylene glycol 400 (Figure a), and the determination of anthraquinone in the same medium (Figures 9 and 10). CONCLUSIONS With the methods described above, the problem of iR potential drop has been almost completely solved. The oscillations, due to slight changes in over-all cell resistance with time, are eliminated by the automatic and fast read884
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
ACKNOWLEDGMENT The authors are grateful to M. Ariel and N. Freedman for the encouragement and constructive criticism and advice given during the development of the instruments. LITERATURE CITED (1) Ch. Yarnitzky and Y. Friedman, Anal. Chem.. 47, 876 (1975). (2) E. E. Wells Jr., Anal. Chem., 43, 87 (1971). (3) H. V. Malmstadt and C. G. Enke, "Digital Electronics for Scientists," W. A. Benjamin, New York, N.Y.. 1969, Chap. 7. (4) N. Klein and Ch. Yarnitzky, in preparation.
RECEIVEDfor review July 25,1974. Accepted December 27, 1974.
