the presence of hydroxylamine at high scan rates are lom-er, probably because of the uncertainty in correcting for charging current and also from using measurements obtained a t the limiting capabilities of the instrument. Measurement of the reaction ratio between Fe(I1) and hydrosglamine is not poscible, since the stoichiometric coefficient is included in the definition of the pseudo first-order late constant. LITERATURE CITED
(1) Alberts, G. S., Shain, I., ASIL. CHEM.35, 1859 (1963). (2) Fischer, O., Drarka, O., Fischerova, E., Collection Czech. Chem. Cornmuns. 2 6 , 130.5 (1961). (3) Fiirlani, C., lIorpiirgo, G., J . Electroanal. Chem. 1, 351 (19.59/60).
(4) Jessop, G., iyature 158,59(1946). (5) Koryta, J., Collectzon Czech. Chem. Communs. 19, 666 (1954). (6) Kicholson, R. S., Shain, I., A s ~ L . CIIEM.36, 706 (1964). (7) Nicholson, R. S.,Shain, I., Ibzd., 37, 178 (1965). ( 8 ) Ibzd., p. 190. (9) Polcvn, D. S., Ph.D. thesii, Uni-
versity of Wisconsin, lladison, WE.,
(15) Shain, I., Polcyn, D. P., J . Phys. Chem. 65, 1649 (1‘361). (16) Smith, 1). E., .%S.\L. CHEM. 35, G10 (1!)63). (17) Piibr:ihnianya, R . P., i n “Advances
i n Polarography,’’ I. F. Loiigniiiir, ed., 1-01. 11, p. 674, Pergnnion Pres., Sew Tork, 1 9 G O . (18) Siibrahnianya, R . S., Proc. Indian
19G
(16jPolcyn, D. S., Shain, I., r l s . 1 ~ . CHEM.38, 370 (1966). (11) Iiiha, J.. Z. Phiisik. Chem. (Sonderheft), p. 152, J~ily,’1938. (12) Saveant, J. AI., S-ianello, E., in
“Advances in Polarography,” I. S. Longmuir, ed., Vol. I, p. 367, Pergamon Press, Sew York, 1960. (13) Saveant. J. 11..Tianello., E.., Electro-
chim. -4ccta’8, 905’(1963). (14) Saveant, J. JI., Vianello, E., Ibid., 10, 905 (1965). ’
1963.
, ‘,Qiiantitative In-
’ 3rd ed., p. 391, John
(21) 1Volf>on, H., .Yalure 153,375 (1044). RECEIVED for review Sovember 10, 1965, Accepted January 10, 196G. \\-ark supported in part by funds from the U. s. Atomic Energy Comniis>ioii Contract
S O .AT( 11-1)-1083.
Continuous Ohmic Polarization Compensator for a Voltammetric Apparatus Utilizing Operational Am pIifiers DIRK POULI, JAMES R. HUFF,’ and JAMES C. PEARSON* Research Division, Allis-Chalmers Manufacfuring Co ., Milwaukee 7 , Wis.
A voltammetric device has been developed to compensate continuously for the ohmic voltage between reference and working electrodes in an electrochemical cell. Compensation is achieved by inserting an “effective” resistance in series with the cell. The value of this effective resistance i s determined by the iR drop as measured between reference and working electrodes when a square wave current pulse is applied across the cell. The voltage developed across this resistance is sensed by a feedback circuit. As a result of the ohmic voltage compensation, the potential difference between reference and working electrodes equals the input voltage. The same technique may b e used in galvanostatic studies to measure the iR free potential of the working electrode. In this manner, the accuracy of galvanostatic potential measurements may be enhanced when the ohmic voltage is appreciable.
