Electronic configurations in potentiostats for the correction of ohmic losses

Electroanalysis, 6( 1994) 531-542

REVlEw ARTlCE

Electronic Configurations in Potentiostats for the Correction of Ohmic Losses

Ricardo M. Souto Depamnent of Pl!sicai Che17~2st1y, C'nav?mt] of La Laguna, Tenenjie, Spaziz Recezr ed April 30, 1992

ABSTRACT Recent trends in the design of potentiostats capable of correcting for ohmic losses occurring in electrochemical cells are reviewed. The various effects of ohmic drop occurrence and their influence on diverse electroanalJ.tica1 techniques are considered, as well as potentiostat configurations and stabilig., with emphasis in the three-electrode cell configuration. Electronic correction methods are discussed according to the following classifications: ( 1) positive feedback, ( 2 ) negative impedance, (3) current pulse, ( 4 ) analogic subtraction. and (5) current interruption.

KEY WORDS: Potentiostat, Ohmic drop, Instrumentation

SCOPE OF THE PROBLEM

In electrochemistry, controlled-potential experimem are performed b!. using a potentiostat. This instrument makes possible the automatic maintenance of the potential of the working electrode (WE) at a programmed value relative to the reference electrode (RE), irrespective of changes in the current passing through the electrolytic cell and/or in the solution resistance. In a three-electrode cell. such operation is continuously achieved by comparing the cell and reference signals, changing the potential of the counter electrode (CE) as necessary to compensate for any difference arising. That is, the cell current is increased or decreased to maintain the equal- iK between rhe cell potential and the reference signal.

Yet, the electrical characteristics of the electrochemical system have not been considered. From an electronic point of view, a three-electrode electrochemical cell can be regarded [ 11 as the network of impedances shown in Figure 1, where Z, and Zll. represent the interfacial impedances at CE and WE and the solution resistance is split into two portions, Rn and R,,, depending on the position of the reference electrode's probe in the current path. Ideally, the potentiostat should control the interfacial potential only, without interference of ohmic losses. However, the potentiostat is capable of compen- sating the ohmic drop in the solution except for its fraction occurring between RE and WE. That is, the controlled voltage contains a portion 1. R, of the total voltage drop in the solution. The presence of this uncompensated resistance loss keeps the potentiostat from giving an accurate control of the desired potential. Thus, a change of potential between these electrodes corresponds to a change of potential across the double layer of UC'E only

if RE is not polarized and the 1. R,, drop between them is negligible. But the potential-measuring probe in the electrol).te cannot measure at a point directly on the solution side of the double layer, thus causing a voltage drop that adds to the measured potential [l-31. The accurate control of potential is most important in cyclic voltammetn. The existence of the uncompensated resistance causes the potential sweep to be nonlinear: the distortion may be large enough so as to invalidate sub- sequent analysis in terms of a preconceived model ( e g , the expected dependence of current on the square root of scan rate for a reversible system). This effect shows up spectacularly at the dropping mercury electrode (DME), because the resistance R, is concentrated in a volume close to the drop and varies with the drop size. making the ohmic loss and the potential of the drop variable also j4-61.

A second effect of R,, occurrence is that it causes a slow cell response due to a finite cell time constant. That is, the charging of the double-laver capacity has a time constant equal to R,, . C,, which defines the shortest time domain over which the cell will accept a significant perturbation. which will be longer the larger R, is [7,81. In ac impedance studies, the series combination of R, and C, produces a phase shift between the actual applied PO- tential and the imposed sinusoidal signal, and in higher harmonic ac polarography, R,, introduces artificial har- monics into the current [ 9 ] .

A third effect is related to its time dependence. The value of Z.R, is a function of time: therefore. a finite capacity current exists throughout the electrochemical

'To =horn correspondence should be addressed.

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532 Souro

5. .l.lathematicnl methods. I ’a l id i~ o f the modified Tafel equation for an electrochemical reaction is assumed. The equation relates the current flowing to the applied potential according to

(1)

A linear relationship can be obtained by differentiat-

+ R,‘ ( 2 ) -

I Ilt.

RU ZW

7 = a + 0- log1 + i .R , ,

0 WE ing this equation, yielding

FIGURE 1. Equivalent circuit of an electrochemical cell. d77 - 0 dl i

experiment [7]. This charging current adds to the current resulting from the potentiostatic perturbation, the measured current being the result of several perturba- tions. Thus. in a potential pulse experiment. the measured current can never be exactl!. equated with the faradaic current.

