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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 7, JULY 2005 1295
Impedance Characterization and Modeling of
Electrodes for Biomedical Applications
Wendy Franks*, Iwan Schenker, Patrik Schmutz, and Andreas Hierlemann
Abstract—A low electrode-electrolyte impedance interface is
critical in the design of electrodes for biomedical applications. To
design low-impedance interfaces a complete understanding of the
physical processes contributing to the impedance is required. In
this work a model describing these physical processes is validated
and extended to quantify the effect of organic coatings and incu-
bation time. Electrochemical impedance spectroscopy has been
used to electrically characterize the interface for various electrode
materials: platinum, platinum black, and titanium nitride; and
varying electrode sizes: 1 cm
, and 900 m . An equivalent
circuit model comprising an interface capacitance, shunted by a
charge transfer resistance, in series with the solution resistance
has been fitted to the experimental results. Theoretical equations
have been used to calculate the interface capacitance impedance
and the solution resistance, yielding results that correspond well
with the fitted parameter values, thereby confirming the validity
of the equations. The effect of incubation time, and two organic
cell-adhesion promoting coatings, poly-L-lysine and laminin, on
the interface impedance has been quantified using the model.
This demonstrates the benefits of using this model in developing
a better understanding of the physical processes occurring at the
interface in more complex, biomedically relevant situations.
Index Terms—Electrochemical impedance spectroscopy, Pt, Pt
black, and TiN bioelectrodes.
I. INTRODUCTION
I
MPEDANCE characterization of the electrode-electrolyte
interface is of paramount importance in the fields of
impedance-based biosensing, neuroprotheses, and in vitro
communication with electrogenic cells. In impedance-based
biosensing, changes in the impedance are correlated to cell
spreading and locomotion [1], to bacterial growth [2], to
DNA hybridization [3] and to antigen-antibody reactions [4].
Neuroprotheses, and in particular cochlear implants, represent
an important application of impedance characterization. The
current applied to stimulate hearing via a cochlear implant is
determined from the known electrode impedance [5], which is
Manuscript received April 13, 2004; revised October 19, 2004. This work
was supported in part by the Information Societies Technology (IST) European
Union Future and Emerging Technologies program, and the Swiss Bundesamt
für Bildung und Wissenschaft (BBW). Asterisk indicates corresponding author.
*W. Franks is with the Physical Electronics Laboratory, ETH, Zurich 8093,
Zurich, Switzerland (e-mail: franks@phys.ethz.ch).
I. Schenker was with the Physical Electronics Laboratory, ETH, Zurich, and is
now with the Nonmetallic Inorganic Materials group, ETH Zurich, 8093 Zurich,
Switzerland (e-mail: iwan.schenker@mat.ethz.ch).
P. Schmutz is with the Laboratory for Corrision and Materials Integrity, Swiss
Federal Institute for Materials Testing and Research (EMPA), 8600 Dübendorf,
Switzerland (e-mail: Patrik.Schmutz@empa.ch).
A. Hierlemann is with the Physical Electronics Laboratory, ETH, Zurich
8093, Zurich, Switzerland (e-mail: hierlema@phys.ethz.ch).
Digital Object Identifier 10.1109/TBME.2005.847523
designed to be as low as possible to avoid cell damage [6]. For
the extracellular, in vitro monitoring of electrogenic cells, where
small microelectrodes are required for high-resolution stimula-
tion and recording, the need for a low interface impedance is
twofold [7]–[10]. During stimulation a certain current density is
necessary to generate activity. A high impedance would result
in a large applied electrode voltage leading to undesirable elec-
trochemical reactions that may be harmful to cellular cultures.
On the recording side, the extracellular signals are low, on
the order of millivolts for cardiomyocytes and microvolts for
neurons. The neural signals will be lost in the noisy, ion-based
electric fluctuations of the surrounding electrolyte media if the
electrode impedance is not low enough. A well-characterized,
fully understood interface impedance leads to an optimized
electrode-electrolyte interface design.
