Conductometric discrimination of electro-inactive metal ions using nanoporous electrodes

Article abstract of DOI:10.1016/j.electacta.2010.12.006

We investigated conductometric analysis of electro-inactive metal ions at high concentration based on nanoporous electrodes by electrochemical impedance spectroscopy (EIS). The three dimensional interconnected nanoporous Pt (L ₂-ePt) was found to enable significantly sensitive and selective conductometric detection of alkali and alkaline earth metal ions of high concentration at low frequency without any additional surface modification, which can be hardly done by flat Pt. The extremely large surface area of L ₂-ePt remarkably suppressed the electrode impedance and the pore effect was additional positive contribution to selective ion sensing by conductometry at low frequency. Importantly, L₂-ePt allowed recognition of fractional ratio reversal of Na⁺ to K⁺ ions in a mixed solution at physiological concentration maintaining the constant total ionic strength. The results suggest the possibility of real time extracellular monitoring of instantaneous ion exchange near ion channels of a cell membrane such as action potential propagation along axons in a neuronal system.

Full text of DOI:10.1016/j.electacta.2010.12.006

Electrochimica Acta 56 (2011) 1947–1954
Contents lists available at ScienceDirect
Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Conductometric discrimination of electro-inactive metal ions
using nanoporous electrodes
Je Hyun Bae, Taek Dong Chung∗,1
Department of Chemistry, Seoul National University, Seoul 151-747, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history:
We investigated conductometric analysis of electro-inactive metal ions at high concentration based
on nanoporous electrodes by electrochemical impedance spectroscopy (EIS). The three dimensional
interconnected nanoporous Pt (L2-ePt) was found to enable significantly sensitive and selective conduc-
tometric detection of alkali and alkaline earth metal ions of high concentration at low frequency without
any additional surface modification, which can be hardly done by flat Pt. The extremely large surface area
of L2-ePt remarkably suppressed the electrode impedance and the pore effect was additional positive
contribution to selective ion sensing by conductometry at low frequency. Importantly, L2-ePt allowed
recognition of fractional ratio reversal of Na+ to K+ ions in a mixed solution at physiological concentration
maintaining the constant total ionic strength. The results suggest the possibility of real time extracellular
monitoring of instantaneous ion exchange near ion channels of a cell membrane such as action potential
propagation along axons in a neuronal system.
Received 15 September 2010
Received in revised form
30 November 2010
Accepted 1 December 2010
Available online 8 December 2010
Keywords:
Nanoporous
Impedance
Metal ion
Action potential
Conductometry
© 2010 Elsevier Ltd. All rights reserved.
1. Introduction
representative approach with attractive features of nondestructive
and ion-selective analytical powers, but problematic in terms of
Most of the aqueous media in nature such as sea water, cytosol,
blood, and body fluid contain high concentration of ions. Ion con-
centration and composition in living organisms may instantly vary
in the immediate vicinity of the ion channels of cell membranes.
For example, the propagation of action potential along the axon in a
neuron accompanies asymmetric ion current through ion channels,
leading to immediate changes in local ion concentration. In case of
mammalian neurons, the intracellular concentrations of K+ and Na+
ions are 140 mM and 5–15 mM at resting states while the extra-
cellular concentrations are 5 mM and 145 mM, respectively [1]. As
recent neuroscience research and related technologies increasingly
require in situ monitoring of extracellular signals without staining
[2–5], prompt recognition of variation in ion composition at high
ionic strength becomes more demanding. In this regard, fluores-
cence techniques and ion selective electrodes (ISEs) are normally
considered. Although fluorescence measurements are most widely
used and provide tremendous information, they need chemical
additives of fluorescent dyes to stain, which may affect the bio-
logical system. In addition, it should be noted that fluorescent
techniques are too sensitive to detect abundant ions at high con-
centration like Na+ and K+ ions. Ion selective electrodes (ISEs) are a
sensitivity, dynamic range, response time, etc. More significantly,
instantaneous variation of composition of Na+/K+/Cl− ions with
high spatial resolution is hardly detected by micro or sub micro
ISE array, which is not easy to fabricate in practice and does not
give stable potentiometric signals either [6,7]. Besides, microfabri-
cated FET array is a reasonable option to take for extracellular signal
monitoring [8]. Recently, silicon nano wire-FET array was applied
to monitor the electrical neuronal signal propagation from single
mammalian neurons [9]. However, these methods have insufficient
ion selectivity and the sensitivity is significantly influenced by the
buffer electrolyte concentration [10].
