Anal. C h e n ~1083, 55, 161-163
161
Instrument for Alternating Current Impedance Measurements Sheng-Min Cai,‘ Tadeusz Mallnski, Xiang-Qin Lin, Jian-Quan Ding, and Karl M. Kadish” Department of Chemistry, University of Houston, Houston, Texas 77004
It has long been recognized that ac impedance measurements can provide much information on electrode processes and double layer structure (1-3). Although the theory of ac impedance measurements is well developed (I),this technique has not found the popularity of other ellectrochemical techniques. The ac bridge method is classic and precise (4,5), but rather inconvenient and time-consuming. Some good nonbridge instruments have been developed, but they are mostly complicated and expeinsive (6-10). The general characteristics desired in an impedance measurement system are good accuracy, precision, lack of difficulty in changing frequency, i,he use of small ac perturbation signals, and a way to internally check for the occurrence of erroneous measurements. In thi,i paper we report, the construction of such an instrument made from common available commercial components. Most available ac impedance instrumentation uses an ac perturbation signal of about 8 mV. In these cases a 1000-R electrode impedance will produce a 5-pA ac perturbation signal. In tlhe system described here we are able to decrease the ac perturbation signal by 10 or more times from that of other instruments so that the perturbation signal is less than 0.5 MA. A small ac perturbation is necessary for cases where a large cuyrent may cause large deviations from equilibrium during the measurement plrocess. CIRCUIT A preliminary descriiption of this circuit has been reported (11) where currents were limited to a lower value of -5 MA. In this paper changes have been effected such that currents as low as 0.5-0.05 pA or less could be routinely obtained. The circuit utilized is shown in Figure 1. An EG&G Princeton Applied Research potentiostat (PAR 1’73)and a signal gonerator together with a saturated calomel reference electrode (RE) and a dc counterelectrode (DCE) were used to control the dc potential of the mercury test electrode (TE) which was either a dropping mlercury electrode (DME) or hanging mercury drop electrode (HMDE). Both ac and dc circuitry are found in Figure 1. The ac current circuit consists of a voltage controlled frequency QScillator (VCFO, Exact IClectronics 502SL), four 340-kQresistors in series (R3-&), and two 200-pF condensers (C, and Cz). The resistors are used in order to keep the amplitude of the ac current constant during the measurement and the condensers (C, and C,) to prevent any dc current from entering the ac current path. The resiistors R, and R, fnrm a voltage divider in order to decrease the voltage output of the VCFO when an ac current perturbation smaller than 0.5 pA is desired. R1 and Rz may be changed as needed in order to obtain the desired low current signal. Typical values utilized were R1 = 1000 R and Rz = 100 R or R, = 1000 Q and R2 = 10 R for reduction of the 0.5 pA current by a factor of 10 and 100, respectively. Disconnecting the lower terminal of R2 from ground will return the ac current to the output value of the VCFO (typically 0.5 ,uA). A 12 H choke (L) and a 45-kR resistor (R7) isolate the dc circuit from the ac current circuit in Figure 1. In order to prevent interference beitween the dc and ac circuits and influencing noise from the potentiostat two On leave from Chemistry Department, Peking University, Neijing, People’s Republic of China.
