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Anal. Chem. 1986, 58,517-523
though such a slope would be obtained also if the adsorption isotherm was logarithmic. It should be also noted that all the results presented in this paper have been obtained under nonequilibrium conditions (injections into the gas chromatograph); therefore no definitive statement about the origin of the signal can be made at this time and this question will be subject of further study. In principle, these devices can be used as new chemical sensors as well as tools of study of gas/solid interactions over wide range of experimental conditions. GLOSSARY activity of species i in phase a aia number of moles of species i mi gate capacitance Ci drain-to-source current ID length of the transistor channel L charge density in the space-charge region QB QSS surface state charge density R gas constant T absolute temperature VD drain voltage VG gate voltage VT threshold voltage W channel width a chemically sensitive phase X semiconductor electron affinity 71, surface dipole on phase a cp inner potential of a phase Pe chemical potential of electron
Pn
4e 4F
4m
mobility of electron in the channel work function of electron Fermi level metal-semiconductor work function difference
ACKNOWLEDGMENT M.J. wishes to thank the Humboldt Stiftung for partial financial support. The authors express their thanks to M. Levy and J. Cassidy for their assistance in this work. Registry No. MeOH, 67-56-1;EtOH, 64-17-5;i-PrOH, 67-63-0; i-BuOH, 78-83-1; polypyrrole, 30604-81-0.
LITERATURE CITED (1) Lundstrom, I.; Shivaraman, M. S.; Svensson, C.; Lundkvist, L. Appl. Phys. Lett. 1975, 26, 55-57. (2) Biackburn, G. F.; Levy, M.; Janata, J. Appl. Phys. Left. 1983, 43, 700-701. (3) Sternberg, M.; Dahlenback, B. I. Sensors Actuators 1983, 4 , 273-281. (4) Trasattl, S. Adv. Nectrochem. Electrochem. Eng . 1977, 70, 213-321. (5) Janata, J. I n "Solid State Chemical Sensors"; Janata, J., Huber, R. J., Eds.; Academic Press: Orlando, FL, 1985. (6) Murray, R. W. I n "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker, New York, 1984; Vol. 13. (7) Diaz, A. F.; Castlllo, J. J . Chem. Sac., Chem. Commun. 1980, 397-396.
RECEIVED for review August 19,1985. Accepted October 21, 1985. This work has been supported in part by the contract from the Office of Naval Research.
Intelligent, Automatic Compensation of Solution Resistance Peixin He and Larry R. Faulkner*
Department of Chemistry, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
Automatic compensation of solution resistance has been Implemented on a cybernetlc potentlostat. The system works about a test potential at whlch no faradaic reactlon occurs. By examinlng the current response to a A€ = 50 mV step across this test point, the Instrument flrst determlnes the amount of uncompensated resistance. Signal-averaged currents at 54 and 72 ps after the step edge are extrapolated backward to provide a zero-time current, whlch Is A € / R , . The system then stages the application of posltlve feedback by using a muttlplying dlgltai-to-analog converter as a digitally controlled potentiometer. A test for potentiostatic stabillty Is made after each stage. This test is carried out by appiylng a 50-mV step across the test potentlai and watching for ringing In the output of the i / V converter. When thls ringing reaches a deflned threshold, the system attempts to stablilze the network capacltlvely. When full compensation Is reached or when the system can take no further action without crossing the allowed ringlng threshold, the process ceases. Normally full compensation is possible. An anaiysls of the stability crlterlon is discussed, and examples of performance are offered.
In controlled-potential electrochemical methods, the uncompensated solution resistance R, causes two problems: a potential control error due to iR, drop and a slow cell response
due to a finite cell time constant. The usefulness of many electrochemical data depends on the precision and accuracy of potential control. Eliminating the effect of solution resistance in electrochemical measurements is very important, and much effort has been spent on this problem (1-5). Several different approaches have been taken, including improved cell design, numerical data correction after the experiment if R, is known, and electronic iR elimination. Better results can often be obtained by using a combination of these approaches. In use of electronic methods, careful design of the potentiostat is very helpful. The current interruption potentiostat (6-9) and the digital potentiostat (10) were designed so that the sensing of the potential between the working electrode and reference electrode is accomplished when no current passes through the electrochemical cell. The potential control is thus free of iR error. With a normal potentiostat, the iR drop can be compensated by making the current-to-voltage converter into a negative resistance element (11,12) or by positive feedback (13-27). The latter method is now widely used because it is compatible with the fastest experimental methods. Figure 1 shows a circuit diagram of the commonly used adder potentiostat, which allows iR compensation to be readily accomplished by positive feedback. The compensation is done by sampling the output of the i l V converter, which is proportional to the iR drop in the cell, and feeding a fraction of the sampled output (through potentiometer P1) into the input of the potentiostat. A widely used technique is to adjust the
0003-2700/86/0358-0517$01.50/00 1986 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
0
Ij_______;
lfRt
Figure 1. Conventional potentiostat with posltive feedback iR com-
pensation.
