Operational-Amplifier, Alternating-Current Pola rogra ph with Admittance Recording JOHN W. HAYES and CHARLES N. REILLEY Department o f Chemistry, University o f North Carolina, Chapel Hill, N. C.
b An alternating current polarograph, which permits automatic recording of the in-phase and quadrature components of the faradaic admittance, has been designed and constructed. Operational amplifiers are the basis of the instrumentation, but tuned amplifiers have been purposefully avoided. Phase selection is accomplished by multiplication of current and voltage signals by an electronic multiplier. Compensation for the effect of series resistance is made by subtraction of the iR drop from the voltage signal before multiplication using the predetermined value of the series resistance at drop fall. Noise levels have been reduced to a negligible level by the use of solid-state amplifiers in the low-signal level parts of the instrument. Stability is excellent, and results are within the expected limits of dummy-cell components.
0
of the disadvantages of alternating current (a.c.) polarography for quantitative work is the tedious vector calculations which must be carried out before useful data are obtained. Although much of this tedium can be eliminated by the use of a digital computer, it was considered desirable to design and construct an instrument which, as far as possible, would eliminate the need for these calculations by giving directly the value of the in-phase and quadrature (90" out-of-phase) components of the faradaic admittance. Because of the versatility of the operational-amplifier approach to electrochemical instrumentation, it was decided to use this technique even though it seriously limits the maximum frequency which can be used. The use of operational-amplifier techniques in a x . polarography has been described by Smith (12). Although his instrument incorporates control of the alternating potential as well as the direct potential, it is still necessary to correct for the alternating voltage drop in the series resistance (mercury thread in the capillary, solution around the drop). An independent measurement of the phase NE
1 Present address, School of Chemistry, University of Sydney, Sydney, N.S.W., Australis.
1322
ANALYTICAL CHEMISTRY
27515
Quadrature signals :
-e,e,
4
Figure 1. Conventional representation of equivalent circuit of polarographic cell R, reriea resistance C, double-layer capacitance 2, faradaic impedance
angle must also be made to obtain useful data. To overcome problems from noise in the vacuum-tube operational amplifiers, Smith ( l a ) used sharply tuned Twin-T filters in his circuit. Experiments carried out in this laboratory (3) have convinced us that the use of such filters introduces considerable inconvenience into the operation of the whole instrument, and we have avoided their use. The amount of noise in t,he circuit was reduced by the use of solidstate amplifiers in the low signal-level parts of the circuit. THEORY
OF
OPERATION
Two parameters are of interest in a.c. polarography-viz. , the magnitude of the faradaic admittance, and its phase angle with respect to the alternating voltage applied across it. These parameters may be obtained from the inphase and quadrature components of the faradaic impedance. When two sinusoidal signals of the same frequency and phase are multiplied together, the resulting signal consists of a steady component and a sinusoidal component of twice the frequency of the original signals. The product of two signals whose phase differs by 90' does not contain a steady component but consists of a sinusoidal signal whose frequency is twice that of the original signal. The following trigonometric identities show these relationships. In-phase signals : asinwtvbsinwt
=
acoswt.bcoswt =
ab -(l-cos2wt) 2
ab
(1 2
+cos24
(1)
(2)
ab w t - b cos ut = - sin 2 w t (3) 2 When the frequencies of the two signals are different, no steady component exists, even for in-phase signals. a sin
a sin ut b sin w't = ab ab - cos(w - w ' ) t - - cos 2 2 9
(w
+ w')t
(4)
The potential usefulness of these principles in a.c. polarography was first pointed out by Smith ( l a ) . When the current and applied voltage signals in a.c. polarography are multiplied together, the steady component in the product will be proportional to the inphase component of the current. If the phase of the voltage signal is shifted by 90°, the product will be proportional to the quadrature component of the current. Figure 1 shows a conventional representation of the equivalent circuit of a polarographic cell ( 5 ) . The applied alternating voltage (el) appears across the whole of the circuit. If a voltage equal to the voltage drop across the series resistance (R) is subtracted from el, the resulting voltage, e2, will equal the voltage drop across the faradaic impedance and double-layer capacitance. If e2 is then used as the multiplying voltage signal, the steady component of the product will represent that component of the current in phase with the voltage e2. The quadrature component of the current may be registered by shifting the phase of the voltage ez by 90' and again measuring the steady component of the product. Another method of compensating for the effect of the series resistance has been used in the Cambridge Univector Polarograph Unit (6, 7). A voltage in phase with and equal to the voltage drop across the series resistance is added to the applied alternating voltage so that the value of e2 is equal in amplitude and phase to the value of the originally applied voltage (el) before compensation. This circuit arrangement involves positive feedback, and, when it is used with our operational amplifier instrument, it is difficult to achieve stability, particulary when the correction voltage approaches the necessary value.