Equivalent circuit models have long been used to model the
interface impedance. In 1899 Warburg first proposed that the
interface could be represented by a polarization resistance in
series with a polarization capacitor [11]. Experimental findings
soon revealed that the polarization capacitance exhibited a
frequency dependency leading to the introduction of Fricke’s
law [12], and the use of a constant phase angle impedance to
represent the impedance of the interface capacitance. Randles’
work with rapid electrode reaction systems resulted in the
well-known Randles model, consisting of an interface capac-
itance shunted by a reaction impedance, in series with the
solution resistance [13]. As the use of platinum electrodes in
medical applications became ubiquitous, more research was
dedicated to the understanding of the electrode—physiological
solution interface. In the case of platinum, the resistive element
due to faradaic current was often omitted as measurement
equipment was not able to measure at low frequencies where
the impedance is finite, and not infinite, as was typically as-
sumed [14]. The work of Schwan and co-workers expanded on
previous work to include low frequency considerations [15]. Of
particular importance to biomedical applications is Schwan’s
limit of linearity: the voltage at which the electrode system’s
impedance becomes nonlinear, which is often exceeded during
stimulation [16], [17]. McAdams and colleagues extensively
studied the platinum pacing electrode (90% platinum and 10%
iridium) in physiological saline, successfully interpreting the
frequency-dependent nonlinear interface impedance [18]–[20].
Kovacs has presented an equivalent circuit model based on the
Randles model, with an additional Warburg impedance due to
the diffusion of faradaic current [7].
In the work presented here, electrochemical impedance spec-
troscopy (EIS) has been used to characterize the electrode-elec-
trolyte interface for various electrode materials commonly used
0018-9294/$20.00 © 2005 IEEE
1296 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 7, JULY 2005
in biomedical applications: platinum, platinum black and tita-
nium nitride. An equivalent circuit model has been used where
each parameter represents a macroscopic physical quantity con-
tributing to the interface impedance: The model consists of an
interface capacitance, shunted by a charge transfer resistance, in
series with the solution resistance. The model parameters have
been fitted to the experimental results. To confirm that the pa-
rameters do indeed represent the physical quantities, theoret-
ical equations have been used to calculate the parameter values
thereby validating the model. With respect to the measurement
technique, the effect of the initial interface conditions on the
charge transfer resistance is demonstrated. Measurements have
been performed for 1 cm
bright Pt, Pt black, and TiN, and for
900
m Pt black. As an extension to models that have been
presented in the past [5], [7], [20], this model has been used to
quantify the effect of organic cell-adhesion promoting coatings,
such as poly-L-lysine (PLL) and laminin, and the effect of incu-
bation time on the interface impedance. This demonstrates the
use of the model to develop a complete understanding of the
physical processes occurring at the interface in more complex,
biomedically relevant situations.
II. M
ETHODS
Both the macroelectrodes and microelectrodes were pro-
duced in-house according to the following procedures. For
the macroelectrodes a bare p-type Si wafer was electrically
isolated with 100 nm SiO
followed by 500 nm of Si N
deposited using plasma enhanced chemical vapor deposition
(PECVD). Sputter deposition was used to coat the substrate
with 50 nm of TiW, an adhesion promoter, followed by 270 nm
of Pt. The wafer was then diced and the chips were cleaned.
The chips were then either coated with Pt black or TiN. Pt
black was deposited using a 0.3–10 A/cm
current density in
a solution containing 7 mM hexachloroplatinic acid, 0.3 mM
lead acetate and hydrochloric acid to adjust the solution pH
to 1.0. Dendritically structured TiN was vapor deposited by
the Naturwissenschaftliche und Medizinische Institut at the
University of Tübingen, Germany [21]. For the microelectrodes
a p-type Si wafer with 100 nm of SiO
and 500 nm of Si N
was used as the substrate. As above, 50 nm TiW and 270 nm
Pt were sputter deposited, and the microelectrodes with leads
and bond pads were structured in a lift-off process. The wafer
was passivated with 500 nm Si
N . A reactive-ion etch (RIE)
was used to open the electrodes, thereby defining their size
and shape. The wafer was then diced, and the chips cleaned.