potentiometer, so as to gradually increase the amount of feedback, until the potentiostat oscillates, and then reduce the positive feedback a little to stabilize the system. Since the critical point where the potentiostat starts to oscillate does not necessarily correspond to full compensation, either undercompensation or overcompensation can result. Another problem is that the potentiostat is pushed out of the control by driving it to oscillation. This procedure can therefore destroy sensitive electrodes, such as some types of chemically modified electrodes, which are now of interest to many electrochemists. A highly desirable goal is to achieve full compensation in a manner based on automatic prior measurement of the resistance that needs to be compensated. Bezman (7) achieved this goal by combining an automatic current interruption scheme with a positive feedback compensator. His system was effective, but only on time scales of about 10 ms or longer. Yarntizky et al. (28,29)devised an analog null balance method that self-adjusted to full compensation during periodic interruptions in potential control, but they used it only with a two-electrode system and never addressed the question of stability in a three-electrode system at full compensation. We have developed a microcomputer-based cybernetic potentiostat (30) having as one of its important features a fully automatic approach to resistance compensation. The compensation procedure is under computer control, but the general principle is the same as the manual case described above involving positive feedback for iR compensation. To apply the correct amount of compensation, the actual uncompensated solution resistance is measured first. If the measurement is accurate and the system is stable under full compensation,
both under- or overcompensation can be avoided. The stability of the system is tested after each increase in the amount of positive feedback until the desired compensation or the maximum allowed compensation is attained. The system is never brought into oscillation during the tests for stability. Through an intelligent circuit-stabilizing approach, 100% compensation is often possible. EXPERIMENTAL SECTION Chemicals. All chemicals used in this work were analytical reagents. Distilled water was used for aqueous solutions. All solutions were degassed prior to the experiments by bubbling nitrogen through them. Instrumentation. A cybernetic potentiostat (30,31)was used in this work. This device is a custom-built Z80-based version that operates in an Intel Multibus chassis. The basic circuit of the potentiostat is the same as that shown in Figure 1, with some modifications (31). The problem of applying a variable, computer-selectabledegree of feedback was solved by using a multiplying digital-to-analog converter (DAC) as a digitally controlled potentiometer. The details are shown in Figure 2. There, IC2 is a 12-bit multiplying DAC, containing essentially a ladder resistor network. The voltage output of the DAC is obtained from IC3. The output of i / V converter is fed into the Vrefinput of the DAC; hence the output of IC2 will be a fraction of this V, with the fraction being digitally controlled by the computer through the 1/0 port. The output and input relationship of the DAC is Vout = -V,,,(A1/2
+ A2/4 + A3/8 + ... + A12/4096)
(1)
where A, = 1, if the A, digital input is high, and A , = 0, if the A,, digital input is low. It is very easy to see that the DAC is functionally a potentiometer, with the advantages of being fast to set, having low noise, offering simplicity, requiring no mechanical parts, and being compatible with digital control. Amplifier IC6 is an inverter that alters the phase of the DAC output to satisfy the requirement for positive feedback. It is also a five-decade gain control amplifier to allow a large active compensation range and to minimize the effects of quantization error in the DAC. For high control precision, the digital input to the DAC corresponding to 100% compensation is usually chosen in the range 40010-400010,and the needed gain of IC6 is then calculated and set. During the stability test (see below) the DAC control number is changed as the amount of feedback is altered, but the gain of IC6 will remain unchanged. Capacitors C1 and C2 are connected across the reference electrode and counter electrode terminals. They are used to
Compute BUS
PORT Decoder
IC1
IC2
IC3
8255
DAC1220
LF351
Figure 2. Schematic diagram of the digital iR compensation circuitry. The resistance R , is a six-decade resistance network controlled by relays operated from the instrument keyboard. The value of R is 10 kQ. The output of the i l V converter in the upper left Is monitored by a 12-bit ADC to give digital readings proportional to current flow, as described in ref 30 and 31.