These effects represent a very severe limitation to relaxation methods and must be corrected.

OHMIC LOSS DETERMINATION The accurate determination of the ohmic loss in electrochemical cells can be performed experimentally. Es- isting methods can be classified into five groups.

1. .l~icrool?zet~--nzounted Lugging pi-ohe. The reference electrode normally is located in a salt bridge and connected to the solution by a Lugging capillary whose tip is placed close to WE. This minimizes the ohmic drop error as the distance between RE and WE is kept small. Nevertheless, the Luggin’s tip cannot be directly placed on the working electrode surface, a certain ohmic loss thus remains. R, measurement can be performed by mounting the Luggin probe in a mi- crometer system and varying the distance between the Lugin‘s tip and the electrode surface. Oven7oltage is measured as a linear function of distance and then extrapolated to zero [ 10,111. At ven short distances, shielding of the capillary has to be considered, which results in a lower current, and the overvoltage values decrease more quickly [ 121.

2 . Gablanostatic methods. Determination of the solution resistance can be performed b!- introducing the electrochemical cell in an arm of a Wheatstone bridge. An adjustable resistor is set to achieve compensation. Next, the cell voltage is measured with an oscillo- scope by applying galvanostatic pulses to the cell [ 12- 141.

3. Impedance and phase-sensitice measurements. The ohmic resistance can be directly determined from impedance [ 15-17] and phase-sensitive measurements [18].

4. Current-intewuption methods. The potential between WE and RE is measured when no current flows through the cell. As these methods constitute a procedure for the IR correction in potentiostats, they will be considered subsequently.

the value of R,, being the ordinate of the dq/dl versus I plot [19!20].

TRENDS IN OHMIC LOSS CORRECTION From the foregoing, it can be concluded that it is very important to correct for the effects of solution resistance in electrochemical determinations. Procedures for the accounting of the ohmic loss across R,, have been the subject of many articles and can be classified into four groups.

1. Imp?-oued cell design. It is by no means a method of ohmic loss correciion, but it may lead to minimization of residual resistance. Thus, potential distribution about many geometrical arrangements of the electrodes. RE and Luggin probe configurations. and WE resistance minimization have been considered [3.21]. Ten years ago, the use of microelectrodes as working electrodes was introduced [22-25] for the attainment of systems with small, constant, and time-independent i - R , , drops [22,23]. as the ohmic drop ZeR,, and time constants R,, . C, relative to the capacitive currents are reduced considerably b>- reducing the electrode size (it decreases proportionally to the electrode diameter since R,, increases proportionally to the inverse of the diameter and the current decreases proportionally to the diameter squared). Nevertheless, Saveant’s and Wightman‘s groups [26-281 have shown that R, and R,, . C, values are not negligible when operating2t ~7en

high voltammetric scan rates (above 1000 V.s ’) and must be corrected. Very recently, a dropping mercun. microelectrode has also been presented [29] which will allow one to minimize R, effects in polarographic techniques.

2 . Numerical data coirection after the experiment, if R,, is known (the “postfactum approach”). This procedure implies a careful and precise determination of R,, in order to take into account the correction. Sev- eral methods have been quoted in the literature, namely, arithmetical rectification of the I . R drop [30,311 and tailoring of measured data before outputting by impedance determinations [ 32-36]. Another procedure often employed in electroanalytical voltammetry makes use of internal electrochemical standards (37- 391, i.e., a reversible electrochemical reaction is monitored in order to compare the real electrode peak

Electronic Configuratioix in Potentiostars for the Correction of Ohmic Losses 533

potential m-ith the measured value E,,,,,,, given b!.

Ep Imc‘.i\ = E p , i- Ii, . R,, ( 3 ) Errors involved in this procedure have been considered recentl!- [39,40]. Matbematical pr-ocedza-es. An exact mathematical de- scription of the response to a voltage perturbation. accounting for the time-dependent ohmic loss, is intended. In this way. the error due to incomplete correction is introduced in rhe theorerical equations describing the system [ 7,30,41]. Distorted qclic voltammograms can also be corrected by (1) the con- volution of the voltammograms with the diffusion op- erator ( 7 ~ . t)-’” [26], and (2) the comparison and fitting of experimental curves to simulated ones incorporating the ohmic and capacitive factors [27,28,42]. Electronic (instrumental) methods, by which a large fraction of the cell resistance can be corrected for. Careful design of the potentiostat must be performed. Faster charging of the double-layer capacitance is suf- ficient sometimes, and diminution of the cell-time constant can be attempted exclusively. In this case, electronic circuitn can be employed in another two ways. a. Polarization zrsing a double-pulse 2 joltage profile.

i.e., superimposition of a short pulse potential with a large amplitude on the voltage-time reference signal of the potentiostat [43-451. In this way, the rate of voltage change on the double-layer capacitance is increased during charging.

b. Charge injection. An injection capacitance is connected in series with the cell and a high-voltage step applied to this combination [46-491. A controlled amount of charge can be injected into the double-layer capacity to accomplish fast charging of c,.