The bond wires of the packaged chips were encapsulated in
polydimethylsiloxane (PDMS) for electrical isolation.
Bright Pt macroelectrodes were coated with two different
cell-adhesion promoting coatings, laminin, and poly-L-lysine,
in the following manner. The samples were cleaned with an air
plasma treatment (2 min. at
mbar). It is known
from x-ray photon spectroscopy (XPS) measurements that,
immediately following plasma cleaning, the surface contains
no carbon, indicating that the surface is free of organic residues.
Additionally, plasma cleaning has the effect of activating the
surface and is believed to lead to better quality protein layers
with respect to coverage and adhesion. Within 45 min of
plasma cleaning the protein coatings were applied. Samples
were incubated (37
C, 5% CO ) overnight in laminin (20
mg/ml phosphate buffered saline, PBS). For PLL the samples
were incubated for 30 min in a 0.05% solution. After incubation
the samples were rinsed three times with PBS.
To investigate the effect of time on the interface impedance,
bright Pt samples were incubated in medium containing 10%
horse serum. Impedance measurements were performed after 7,
14, and 35 days using medium with serum as the electrolyte.
Measurements were performed using a commercially avail-
able Autolab PGSTAT30 potentiostat system with Frequency
Response Analysis software (version 4.9, Eco Chemie B.V.,
Netherlands). In this three-electrode system, a standard calomel
electrode (SCE) is the reference electrode, the counter elec-
trode is large-area Pt, and the electrolyte is physiological saline,
0.9% NaCl. In addition to the time dependency measurements,
neuron medium with 10% horse serum was used as the elec-
trolyte in one set of measurements. The perturbation potential
was 10 mV and the scan range was
to Hz, unless oth-
erwise noted. Measurements were typically performed with re-
spect to the open-circuit potential (OCP), the potential naturally
occurring between the working and reference electrodes. The
OCP is a function of the chemical composition of the interface,
and can significantly affect the impedance results. Accordingly,
special attention was paid to the preparation of the samples to
ensure that the interface was as defined as possible. It is known
that organic residues on the substrate surface can contribute to a
faradaic current, which decreases the charge transfer resistance
and polarizes the electrode. An
in situ cleaning process was,
therefore, used where the Pt and Pt black electrodes (without
coatings) were treated by voltammetric cycling from
to
1.0 V for typically 6 cycles, at which point the measurement sta-
bilized. Cyclic voltammetry potentially results in the formation
and reduction of Pt oxide and Pt dioxide layers, as indicated by
the Pt-H
O Pourbaix diagram [22]. Since the OCP is a function
of the interface composition, the OCP can be altered through
the cycling process. Additionally, the OCP can be used as a
quality control to ensure that the initial conditions are the same
from measurement to measurement. The average OCP values
for Pt, Pt black, and TiN were
,
and
V, respectively. The relatively large range of
OCP values for TiN can be attributed to the fact that the samples
were not treated with cyclic voltammetry for fear of damaging
the dendritic structure.
Measurements were first performed with relatively large area
samples (1 cm
) to establish the measurement technique and
equivalent circuit model under stable experimental conditions.
Difficulties with respect to stability were encountered during the
measurement of the microelectrodes as the current approached
the system measurement limit of 10 nA at low frequencies. As a
result, the frequency range for the microelectrode measurements
was reduced to
to Hz.
III. E
QUIVALENT CIRCUIT MODEL
The equivalent circuit model presented in this work com-
prises a constant phase angle impedance
, that represents
the interface capacitance impedance, shunted by a charge
FRANKS et al.: IMPEDANCE CHARACTERIZATION AND MODELING OF ELECTRODES FOR BIOMEDICAL APPLICATIONS 1297
Fig. 1. Equivalent circuit model of electrode-electrolyte interface.
transfer resistance , together in series with the solution
resistance
, see Fig. 1, [23]. This model is an adaptation
from the theoretical models typically used to represent the
electrode-electrolyte impedance [7], [19], [24]. The Warburg
impedance due to diffusion of the chemical reactants in solution
is not included in this model. For the materials and frequency
range employed here, it was experimentally determined that
the Warburg impedance does not significantly contribute to the
overall impedance.