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
519
REFERENCE
%e
Flgure 3. Simplified equivalent circuit of an electrochemical Cell.
stabilize the system in a manner that will be discussed in more detail later. Compensation can be enabled or disabled by closing or opening the switch F. The electrochemical cell used for polarographic experiments was an EG&G PARC Model 303 static mercury drop electrode (SMDE). A Pt disk working electrode with 0.2 cm diameter was used for voltammetric work. In both cases, a Ag/AgC1(1 N KC1) reference electrode and a Pt auxiliary electrode were used. A dummy cell was used for the functional trials described below. The circuit shown in Figure 3 was used as a dummy cell, but with Zf at open circuit. The capacitance Cd was fixed at 1pF. The resistances R, and R, always had equal values, but they were variable. All of the components had 1%precision.
RESULTS AND DISCUSSION iR compensation is one of the cybernetic potentiostat's system ("star") functions. By invoking the "IR" command and then answering queries for test potential, desired percentage of compensation, and allowed overshoot level, the operator initiates an automatic sequence involving evaluations of resistance, cell time constant, and stability. The measured resistance, cell time constant, percentage of compensation achieved, and remaining uncompensated resistance will be reported on the screen. The process takes about 4 s. Resistance Measurement. To make iR compensation correctly, the actual solution resistance has to be measured. Well-established methods include bridge impedance measurements (2) and conductance measurements at very high frequency (3). However, these are tedious and involve some additional fairly complex circuitry. Also, the uncompensated solution resistance depends on electrode position and cell geometry, so the solution resistance measurement and compensation should be done under the same cell conditions that will be used in the controlled potential experiments. Figure 3 shows a simplified equivalent circuit of an electrochemical cell. The value of R,, regarded as "compensated solution resistance", is of no interest. The solution resistance between working electrode and reference electrode is R,, which is the uncompensated solution resistance that must be measured. The impedance 2, represents the faradaic impedance, and C d is the double layer capacitance of the working electrode. At any potential where no faradaic reaction occurs, the faradaic impedance is very large and can be considered as approximately an open circuit. Between the reference and working electrodes, there are only two elements, a resistance R, in series with a capacitance c d . If one applies a potential step AE across the reference and working electrodes, the current response will be a pure charging current with an exponential decay
i(t) = W / R J exp(-t/R,Cd)
(2)
If the current is measured a t t = 0, the exponential term will be unity, the parameter C d disappears, and i(0) = aE/R,. Since AE is known R, can then be calculated. It is not difficult for the computer to sample the current response a t a time very close to zero. However, due to finite potentiostat rise time, the current response will not have reached its maximum. In our instrument, it continues to rise for about 40 ps after the step function is applied. Thus the current has to be measured after some delay time. We sample
L 0 54 tips 72
Figure 4. Current transient after application of AE and extrapolation back to t = 0: (A) applied potential wave form, (B) current response.
Table I. Calculated Measurement Error measure-
cell time constant/ps
measurement error/%"
cell time
ment
constant/ps
error/%"
50 100 150 200 250
35.24 12.92 6.56 3.95 2.63
300 350 400 450 500
1.88 1.41 1.09 0.87 0.71
"For i(0)estimated by linear extrapolation from samples at 54
and 72 us.