Not only for neuronal signal monitoring but for general analysis
of electrochemically inactive species in aqueous phase, conductom-
etry has been widely regarded as an inexpensive, nondestructive
and simple conventional method [11–13]. As chemical or biological
monitoring within a limited volume is increasingly demand-
ing, high resolution conductometric analysis of ions based on
miniaturized electrode array attracts keen attention. For instance,
microfluidic technology needs smaller and more sensitive conduc-
tometric detectors to extend its applications. As a result, electrodes
for biological process and analysis are ceaselessly miniaturized and
integrated on a chip [14–16].
In conductometry, ions are discerned by equivalent conduc-
tance which is a function of intrinsic mobility in the solution
[17,18]. As the electrodes for conductometry are reduced in
size, the impedance at the electrode–solution interface, electrode
∗
Corresponding author. Tel.: +82 2 880 4362; fax: +82 2 887 4354.
E-mail address: tdchung@snu.ac.kr (T.D. Chung).
ISE member.
1
0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2010.12.006

1948
J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
(Triton® X-100, Sigma), sodium chloride (DAE JUNG, Korea), sulfu-
ric acid (Sigma), lithium perchlorate (95+%, A.C.S reagent, Sigma),
sodium perchlorate mono-hydrate (98%, A.C.S reagent, Sigma),
potassium perchlorate (99+%, A.C.S reagent, Sigma), magnesium
perchlorate (A.C.S reagent, Sigma) and calcium perchlorate tetrahy-
drate (99%, Sigma) were used without further purification. All the
aqueous solutions in this experiment were prepared with ultrapure
deionized water produced by NANOpure (Barnstead).
impedance called in this report, increases correspondingly. Higher
electrode impedance leads to smaller contribution of the solu-
tion resistance to the total impedance, which makes less sensitive
and selective analysis of ions. This problem becomes worse in the
higher ion concentration that results in solution resistance as well
[12]. That is why maximum concentration of the dynamic range in
conductometric detection does not exceed several tens mM [19].
Although contribution of solution resistance to total impedance
can be raised by using a high frequency, conductometry in high
ion concentration is inaccurate due to a few problems such as
impedance artifacts [20] and interference by the electrodes that
are not in contact with the solution [21]. Specifically, miniaturized
electrode array on a chip has inevitably thin insulating layer with
relatively wide area, which may not be assumed to be perfect insu-
lator. Cross-talk among the electrodes in a cellular medium upon
high frequency input signals is a serious problem in practice caused
by such a condition.
Platinization of electrode surface like a Pt black is a well known
treatment to help reduce the electrode impedance with the aid
of enlarged electrode surface area and better electrode material,
Pt, that allows relatively high exchange current [13,22]. Higher
surface-to-volume ratio leads to lower impedance at the electrode
surface and larger contribution of the solution resistance to the total
impedance [23]. As apparent size of the electrode reduces, porosity
of the electrode surface becomes crucial to effectively diminish the
impedance [24]. For microelectrodes, only nanoporous electrode
surface can make significant contribution. Therefore, the presence
of nanopores and high roughness factor of the electrode surface
have a great deal of importance, especially for the electrodes on a
few micro or sub micro meter scale.
2.2. Electrodeposition of L2-ePt
The nanoporous Pt denoted by L2-ePt was prepared by electro-
plating of Pt in reverse micelle solution as described in our previous
report [27]. Hydrogen hexachloroplatinate hydrate (5 wt%), 0.3 M
sodium chloride (45 wt%), and Triton X-100 (50 wt%) were mixed
and heated to 60 ◦C. The mixture as made was transparent and
homogeneous. The temperature of the mixture solution was
maintained around 40 ◦C using a thermostat. L2-ePt was elec-
trochemically deposited on a Pt disk electrode (d = 1 mm, and
Ag = 0.00785 cm2) at −0.1 V vs. Ag/AgCl. The resulting L2-ePt elec-
trode was in distilled water for 1 day to extract the Triton X-100 and
this procedure was repeated 3–4 times. It follows that the electrode
was electrochemically cleaned by cycling potential between +0.68
and −0.72 V vs. Hg/Hg2SO4 in 1 M sulfuric acid until reproducibly
identical cyclic voltammograms were obtained. The surface rough-
ness of the L2-ePt was determined by measuring the area under the
hydrogen adsorption peak of the cyclic voltammogram (scan rate
of 0.2 V s−1) in 1 M H2SO4, using a conversion factor of 210 ␮C cm−2
[40].