A. Interface Capacitance
The constant phase angle impedance is a measure of the non-
faradaic impedance arising from the interface capacitance, or
polarization, and is given by the empirical relation [20]
(1)
where
is a measure of the magnitude of is a con-
stant
representing inhomogeneities in the surface
and
. In a Nyquist plot the angle between the data
and the abscissa axes gives
according to . When
represents a purely capacitive impedance element
corresponding to the interface capacitance.
A theoretical derivation of the interface capacitance is given
by the Gouy-Chapman-Stern model (GCS) [25]. The interface
capacitance is taken to be the series combination of the double-
layer capacitance, termed the Helmholz capacitance
, and
the diffuse layer capacitance, the Gouy-Chapman capacitance
, and is given by the following formula:
(2)
where
is the thickness of the double-layer, is the per-
mittivity of free space,
is the permittivity of the double layer,
is the charge on the ion in solution, is the applied electrode
potential, and
is the thermal voltage. The Debye length, ,
is given by
(3)
where
is the bulk number concentration of ions in solution
and
is the elementary charge. See Table I for the values of the
constants and variables used here.
B. Equilibrium Exchange Current Density and
At equilibrium, equal, and opposite reduction and oxidation
currents flow across the electrode-electrolyte interface. The
magnitude of these currents is termed the equilibrium exchange
current density
and is given by
(4)
TABLE I
S
UMMARY OF THE VALUES USED FOR VARIABLES AND CONSTANTS USED TO
CALCULATE THE THEORETICAL VALUE OF USING (2). INTHE“NOTE”
C
OLUMN ALL ASSUMPTIONS ARE GIVEN
for the reduction reaction where
is Faraday’s constant, is
reduction reaction rate constant,
is the concentration of elec-
tron-acceptor ions A in solution plane of the interface,
is the
symmetry factor,
is the equilibrium potential, is the gas
constant and
is the temperature [26]. The equilibrium current
is a measure of the electrode’s ability to participate in exchange
current reactions, and, hence, is of particular relevance to this
work. For an ideally polarizable electrode
equals zero and for
an ideally unpolarizable electrode
tends to infinity; in reality,
lies somewhere between these two extremes. It is tempting
to use literature values of
to compare various electrode ma-
terials, however, since
is a function of ion concentration and
temperature, literature values must be carefully considered.
The equilibrium exchange current and
can be experimen-
tally determined through the application of the low-field approx-
imation to the Butler-Volmer equation
, which
yields
(5)
where
is the measured current density, is the applied over-
potential,
is the number of electrons involved in the redox
reaction, and
mV at 298 K. Under the low-field
approximation, the Butler-Volmer equation reduces to Ohm’s
law. A plot of the current versus overpotential yields a straight
line and the charge transfer resistance is given by the slope as
. Cyclic voltammetry was used to determine
under the following conditions: 5 mV perturbation signal
with respect to the OCP, 0.5 mV/s scan rate, 0.15 mV step po-
tential, averaged over 10 scans. For the case of Pt the charge
transfer arises from the electrolysis of H
O and reduction of O
according to where the equilibrium
potential is
(6)
with respect to the SCE [27]. For the calculation of
was,
therefore, assumed to be 4. It should be noted that the pres-
ence of contaminants at the interface will also contribute to the
faradaic current.