THE POTENTIOSTAT The instrumental voltage-control operation was first performed by Hickling [ j O ] in 1942, though the first mod- ern-form potentiostat can be attributed to Hodgkin et al. [51,52] at the end of the 1940s. Many of the early potentiostats were servo devices, thus very slow and badly suited to transient studies. But the introduction by Booman and co-workers [ 53,541 of operational amplifiers in potentiostat design revolutionized electrochemical instrumentation. Operational amplifiers permit the perturbation of an electrode from equilibrium or steady state to be made much faster than was previously possible. In fact, the operational amplifier is basically a control circuit trying to maintain its inverting (negative) input at zero potential by means of the feedback current.

Extensive work on potentiostat design has been performed since then; as a result, the features, characteristics, and applications of the potentiostat are now well established [3, j 5-58], Potentiostats are built around an operational amplifier CA which is the conh-ol ampl@er,

(b)

FIGURE 2. Typical three-electrode potentiostat configurations: (a) differential input mode and (b) additive input mode.

and the electrochemical cell is introduced in its feedback loop. Attending to their basic configuration, potentiostats can be classified into two groups, depending on whether the input signals are introduced to the CA using its noninverting input (Figure 2a) or its inverting input (Figure 2b). The former configuration presents a differential input mode, and the second an additive input mode. The diffevential mode was extensively used in the earlier potentiostats due to its high input impedances, but only one signal can be introduced in it. In the addevpoten- tiostat, both inputs to CA are at virtual ground and allow addition of several signals to form the desired control function to be applied to the electrochemical cell. At present, the adder potentiostat is extensively used because operational amplifiers exhibit high input impedances and allow the application of complicated potential waveforms to the cell by adding various simple input waveforms at the inverting terminal. The summing char- acteristic of the adder configuration requires that the currents from the input signals be nulled by a current provided by the reference electrode. Therefore, a voltage follower (VF) is introduced into the feedback loop of CA (cf. Figure 2b) so that the RE is not loaded by the current fed into the summing point. In addition, the follower’s output is also available externally. Thus, two operational amplifiers are used in the feedback loop between CE and WE. To ease tailoring gain and speed independently, the introduction of a third operational amplifier has been proposed [59]. That is, CA is replaced b>- a series combination of a.differentia1 amplifier and

534 Sour0

- (b)

FIGURE 3. Current measurement techniques: (a) differential-amplifier mode and (b) current-follower mode.

an integrator. Nevertheless, applicabiliv of such a procedure seems to be rather restricted, only applicable to dc techniques.

Next, a current-sensitive device is necessary to measure the values of the current 2 in the cell. This element operates by converting the current to be measured to the voltage drop caused through the current-measuring resistor R,. Most widely, this element is placed in the counter electrode circuit (differential-amplifier mode operation) or is a part of the voltage clamp at the working electrode (current-follower mode operation) [ 56,571.. The basic scheme of the two operation modes is shown in Figure 3: in which the dflerential potentiostat has been used for the sake of clarity in the diagram. (The same procedure will often be followed in the figures below). In the differential-amplifier mode configuration, WE is truly grounded, making it less sensitive to noise pickup. Nevertheless: this configuration requires the use of the diffevential amplifier (DA) for which both inputs may be operating at high potentials with respect to ground since both ends of R, can be a long way off ground, which are common mode errors. Moreover, a DA presents higher drift than a single-ended amplifier, thus the latter is preferred.

Common mode error problems are avoided in the current-follower mode: because WE remains at virtual ground since it feeds a currentfollower. But WE now is

I Ri

s (b)

FIGURE 4. Current follower’s stabilization procedures: (a) by introducing a capacitance in parallel to R, and (b) by using two operational amplifiers.

more sensitive to noise. and the circuit is less stable. The analysis of the instabiliv of current followers and their stabilization have been extensively studied [ 60-641. It is a common practice to introduce stabilizing capacitors in the circuit when current followers are used as current- measuring devices [ 2,18,62-64] (Figure 4a). Alterna- tively, the current follower circuit can be stabilized by the use of two operational amplifiers [6j] (Figure 4b) which must operate with RJR? = Rj/R, to keep the’ input virtually zero.