i(tJ after a 54-ps delay and i(t2) after a 72-ps delay. Provided that t2is small compared to the cell time constant, the decay of charging current is nearly linear, so that i(0)can be calculated by extrapolation. This procedure is shown graphically in Figure 4. The error of i(0)measurement resulting from curvature in the decay is always negative and depends on the cell time constant error (5%) =
(
- t 2 exP(-tl/R,Cd)
- t , exP(-t2/RuCd) t2
- tl
)
x 100 (3)
Table I lists the measurement error as a function of cell time constant, calculated according to eq 3. If R,Cd is bigger than 500 ps, the error will be smaller than 1% ;however the error could be considerably bigger than 10% if R,Cd is less than 100 ps. Some error of this kind is quite natural, since it is very difficult for a measurement system to precisely measure the transient response of a network that has a time constant comparable to or smaller than that of the measurement system itself. If a faster potentiostat could be used, a shorter measurement delay time could be allowed, and the resistance in a cell of smaller time constant could be measured. In practice, once the time constant of an electrochemical cell is comparable to the response time of the potentiostat, the iR compensation no longer makes much sense, unless very large currents are to be measured. A 50-mV potential step is applied in measuring the resistance. The step is from a potential 25 mV more negative than the specified test value to a potential 25 mV more positive than the test point. The test potential should be chosen as a value where no faradaic reaction occurs. The gain of the i/ V converter is autoranged, in order to obtain a maximum digital reading. To reduce interference from electrical noise, both i(tJ and i(tJ are sampled 256 times in repeated step
520
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
Table 11. Measured Resistance and Time Constant via Linear Extrapolation
Table 111. Measured Resistance and Time Constant via Exponential Extrapolation
measured
measurement/
R,/Q
measured RC time constant/ps"
Ru/Q
90
50.1 100.5 147 200 250 301 347 403 452 502 998 9990 99700
50 100 150 200 250 300 350 400 450 500 1000 9700 >50000
96 109 156 207 255 306 348 40 1 450 499 981 10065 99610
92 8.5 6.1 3.5 2.0 1.6 0.3 -0.5 -0.4 -0.6 -1.7 0.7 -0.4
error of Ru
error of R, measured
measurement/
R,/Q
time constant/rsa
Ru/Q
90
50.3 100.4 150 200 250 300 347 401 452
38 94 146 198 250 302 350 406 460
29 92 145 198 249 301 349 404 449
-42 -8.4 -3.3 -1.0 -0.4 +0.3 +0.6 +0.7 -0.7
" A 1.0-pF capacitor was used for the measurements. See Table 11.
" A 1.0-pF capacitor was used for all the measurements, so the true cell time constant in microseconds is equal numerically to the value of R, in ohms.
cycles and the values of i(0)and R, are then calculated. By measurement of the time that it takes for the current to decay to 37% of the initial current i(O), the cell time constant is evaluated, although this is done only within 50-ps resolution. Table I1 shows resistance and time constant measurements for a dummy cell. The error is quite large when the RC time constant is low, but the errors found were close to the estimated values (Table I). The accuracy was within 1% when the RC time constant was longer than 350 ps, except a t one point. Also, for most measurements, the reproducibility was better than 1%. We also explored the possibility of reducing the error due to the linear extrapolation by using an exponential extrapolation instead. In this case, il was sampled a t a fixed time tl (54 ps) and i2 a t a variable time, t2. From eq 2, we have il/& = eXP[(h - tl)/R,Cd] = exP[At/&Cd] (4) The time constant of the cell is
R,Cd = At/[ln (il/i2)]
measured RC
(5)
and the current at zero time is The error of the logarithmic factor in eq 5 can be large if il and i2 have similar values. For this reason, At was chosen to be 0.7R,Cd so that il is about twice i2. The value R,Cd was estimated preliminarily as described earlier. Since At is excessively long if the cell time constant is long and since 256 repetitions are necessary for noise rejection, the exponential extrapolation was used only if the cell time constant was shorter than 500 ps. For a cell with longer time constant, the linear extrapolation was used to save time, because the measurement error is not significant anyway. Resistance measurements for various dummy cells via the exponential extrapolation are listed in Table 111. The reported RuCd values were computed by using eq 5. The measurement error is generally smaller than with linear extrapolation, but a sizable error still exists when the cell time constant is very short. It is likely that this residual error is a consequence of nonideal rise in the current response, as discussed above. The exponential extrapolation was made possible by introducing the arithmetic processor AM9511 into a new version of our instrument. In the old prototype and in the BAS-100 (see below), only linear extrapolation can be carried out. The remainder of this paper deals with studies that were carried out on the original BAS-100 prototype and involve mea-
surements of R, via linear extmpolation. System Stability. Even given the known resistance, one must still know if it is possible to make full compensation, that is, if the circuit is stable with compensation. In the cybernetic system, the computer regards the measured resistance as the full compensation amount and applies compensation gradually toward this amount with a test for stability after each increase. At high degrees of compensation, there is often an instability in the potentiostat due to the nonideality of the potential control amplifier and the phase shift in the electrochemical cell. For an adder potentiostat, the circuit is stable if the phase shift is smaller than 180' at the reference electrode point vs. the ideal response expected there. However, the transfer function of any amplifier is frequency dependent. For an amplifier with a single-pole characteristic, a -90' phase shift can apply at frequencies much higher than the corner frequency, The electrochemical cell introduces