C. Solution Resistance
The resistance measured between the working electrode and
the reference electrode is termed the solution resistance. It can
1298 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 7, JULY 2005
Fig. 2. Impedance modulus and phase as a function of frequency for 1 cm Pt,
Pt black, and TiN electrode materials [28]. Modeled results are indicated by the
smooth lines.
be determined from the spreading resistance, the resistance en-
countered by current spreading out into solution, under the as-
sumption that the counter electrode is infinitely large and the
working electrode is surrounded by electrolyte. The spreading
resistance is given by
(7)
for square electrodes (
is the solution resistivity, 72 cm for
physiological saline [7],
the electrode side length), and
(8)
for round electrodes (
is the radius) [7]. It is worth noting that
unlike
and , which scale with the total electrode area, the
solution resistance is dependent upon the geometric area only
(where geometric area refers to the planar two-dimensional area,
and not the larger total area which increases with roughness).
IV. R
ESULTS
EIS measurements and model results for 1 cm Pt, Pt black,
and TiN are given in Fig. 2, [28]. Table II gives a summary of
the averaged, fitted parameter values with corresponding stan-
dard deviations. For
, and the standard deviation is 10%,
or less, in almost all cases. In the case of
the standard devia-
tion is as high as 110%. This large standard deviation can be at-
tributed to the high sensitivity of
to the electrode-electrolyte
interface conditions. Furthermore,
is extrapolated from the
low frequency data which leads to increased uncertainty. The
sharply decreasing phase angles at high frequencies is an arti-
fact of the measurement system.
A. Verification of Model Parameters
To confirm the validity of the model, the model parameters
have been calculated based on the theoretical principles pre-
sented above. A comparison between the fitted and theoretical
parameters has been performed for the simplest case of bright
TABLE II
S
UMMARY OF THE AVERAGED,FITTED PARAMETER RESULTS,WITH
CORRESPONDING STANDARD DEVIATIONS, FOR THE FOLLOWING MATERIALS
AND
MEASUREMENT AREAS:BRIGHT Pt 1 cm ,PtBLACK 1cm , TiN 1 cm ,
Pt B
LACK MICROELECTRODE 900 m , PLL-COATED BRIGHT Pt 1
cm
,LAMININ-COATED BRIGHT Pt 1 cm ,BRIGHT Pt WITH NEURON
MEDIUM AS THE ELECTROLYTE,1cm
Fig. 3. Equilibrium exchange current density measurement: current versus
applied electrode overpotential measurement results for 1 cm
bright platinum.
A
mV overpotential with respect to an OCP of 351.5 mV was applied.
Pt. Using (2) and the variable values given in Table I, the theo-
retical interface capacitance was found to be 0.545 F/m
. The
impedance of the interface capacitance was calculated using
, and at an angular frequency of 1 s ,
is (for 1 cm ). Similarly, using the values of and
(given in Table II) for 1 cm bright Pt, and (1), was
found to be
.For , cyclic voltammetry was used
to generate a current versus overpotential plot, see Fig. 3. From
the slope of the plot,
was found to be 300 k ; the fitted
value was found to be 450 k
. From (5), the exchange current
density was calculated to be
A/cm . Finally the solu-
tion resistance was determined to be 32.0
using (8). The fitted
parameter value is 28.0
.
B. Effect of OCP on Model Results
Throughout the course of this work it has been observed that
the model parameter
is highly dependent on the initial elec-
trode-electrolyte interface conditions. To demonstrate this de-
pendance, the OCP was set to various values, either by cyclic
voltammetry or by an applied potential. The EIS phase results
(the modulus results show no variation) and the fitted values for
are given in Fig. 4.
FRANKS et al.: IMPEDANCE CHARACTERIZATION AND MODELING OF ELECTRODES FOR BIOMEDICAL APPLICATIONS 1299
Fig. 4. Effect of OCP on measurements results. Measurements were
performed using 1 cm
bright platinum samples. The table shows the fitted
values for
.
Fig. 5. Impedance modulus and phase experimental results for Pt black
microelectrodes (geometrical area 900
m ). The modeled results are indicated
by the solid lines [28].