A severe limitation for the use of the current-follower configuration appears when ultrafast measurements are intended. The introduction of stabilizing capacitors in the circuit severely limit bandwidth. Furthermore, rather large values for R, must be used when performing low current determinations. To overcome these problems, two new configurations for current monitoring have recentl!. been proposed. In the first one (Figure ja j , a voltage follower is introduced in the working electrode clamp instead of the current follower [%], because the \‘F configuration easily satisfies the mini- mum gain requirement. The main objection to this procedure arises from the fact that “E is no longer at ground potential, which is a common mode problem again. In addition, the current sensitive element R, becomes a part of the uncompensated resistance, thus keeping the system from giving an accurate control of the applied potential. The potential of WE relative to RE can be mon-

Electronic Configurations in Potentiostats for the Correction of Ohmic Losses 535

technique). In elinzinntion metbody. the electrode potential is left at the incorrect potential, but any uncer- taint\- of the value of the electrode potential is elimi- nated. In this case. a portion of the cell current can be driven out to get direct control of the true potential (analog elimination technique) or a precise measurement of R,, can be performed to provide direct monitoring of E,,,,, (current interruption technique). Thus, electronic IR correction methods can be grouped as follows:

positive feedback

compensarion techniques negative impedance i current pulse

analog elimination

current interruption elimination techniques

-I- - - (b)

FIGURE 5. Current measurement by using: (a) the voltage follower configuration and (b) a current feedback operational amplifier.

itored by introducing a differential controller circuit at the output of \‘F [66]. A more interesting procedure consists in the use of a current feedback configuration at the working electrode clamp instead of a voltage feedback configuration as considered so far [67] (Figure %). The bandwidth of current feedback operational amplifiers depends much less on the voltage gain, the use of stabilizing capacitors not being necessary now.

Potentiostat development now aims at faster response [ 64,66401, lower noise [ 69,71,72], multiple electrode [ 731, high power [ 74,751, and microprocessor [ 59,64:76-83] controls, with most of these circuits incorporating IR compensation in some form. Effort is also devoted to the design of four-elearode potentiostats [ 84- 941.

ELECTRONIC TECHNIQUES FOR OHMIC LOSS CORRECTION Electronic procedures to achieve IR correction have been the subject of a large number of publications and are based on rather diverse principles. In order to consider them, classification must be attempted according to their operating principle. Ohmic losses can be corrected in two ways, namely. compensation and elimination. In compensation procedures, direct correction of the cell electrode potential is intended. The electrode potential is forced to approach the desired potential as close as possible. To this end, an electrical signal equalizing Z.R, must be driven in or out of the electrochemical cell. This signal can be generated both from the current flowing in the cell (positive feedback and negative impedance techniques j or externally (current pulse

Positive-Feedback Methods

The uncompensated resistance causes a potential control error equal to I R,,, and correction can be attempted by adding into the input of the potentiostat a correction voltage proportional to the current flow. This idea is the basis for posititie feedback compensation circuits. Such effect is achieved by adding a new (posirivej feedback loop to conventional potentiostats in parallel to the reference electrode voltage clamp. The function of the new- loop is to drive to the control amplifier a signal derived from the current-measuring part of the instrument. Ide- ally, the positive feedback loop allows addition to the potentiostat input potential of a signal equal to the I.R,, drop. That is, a voltage signal, E,. is generated that is proportional to Z.R, and is added to the control input voltage Eo. This principle has been applied to potentiostats both in the differential-amplifier mode operation [ 95-97] and in the current-follower mode operation [63,98-100) (Figure 6). Positive feedback compensation in two-electrode [8 5-87] and four-electrode [ 101,1021 potentiostats has also been given.

The use of positive feedback compensation in the differential-amplifier mode operation presents the following characteristics: the dynamic behavior is not affected significantly by ohmic drop compensation provided R, is small compared to the cell resistance. This configuration requires the use of a DA, which shows common mode error. In order to avoid the differential mode operation of the amplifier, DA can be used as a unity gain inverter feeding a fourth operational amplifier to achieve full compensation [96]. In this way, the circuit can operate at high currents as well. Nevertheless, common-mode errors remain present, and full compensation is likely not to occur since instabilities in the system must appear, as a high compensation rate is intended. On the other hand, the use of positive feedback compensation in the current-follower mode operation ex- hibits the typical limitations of the current-follower configuration. They are, namely, WE at virtual ground, degradation of the signal at high frequencies, and dynamic behavior affected b!- ohmic drop compensation.

