Fitting Improvement Using a New Electrical Circuit Model for the ...

Proceedings of the 3rd International
IEEE EMBS Conference on Neural Engineering
Kohala Coast, Hawaii, USA, May 2-5, 2007
SaD1.9
Fitting Improvement Using a New Electrical Circuit Model for the
Electrode-Electrolyte Interface
Jong-hyeon Chang, Student Member, IEEE, Jungil Park, Student Member, IEEE, Youngmi Kim Pak,
and James Jungho Pak, Member, IEEE
Abstract— The characteristics of impedance for the
electrode-electrolyte interface are important in the electrode
researches for biomedical applications. So, the equivalent
circuit models for the interface have been researched and
developed. However, the applications of such previous models
are limited in terms of the frequency range, type of electrode or
electrolyte. In this paper, a new electrical circuit model was
proposed and demonstrated its capability of fitting the
experimental results more accurately than before. A new
electrical circuit model consists of three resistors and two
constant phase elements. Electrochemical impedance
spectroscopy was used to characterize the interface for several
materials of Au, Pt, and stainless steel electrode in 0.9% NaCl
solution. The new model and the previous model were applied to
fit the measured impedance results, and were compared their
goodness of fit.
E
I. INTRODUCTION
LECTRODES are widely used for measuring
electrochemical reaction in various electrolyte solutions
and for stimulating tissues or cells. When a metal electrode is
in electrolyte solution, electrical double layer is formed at the
electrode-electrolyte interface. Characterization of the
electrode- electrolyte interface is very important in the fields
of impedance-based biosensor, neuroprothesis, and in vitro
communication with cells[1-3]. So, if the interface impedance
is characterized well, then it is possible to make an optimized
microelectrode for various biomedical applications.
The Warburg capacitance(C W ) varies inversely with the
square root of frequency and the phase angle is constant of
π/4 as shown in Fig. 1a. In 1932, Fricke renewed the Warburg
model(Fig. 1b). The phase angle of the Fricke model is
constant of mπ/2, and m depends on the metal species. In
1947, well-known Randles’ model consisted of a
double-layer polarization capacitance(C p ) in parallel with a
series resistance(R) and capacitance(C) was proposed(Fig.
1c). In 1970, Sluyters-Rehbach proposed a more complex
model with electrochemical considerations(Fig. 1d). All the
models mentioned above refuse permission for the passage of
direct current(DC) through the interface. In 1994, Kovacs
proposed a currently used equivalent circuit model which is
based on the Randles’ model with additional Warburg
impedance due to the diffusion of Faradaic current(Fig.
1e)[7-8]. Here, C dl , R ct , Z W , and R S are double layer
capacitance, charge-transfer resistance, Warburg impedance,
and solution resistance, respectively. Warburg impedance,
which is caused by diffusion of ions from bulk electrolyte to
the interface, is written by the following equation[6].
Z W = (1-j)/[k·ω 0.5 ]
As frequency decreases, Warburg impedance increases.
When DC voltage is applied to the electrodes in electrolyte
solution, the total impedance becomes infinite value due to
II. ELECTRICAL CIRCUIT MODEL
Many researchers have studied about the interface and
developed several electrical circuit models[4-6]. Helmholtz
proposed a double layer of charge existed at the interface for
the first time in 1879. In 1899, Warburg proposed an
electrical circuit model for an infinitely low current density.
Manuscript received February 16, 2007. This work was supported by the
Korea Science and Engineering Foundation(KOSEF) through Nano
Bioelectronics and Systems Research Center and the Brain Korea 21 program
of the Ministry of Education of Korea.
James Jungho Pak is with the Department of Electrical Engineering,
Korea University, Seoul 136-713, Korea(phone: 82-2-3290-3238, fax: 82-
2-921-0544; e-mail: pak@korea.ac.kr).
Jong-hyeon Chang is with the Department of Electrical Engineering,
Korea University, Seoul 136-713, Korea(e-mail: ican@korea.ac.kr).