an additional phase shift at the reference electrode, due to the double layer capacitance load. This phase shift will approach -90' if the uncompensated resistance is very small and the frequency is high. The total -180' phase shift a t the reference electrode point makes the potentiostat circuit actually experience positive feedback, with a total gain greater than or equal to unity; hence the system becomes unstable and oscillates. The situation could be even worse. The distributed parameters of the potentiostat, such as stray capacitance, can also cause some additional phase shift. In practical operation the potentiostat often oscillates at a point where the solution resistance is not fully compensated. According to stability analysis for electronic circuits (32), for any system to be stable, its poles should lie in the left half of the Laplace plane. The system response to a step function will approach the ideal response for infinite bandwidth either with or without an underdamped oscillation showing an exponential decay of its amplitude envelope, depending on the phase margin of the whole System. The overshoot increases as the phase margin is reduced, eventually approaching infinity when the phase margin is zero. Zero phase margin, of course, implies that the potentiostat will sustain free oscillation. On the other hand, the amount of overshoot is closely related to the phase margin and can be used to test the stability of the system. In principle, the overshoot could be monitored in our system at the output of the reference electrode follower. However, a spike, which is the positive feedback voltage corresponding to the charging current due to the potential step, is superimposed on the output of the reference electrode follower. This spike could be misunderstood as the overshoot, even though the extent of positive feedback might be far away from full compensation, with the system remaining very stable. Al-
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
0
t/ms
521
3
E[UOLTI
Flgure 0. Phase-selective ac polarograms of 5 X 10" M &I2+ in 0.002 M KCI solution (A) without compensation and (B) with compensation.
t/ms
Figure 5. Stability test wave form and current response: (A) test potential wave form, (B)current response when iR compensation is applied and critical point is approached.
ternatively one could relate the stability to the negative swing, below the potential step setting, which appears only when overshoot happens. On the other hand, the signal at the output of the reference electrode follower is inadequate for precise A/D conversion. An additional amplifier would be necessary and an analog multiplexer would be needed for the sampling APC. These problems make the observation of overshoot difficult at the follower output. Fortunately, the underdamped oscillation can also be obtained, with a much larger signal level, at the output of the current-to-voltage converter. Observing at that point greatly simplifies the test circuitry. In the stability test, a potential step is applied exactly as in the resistance measurement. The test starts from 0% compensation, gradually increasing to 80% in 5% increments, then to 90% in 2% increments, and to 100% in 1%increments. The test is carried out on the sensitivity scale that will be used for later voltammetric experiments. To test for overshoot, the computer first samples the current io before the step is applied. After the step is applied, the computer samples data at 20 kHz for 3 ms. Both the forward maximum current,,,i which is mainly a charging current spike, and the reverse minimum current i,,, are determined. Figure 5 shows the typical response. If i,,, is not less than io, then the overshoot is zero. Otherwise it is defined as overshoot (%) =
1-
- 10 lmax - ZO lmin
X
100
(7)
Sometimes, noise can affect the stability test, especially when the electrochemical cell is very resistive or an improperly coarse sensitivity scale is used in the experiment. In these cases, the signal is very low, and the noise may produce an apparent current below io,which would be regarded as overshoot. In this circumstance, the system can stap the stability test at an unnecessarily low compensation level. To avoid this problem, our system repeats the test procedure eight times for signal averaging, whenever the overshoot level exceeds the declared limit. The potentiostat circuit as a whole has two poles. One is the single-pole of the control amplifier and another is due to R,, R,, and Cd of the electrochemical cell. For a two-pole system, if the overshoot in the response to a step-function input, as normally measured (i.e., voltage output), is less than lo%, the phase margin is at least 60' (33),and the amplifier is quite stable. For the stability test in our system, the default value of allowed overshoot is thus chosen at 10%. Since the overshoot in our case is defined differently than for a normal
test, this percentage of overshoot may not correspond to a 60' phase margin, but in practice we find that the actual margin is very safe. A large overshoot will lengthen the settling time, so if the response time is paramount, a very large overshoot may not be acceptable. If precision and accuracy of potential control are wanted, full compensation is important, and a high overshoot level could be allowed. In practice, the system is still stable with even a 50-80% overshoot level. For electrochemical systems, it is quite often true that the circuit becomes unstable before 100% compensation is reached. In order to make full compensation possible, some sort of stabilizing circuit has to be used. One fairly effective approach is to insert a capacitor between the reference electrode and counter electrode (14), e.g., as C1 and C2 are shown in Figure 2. Since the double layer capacitance causes a negative phase shift at the reference electrode point, adding this capacitor tends to introduce a positive phase shift at the same point. The combined effect is then that the total phase shift is reduced. This approach can effectively stabilize the system, as one can readily verify by the reduced overshoot observed