counterelectrodes were used. In addition to the dc counterelectrode a 2-cm2 Pt mesh served as an independent ac counterelectrode (ACE). The use of a two counterelectrode system has been discussed in ref 6 but in this case the configuration is quite different than that reported in this paper. Ordinary impedance measurement systems using constant ac voltage perturbation prevent the use of two counterelectrodes because the currents from dc circuit and from the ac circuit are mixed together in the potentiostat. In the presented system the dc current and ac current are well separated by the condensors C, and Cz so we can utilize two counterelectrodes. A PAR Model 5204 lock-in analyzer was used to measure the impedance of the TE. This instrument contains in-phase and quadrature meter reading (12). Since the output voltage of the VCFO is used as the reference signal of the lock-in amplifier, the ac current is in phase with the lock-in amplifier output voltage (because the circuit is resistive in character). The in-phase meter reading of the lock-in analyzer shows the resistive component, ZR, of the impedance value, while the quadrature meter reading shows the negative value of the capacitive component, Zc. In the electrochemical cell equivalent circuit (Figure 2a), the 2, and Zc components are connected in series (12, 13) and can be recorded simultaneously as output from the lock-in amplifier using a storage oscilloscope, an X-Y recorder, or a digital voltmeter as a recording instrument. Alternatively, they may be read directly from the meter. The two floating inputs of the lock-in analyzer are connected to both the ACE (input A) and the T E (input B), and the T E is not grounded. The ac signal flows from the “live” terminal of the VCFO output (labeled OUT 1) via resistors R3 to R6 and the condensers C1 and Cz to the ACE. An ac path to ground from the test electrode must be provided because one terminal of the VCFO output is grounded (labeled OUT 2 in Figure 1). The test electrode cannot be directly grounded because the design of most potentiostats prevent this. However, the working electrode terminal of the PAR Model 173 potentiostat is connected to ground via internal resistors in the potentiostat and this provides the path to ground for the ac current. These internal resistors vary between l R and 10 kQ depending on the current sensitivity of the potentiostat. For the specific currents utilized the range is between 1 R and 1000 R. Since these resistors are small compared to the sum of R3, R4, R5, and R6 (1360 kR) they do not influence the amplitude of the ac current. A 20-kR resistor (R,) and a 1-pF capacitor (C3)form a filter preventing the ac signal from entering the potentiostat which would cause self-oscillation. The time constant of RsC3 is large enough to reject the ac signal but not so large as to influence the dc voltage which is scanned linearly. For this voltage scan an external signal generator must be used in conjunction with the Model 173 potentiostat. Other potentiostats such as the IBM Model EC 225 have a built-in signal generator and an external triangular function is not needed. The main problem of making the system an automatic frequency scanning one is the necessity to adjust the phase shift of the lock-in amplifier to make the resistive component measurement exactly in phase with the ac current flowing in the circuit. One solution to this problem is to keep the stray capacitance of resistors R3 to R6 in the ac current circuit as
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 1, JANUARY 1983
Table I, Frequency Dependence of Current, Resistance, and Capacitance at Fixed Phase Shift with a Dummy Cella
VCFC
dc current, pA without with ac ac pertur- perturbation bation
I
frequency, Hz 5 50 500 5000 50000 a
a
C, p F
R,
1.00 1.00 1.00 1.00
103
0.95
99
10.0 10.0 10.0 10.0 10.0
100
101 100
10.0 10.0 10.0
10.0 10.0
The following conditions were set for the experiment:
R = 100 0 and C = 1.00 pF in series connection; phase shift = +0.3";ac current = 0.5 pA. Figure 1. Alternating current impedance circuit diagram: voltage control frequency oscilator (VFCO); lock-in analyzer (LOCK-IN); test electrode (TE); reference electrode (RFE); alternating current counterelectrode (ACE); direct current counterelectrode (DCE); reference electrode, working electrode, and counterelectrode inputs of the potentiostate (RE, WE, CE); floating inputs of lock-in (A, B): reference signal input of lock-in (S);in-phase output of lock-in (I); quadrature phase output of lock-in (Q); output terminals of VCFO (OUT,, OUT2); resistors (R,-R9); capacitors (Cl-C3); resistors of 1 0, 10 Q, 100 Q, and 1000 Q for current range 1 A, 0.1 A, 0.01 A, and 0.001 A which are built into the potentiostat (Rg, Ria, R,,, and R12).