536 Souto

FIGURE 6. Positive feedback configurations for I . R, compensation: (a) differential- amplifier configuration: (b) current-follower configuration; and (c) potentiostat with the current-measuring resistor outside the negative feedback loop.

h third configuration with positive-feedback compensation has also been presented [103-1061, in which the current-measuring resistor is placed between WE and ground. that is, outside the negative feedback loop (Fig- ure 6c). This confguration eliminates the common-mode problem and may be preferred for high-frequency work. because no current follower is used. It must be observed that in this configuration, R, has to be compensated for too, the total uncompensated resistance being R,, + R,.

Though positive feedback compensation has often been employed with success, degradation of the potentiostat stabiliy margin accompanies the use of the feedback loop. The various components of the measuring and controlling system, i.e., the potentiostat, the current measuring device, and the positive feedback device, have limiting characteristics which can contribute to the in- stability of the system when the rate of positive feedback is increased. Though some controversy arose on the subject in the past, it is well established that the positive feedback technique leads to instabilities and signal degradation. Instabilities are not the direct result of the positive feedback technique, but they arise in IR compensation because it makes the system behave as if a purely capacitive electrode is being controlled [3]. Therefore, every method devised in order to fully compensate for IR in the cell, and not only the positive feedback technique, is suitable for destabilizing the system as 100% compensation is approached. Furthermore, certain kinds

of faradaic impedances destabilize the circuit in addition to the capacitive charging process [ 107-1091.

Delay times through the various operational amplifiers severely distort the control voltage signal provided by the potentiostat when operating at very high scan rates (11 > 1000 V - s - ’ ) in qclic roltammetn [67,110]. To overcome this limitation in potentiostats incorporating feedback compensation, effort is devoted to the design of potentiostats in which the number of operational amplifiers involved in the feedback/potentiostat circuit is decreased [ill].

The establishment of a safe standard stability margin for the application of the positive feedback technique to real systems has been the subject of extensive work. A first attempt consists in operaring with less than the ideal of 100% 1. R,, compensation; that is, Compensation rate is set to a value at which instabilities are not observed and a high portion of the total ohmic loss is compensated for. It has became a rather extended procedure to consider 80% as such limit [63], but the establishment of a standard limit is not possible because the initiation of instabilities depends upon the magnitude of R, itself.

On the other hand, stabilization of the system can be attempted. Smith and co-workers [98] introduced stabilizing capacitors in the potentiostat’s circuit. An ap- propriate choice of the capacitance values apparently al- lowed the achievement of full compensation both in three- electrode [ 112-1 151 and four-electrode configurations [ 1161. Nevertheless, Britz 131 computed the cell transfer


function of this network and showed that important phase shifts are introduced on the potential signal as taken at the electrometer output. A way to circumwnt this problem when highl!. precise phase-sensitive measurements. such as impedance determinations, are performed consists of taking the ac potential signal at the counter electrode [l-.lS]. Doing so. the total impedance of the cell is non- determined, and this is the magnitude for m.hich to compensate.

Stabilization of the system can also be achieved by utilizing damping compensation in the feedback of the control amplifier [68,110,116]. A similar effect has been achieved by using a dual reference electrode [ll:,llS]. that is. by coupling capacitively the reference electrode to a platinum wire to provide a low impedance. As damping introduces a severe loss of bandpass. such procedures can be indicated for situations in which zero I.R,, error is wished and loss of bandpass is not critical, as in linear sweep voltammetry.

For exacting work, it is often interesting to know the amount compensated. Therefore, monitoring of R,, has also received some attention. Usually, the amount of feedback to the control amplifier is established by step- ping down the output of the current follower by a potentiometer which can be set manually [99,119] or au- tomatically [77,113]. As the exact amount of feedback cannot be determined because it is not a simple function of the potentiometer setting due to the loading by the control input resistor. it has been proposed [116] that the introduction of a voltage follower between the PO- tentiometer and the control input resistor monitors the ohmic loss.