2
Figure 2.
Flow sheet of multiplier and divider' circuits for in-phase signals
Operations 1 and 3 are performed in SK5-M multiplier-divider; operation 2, rectifier; operation 4, low-pass filter; operation 5, division b y recorder 1 Y = - = )2 :( where Y = faradaic admittance Z
Because the magnitude of the voltage signal, e*, is not constant but depends upon the voltage drop across the series resistance, which is, in turn, dependent upon the total current flowing through
the cell, the steady components of the products of the multiplication processes are not simply related to the in-phase and quadrature components of the cell impedance. To obtain signals pro-
scan 300
AOOER
OIFFERENCE AMR
DESCRIPTION OF INSTRUMEN1
A detailed circuit diagram of the instrument is given in Figure 3, along with the function of each amplifier or group of amplifiers.
B
2OK
40K
I.P.
portional to the in-phase and quadrature components of the cell impedance, it is necessary to divide the products of current and voltage by a direct voltage proportional in magnitude to the voltage e2. If the resulting signals are divided a second time by the voltage proportional to ea, the quotients are proportional to the in-phase and quadrature components of the cell admittance. The admittance due to the double-layer capacitance may then be subtracted algebraically from the quadrature component of the total admittance-a relatively simple process compared with vectorial calculations. Figure 2 is a flow sheet indicating the mode of operation of the multiplier and divider circuits for in-phase signals.
AMPLIFIER
CURRENT AMP.
,
ti.-' P
I
I I
1
I
I II
HIOH PASS FILTER
Figure 3.
Circuit diagram of operational amplifier a.c. polarograph
Amplifier 1, 4-1 1, Philbrick USA-3; amplifier 2, Philbrick P65; omplifler 3, Philbrick P45A; OSC, Hewlett-Packard 241 A Oscillator. MULT./DIV.: Philbrick SK5-M Universal multiplier-divider. Inputs 1 and 2, multiply; Input 3, divide; 4, output; REC. Sargent Model SR recorder (modified as described in text); R1, current range resistor; Rz, iRcompensator input resistor (lee below); PI, Pz, Fluke Vernier potentiometers Model 22A, 100 kohms; Pa, Pa, carbon potentiometers; CI,Mylar capacitor (0.002, 0.005,0.01, 0.02, 0.05 pf.1; D, Sylvania silicon diodes, Type 1 N485A; S, in-phase quadrature switch; Position 1, quadrature component; Position 2, in-phase component All resistor values are in ohms; all capacitor values are in microfarads
-
Sensitivity ( l a . full scale) 0.1 0.2 0.5 1 .o 2.0
5.0 10.0 20.0 50.0 100.0 200.0
500.0
R1
ohms
2M 1M 400K 200K 1OOK 40K 20K 1OK 4K 2K 1K 400
RZ ohms 1OM 5M 2M 1M 500K 200K 1OOK 50K 20K 1OK 5K 2K
VOL 37, NO. 11, OCTOBER 1965
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Scan Generator. The scan generator is a conventional unit in operational amplifier polarographs (2, 11) and will not be described in detail. The voltage source for the scan generator is obtained from the stabilized power supply. The output of the scan generator is designed to be 0 to *50 volts. Adder. I n this unit, the scan voltage is added to an initial voltage (I. P., 0 to *lo0 volts) obtained from the stabilized power supply and an alternating voltage supplied from an oscillator. The sum of these voltages is then fed to a 25: 1 attenuator to provide a voltage of the correct magnitude for application to the polarographic cell. This results in a good signal-to-noise ratio a t the input to the difference amplifier (Figure 4). Difference Amplifier. This is a Philbrick Model P65 amplifier with both inputs active and is used in a conventional controlled-potential configuration (%', 11) Current Amplifier. This is a Philbrick Model P45A amplifier used with the positive input grounded in the conventional configuration (2, 11). To improve the stability of the amplifier toward oscillation, the brute force stabilization technique (4) is used, This consists of placing a resistor and a capacitor in series between the summing point and ground. The values-viz. 0.5 pf,, 300 ohms-are optimum for this amplifier. A further increase in stability is obtained by loading the output of the amplifier with another RC series network. Stability could also have been achieved by placing capacitors across the feedback resistors, but this introduces phase shift and so was avoided. The output of this amplifier is designed to be 0.2 volt for full-scale sensitivities between 0.1 and 500 pa. High Pass Filter (Amplifier 4). This conventional unit was introduced to reject the d.c. polarographic current and has a gain of 10 a t high frequencies. The output of this amplifier is also loaded as indicated t o increase overall stability. Amplifier. This gain-of-10 amplifier increases the magnitude of the signal t o the required 0 to 20 volts for the input of the multiplier and, as an inverter, supplies the correct phase relationship. High Pass Filter (Amplifier 6). This unity-gain amplifier (at high frequencies) has a time constant identical with the other high pass filter. It rejects direct voltage from the oscillator and compensates for any phase shift and attenuation introduced by the other high pass filter a t low frequencies. iR Compensator. This device subtracts the iR drop in the polarographic cell from the applied voltage signal. 1324
ANALYTICAL CHEMISTRY
Figure 4. Waveforms observed at various points in instrumenf A.