C. Microelectrode Results
The impedance modulus, phase, and standard deviations
for the Pt black microelectrodes (geometric area 900
m )
are presented in Fig. 5; fitted parameter values are given in
Table II. A variation in the total electrode area within the
sample population arising from the platinization procedure
results in a large measurement standard deviation apparent in
the phase measurements at high frequencies. The theoretical
value for the interface capacitance, 0.545 F/m
[from (2)] and
the relation
, which simplifies
to
, were used to determine the total area of
each of the 6 microelectrodes measured. The areas ranged
from
to m , with a standard deviation of
m . Development of a more uniform platinization
process is currently under investigation.
D. Effect of Coatings and Neuron Medium as Electrolyte
Fig. 6 shows the impedance modulus and phase results for
the two cell—adhesion promoting coatings, laminin
and PLL , and for the measurements performed with
neuron medium
as the electrolyte (see Table II for fitted
parameter values). The charge transfer resistance of PLL and
laminin is 1.24 and 0.25 M
, respectively, a difference which
quantifies the relative reactivity of the materials at the given
conditions. For the PLL and laminin coatings the value for
was found to be 8.6 and 5.0 s/ , respectively. In the case
of the neuron medium as the electrolyte, the parameter value for
is similar to that of bright Pt. The value of was found to
be 14.6
s/ which is smaller than that of bright Pt. The
solution resistance of the neuron medium was found to be 40.4
, which yields a value of 90.3 cm [from (8)] for the neuron
medium resistivity.
Fig. 6. Impedance modulus and phase for the laminin and PLL protein
coatings, and the neuron medium as electrolyte. The modeled results are
indicated by the solid lines.
Fig. 7. Relative change in modeled parameter value as a function of time for
1cm
bright Pt incubated in medium containing 10% horse serum for up to 35
days.
E. Effect of Time
The percent change in model parameter results for impedance
recordings performed at days 1, 7, 14, and 35 in incubation are
given in Fig. 7. In all cases, the parameter value increases from
day 1 to day 7, and then levels off. This demonstrates the effec-
tive encapsulation of the electrodes, as is discussed in the fol-
lowing section.
V. D
ISCUSSION
An equivalent circuit model has been used to describe and
analyze the EIS experimental results. A good match between
the curves generated using the equivalent circuit model and the
measurement results indicates that the appropriate model has
been selected. For the simplest case of bright Pt, equations de-
scribing the macroscopic physical processes occurring at the
electrode-electrolyte interface yield parameter values for
and
that are in good agreement with the experimentally derived
parameters. The difference between
and repre-
sents a 15% deviation from the experimental value, which is
evidence that the GCS model describes well the interface ca-
pacitance. The difference between the fitted and calculated the-
oretical value could be a result of impurities at the interface that
are not accounted for in the GCS model. A 14% deviation from
1300 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 7, JULY 2005
the measured value of the solution resistance indicates that (7)
can be used to calculate
.
Cyclic voltammetry was used to measure
for the bright
Pt-0.9% NaCl system. There is a 50% difference between the
fitted
value and that determined from cyclic voltammetry.
The source of this difference is difficult to quantify, however,
is most likely a result of sensitivities, in both the EIS and the
cyclic voltammetry measurements, to the interface conditions.
It is worthwhile to mention that the
value reported here
is four orders of magnitude greater than the values reported
in literature,
cm [10], [29]. The literature values are
erroneously based on the assumption that the faradaic current
flowing across the interface is due to a hydrogen redox reaction.
For a neutral pH, the equilibrium potential of the hydrogen re-
action is
V, significantly negative of the OCP value of
V. Given the positive OCP value, the theoretical
reaction would be the oxidation of hydrogen gas according to:
, although the limited amount of hydrogen
gas available in solution precludes this reaction from occurring.