Some dynamic procedures for the correction of ohmic drop have also been proposed. First, R, can be monitored by means of a high-frequency current that is applied to the cell [120,121]. Under these conditions, the high-frequenq voltage drop between RE and ViE is a measure of R,. The ac voltage is then amplified and rec- tified to get a dc voltage equal to the ohmic loss voltage. Automatic IR correction can also be attempted by con- sidering the properties of the analogue multiplier. as it detects any variations arising in the ohmic drop when introduced in the feedback circuit [122>123]. Some electronic circuitry is necessary for providing the control voltage signal necessary for its operation. This procedure was first employed for double-laver capacitance determinations [ 1221. The current measuring resistor R, can be introduced between WE and ground, and WE shows a voltage V, with an ac component. Then, v, is fed to an analogue multiplier together with Vreh the last being measured across the impedance given by the series sum of this resistor, the double layer, and R, (Figure 7). There will be certain phase shift between these two voltages, and their product will thus contain a dc component dependent on the phase angle. The output signal from the multiplier (afier having passed through a low-pass filter) is directly proportional to V, + Vi, where V,? is the ohmic drop Z. R,. Nevertheless. such proportionality will be found only under fixed frequency, small phase angles, and purely capacitive double-layer impedance [ 31. R, can

R

I @ A

- - FIGURE 7. Analog-multiplier based circuit for dynamic compensation of the ohmic loss in potentiostats with positive feedback. AM-analogue multiplier; LPF-low- pass filter.

be monitored on a digital panel meter to get direct read- ing of electrol!-re resistance [ 1241. Very recently. further development of the electronic circuitv for the control voltage to the multiplier has been presented [123]. which alloxvs its implementation for cyclic voitammetv at scan rates up to 1000 V. s-' with the dropping mercury electrode.

Continuous automatic gain adjustment in the positive feedback can also be performed if an automatic prior measurement of the solution resistance is done. Both impedance [86.89.12 j] and galvanostatic pulse methods [ 116.126,127] have been employed for such determination. An analog null-balance method that self-adjusts to full compensation during periodic interruptions in potential control was proposed by Yarnitzln- and co-workers [128.129]. A small square wave is input to the cell. The amplitude of the resultant current signal is compared with the input one, and equalin. of both signals is intended.

Negative-Impedance Methods 1. R,, compensation during the measurement can be achieved by introducing into the cell circuit, outside the negative feedback loop, a negative resistance of magnitude equal to R,. That is, the ohmic drop can be compensated by means of a circuit containing a phase re- v e r b ~ This principle was first employed by Kooijman and Sluyters [130] in galvanostatic single- and double- pulse methods and, more recently, by Gabrielli and Ked- dam [131] in impedance measurements. In the former case, a triode was used as a phase reverter. The signal to be introduced in the cell was previously fed to the grid of the triode. Then, provided the cathode and an- ode resistances were almost equal, both outputs had nearly the same amplitude but of opposite sign. Thus one output provided the polarizing signal for the cell, and the other one was used to compensate the ohmic drop.

The negative impedance effect can also be achieved with an operational amplifier. The modified current-follower configuration (Figure 8a) provides a negative impedance 2, = VJZ, i.e., the voltage V, is out of phase with the Z . R,, voltage. The negative impedance element

4

I

FIGURE 8. (a) Negative-impedance current follower and (b) potentiostat provided with a negative-resistance compensator.

has been implemented in a differential-amplifier mode potentiostat by inserting it between the working electrode and ground (131,1321 (Figure 8b). The new operational amplifier polarizes the electrodes as a negative impedance input; that is, the current-to-voltage converter has been modified into a negative impedance device. The compensation is then achieved by choosing the appro- priate set of resistor values in the negative impedance branch.

The need for the differential amplifier can be cir- cumvented if the current-to-voltage converter is used both for the attainment of the negative impedance effect and for the determination of the current by operating as a current-to-voltage converter. But the output voltage of the device depends upon the degree of compensation and is not simply proportional to the product of cell current and feedback resistor. Therefore, a second operational amplifier must be introduced in order to subtract the output voltage and the voltage applied to the noninverting input [133]. In this case, the compensation loop involves only one amplifier and therefore only one pole, so loop stabilin- is easy to ensure. Though such a system presents the advantages of no existence of a feedbaek

FIGURE 9. Digital potentiostat. For the sake of clarity, the DA is drawn as a comparator. CPG-current pulse generator.

loop and no limitation of the cell current produced, there are some problems as well. Common-mode problems are increased, because the inverting input terminal is no longer at virtual ground but moves away from the input signal (i.e., CE and WE are now longer way off ground). thus full compensation cannot be achieved due to capacitive behavior of the electrochemical cell, and this circuit is not very stable at high frequencies.