on an oscilloscope when the stabilizing capacitor is inserted. For different electrochemical systems, the optimum stabilizing capacitor may be different. At the beginning of the test, no stabilizing capacitor is connected. Only when positive feedback is applied and the current response yields a bigger overshoot than that allowed will C1 or C2 be connected. The system will make further tests and decide the best option. If the stability is satisfactory, more positive feedback will be applied. If the declared compensation level is achieved, the computer stops increasing the positive feedback, and sets this amount of feedback for later experiments. However, if the computer stops testing because the system is close to oscillation, it will reduce the positive feedback to the last stable test level, to ensure that the system is stable for experiments. By use of this system stabilizing approach, full compensation is often possible. All of the tests are monitored by the computer, and oscillations that will take the system out of control and permanently damage some electrodes will not happen. If the resistance measurement is correct, overcompensation can also he avoided. In the manually controlled compensation case, overcompensation sometimes happens without oscillation of the system. This is definitely unwanted (16). Performance. As a test of the system, several resistive electrochemical syetems were examined. For comparison, experiments with and without iR compensation were both carried out. Figure 6 shows phase-selective ac polarograms of 5 X M Cd2+in 0.002 M KC1 solution. The resistance measured was about 10 kQ and the cell time constant was 4.5 ms. In
ANALYTICAL CHEMISTRY, VOL. 58, NO. 3, MARCH 1986
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E IUOLT I
Figure 7. Square wave polarograms of 5 X M Cd2+ in 0.002 M KCI solution (A) without compensation and (B) with compensation.
ideal ac polarography, the charging current leads the applied potential by 90°, so a software lock-in amplifier set to zero phase shift ought to detect no charging current. Because the double layer capacitance of any real system is in series with a solution resistance, the charging current phase shift is smaller than 90°, and there will be a detected component of charging current at 0'. As R, increases the detected component grows larger. Figure 6A is the result obtained for our experimental case without iR compensation. As a consequence of the large R,, the charging current contribution at 0' is appreciable, and it gives a sloping background. For the same experiment with automatic iR compensation, as shown in Figure 6B, a much higher signal-to-background ratio is obtained. Figure 7 shows Barker square-wave polarograms of the same chemical system. In this experiment, the modulation frequency is 50 Hz, and the sample delay time is 5 ms. For complete charging current decay, a five time-constant delay is necessary. With a 4.5-ms cell time constant, this condition is not satisfied at all, so the polarogram without compensation (Figure 7A) is severely distorted by the charging current. In contrast, the base line shown in Figure 7B is close to zero tmd flat, because the solution resistance has been compensated and the cell time constant is shortened enough to allow full decay of charging current before sampling. Resistance problems are usually more serious in nonaqueous solutions. Figure 8 is a set of cyclic voltammograms for 1mM ferrocene in a CHzClzsolution containing 0.1 M TBABF4. Without iR compensation, the separation between anodic and cathodic peaks is 224 mV. As the compensation level is increased, the peak heights become higher, and the peak separation becomes smaller. With full compensation, the peak separation is about 59 mV, which is the expectation for reversible one-electron transfer. In these three examples, the existence of the uncompensated solution resistance caused different problems. However, all of them were very well solved by intelligent automatic iR compensation. We have used this approach for 3 years under a wide variety of circumstances and have found it to be extremely reliable. As an example of the ability of the system to adapt to rather extreme conditions, we can mention a case in which a reversible cyclic voltammetric response was obtained for ferrocene in an LCEC cell. The amount of com-
Figure 8. Cyclic voltammograms of 1 X M ferrocene in CH,CI, solution containing 0.1 M TBABF,: curve (1) 0, (2) 20%, (3)40%, (4) BO%, (5) 80%, (6) 100% iR compensation. Electrode is a Pt dlsk of 0.2 cm diameter. Results in lower right corner are for curve 6.
pensation required and applied was 204 kR. Since the currents were of microampere magnitude, the compensated error was several hundred millivolts. We have found occasional measurements of uncompensated resistance to be unexpectedly useful in indicating degradation (e.g., by filming) of the working electrode surface during a series of experiments. In these instances, there is a progressive rise in the uncompensated resistance measured after each experimental run in a sequence. This compensation scheme will not be effective for systems in which the uncompensated resistance changes appreciably during an experimental run. Many electrode processes involving a change in the electrode surface can give rise to such an effect. A dynamic compensator like that of Bezman (7) or Yarnitzky and Klein (28,29) would be required. A related matter is that Cd may be a sufficiently strong function of potential to reduce the phase margin unsatisfactorily as a sweep is carried out. Such a circumstance is fairly rare, but if it is encountered, dynamic compensation by an interrupter would be necessary. The hardware design and algorithms described here are virtually the same as those operating in the BAS-100 cybernetic potentiostat commercialized by Bioanalytical Systems, Inc. However, the signal averaging procedure used upon exceeding the overshoot threshold postdates the BAS-100 and now exists only on our prototype system. In addition there are some variations in component selection between our system and the BAS-100.