It is known from literature that, given the experimental condi-
tions used in this work, it is the O
redox reaction that is mainly
responsible for the faradaic current (although contamination at
the interface will also contribute to charge transfer) [27]. Exper-
iment results presented here support this assumption. When the
OCP is set to value higher or lower than the equilibrium value
of approximately 0.6 V [from (6) using a pH of 7.0], the
is
lower than if the OCP were equal to the equilibrium value. The
higher or lower potential shifts the reaction from equilibrium
conditions, more faradaic charge transfer occurs, and
is re-
duced. For example, for an OCP of 0.66 V the change transfer
resistance is 1.0 M
(Fig. 4). For an OCP of 0.39 and 0.92 V the
charge transfer resistance reduces to 0.43 M
and 0.23 k , re-
spectively. Since
depends on , it is interesting to compare
the
value measured here with those reported in literature. The
value reported by Kovacs for the oxygen reaction is
A/cm , which was experimentally determined using a platinum
electrode and aerated frog Ringer’s solution (115 mM NaCl, 2.0
mM KCl, 1.8 mM CaCl
) [7], [30]. Aeration of the electrolyte
will increase the amount of O
available for reaction, thereby in-
creasing the equilibrium exchange current, which explains the
deviation from the value reported here. The value reported by
McAdams [19] for a platinum pacing electrode in physiological
saline is
A/cm , which is similar to our measured
value of
A/cm , albeit a direct comparison is invalid
due to the 10% iridium content in the pacing electrode.
It has been the goal of this study to use the EIS results
and model parameter values to develop an enhanced under-
standing of the effect of the physical processes on the interface
impedance, with the expressed purpose of improving the inter-
face design. For example, the impedance modulus of Pt black
and TiN is two orders of magnitude smaller than for bright Pt,
clearly demonstrating the effect of increased total surface area.
This finding is expected and is well documented in previous
studies [10], [29], [31]. A more interesting use of the results
can be found in the effects of PLL and laminin on the interface
impedance. Qualitatively, there is little difference between the
impedance modulus of PLL and laminin, however, the phase
results show that the phase decreases more rapidly for laminin
that PLL, indicating a lower
for laminin. Quantitatively,
this difference manifests itself in the fitted parameter results,
where
is 1.24 M for PLL versus 0.25 M for laminin.
Although laminin is a thicker coating
nm compared to
nm, it appears to facilitate charge transfer rather than
to impede reactions. The effect of the coating thicknesses is
apparent in the modeled parameter
, which is approximately
of for bright Pt. Since is representative of the interface
capacitance, which is inversely proportional to the “dielectric”
thickness (in this case the coating), it follows that the coatings
would reduce
. Such effects are important when considering
an optimized interface design for the stimulation and recording
of electrical activity from electrogenic cells, or when designing
biosensors based on changes in the interface capacitance.
Additionally, the model has been used the quantify the ef-
fect of incubation time on the interface impedance. The relative
change in the model parameter results over time show a sharp
increase from day 1 to 7, followed by a plateau. Indeed, the
impedance results themselves (not shown here) do not change
significantly from day 7 to 35. This indicates that the electrodes
have been encapsulated, most likely by proteins contained in
the medium. For example, the value of
increases from 0.91
at day 1 to 0.95 at day 35, indicating that the interface has be-
come more capacitive. Similarly,
increases from 217 k at
day 1 to 556 k
at day 35, again demonstrating that the inter-
face has become more capacitive, or less conducive to charge
transfer. The same is true of
, which increases from an ini-
tial value of 6.5
s/ to 9.7 s/ by day 35. These
results are relevant to researchers who are performing electro-
physiological measurements over extended periods of time. The
changing electrode impedance of electrodes covered by cell cul-
tures would additionally provide useful insights and shall be in-
vestigated in the future.