4r
t -
Qe Rct
a
R w CY
b
Figure 2. Interconversion of (a) series and (b) parallel equivalent circuits: Z,, resistive component of the impedance; Z,, capactive component of the impedance; Re, electrolyte resistance: R, charge transfer resistance: Cd, double layer capacitance; R, diffusion resistance (Warburg resistance); C,, diffusion capacltance (Warburg capacitance). low as possible. This is best accomplished by connecting several smaller resistors in series rather than utilizing one large resistor. In Figure 1 four 340-kQ resistors are utilized to produce a total 1360-kQresistance. These small resistors are separated 5 cm from each other and aligned in a straight line and the whole chain of resistors is a t least 10 cm from any circuit. Finally, in order to shield the electronics from external electrical interference in the laboratory, all resistors, condensers, and filters and the electrolytic cell were put into a grounded 40 X 40 X 60 cm metallic box constructed from 0.5 mm sheet metal. This is shown by the dashed line in Figure 1. A square wave is usually utilized as the reference signal of lock-in amplifiers (13). In this case manual adjustment of the phase is required because a 5' or more shift of the phase with frequency is observed, making an automatically obtained complex plane spectrum (impedance diagram) almost impossible. On the other hand, when a sine wave of approximately 3 Vp, is used as the reference signal, one can obtain a complex plane spectrum between 5 and 50 kHz automatically with less than a 2' phase shift over the total range of frequency. Better precision may be obtained by manual adjustment. Calibration, Operation, and Performance. For high precision measurements manual adjustment of the lock-in amplifier phase shift may be made prior to each experiment a t a specified frequency in order to offset the phase change in the exterior circuit. For calibration, a standard resistor
R:t
-
Figure 3. Complex plane spectrum (impedance diagram of Zn(Hg) M)/Zn2+ M), 1 M KCI system at -1.00 V (vs. SCE); ac current 0.5 MA). Numbers by points are frequencies in kilohertz. (Rstd) is used in place of the test electrode and connected to the ACE. The phase shift of the lock-in amplifier is set so that the quadrature meter reading (V,) is zero and at the same time the reading of the in-phase meter (Vi) reaches a maximum. Manual phase shift adjustment also serves as a useful criterion to prove the instrument is functioning correctly. The frequency dependence of current, resistance, and capacitance a t fixed phase shift is shown in Table I. Since the reading of in-phase meter Vi is known, one can calibrate the ac current by using eq 1.
Vi = i,,Rstd The output voltage of the VCFO should be slightly adjusted in order to make io exactly equal to the ac current expected (such as 0.05 MA,0.005 MA,etc.). This calibration is standard procedure before measurements of impedance vs. potential, and phase shifts of less than f2' are satisfactory. Calculation of resistance and capacitance can be done by using the following equations:
Zc = VJi0
(3)
2, = 1 / 2 7rfC
(4)
where f is the frequency. An equivalent circuit of the electrochemical cell is shown on Figure 2b. The electrolyte resistance, Re, charge transfer resistance, Rd, double layer capacitance, cd)Warburg resistance, Rw, and Warburg capacitance, Cw, can be calculated from the impedance measurements under different experimental conditions (1). For automatic measuring ZRand Zc are simultaneously recorded on an X-Y recorder. In order to test the performance of the instrumentation, we made impedance measurements of an organic and an inorganic system. In addition the response of the instrumentation was examined under conditions of both changing fre-
Anal. Chem. 1983,55, 163-166
Table 11. Kinetic Parameters of the (Hg)Zn Mi) Couple at an HMDE in 1.0 M)/Zn2+ Molar Supporting Electrolytea
-i o ' , A/cmz
k " , cm/s
supporting electrolyte
-___
this work
this
work
KNO,
2.3
K C1
10-3 2.6 X
X
10-3
lit.
3.5 X
4.5
X
5.0
X
lit. 6.3 X 1 0 - ~ c
b
4.0 X 10-3b
Refer-
a Measured at 50 Hz and at -1.00 V (vs. SCE). ence 14. Reference 16.
2 ,--
54
v
% -0.2 -c4
-c.6 -3 a
-1.9
-$
2
-$.4
-I 6
POTER' I A L ,1 vs %E Figure 4. Potential dependlence of the capacity component of adenine in a borate buffer pH 9 at a DME. Adenine concentration was as (A) 0.0; (B) 0.031 mM; (C) 0 083 mM; (D) 0.125 mM; (E) 0.25 mM; (F) 0.5 mM; (G)1.0 mM; (H) 2.0 mM; (I) 4.0 mM; (J) 5.0 mM; (K) 8.0 mM. Curves were taken at 100 Hz; ac current was 0.5 pA and scan rate was 5 mV/s.
quency and changing potential. The first system selected was that of the Zn(II)/Zn(Hg) reaction in aqueous KNOBor KC1 media (Figure 3). This reaction has been investigated by using ac impedance methods. Results from the literature and our expermental data under the same solution condition are listed in Table 11. Both ',i and k" were calculated according to literature procedures (1, 14). Given the uncertainties in solution purification and the usual systematic errors from laboratory to laboratory, the values obtained by our instrumentation appear to be acceptable. More importantly, however, is the fact that a typical impedance diagram used for the calculation of id (or k o ) can be made in 5 min as compared to 1 h or more needed for manual determination. In Figure 4 a plot of the impedance of double layer capacity c vs. potential is shown for adenine at different concentrations. Measurements were dame at a DME in borate buffer solution (ionic strength 0.5 M) using sampled measurements. The adsorption of adenine on Hg has been studied before using a quadrature component of ac sinusoidal polarography (15).