S
applications of operational amplifiers in electrochemical equipmcnt have been reviewed by Schwarz niid Shain ( 7 ) . Further special adaptations of these electronic components were considered in a sympo,’qium on operational amplifiers (1). The problems associated with appropriate earthing points and compensation for EVERAL
382
ANALYTICAL CHEMISTRY
voltage drops across measuring resistors are fully discussed in the articles cited above. One of the major difficulties in electrochemical experimentation is the precise measurement of the potential of the working electrode with respect to a reference electrode. When a continuous current flow betlveen working and counter electrodes, the measured potential of the former always includes an ohmic component. Similarly, when a voltage is applied to the working electrode by means of a potentiostat, the electrochemical potential of this electrode with respect to a reference electrode differs from the imposed voltage by an iR term. The ohmic voltage referred to is due to the fact that the completed circuit for measuring the potential partially coincides with the current path from the xorking to the counter electrode. I n subsequent discussions, “the iR and/or ohmic voltage” refers to this ohmic voltage between reference and working electrodes. A Luggin capillary often has been used to decrease the ohmic voltage to a small value. It is, hoivever, not possible to eliminate the iR term completely in this manner. I n addition, the geometry of the cell precludes the use of the Luggin capillary in some systems. Even when a Luggin capillary can be incorporated, the ohmic voltage may be
appreciable a t current densities of the order of 100 ma. per sq. cin. (based on geometric area) or if the electrolyte concentration is low. For esample, Bockris (2) has calculated the iR drop to be in excess of 1 volt under the following conditions : electrolyte concentration of 10-2 gram ion per liter, a distance of 1 mm. between the tip of the Luggin capillary and the working electrode, and a current’ density of 10 ma. per sq. cm. Correction after measurements have been made is possible only if a steadystate current-voltage characteristic is required. I n voltammetry with a linearly varying potential (LT’P) signal, the current-voltage characteristic often exhibits maxima and minima-Le., the potential is a multivalued function of the current. Many examples of this type of curve are to be found in the literature-e.g., see (8). Correction for the ohmic voltage afterwards is impossible without accurate knowledge of the true current-potential curve. The electrochemical determined parameterse g . , the Tafel slope-may thus be considerably in error. I n addition, small current, maxima or inflections may be lost completely or in part whenever the ohmic voltage is appreciable. 1 Present address, Research Laboratories, Globe-Union, Inc., Milwaukee, \Vis. * Present address, LECO Laboratory Equipment Corp., St. Joseph, llich.
4-l
Figure 2. Galvanostatic circuit for iR free potential measurements
s
AI.
Figure 1 , Voltammetric circuit for continuous ohmic voltage corn pensation AI, A?. Stabilized adder (Philbrick KSYJ, KSPJ) inverting amplifiers 6.
Current amplifier 10 pf. Co. Counter electrode el, e2. Voltage sources I . Stabilized omplifiers (Philbrick KSYJ, KSPJ) In conventional integrator circuit R. 100 kiloohms R,. Compensating resistor, continuously variable to 10 ohms Re. Reference electrode RL. Load resistor W. Working electrode
c.
CONTINUOUS FEEDBACK OF OHMIC VOLTAGE FOR LVP AND POTENTIOSTATIC OPERATION
The instrument developed in this laboratory continuously compensates for the ohmic voltage. The principle of the compensation technique is as follows. The i R drop for a known current i is determined by applying a square wave current signal between the working and counter electrodes. (The square wave current generator is a transistorized device producing a signal with rise and decay times of a fraction of a microsecond.) The potential difference between reference and working electrodes is then measured with an oscilloscope. The i R voltage corresponds to the vertical portions of the voltage-time trace. An “effective” resistance may then be calculated using the value of the current of the square wave pulse. Only the iR, and not i and R individually, is measured by this technique. The calculated value of the resistance is then inserted in the feedback circuit of the voltammetric (potentiostatic) instrument. The feedback circuit feeds a compensating ohmic voltage, which is dependent on the calculated resistance and the current flowing in the circuit, into the adder. Since the sign of this compensating voltage is inverted, it acts to cancel the ohmic voltage between the reference and working electrodes. Thus, the potential of the working electrode is known more accurately. A schematic diagram of a possible voltammetric circuit for continuous
Stabilized adder used as inverter Stabilized adder (Philbrick K2YJ, KSPJ) inverting amplifiers Current amplifier Counter electrode Voltage source Stabilized follower (Philbrick KSYJ, KSPJ) 100 kiloohms Compensating resistor, continuously variable to 10 ohms Reference electrode 100 kiloohms Working electrode
A*, A8. B. C,. e.
F. R.
R,. Re. RL. W.
ohmic voltage compensation is depicted in Figure 1. The integrator inverts the sign and integrates the input voltage with respect to time. The adders add all inputs algebraically and invert the sign of the sum. The follower amplifiers, which are high impedance devices ca. 10’0 ohms, are inserted to prevent the flow of excessive currents lvhen these are undesirable. The performance of all these components is determined by the properties of the operational amplifiers used in their construction. In Figure 1, R, is the compensating resistor referred to above. I n order to measure the current through the cell accurately, the requirement RL