Dynamic correction can be attempted by employing an analogue multiplier, in which case variable resistance values are achieved by introducing a field-effect transistor (FET) in place of resistor R, in F ipre 8b [134].

Finally, the circuit proposed by Svetska and Bond for the stabilization of the current-to-voltage converter [65] can also be employed to provide a negative input resistance for I . R,, correction. In this case, the input resistance can be altered as necessan by changing the value of R, (Figure 4b) in a way that R3/R2 > R,/R,.

Current-Pulse Methods

In 1971, Goldsworthy and Clem [135.136] designed a PO- tentiostat in which a train of current pulses is used instead of a potential. In this way, conversion of the charge involved in the system to digital information is directly performed by the system. Actually, the digital potentiostat consists of a current pulse generator (CPG), a comparator, and a digitizer (Figure 9). The reference electrode is connected to a comparator which compares its potential with an externally driven control potential. As a result of the operation, potentiostat function is achieved by forcing charge injection or charge extraction in the cell to maintain the desired cell control potential. Such effect is achieved by connecting the CPG to the CE. A digitizer is introduced to digitize the comparator’s output. The circuit operation is clocked, and the comparator performs its task between current pulses. Thus, the circuit measures the true electrode potential sensed at WE: since measurements are performed when the current is not flowing through the cell (e.g., between current pulses). In this way, direct I . R, correction is achieved and no stability problems are encountered in the system.


E0*-&-,

EO

L (b) - FIGURE 10. Analogic subtraction correction in: (a) the differential-amplifier mode potentiostat and (b) the adder- mode potentiostat with analogic subtraction correction.

Analog Elimination Methods

Ohmic drop correction can be performed by subtracting two signals, one of them proportional to the ohmic loss I . R,, [ 13-,138] and the other is the voltage existing between RE and K T . This analogic subtraction is performed by means of a new operational amplifier, whose output directly monitors the effective potential in the system. No feedback to the control amplifier is performed, thus avoiding instabilities in the circuit.

The first device based on this idea was proposed by Gabrielli et al. [137] in 1977 It is built around a differential-amplifier mode potentiostat by introducing a second differential amplifier DA2 in the circuit (Figure 10a). In this circuit: a portion proportional to the current flowing through the cell, the extent of which is fixed by the gain of the differential amplifier DAI, is fed to DQ. The operational amplifier DA2 performs the analogic subtraction. Ohmic correction can then be attempted by vaFing R, in such a way that the output of DA2 gives the actual voltage difference at the interface when the product of R, by the gain of DAl equals the ohmic drop.

To avoid the problems inherent to the differential- amplifier configuration, the adder potentiostat configuration is preferred. A commercial potentiostat based on this principle for the correction of the ohmic loss is available [139]. It is built around an adder-type potentiostat, with the current-measuring device in the working electrode clamp. Nevertheless, the operational amplifier is still built in the differential operation mode. An alter- nate procedure has been proposed by Souto and Shy- ters [138]. In this case, operational amplifiers are always used in the adder configuration (Figure lob). The circuit is very simple but appears to be very stable, and common mode error problems are avoided. By choosing ap- propriate operational amplifiers for both CF and OA2

L

FIGURE 11. Current-interruption technique: (a) principle and (b) circuit.

(i.e., meeting the desired requirements), the circuit can offer very interesting bandpass characteristics.

So far, these circuits were designed for electrochemical impedance studies, for which they are very suitable, as the critical bandpass limitations presented by the other methods are avoided. Full correction can be achieved, even desired overcorrection, with the aid of a potentiometer [ 1381 or an adjustable gain amplifier [ 1371. This simple operating principle seems to be applicable for other electrochemical techniques.

Curren t-In terrup tion Methods

In current-interruption methods, the sensing of the PO- tential between WE and RE is accomplished when no current passes through the cell. These methods have no stability problems as they leave the electrode at the incorrect potential. In them, a highly precise determination of R, value is performed, thus allowing for the later calculation of the actual potential difference sensed by the double layer. (Current interruption can be achieved simply by opening the counter electrode loop with a switch S: as shown schematically in Figure l la ) . As current flow is interrupted, the working electrode achieves the double-layer potential because the solution resistance instantaneously drops to zero. Next, W'E relaxes because of double-layer discharge and because of equal- ization of potential nonuniformities over the electrode surface, processes which exhibit time constants in the interval 0.3 to 0. j ms [140.141]. Thus, if the potential difference between the electrodes is measured within a time following the interruption sufficiently short compared with the rate of the decay, e.g., up to 20 ps, no significant errors will be introduced. The difference between the electrode potentials measured before and just after the

540 Souto

current interruption is merely the ohmic drop in the cell. Thus. obsenation of potential shortly after the current interruption will give the true potential directly.