163
The data obtained in the present work suggest that using impedance measurements one can obtain a Zc-V curve in approximately the same period of time as in ac polarography but with better accuracy. The accuracy of measurement of Zc by the described ac impedance method is about 0.5% in comparison to the 1-2% accuracy in quadrature ac polarography. In conclusion the instrument described in this paper offers advantages not only in cost but in a substantial savings of time. If the frequency is changed automatically, numerous complex plane spectra may be rapidly obtained in the time that is usually needed for the obtaining of a single measurement set using the classical ac bridge technique. In addition, through the use of small amplitude ac currents one is not faced with the problem of deviations from equilibria which may occur with large currents. Finally, this method, using the described instrumentation, leads to higher accuracy than that obtained by sinusoidal ac polarography.
ACKNOWLEDGMENT We acknowledge the loan of a lock-in analyzer from EG&G Princeton Applied Research. Registry No. Zn, 7440-66-6;KN03, 7757-79-1;KC1,7447-40-7; Zn(Hg), 11146-96-6;Hg, 7439-97-6;adenine, 73-24-5. LITERATURE CITED (1) Sluyter-Rehbach, M.; Sluyters, J. H. "Electrochemical Chemistry"; Marcel Dekker: New York, 1970; Voi. 4, pp 1-121. (2) Archer, W. I.; Armstrong, R. D. "Electrochemistry"; Burlington House: London, 1978; Vol. 7, pp 157-201. (3) Armstrong, R. D.; Bell, M. F.; Metcalfe, A. A. "Electrochemistry"; Burlington House: London, 1978; Vol. 6, pp 98-121. (4) Grahame, D. C. Chem. Rev. 1947, 4 7 , 441-501. (5) Grahame, D. C. J. Am. Chem. SOC.1941, 6 3 , 1207-1215. (6) Gabrlelli, C. "Identificatlon of Electrochemlcal Processes by Frequency Response Analysls"; Solartron: Paris, 1980. (7) Brleter, M. W. J. Electrochem. SOC.1965, 772, 845-849. (8) Tshernikovskl, N.; Glleadi, E. f/ectrochlm. Acta 1971, 76, 579-584. (9) Bower, 0. P.; Caldwell, I. flectrochim. Acta 1981, 26, 625-629. (10) Feller, H. G.; Ratzer-Schelbe, H. J.; Wendt, W. Electrochim. Acta 1972, 77, 187-195. (11) Cai, S. M.; Liu, C. Y.; Wilhelm, S. M.; Hackerman, N. Extended Abstract of Electrochemlcal Society 161th Meeting, No. 697, Montreal, 1982. (12) Operating and Service Manual for EG&G Prlnceton Applied Research Model 5204 Lock-in Analyzer, Prlnceton, NJ. (13) O'Haver, T. C. J. Chem. fduc. 1972, 498 A131-134 and A211-222. (14) Vetter, K., "Electrochemische Klnetik"; Sprlnger-Verlag: Germany, 1981. (15) Knoshila, H.; Chrlstian, S. D.; Dryhurst, G. J. Necfroanal. Chem. 1977, 83, 151-166. (16) Parsons, R. "Handbook of Electrochemlcal Constants"; Butterworths: Longon, 1959.
RECEIVED for review August 19, 1982. Accepted October 7, 1982. The support of the National Science Foundation (Grant CHE 7921536) and the National Institutes of Health (Grant GM 25172) is gratefully acknowledged.
Impedance Measurements for Evaluating the Stability of Aqueous Saturated Calomel Reference Electrodes in Nonaqueous Solvents Karl M. Kadish, * Sheng-Min Cal,' Tadeusz Malinski, Jlan-Quan Dlng, and Xiang-Oin Lin Department of Chemistry, University of Houston, Houston, Texas 77004
The increased use of nonaqueous solvents for electrochemical studies has led to the utilization of numerous novel reference electrodes suitable for these solvents. These electrodes On leave from the Chemistry Department, Peking University, Beijing, People's Republic of China.
and their specific advantages and disadvantages are discussed in several comprehensive monographs (1-4). In almost all cases the authors recommend against the use of an aqueous saturated calomel electrode (SCE) in nonaqueous media, However, despite these warnings, the most often utilized electrode in nonaqueous media remains as the saturated
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