ACKNOWLEDGMENT We appreciate the suggestion by D. K. Roe that exponential extrapolation be explored. Registry No. Cd, 7440-43-9; KCl, 7447-40-7; TBABF4,42942-5; ferrocene, 102-54-5. LITERATURE CITED ( 1 ) Britz, D. J. Electroanal. Chem. 1978, 88, 309. (2) Sawyer, D. T.; Roberts, J. L. "Experimental Electrochemistry for Chemists"; Wlley: New York, 1974; Chapter 5. (3) Roe, D. K. I n "Laboratory Techniques In Electroanalytical Chemistry"; Klssinger, P. T., Heineman, W. R., Eds., Marcel Dekker: New York, 1984. (4) Bard, A. J.; Faulkner, L. R. "Electrochemlcal Methods"; Wiiey: New York, 1980; Chapter 13. (5) Smith, D. E. CRC CrM. Rev. Anal. Chem. 1971, 2 , 247. (6) McIntyre, J. D. E.; Peck, W. F., Jr. J. Nectrochem SOC. 1970, 1 1 7 , 7I _ A ,f
.
(7) Bezman, R. Anal. Chem. 1972, 4 4 , 1781. (8) Britz, D.; Brocke, W. A. J. Electroanal. Chem. 1975, 5 8 , 301. 1% Moors. M : Demedts. G. J \_, . . Phvs. E 1976. 9. 1087. (IO) Goidsworthy, W. W.; Clem, R.'G. Anal. Chem. 1972, 4 4 , 1360. (11) Gabrielii, C.; Keddam, M. Electrochim. Acta 1974, 19, 355. (12) Lamy, C.; Herrmann, C. C. J. Electroanal. Chem. 1975, 5 9 , 113.
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~
523
Anal. Chem. 1986, 58,523-526 (13) Booman, G. L.; Holbrook, W. B. Anal. Chem. 1963, 35, 1793. (14) Brown, E. R.; Smith, D. E.; Booman, G. L. Anal. Chem. 1968, 4 0 , 141 1. (15) Brown, E. R.;Hung, H. L.; McCord, T. G.; Smith, D. E.; Booman, G. L. Anal. Chem. 1988, 4 0 , 1424. (16) Bewlck, A. Nectrochim. Acta 1968, 73,825. (17) Garreau, D.; Saveant, J. M. J . Nectroanal. Chem. 1972, 35, 309. (18) Brown, E. R.; McCord, T. G.; Smith, D. E.; DeFord, D. D. Anal. Chem. 1966, 38, 1119. (19) Schroeder, R. R.; Shain, I. Chem. Instrum. 1969, 7 , 233. (20) delevie, R.; Husovsky, A. A. J . Elecfroanal. Chem. 1969, 2 0 , 181. (21) Piiia, A. A.; Roe, R. 6.; Herrmann, C. C. J . Nectrochem. Soc. 1969, 116, 1105. (22) Piila, A. A. J . Electrochem. SOC. 1971, 718,702. (23) Weiis, E. E., Jr. Anal. Chem. 1971, 4 3 , 87. (24) Sarma, N. S.; Sankar, L.; Krishnan, A.; Rajagopaian, S. R. J . Electroanal. Chem. 1973, 4 7 , 503.
(25) Deroo, D.; Diard, J. P.; Guitton, J.; Gorrec, B. J . Nectroanal. Chem. 1976. 67. 269. (26) Gabrkili, C : Ksouri, M.; Wlart, R. Electrochim. Acta 1977, 22, 255. (27) Garreau, D.; Saveant, J. M. J . Nectroanal. Chem. 1978, 86, 63. (28) Yarnitzky, C.; Friedman, Y. Anal. Chem. 1975, 4 7 , 876. (29) Yarnitzky. C.; Klein, N. Anal. Chem. 1975, 4 7 , 880. (30) He, P.; Avery. J. P.; Fauikner, L. R. Anal. Chem. 1982, 12, 1313A. (31) He, P. Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1984. (32) Sedra, A. S.;Smith, K. C. "Microelectronic Circuits"; CBS College Publishing: New York, 1982. (33) Shea, R. F. "Amplifier Handbook"; McGraw-Hill: New York, 1966.