Jungil Park is with the Department of Electrical Engineering, Korea
University, Seoul 136-713, Korea(e-mail: niipark@korea.ac.kr).
Youngmi Kim Pak is with the Asan Institute for Life Sciences, University
of Ulsan College of Medicine, Seoul 138-736, Korea(e-mail:
ymkimpak@amc.seoul.kr)
Fig. 1. Previous electrical circuit models for the electrode-electrolyte
interface; (a)Warburg in 1899, (b)Fricke in 1932, (c)Randles in 1947,
(d)Sluyters-Rehbach in 1970, (e)Kovacs in 1994.
1-4244-0792-3/07/$20.00©2007 IEEE. 572

the frequency dependence of the Warburg impedance.
However, the Kovacs’ model, omitting the circuit element R ct
or Z W , in accordance with experimental conditions is often
used[6, 9-12]. In Fig. 1e, constant phase element(CPE) was
used instead of C dl , because a capacitor in electrochemical
impedance spectroscopy(EIS) normally does not behave
ideally and act like a CPE[6].
Z CPE = 1/[A·(jω) a ]
When this equation describes a capacitor, the exponent a is 1.
For a CPE, the exponent a is less than 1.
To overcome the problem of the previous model, we make
a new electrical circuit model for the electrode-electrolyte
interface as shown in Fig. 2. In this model, Warburg
impedance was replaced by CPE b and R b paralleled for the
passage of DC through the interface. With this model, total
impedance becomes a finite value even at 0 Hz due to R b . then
the total impedance is given by
Z(0) = R a +R b +R S
the Kovacs’ model. So, the applicable range of this model is
broader than Kovacs’ model at least.
III. EXPERIMENTS
To measure and analyze the impedance characteristics
according to the frequency, EIS was used. Fig 3 shows
3-electrode system consisted of a working electrode(WE), a
reference electrode(RE) and a counter electrode(CE) for
stable EIS. Each of Au, Pt and stainless steel(SUS) wire with
5.0 mm 2 in the surface area was used as a WE. Where, the
diameter of each wire electrode was 0.4mm, and the length
was 4mm. A commercial Ag/AgCl electrode(RE-5B,
Bioanalytical Systems Inc.) was used as a RE, and Pt coil with
about 400 mm 2 in the surface area was used as a CE. The
electrolyte solution was physiological saline, 0.9% NaCl,
with the volume of 15mL.
AC voltage of 10mV rms with respect to the open-circuit
potential was applied typically and impedance according to
the frequency was measured by Potentiostatic EIS(PCI4/750,
Gamry Instruments Inc.). As the frequency is lower, the
If R b has infinite value and the parameter of CPE b , b has a
certain value of 0.5, then the new model can be converted to
Fig. 2. A New electrical circuit model for the electrode-electrolyte
interface.
Fig. 3. 3-electrode system for electrochemical impedance spectroscopy.
Impedance Magnitude [Ω]
10 10 10 8
10 7
10 6
10 5
10 4
10 3
10 2
Frequency [Hz]
10 9
0
10 1
-90
10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6
10
-10
-20
-30
-40
-50
-60
-70
-80
Impedance Phase [degrees]
Impedance Magnitude [Ω]
10 10 10 8
10 7
10 6
10 5
10 4
10 3
10 2
Frequency [Hz]
10 9
0
10 1
-90
10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6
10
-10
-20
-30
-40
-50
-60
-70
-80
Impedance Phase [degrees]
Impedance Magnitude [Ω]
10 10 10 8
10 7
10 6
10 5
10 4
10 3
10 2
Frequency [Hz]
10 9
0
10 1
-90
10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6
10
-10
-20
-30
-40
-50
-60
-70
-80
Impedance Phase [degrees]
-imag Z [Ω]
20.0M
15.0M
10.0M
5.0M
0.0
0.0 5.0M 10.0M 15.0M 20.0M 25.0M
real Z [Ω]
-imag Z [Ω]
2.0M
1.5M
1.0M
500.0k
0.0
0.0 500.0k 1.0M 1.5M 2.0M 2.5M 3.0M
real Z [Ω]
-imag Z [Ω]
120.0k
100.0k
80.0k
60.0k
40.0k
20.0k
0.0
0.0 20.0k 40.0k 60.0k 80.0k 100.0k 120.0k 140.0k
real Z [Ω]
(a) (b) (c)
Fig. 4. Impedance magnitude and phase experimental results, and Nyquist diagram for (a)Au, (b)Pt, and (c)SUS wire electrodes in 0.9% NaCl with fitting by
Kovacs’ model(dashed line) and new model(solid line).