In recent years, there has been growing interest in the
nanoporous Pt as an electrode material, for which a few novel
2.3. Electrochemical measurements
fabrication methods were developed [25–30]. Particularly,
3
All electrochemical measurements were performed in a three
electrode system, using Model CHI660 (CH Instruments) as electro-
chemical analyzer. Hg/Hg2SO4 (saturated K2SO4, RE-2C, BAS Inc.)
and Pt wire (dia. 0.5 mm, Sigma) were used as reference elec-
trode and counter electrode, respectively. The Pt disk electrode (dia.
1 mm) was used as a flat working electrode to compare with L2-ePt.
All experiments were carried out at room temperature. The solu-
tion was purged with high purity nitrogen gas for 15 min prior to
use and nitrogen environment was maintained over the solution
throughout the experiments. For electrochemical impedance spec-
troscopy (EIS), a programmed ac input with 10 mV amplitude over
a frequency range from 1 Hz to 10 kHz was superimposed on the dc
potential, −0.5 V vs. Hg/Hg2SO4 where no faradaic reaction occurs.
dimensional (3D) interconnected nanoporous Pt, which is denoted
by L2-ePt, possesses the 3D interstitial pores of 1–3 nm in width
as well as a high roughness factor [27]. Considering characteris-
tic thickness of the electrical double layer [31], L2-ePt is regarded
as the ultimate electrode with the highest surface-to-volume ratio
that can suppress the electrode impedance to the lowest limit.
Harnessing extremely high surface roughness and extraordinary
spatial environment raising collision frequency inside the pores,
L2-ePt exhibits remarkably enhanced electrocatalytic activity that
allows very sensitive detection of electroactive species such as
H2O2 [32]. Therefore, it is no wonder that much attention has been
paid to its attractive applications such as electrochemical sensors
[33–35], catalyst [36,37], and energy device materials [38,39]. Neu-
ral recording and stimulation electrodes are another class of such
electrodes with extremely low electrode impedance. Compared
with the conventional electrodes for this purpose like titanium
nitride, platinized Pt, and carbon nanotube, L2-ePt is reportedly
excellent in electrode impedance, electrode capacitance, and max-
imum charge injection limit [23].
3. Theory
In the absence of electroactive species in solution and specific
adsorption, equivalent circuit is assumed to be expressed by a serial
combination of solution resistance, Rs, and double layer capaci-
tance, Cdl. This is the case for ideal double layer on an electrode.
In real systems, however, the curve in a Nyquist plot as a function
of frequency may deviate significantly from the ideal vertical linear
plot that is simply expressed as 1/jwC. Such a non-ideal behavior,
which usually comes from time constant dispersion at solid elec-
trodes, is reportedly caused by roughened surface, non-uniform
polycrystallinity, anion adsorption, and so on [41,42]. The deriva-
tion from the linear behavior assuming a sing pure capacitance
would be empirically represented by a constant phase element
(CPE) in equivalent electrical circuit. Considering this factor, the
equivalent circuit is normally presented by a solution resistance,
Rs, and a CPE in series. The total impedance is given by
In this work, we realize conductometric detection of alkali metal
and alkaline earth metal ions at low frequency at high concentra-
tion by employing a nanoporous Pt of L2-ePt. Following theoretical
impedance modeling of the proposed system, we systematically
examine the experimental results of electrochemical impedance
spectroscopy (EIS) for conductometric ion analysis in comparison
with a flat electrode that has same apparent electrode area.