RECEIVED for review June 25, 1985. Accepted October 10, 1985. We are grateful to the National Science Foundation for supporting this work through Grant CHE-81-06026.
Immobilized Enzyme Electrode for the Determination of Oxalate in Urine Mohammad A. Nabi Rahni and George G. Guilbault*
Department of Chemistry, University of New Orleans, Lakefront, New Orleans, Louisiana 70148 Net0 Graciliana de Olivera
Instituto de Quimica, Unicamp, Campinas, Brazil
An lmmobllized enzyme electrode for the assay of oxalate, particularly In urlne, was constructed. I t Is based on the lmmoblllzatlon of the enzyme oxalate oxidase on pig Intestine, mounted on the tip of an oxygen electrode. The oxygen partial pressure was amperometrlcally monitored, the current change being converted to a voltage through an adapter, whlch could then be monitored directly on a dlgttal voltmeter. The experimental parameters were all optimlzed, and callbration curves based on both the initial rate and the steady state were constructed. The enzyme electrode response to oxalate in urlne samples from 14 patlents was compared to that obtained by the establlshed spectrophotometric method. The proposed method exhibits high sensitivity and speclflclty to oxallc acid with almost no loss of relative activity due to interferences studied. There Is no sample pretreatment required and the method can be modlfled to be equally useful for the assay of oxallc acid in any blologlcal or nonblologlcal samples.
During recent years, there has been an increasing interest in the determination of oxalic acid in a wide variety of biological and nonbiological materials (1);oxalate has also been used in analytical (2) and manufacturing procedures (3). It has also been shown that increased urinary oxalate excretion may lead to the development and formation of renal calculi and urinary tract stones ( 4 , 5 ) . The determination of oxalate in urine is also clinically important for the diagnosis of various forms of hyperoxaluria, a genetic disorder of oxalate metabolism characterized by the early onset of calcium oxalate nephrolithiasis and nephrocalcinosis (6, 7). Current methods for determination of oxalic acid can be divided into three main groups: (1) solvent extraction and precipitation; (2) isotopic dilution; and (3) enzymatic analyses. Excellent reviews of these methods can be found elsewhere
(8, 9). Among these, enzymatic methods generally seem to be promising in terms of specificity, selectivity, and sensitivity where sample preparation (preconcentration, extraction, etc.) is minimal. Two enzymes have now been identified in purified form: oxalate decarboxylase [EC 4.1.1.21 from the wood rot fungus (Colybia velutipes ref lo), which has been shown to be highly specific in catalyzing the stoichiometric reaction: oxalate COz + formate; and oxalate oxidase [EC 1.2.3.41 prepared from plant tissue (11,12), which catalyzes the reaction
-
(C0OH)Z + 0
oxalate oxidase 2
2C02
+ HzOz
The immobilization of enzymes has found ever increasing popularity, since in most cases the enzyme stability is increased, the effects of enzyme inhibitors greatly reduced or eliminated (13, 14), and the immobilized enzyme useful for many assays. Enzyme electrodes have opened a new era in clinical analysis (13). The method presented herein utilizes the purified enzyme oxalate oxidase, immobilized on an oxygen electrode, for the determination of oxalate in urine. An amperometric method is more sensitive than a potentiometric based oxalate decarboxylase electrode method (15,16). It can be applied to small volumes of untreated urine and is therefore not subject to errors introduced by preliminary treatments. The method outlined here is a rapid, one-step procedure suitable for the analysis of any samples containing oxalate.
EXPERIMENTAL SECTION Apparatus. A PHM 84 Research pH meter coupled to a REC 61 Servograph recorder (Radiometer America, Inc.) through a dc offset module and potentiometric amplifier (Model EV-200-1and 2, Schlumberger) was used for all measurements. To eliminate the necessity of using a polarograph to monitor the amperometric oxygen electrode, an adapter (Model No. CP-960, Universal Sensors, Inc., P.O. Box 736, New Orleans, LA) was used. It is a device that will simultaneously apply the desired potential to the amperometric enzyme electrode, take the resulting current
0003-2700/86/0358-0523$01.50/0 0 1986 American Chemical Society