Signal ot summing point of difference amplifler. Sensitivity, 1 mv. per cm. B. Signal at output of current amplifier. Sensitivity, 100 mv. per cm. C. Voltage signal at multiplier input. Senritivity, 10 volts per cm. D. Current signal at multiplier input. Senritivity, 5 volts per cm. Dummy cell, 100 ohms in series with 10.0 rf. Applied voltage, 1 .O mv. at 80 cycles per second
Amplifier 7 provides a signal proportional in amplitude and equal in phase to the i R drop, and the subtraction is accomplished in amplifier 8. The resistor Rz is adjusted according t o the setting of R1, the feedback resistor in the current amplifier, and the potentiometer PI is adjusted according to the value of the series resistance, which is measured in a separate experiment (1). X constant current of 100 pa. a t 50 kc. per second is passed between the auxiliary electrode and the D.M.E. (ground). The series resistance a t the end of drop life is calculated from the voltage drop between the reference electrode and ground. 90" Phase Shifter. For recording the quadrature component of the cell impedance, the phase of the voltage signal must be shifted by 90". This is accomplished using an integrating circuit. Because t h e gain is dependent on the frequency, i t is necessary to adjust the values of the input resistor and/or capacitor in the feedback circuit to achieve unity gain a t each frequency. This amplifier is fitted with a diode circuit (10) which limits the output to 1 3 0 volts. This prevents the summingpoint error device from operating when the large voltage surge occurs a t drop fall. A 10-megohm resistor (not shown in Figure 2) is connected in parallel with C1 to minimize erratic long-time d.c. drift. Rectifier and Low Pass Filter. This precision full-wave rectifier-filter combination (9) provides a direct voltage proportional in magnitude to the amplitude of e2.
Multiplier and Divider Circuits. The Philbrick SK5-M multiplierdivider was modified as suggested (8) to allow the use of input and output voltages of maximum amplitude 20 volts. The coefficient switches are set a t 1.00 X 10' and are not altered; the form switch is set in the multiplydivide position. The current and voltage signals are applied to the multiply inputs-i.e., numbers 1 and 2of the instrument through capacitors (which help to filter the large voltage surges a t the drop fall). These capacitors are chosen to provide equal phase shifts in both inputs. The direct voltage from the rectifier (proportional to the magnitude of the sinusoidal voltage signal) is applied to the divide input (number 3). The output of the multiplier-divider is fed to the input of a Sargent Model SR recorder after suitable low pass filtering and voltage division. The recorder is modified in the following way. The normal voltage supply for the slidewire (1.35-volt mercury cell) is disconnected and is replaced by the direct voltage output of the rectifier after suitable low pass filtering and voltage division. The displacement of the recorder pen is proportional to the quotient of the recorder input voltage divided by the voltage across the slidewire. The recorder displacement is proportional to the admittance of the polarographic cell (Figure 2). EXPERIMENTAL
The operational amplifiers used in all positions except the difference amplifier and current amplifier are Philbrick USA-3 amplifiers housed in a K7-AlO manifold. The passive networks are built into plug-in cans. The power supply for these amplifiers is a Philbrick Model R-300. The difference amplifier (Philbrick P65) and the current amplifier (Philbrick P45A) are powered from separate packs of mercury batteries. A Hewlett-Packard 241A oscillator is used to provide the alternating voltage in most experiments. In early experiments, a Hewlett-Packard 202A function generator was used, but it was unsuitable for a x . polarography because of the wave-shaping technique used to produce the sinusoidal signal. This causes a distorted polarographic current signal due to the differentiating action of the cell impedance. Carbon-film resistors (1%) are used in the passive networks. Mylar or ceramic capacitors (10%) are used everywhere except for the integrating capacitor in the scan generator which is a Southern Electronics polystyrene capacitor (1 fif, 1%). Fluke Vernier potentiometers (Model 22A) are used in the a x . parts of the circuit, and Beckman Helipots are used in the d.c. parts of the circuit. The diodes are Sylvania Type 1N485A. A conventional three-electrode polarographic cell is used. The polaro-
