Dynamic Compensation of the “Over All” and “Uncompensated” Cell Resistance in a Two- or ThreeElectrode System-Steady State Techniques Chaim Yarnitzky and Yaakov Friedman Department of Chemistry, Technion-lsrael lnstitute of Technology, Haifa, lsrael
The construction of two modified systems which utilize the common positive feedback is described. One system has proved to be very useful and effective in slow scan voltammetry while the other has been adopted to fast techniques, such as cyclic voltammetry and pulse polarography. The new positive feedback is self-adjusting and is effective for cell resistances up to 1 MQ. The basic idea underlying the first system is discussed. Details of a unit, designed for use in polarography and in a three-electrode system for electroorganic synthesis in high resistance media, are given.
The compensation of the ohmic potential ( i R ) drop accompanying the passage of current through solution has been the subject of continued investigation ( I ) . The prevalent 3-electrode method has been the target of critical scrutiny and its shortcomings in high resistance solutions, as encountered frequently in nonaqueous media, have been generally recognized; the use of Luggin-Haber capillaries for minimizing the iR drop has been shown to have practical limitations (2). Methods employing positive feedback (3, 4 ) , while apparently providing a complete solution to the problem, have hardly penetrated the field of applied analysis, because of severai deterring factors; indeed, they have been the subject of outspoken criticism ( 5 ) .As a result, in spite of the twelve years which have already passed since this was first proposed, only a few commercial attachments for existing chemical apparatus are available. This may be explained by considering the following: a) The methods described to date are all based on positive feedback in a 3electrode system without an adequate emphasis and differentiation of the situations in which the positive or negative feedback present operate. b) As in all electronic systems employing positive feedback, the electronic stability deteriorates; the negative feedback operates in a small part of the system only, and does not improve stability, merely permitting the definite fixing of potential vs. the reference electrode. In addition, adjustment of the positive feedback requires the performance of preliminary experiments, involving either the determination of cell resistance (e.g., with a square wave technique) or the adjustment of the positive feedback until the system starts oscillating and then decreasing it again by a small fraction. Every change in the chemical system (solution composition, working electrode, auxiliary electrode, etc.) requires readjustment. A novel and entirely different approach is the basis of the new digital potentiostat (6). In contrast to previous methods, the potential of the working electrode with respect to the reference electrode is measured with no current flowing through the cell, i.e., with the iR drop equal to zero. This potential is compared to the desired value and, if the difference is too high, a charge of the proper polarity is injected, the total charge per unit time giving the average current through the cell. The sampled data approach (the 876
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
current interruption technique) ( 7 ) is closely related to the digital potentiostat. The problem may also be solved by sensing the cell resistance (or conductance) and applying the positive feedback, providing its amount is linearly correlated (and adjusted automatically) to cell resistance. A very similar idea has been suggested by J. DBvay, B. Lengyel, and L. MBsz6ros (8). Unfortunately, the over-all performance of their instrument limits its usefulness for regular work. A system consisting of reference and working electrodes suffices whenever the currents measured are small and polarization of the reference electrode is negligible. However, when a flow of high current is expected, a counter electrode is added. In the latter case, the desired potential difference across the double layer is controlled by sensing the “uncompensated resistance” which exists between the tip of the reference and the working electrodes, and applying the appropriate positive feedback. Development of the Instrument. Keeping in mind that the elimination of the need for preliminary adjustment of the feedback is the main target of this work, the idea of exploiting changes in the electrical parameters of the cell for adjusting the feedback is the first to be considered. An experimental system, constructed to demonstrate this idea, is shown in Figure 1. Four operational amplifiers form the well known positive feedback except for the capacitor C which considerably reduces the response rate of the system a t high frequencies (RC = 0.1 sec). This system is therefore applicable for slow scan voltammetry (or regular polarography) only. The capacitor has been introduced for reasons to be discussed below. Now suppose a square wave signal of amplitude to be continuously applied in parallel with the slowly changing potential, Vi,. The direct voltage a t point A equals the current flowing through the cell, icell, multiplied by the resistor R, of the operational amplifier. At point B, the direct voltage VB, equals:
I‘, = icelll?Rr’/R’
(1)
The voltage V g is returned, in inverted phase, to the first operational amplifier. The condition for complete compensation of cell resistance Rceliis: L’B
= icellRce11
or Rcell = RR“/R’
(21
Applying a square wave a t the input results in a square wave a t point A, with an amplitude, V A ~ ~ : \’*SW
-
J‘inswWRcell
(3I
and a t point B: lrgsw = T ’ l n S w R R f ’ / K c e l l R f
(4 )
By means of a comparator, the ratio R”/R’ is adjusted until
R
R
R
ELECTRONIC GATE
Figure 4. Variable positive feedback via an electronic gate
e Figure 1. Simplified positive feedback circuit employing two electrodes
--i Eapp
Figure 2. Equivalent circuit of the electrochemicalcell
portional to cell conductance. The alternating and direct currents may be separated, and the rectified and filtered ac component (Otl/R,,~~) fed into an analog divider along with the dc component ( i c e l l ) . The resulting output ( i c e l l R c e i l ) is applied to the cell through a voltage adder. A block diagram of the system is given in Figure 3. Clearly, the higher the frequency, the faster the desired Eappis achieved. The diagram shows that complete compensation can be attained continuously in all solvents, under all conditions, using a two-electrode system. If a three-electrode system is used, the alternating current component is proportional to the “uncompensated conductances.” Thus, the additional compensation covers that part of the cell resistance which has not been compensated (because of geometrical limitations) by the arrangement of the auxiliary reference electrodes.
ALTERNATING
OL1TPU T VOLTAGE 01: T H E P’3LAROGRAPH
TO VOLTAGE C 0NV E R T ER
LOW PASS FILTER
Figure 3. Block diagram of an electronic system, consisting of an analog divider for the complete compensation of iR potential drop
the square wave amplitude a t B is made equal to that a t the input Trinsw
= VinSWRK”/RcelItl’
(5)
so that Rceil = RRN/€I‘. The condensator i n amplifier 4 shorts the square wave in the feedback, eliminating the error which would otherwise result from changes in the amplitude of the square wave applied to the cell; its main disadvantage is the limit it imposes on the response rate of the system. A dynamic system in which two photo-resistors control the positive feedback was tried, and did not work satisfactorily. A second approach to the problem of compensation is to multiply the resistor Rcell by the current flowing through the cell (Figure 2) and add the result to the applied potential. This can be carried out in the following way: superimposing an alternating component on the existing applied emf, causes the flow of an alternating current which is pro-
T o illustrate this approach, a system which has an analog divider based on the time division multiplier (9) has been designed ( 1 0 ) . This is identical to the system shown in Figure 1 except for an electronic gate added between operational amplifiers 3 and 4 (Figure 4). The gate is closed periodically, a t a rate determined by the frequency of the applied square wave. The combination of the resistance, R, and the gate between operational amplifier 3 and 4 gives an apparent resistance Rapp, equal to:
where t is the square wave period and At is the switching on time. In order that this point be well understood, let the potentials a t points B and C be V B and VC, respectively. T h e charge injected to the capacitor Cs of operational amplifier 4 is gin = VBAt/R. This capacitor is discharged in time t by the amount q d , 9 d = V c t / R ( t