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TABLE I
FITTING PARAMETER RESULTS FOR THE ELECTRODE-ELECTROLYTE INTERFACE
Parameter
Au/0.9% NaCl Pt/0.9% NaCl SUS/0.9% NaCl
Kovacs’ model New model Kovacs’ model New model Kovacs’ model New model
R S [Ω] 88 87.3 83.7 83.8 90.6 91.1
Deviation 1.59 1.13 0.807 0.926 1.23 1.43
R b [Ω] ∞ 1.62e7 ∞ 1.27e6 ∞ 8.45e4
Deviation - 2.07e7 - 1.00e6 - 4.18e4
R ct or R a [Ω] 3.52e3 7.54e6 1.55e6 1.34e6 5.24e4 4.93e4
Deviation 1.56e6 3.19e6 1.14e5 4.46e5 8.71e2 3.03e3
k or B [S·s b ] 3.36e-7 1.09e-6 5.53e-6 4.80e-6 1.12e-4 8.06e-5
Deviation 4.10e-8 1.61e-6 9.77e-7 7.49e-6 5.76e-6 1.99e-5
b 0.5 0.888 0.5 0.767 0.5 0.543
Deviation - 5.14e-1 - 4.43e-1 - 1.25e-1
A [S·s a ] 2.22e-6 2.42e-6 5.54e-6 5.49e-6 3.68e-6 3.57e-6
Deviation 1.51e-7 3.74e-8 6.40e-8 1.01e-7 7.78e-8 1.14e-7
a 0.876 0.865 0.893 0.895 0.772 0.776
Deviation 1.55e-2 2.65e-3 2.23e-3 3.43e-3 3.08e-3 4.40e-3
Goodness of fit 6.67e-4 1.96e-4 1.11e-3 1.06e-3 6.92e-4 1.64e-4
impedance magnitude is higher, and the current approaches
the system measurement limit. So, the frequency range was
set between 10 -2 ~ 10 5 Hz. To obtain the appropriate electrical
circuit model from the measured result, the analysis was
performed by using Echem Analyst(Gamry Instruments Inc.).
Both of the Kovacs’ model and new model were applied to fit,
and the fitting parameters are obtained.
Fig. 4 shows the EIS measurements and model results for
5.0mm 2 Au, Pt, and SUS wire electrodes with fitting by
Kovacs’ model and new model, and Table I shows the fitting
parameter results for the Au/0.9% NaCl, Pt/0.9% NaCl, and
SUS/0.9% NaCl interface.
In the fitted results by the Kovacs’ model, the impedance
magnitude goes up with the frequency goes down at the very
low frequency. However, in the results by the new model, the
impedance goes to a finite value. Both of the two models
seem to be fitted well, but the new model was fitted more
precisely. Small goodness of fit in Table 1 presents high
accuracy.
V. CONCLUSIONS
A new electrical circuit model for the electrode-electrolyte
interface was proposed and used to analyze the EIS
experimental results comparing with a previous model. Au, Pt
and SUS wire electrode and 0.9% NaCl solution were used to
measure the impedance characteristics according to the
frequency range of 10 -2 ~ 10 5 Hz. The new model was fitted
better than Kovacs’s model at the low frequency range, and it
was possible to predict the impedance at very low frequency
inclusive of DC using the new model. This model will be
applicable to various biomedical applications instead of
previous models for accurate analysis.
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