The ease in analyzing surface conditions using EIS and its
widespread applicability gives merit to a short discussion on
how this technique may be extended to other electrode-elec-
trolyte systems and smaller electrode sizes. In order to use this
technique with different systems, such as iridium oxide, gold,
stainless steel and other biomedical metals with electrolytes of
varying concentrations and compositions, the appropriate equiv-
alent circuit, which is highly dependent on the equilibrium ex-
change current density, must be selected. For nonpolarizable
electrodes, corresponding to a high equilibrium exchange cur-
rent, the charge transfer resistance becomes low and a War-
burg element, representing the effect of diffusion on the cur-
rent-carrying ions, may be necessary to accurately model the
interface conditions (the reader is referred to general references
on EIS [25], [26], [32]). Due to the sensitivity of
to the inter-
face conditions, as demonstrated in this work, the equilibrium
exchange current varies significantly with electrode and elec-
trolyte and, hence, care must be taken when using values from
literature. It is, therefore, recommended that
be experimen-
tally determined. Although values for
are reported in litera-
ture, for example Kovacs provides a table with various values
[7], it is unlikely that the experimental conditions are exactly
the same. Pourbaix diagrams may be used to determine the re-
actions giving rise to
, and will provide a value for that is
required to determine
using (5). Many cases of EIS applied
FRANKS et al.: IMPEDANCE CHARACTERIZATION AND MODELING OF ELECTRODES FOR BIOMEDICAL APPLICATIONS 1301
to different electrode-electrolyte systems can be found in litera-
ture, for example: Bates, et al., have analyzed a system of rough-
ened Pt and aqueous H
SO [33], Valoen, et al., have developed
an impedance model for metal hydride electrodes in KOH [34],
and Chou and colleagues have used EIS to investigate the effect
of a self-assembled monolayer on a Au electrode inside a rat
heart [35]. As a final extension to the model, it should be noted
that while this theory may be applied to infinitely small elec-
trodes, the experimental measurement becomes increasingly un-
stable with shrinking electrode dimensions because the current
flowing across the interface becomes too small to be measured.
Very small electrodes,
m , must be measured at higher
frequencies requiring special equipment.
VI. C
ONCLUSION
A measurement technique with a corresponding equivalent
circuit model has been established for the quantification of
the electrode-electrolyte interface impedance using electro-
chemical impedance spectroscopy. Equations describing the
macroscopic physical processes occurring at the interface are
presented, and, for the case of bright Pt, yield results that are
in good agreement with the fitted parameter values. The effect
of various characteristics, such as total area, protein coating,
and time on the EIS and fitted parameter results has been used
to elucidate the processes occurring at the interface, thereby
demonstrating the usefulness of the model in the impedance
analysis of more complex, biomedically relevant situations.
A
CKNOWLEDGMENT
The authors would like to thank Prof. H. Baltes (on leave)
for sharing laboratory resources and for his ongoing stimulating
interest in their work.
R
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1302 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 52, NO. 7, JULY 2005
Wendy Franks received the B.Sc. degree in chem-
ical engineering in 1998 and the M.Sc. degree in
electrical engineering in 2000, both at the University
of Waterloo, Waterloo, ON, Canada. She received
the Ph.D. degree from the Swiss Federal Institute of
Technology, Zurich (ETHZ) in the field of bioelec-
tronics.
Iwan Schenker received the Diploma in physics
from the Swiss Federal Institute of Technology
(ETHZ), Zurich, Switzerland, in 2003. He is cur-
rently working towards the Ph.D. degree in the
Nonmetallic Inorganic Materials Group, Department
of Materials, ETHZ, Zurich, Switzerland.
Patrik Schmutz received an undergraduate degree in
solid-state physics in 1991 from the University of Fri-
bourg, Switzerland, and a Ph.D. degree in science in
1996 from the Swiss Federal Institute of Technology
in Lausanne (EPFL).
He is currently Head of Corrosion Research at the
EMPA (National Laboratory for Material Science
and Technology) and is a Lecturer at the Swiss
Federal Institute of Technology in Zurich (ETHZ),
Switzerland. His main research topic is investigation
of localized physico-(electro)chemical processes on
reactive metallic surfaces.
Andreas Hierlemann received the Diploma in
chemistry in 1992 and the Ph.D. degree in physical
chemistry in 1996 from the University of Tübingen,
Tübingen, Germany.
Having been a Postdoc at Texas A&M Uni-
versity, College Station, TX (1997), and Sandia
National Laboratories, Albuquerque, NM (1998),
he is currently Professor at the Physical Electronics
Laboratory at ETH Zurich in Switzerland. The
focus of his research activities is on CMOS-based
microsensors and interfacing CMOS electronics
with electrogenic cells.