2. Experimental
2.1. Reagents
1
All chemicals including hydrogen hexachloroplatinate hydrate
(KOJIMA chemicals, JAPAN), t-octylphenoxypolyethoxyethanol
Z = Rs + Ze, Ze
=
,
w = 2ꢀf
(1)
Q(jw)˛

J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
1949
where Rs, Ze, Q, and ˛ stand for solution resistance, electrode
impedance, a constant containing the double-layer capacitance,
and a function of the phase angle ꢁ with the relation of ˛ = ꢁ/(ꢀ/2),
respectively. The exponent ˛ is mostly in the range 0.9–0.99
depending on the electrode material. Q is a constant which would
equal the capacitance at ˛ = 1. When ˛ =/ 1, the impedometric
behavior is governed by the surface heterogeneity. Ze as a function
of the CPE can be expressed as follows.
significantly different from each other, up to 100 times (rough-
ness factor, fR) while the apparent geometric areas were the same.
The enlarged surface area of L2-ePt substantially reduced the elec-
trode impedance so as to raise the relative contribution of solution
resistance to the total impedance.
In addition to the surface area effect, nanoporous electrode
provides another factor that should be concerned. Micro- or meso-
porous materials like L2-ePt have numerous pores with nanometer
scale in diameter. The pore diameter is comparable to the char-
acteristic thickness of the electrical double layer so called Debye
length (ꢃ−1), so that the electrochemically effective area of the
electrode surface is not necessarily identical to the real surface
area at a low ionic strength [31]. Gouy-Chapman theory states
ꢃ = (3.29 × 107)zC*1/2 where C* is the bulk z:z electrolyte con-
centration in mol L−1 and ꢃ is given in cm−1. Theoretically, the
Debye length is about 1.5 nm at the electrolyte concentration of
4.1 × 10−2 M. Since L2-ePt has narrow interstitial pores of 1–3 nm
in diameter [27], the Debye length is similar or longer than the
pore radius. This means that the electrochemically effective inter-
face, which corresponds to the equi-potential surface in the electric
double layer, does not exactly follow the porous geometry of L2-ePt
electrode. In other words, L2-ePt may fail to reduce the electrode
impedance as much as its roughness factor, that is the surface
enlargement, at an ionic strength lower than 0.04 M. Based on this
consideration, we can learn that L2-ePt will be much more effective
at a high ion concentration through its low electrode impedance.
The sensitive admittance results from L2-ePt shown in Fig. 1 were
ascribed to the low electrode impedance, which leads to corre-
spondingly low total impedance. And the selective responses to
various aqueous ions came from the large contribution of solu-
tion resistance to the total impedance, as a result of the electrode
impedance reduced by not only the enlarged surface area but also
high ion concentration ensuring the sufficiently thin electric double
layer compared with the pore radius of L2-ePt. For conductome-
try, the ion concentrations higher than 0.1 M are often encountered
everywhere, as confirmed by noting that sea water and physiologi-
cal media belong to the samples with this condition. However, such
range of ion concentration has been a tough condition for conven-
tional conductometry because higher ionic strength means lower
ꢀ
ꢁ
ꢂ
ꢁ
ꢂꢃ
1
˛ꢀ
˛ꢀ
Ze = Zre,e + Zim,e
=
cos
− j sin
(2)
Qw˛
2
2
where Zre,e and Zim,e are the real and imaginary parts of the elec-
trode impedance, respectively. The real part of Ze is attributed to
non-ideality of the capacitance in the electrochemical system. The
magnitude of Z, that is, |Z| is given by
ꢅ
ꢄ
ꢁ
ꢂ
2Rs
Qw˛
˛ꢀ
1
|Z| =
Zr2e + Z2
=
Rs2
+
cos
+
(3)
im
Q2w2˛
2
The relationship between CPE parameters and the interfacial
capacitance is given by [43]
1/˛
C = [QRs(1−˛)
]
(4)
Assuming that current density across the surface of a planar
electrode is uniform, the solution resistance is given by [17]
L
Rs =
(5)
ꢂAg
where L is the distance between the electrodes. Ag and ꢂ are the
geometric area of the electrode and the conductivity of solution,
respectively. Capacitance is expressed by
εε0Ar
C =
(6)
d
where εε0 and d are the electric permittivity of the medium and
the interpolate spacing, respectively. Ar denotes the real area of the
electrode assuming that any pore on the surface is larger than the
characteristic thickness of the electric double layer [31]. Typical
ranges of capacitance values lie between 1 and 50 ␮F cm−2 [42].
By substituting Eqs. (4)–(6) into Eq. (3), we obtain the equation as
follows.
