Abstract:

A.C. impedance is an extremely valuable tool for the interpretation of electrochemical reaction mechanisms and

cell characteristics.
We describe here instrumentation capable of measuring the capacitance and resistance of electrochemical cells under

conditions of varying cell voltage and/or measuring frequency.
Circuit
The principle on which the circuit is based (Figure 1) is that of phase-sensitive detection and is similar to methods

described previously [1] with two exceptions. In most impedance measurement circuits, the cell voltage is modulated and the

corresponding response of the cell current monitored. This sometimes presents aproblem in separating the cell response from

that of the control circuit and generally requires larger perturbation signals. In this case, a small (<10 μA) current

signal is applied with the control circuit isolated through L. Second, in this system, the measuuring frequency can be varied

using a ramp generator coupled to a voltage-controlled frequency oscillator.
The lock-in amplifier that was used (PAR Model 5204) contains two phasesensitive detectors that are driven by orthogonal

reference signals. Both cell resistance (in phase) and cell reactance (-1/ωC, quadrature) can be monitored simultaneously.

Any phase shift caused by the measurement circuit can be offset by substituting a standard resistor for the electrochemical

cell and adjusting the phase control of the lock-in amplifier. In all cases tested, this adjustment was less than ±2°.
Applications
The response of the measuring system to a dummy cell consisting of a 50 Ω resistor in series with a 50 Ω resistor and 1 μF

capacitor in parallel gave a spectrum that agreed with the theoretical prediction within 2%. In Figure 2, the differential

capacitance of a dropping mercury electrode in 1 molL~(-1) Na_2SO_4 solution obtained using the system under discussion is

compared with Grahame′s original data [2,3]. Curve b is for a solution saturated with N-heptyl alcohol. The agreement is

quite good with the exception of the adsorption peaks. The peak heights should be sensitive to the perturbation signal

magnitude in that higher amplitude perturbations tend to “average out” sharp peaks. The small current signal that was used

in the present case seems to improve the resolution of the capacitance peaks.
There an error in the original report by Grahame(2). The abscissas in Figures 20 and 21 should read, “E relative to the

normal mercury/mercurous sulfate electrode” instead of “E relative to the normal calomel electrode”. The reasons are as

follows:
1) Our numerous experiments using SCE reference electrode and normal mercury/mercurous sulfate reference electrode show

Grahame′s abscissa (in fig.21) is incorrect.
2) The related fig.20 of Grahame′s paper was quoted from Gouy (Ann. Chim. Phys. 8, 291). However, we found out in this

original paper Gouy used a large mercury pool asreference electrode. Since it is a normal sulfate solution, the

electrodepotential should related to mercury/mercurous sulfate electrode but not to NCE electrode.
3) From table 1 on page 451 in Grahame′s paper, the E~(MAX) (potential of the electrocapillary maximum) in Na_2SO_4 solution

is -0.48 V versus NCE. It agrees well with Frumkin′s data -0.47 V versus NCE (A.H.фрумкин et.al. КИНЕТИКА Э

ЛЕКТРОДНЫХ ПРОЦЕССОВ. 1952, p.31, table 1). If in fig.20 the maximum is -0.85 V “relative to normal

mercury/mercurous sulfate electrode”, since N-mercury/mercurous electrode is 0.335 V more positive that NCE, now the maximum

appears at -0.515 V releative to NCE electrode. It agrees well with other data.
Our intention of pointing out this minor error in Grahame′s paper is merely because this paper is generally accepted as the

classical paper with most authority in its own field and Figure 21 is widely quoted in numerous papers and text-books (e. g.

A. J. Bard, L. R. Faulkner, “Electrochemical Methods, fundamentals and Applications.” 1980. p.550, 551).
The performance of silver oxide electrodes is knowng to be sensitive to the magnitude of the charging current (4). Upon

chargin at 17 mA/cm~2 (Curve a, Figure 3), potential plateaux corresponding to
2Ag+2OH~-→Ag_2O+H_2O+2e~-
and
Ag_2+4OH~-→Ag_2O_3+2H_2O+4e~-
are observed prior to oxygen evolution (highest plateau). The potential decay curve displays three plateaux corresponding to

the reverse reactions
Ag_2O_3→AgO→Ag_2O→Ag
In concentrated electrolyte, the cell resistance reflects primarily the resistance of the surface layer. Verification of this

fact was achieved by measurement of the resistance during potential decay. The initial decay of Ag_2O_3 to AgO proceeds at

low resistance in accordance with the relatively high conductance of these compounds Ag_2O_3, 2×10~2 Ω~(-1)cm~(-1); AgO,

10~(-1) Ω~(-1)cm~(-1)). The transformation of the surface layer from AgO to Ag_2O proceeded concurrently with an increase in

resistance (Ag_2O3, 10~(-8) Ω~(-1)cm~(-1)). The resistance diminished upon discharge of Ag_2O to Ag. Rapid measurements of

this type facilitate successfull evaluation of Ag battery characteristics.
Complex plane spectra of iron oxide electrodes (s) were generated by continuous variation of measurement frequency during

experiments with both illuminated and non-illuminated electlodes. Analysis of the curves (Figure 4) provided an equivalent

circuit that explained the observed results. It was found that the internal resistance of the semiconducting oxide (R_(SC))

diminished under illumination simultaneousry with an increase in space charge capacitance. The capacitance and resistance

data obtained show promise toward routine evaluation of semiconducting materials and may facilitate optimization of

photoelectrochemical devices.
(This paper has been presented on 161st meeting of the Electrochemical Society, 1982, Montreal, Canada)