This technique is based on the commutator method introduced by Hickling in 1937 [ 1421. The technique was further developed by using diverse electronic components for current interruption achievement. namely, electronic valves [ l43.l-i4] and mechanically activated switches [ 14 j], but this technique could not be widely employed until electronic switching was introduced by McInvre and Peck in 1970 [146]. allowing the interruption time to be reduced from about 1 ms to times on the order of 1 ps. They used a diode as a switch! and current interruption could be achieved by applying a short-duration pulse to the potentiostat input driving the diode to its nonconducting state. Their system was un- stable when operating with less than 100 pi%. and it had to be adapted when changing from positive to negative currents. The introduction of FETs as electronic switches made it possible to work on both positive and negative currents and without limitations at low currents [ 1471. In this case, the gate-source capacitance of the FET limited the recove? time of the circuit after the interruption to 20 ps.

Fast current-interruption potentiostats were later designed by combining an FET as electronic switch with a sample and hold unit (SH) [ 1481. The introduction of SH allows one to keep a record of the instantaneous voltage drop occurring as the interruption takes place. To this end, SH can be controlled by the same trigger as the electronic switch. Compensation can also be tended by feeding back to the control amplifier the amount I . Rzi.

The continuous monitoring of the potential sensed at the electrochemical interface can also be performed [149]. In addition, the control amplifier can be made into a short-time constant integrator br; placing a capacitor in the feedback loop (Figure l lb ) . At the moment that the switch at the counter electrode loop is opened, the sum of the cell potential plus the input voltage is fed to CA and integrated. This sets the output to the necessan level to compensate for Z.R,, drop in the cell.

The current interrupter and the sample and hold circuit can be built in a separate instrument [ I j O ] . In this way, a resistance polarization can be obtained, which can be connected to any potentiostat or current source of interest. The output voltage of this instrument is continuous and equal to the actual potential sensed at the interface. To achieve further stabilization of the instrument, a filter is introduced in the sample and hold circuit, but filtering slows down the transient response of the instrument, making it unsuitable for transient electrochemical determinations.

At present, design trends are directed to the auto- matization of the circuit [ 151-153]. Both the interfacing of the circuit to a computer and the design of analog autocompensators are intended. At this point, the circuit designed by Williams and Taylor [ljl] is worth some attention. To get a computer-controlled compensator, they introduced an optoisolator to control the electronic switch (a bipolar transistor again), which made it possible to

build a fully floated device. In this way, switching could be safel!. produced in the counter electrode loop.

The current-interruption technique has also been employed in four-electrode potentiostats [ 1 ji] and in in- dustrial processes. particularly in batter) testing for the measurement of the "resistance-free potential" of a cell under load conditions [lSj-159].

CONCLUDING l2.?34ARkS

To achieve ohmic loss correction, a number of methods are available in the literature. Some of them are designed in order to get the true potential difference be- meen the electrodes of interest, and full compensation is often claimed in literature in relation to potentiostat designs; but full compensation leads to oscillations in the system. and reliable measurements cannot be performed. In other cases, exact determination of the ohmic drop is intended instead. A new classification procedure consists of grouping the methods as compensation or elinzinution. whether direct compensation of the electrode potential in the electrolytic cell is intended or not. respectively. In the first case, only partial compensation can be performed, as the system gets into oscillation as full compensation is approached. Therefore, a precise determination of ohmic resistance both in the absence and in the presence of I . R, compensation must be done in order to allon for later correction of experimental data. Compensation methods are specially suited when electrolytes with low conductivities, or large currents. are involved. On the other hand, elimination techniques allow for the continuous monitoring of the actual potential sensed by the electrodes in the electrochemical system. No stability problems are encountered, as the electrodes are left at the uncompensated potential.

Combination of compensation and elimination techniques in a potentiostat is often interesting as well [138,148]. In this way, an increase in cell conductivity, a decrease in the cell-time constant, and the continuous monitoring of the true potential can be achieved at the same time.

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Electronic configurations in potentiostats for the correction of ohmic losses

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