polarogram, the wave heights are identical, indicating, as expected, a phase angle of 45” for this system. The reproducibility of replicate polarograms is better than 0.5%. Phase-selective a.c. polarography is inherently sensitive (6),and reasonably good waves have been obtained from as low a concentration as 10+M cadmium ions using 1-mv. applied voltage. For fundamental work in ax. polarography, it would be desirable to make use of higher frequencies, but at present operational amplifiers with sufficient bandwidth are not available. With a small extension (12) of the present instrumentation to provide a second harmonic voltage signal from e*, second harmonic a.c. polarography could be performed because the multiplication technique is frequency selective as well as phase selective. V o l t s ye. S.C.E. Figure 5. In-phase and quadrature component a.c. polarograms for 1.09mM Cd+2 in 0.5M KCI Applied voltage, 1 .O mv. at 1 6 0 cycles per second
graphic cell, difference amplifier, and current amplifier are housed in an open-front Faraday cage constructed of copper screen. A dummy cell consisting of 1% resistors and capacitors is used to check instrument performance. Slight phase shifts in the amplifiers, caused by imperfect passive networks, were balanced by the use of smallvalue ceramic capacitors in the input or feedback circuits. Each amplifier was balanced independently. EVALUATION OF INSTRUMENT PERFORMANCE
The frequency of operation may be altered simply by changing the frequency of the oscillator and the gain of the 90” phase shifter; no further adjustment is required for frequencies up to 1000 cycles per second. Using a dummy cell with 1% components, the results obtained were within 1% of the expected values. Short-term stability (20 minutes) was excellent and within the limit of reading of the recorder scale (o.2570). Over a period of 4 hours a drift in the instrument of less than 0.5% was observed (including warm-up drift).
The iR compensator can correct for series resistances up to about 100 ohms and, if necessary, this range can be increased (with some loss of accuracy) by increasing the value of the feedback resistor in amplifier 7. The displacement of the recorder pen is proportional to the cell admittance provided that the voltage signal (ez) does not fall below 10% of the applied voltage (el). This can only occur when the series resistance is much greater than the faradaic impedance in parallel with the doublelayer capacitance. Under these circumstances, the multiplication and division processes introduce large errors. Noise has been reduced to negligible limits relative to the applied alternating voltage of 1 mv. Figure 4 shows waveforms observed a t various points in the circuit. Figure 5 shows in-phase and quadrature-component a.c. polarograms for a millimolar solution of cadmium ion in 0.5M KC1. The applied alternating voltage is 1 mv. at 160 cycles per second. When the base admittance is subtracted from the quadrature-component
LITERATURE CITED
(1) Bauer, H. H., Elving, P. J., ANAL. CHEM.30, 334 (1958). (2) De Ford, D. D., mimeographed notes, Northwestern University, Evanston. Ill. (3) Fkost, J. G., Reilley, C. N., University of North Carolina, Chapel Hill, N. C., un ublished data. (4) . , 6AP/R Amhation Brief D4, February ‘1961,-George A. Philbrick Researches. Inc.. Dedham. Mass. Electioanal. Chem. 3, 336 (1962). ( 7 ) Jessoz; G. (to Cambridge Instrument ., Ltd.), Brit. Patent 640,768 (July 26, 1950); Ibid., 776,543 (June 12, 1957). (8) “Model SK5-M Universal Multiplier - Divider, Tentative Instruction Manual,” George A. Philbrick Researches, Inc., Dedham, Mass. (9) Morrison, C. F., “Generalized Instrumentation for Research and Teaching,” p. 39, Washington State University, 1964. (10) Ib;dl, p. 52. (11) Reillev. C. N.. J . Chem. Educ. 39. 6853, A333 (1962). (12) Smith, D. E., ANAL.CHEM.35, 1811 (1963). ~
RECEIVEDfor review May 18, 1965. Accepted July 21, 1965. Division of Analytical Chemistry, 149th Meeting ACS, Detroit, Mich., April 1965. Work supported by the Directorate of Chemical Sciences, Air Force Office of Scientific Research, Grant No. AF-AFOSR584-64.
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