Table I shows typical heater calibration data obtained from titrations of 0.005N HC1 with 1.ON NaOH. The enthalpy of this neutralization reaction was taken to be -13,375 cal./mole at 25.0’ C. ( 2 ) . -4 sufficiently accurate first-order temperature correction of +50(t - 25.0) cal./mole (4), where t is the temperature in ‘C., was added to AH when the titration was run at a temperature slightly higher than 25.0’ C. (up to 25.5’ C.). The calibration data in Table I were obtained over a period of twelve weeks. The heater was used extensively between calibration sets. A typical breaking-in period for a new heater is illustrated by the data. The
ed., Sect. 8, p. 3 ff., McGraw-Hill, New York, 1963. (4) Pitzer, K. S., J . Am. Chem. SOC.59, 2365 (1937). (5) Raffa, R. J., M.S. thesis, College of Pharmacy, Columbia University, New York, N. Y., 1966; Raffa, R. J., Stern, hI. J., Malspeis, L., unpublished data. (6) W:pdlandt, W. W., “Chemical Analysis, Vol. 19, P. J. Elving and I. M. Kolthoff, eds., Chap. 8, p. 271 ff., Interscience, New York, 1964. (7) Zenchelsky, S. T., ANAL. CHEM.32, 289R (1960).
error limits are probably more indicative of the experimental error in the measurements than of irreproducibility of the heater output. ACKNOWLEDGMENT
The authors thank J. J. Christensen for a preprint of Ref. (1) prior to its publication. LITERATURE CITED
(1) Christensen, J. J., Izatt, R. RI., Hansen, L. D., Rev. Sci. Inst?. 36, 779
Research a t Columbia University supported in part by the Ciba Pharmaceutical Co., Summit, N. J. Research at Brookhaven Xational Laboratory carried out under the auspices of the U. S. Atomic Energy Commission.
(1965). (2) Hale, J. D., Izatt, R. M., Christensen, J. J., J . Phys. Chem. 67, 2605 (1963). (3) Jordan, J., Ewing, G. J., “Handbook of Analytical Chemistry,” L. Meites,
A n Electronic Coulostat George Lauer, North American Aviation Science Center, Thousand Oaks, Calif., 91 360, and California Institute of Technology, Pasadena, Calif.
electrochemical investigations it is desired to control the quantity of charge passed, e.g. in coulostatic experiments (2, 7 ) . The published coulostatic circuits inject the charge via a capacitor charged t o a very high voltage. The high voltage is required since the capacity of the injector must be much smaller than the double layer capacity of the indicator electrode. When the injector is initiated, large spikes and spurious noise are observed for 10 t o 100 pseconds. IN MANY
It is therefore of interest t o consider the development of a n electronic coulostat. This can be most easily accomplished by considering a potentiostat and feeding back the charge rather than the potential. Such a scheme can be most easily accomplished by inserting a capacitor in series with the indicator electrode and feeding back the potential drop across the capacitor. Figure l a depicts the simplest configuration. This requires a fairly stable differential input amplifier. The
potential across the capacitor must be equal to E,. If E , is constant, the current through the cell will be zero. If a potential step, AEc, is applied, the circuit acts as a coulostat in the sense of Delahay (2, 7 ) ; a net charge, &, will pass through the cell in a time determined by the rise time, current capabilities, and maximum voltage output of the amplifier. Figure l b shows the equivalent circuit if a single-ended operational amplifier is used. I n this case, the voltage across the capacitor is the negative of the value of E,. Both of these methods have the disadvantage of requiring that the electrode potential be measured differentially. With available equipment it is very difficult t o measure small changes in electrode potential, differentially, a t the fast times required (< 100 pS). This problem can be overcome by using the circuit shown in Figure 2. Amplifier Az is wired as a unity gain follower, A3 as a current follower, and A4 as an integrator. The output of A b is given by
(a) L
E,
=
1 E I‘iR,dt
(1)
where i is the current that flows through the cell.
-Figure 1. Basic charge control circuits
--
Figure 2. Charge control circuit using amplifier feedback VOL 30, NO. 9, AUGUST 1966
1277
Considering A1 only, the basic equation is (2)
eout = --e?
where G is the open loop gain of the amplifier, assumed to be very large (> lo7). The bridge equation is
and if Rt = Ri, solving for e2 and substituting into Equation 2 we obtain
-
If we make the usual assumption that the gain is sufficiently high so that 2eout/ G 0, Equation 4 reduces to
-E,
=
E1
1‘
iR,dt
(5)
Thus this circuit allows the control voltage to be scaled in addition to obviating the necessity of making a differential measurement. The control of coulombs has certain advantages over other methods. As an illustration, consider the double pulse galvanostatic technique developed by Gerischer and Krause (3, 4) and by Matsuda, Oka, and Delahay (6). The objective in the procedure is to charge up the double layer rapidly with the initial pulse of short duration and large magnitude; this is then followed by the galvanostatic current proper. The quantity of charge injected by the first pulse is determined by the product of current and pulse duration; both vari-
0 Figure 4. run
Voltage-time behavior at E, in typical galvanostatic
ables must be precisely controlled. On the other hand, the coulostatic technique can inject the precise amount of charge required, and that is the quantity of interest. The circuit shown in Figure 3 will inject the desired charge followed by aconstant current. Amplifiers 1 through 4 are as in Figure 2. Amplifier 5 is wired as a sweep generator. The field-effect transistors act as simple electronic switches; they have a very large drain to source resistance ( R > 100 megohms) when a negative voltage greater than 8 volts is applied and a low resistance (R < 100 ohms) when the emitter voltage is zero. (It may be noted that all the field effect transistors may be replaced by suitable mercury relays.) In operation, the sweep is initiated by putting T1into
E0“t
the high resistance state. When the potential of -45 reaches the predetermined trigger value of the voltage sensitive switch (5) this fires and takes T,from the high resistance to the low resistance state. The net effect, insofar as the control voltage to d lis concerned, is a trapezoidal potential function as shown in Figure 4. One can choose a AQ necessary to bring the potential to the desired value, and since dQ/dt = i, the current can be easily varied by adjusting the potentiometer until the E - t plot resembles that shown by Delahay (1). The charging time will be determined by the control amplifier used and the total resistance between counter and indicator electrodes. If it is desired to inject 0.1 pc. in one microsecond through a cell with 50 ohms resistance, the control amplifier will have to be capable of delivering 0.1 ampere a t 5 volts with the required rise time. The control of charge passed through the cell rather than control of potential or current can be used for a variety of other purposes by supplying suitable voltage functions a t E,. ACKNOWLEDGMENT
The author thanks F. C. Anson and R. A. Osteryoung for helpful discussions. LITERATURE CITED
(1) Delahay, P., “Advances in Electro-
chemistry and Electrochemical Engineering,” Vol. I, p. 259, Interscience,
New York, 1961. (2) Delahav. P.. ANAL.C n m . 34. 1267
voltage sensitive switch Figure 3. Improved galvanostatic circuit
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ANALYTICAL CHEMSTRY
CONTRIBUTION No. 3345 from the Gates and Crellin Laboratories of Chemistry.