ꢆ
ꢇ
ꢇ
ꢇ
2
2−˛
2−2˛
ꢁ
ꢂ
ꢁ
ꢂ
ꢁ
ꢂ
˛
2˛
L
L
d
1
w˛
˛ꢀ
L
d
1
w2˛
|Z| =
+ 2
cos
+
(7)
ꢂAg
ꢂAg
εε0Ar
2
ꢂAg
εε0Ar
The experimental results were analyzed and interpreted based
on Eq. (7).
contribution of solution resistance to the total impedance. That is
why higher frequency is required to obtain reasonable ion sensi-
tivity and selectivity for conductometry at high ionic strength. In
these respects, the results in Fig. 1 suggest nanoporous electrode
like L2-ePt as a promising way to enable both sensitive and selec-
tive conductometry in high ion concentration without increasing
frequency. The dc offset in Fig. 1 was −0.5 V vs. Hg/Hg2SO4.
4. Results and discussion
4.1. Impedance of aqueous alkali and alkaline earth metal ions
Fig. 1 shows the impedometric results from 0.01 to 0.5 M
alkali and alkaline earth metal ions. We monitored the admit-
tance that was straightforwardly converted from the measured
impedance and proportional to concentration of ions. For this
experiment, 1 kHz was selected as the frequency, which is the typ-
ically employed for conductometry. As clearly and quickly noted
from Fig. 1, the nanoporous Pt (L2-ePt) was superior to flat Pt in
sensitivity as well as selectivity in terms of conductometric recog-
nition of ions. This result is well consistent with what was expected.
In conventional conductometry, electro-inactive ions such as alkali
and alkaline earth metal ions should be discerned via the differ-
ences among their own ion mobilities. Therefore, it is obvious that
larger contribution of solution resistance, which is a function of
ion mobilities, results in better selectivity. In this experiment, the
real surface areas of the nanoporous and flat Pt electrodes were
4.2. ac frequency and roughness factor
Suppose that there are two different solutions of alkali or alka-
line earth metal ions and we apply ac inputs with certain frequency
to measure the total impedance of each sample. The ratio of the dif-
ference between the two absolute total impedances to the average,
ı|Z|/[|Z|] ≡ ꢄ, is a good index of how discriminative the ion ac con-
ductometry is. At a given frequency, higher ꢄ value indicates better
resolution in distinguishing one ion to the other. ꢄ values for two
different solutions, for example aqueous NaClO4 and KClO4, can
be calculated from Eq. (7) and plotted as a function of the input
ac frequency as shown in Fig. 2a. As the frequency increases, the
respective curve in Fig. 2a undergoes a transition to the upper

1950
J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
plateau at its own characteristic frequency regime. The plateau in
the high frequency regime can be quantitatively estimated from
Eq. (7), which is reduced to |Z| = L/ꢂAg = Rs. As a consequence, ꢄ is
expressed by
ıRs
ꢂ2 − ꢂ1
ꢂ1 + ꢂ2
ꢄ =
= 2
(8)
[Rs]
In this ultimate condition, the total impedance is completely
determined by the solution resistance so that the resolution, ion-
discriminating power, reaches a maximum. However, exceedingly
high frequency is not favorable for ion conductometry. Negligible
electrode impedance due to high frequency significantly reduces
the total impedance, which may become too low to be reliably
measured. In particular, the total impedance is seriously lowered
in high ion concentration because the solution resistance substan-
tially drops as well. Moreover, high frequency condition imposes
another practical restriction that electronic cross-talk should be
concerned during the design and fabrication of the conductometric
devices. This may be more important concern when such a conduc-
tometer should be integrated with other electroanalytical cells for
advanced systems, e.g. multiplex detection or sequential processes
on a chip-based analyzer.
On the other hand, the total impedance at sufficiently low fre-
quency is overwhelmingly regulated by the electrode impedance
rather than the solution resistance. Eq. (7) reduces to
ꢇ
1−˛
ꢁ
ꢂ
˛
L
d
1
w˛
1
Qw˛
|Z| =
=
= |Ze|
(9)
ꢂAg
εε0Ar
ꢈ ꢈ
ꢈ ꢈ
where Ze is the magnitude of electrode impedance. In Eq. (9),
there is no parameter dependent on ion concentration and compo-
sition but the solution conductivity, ꢂ. Actually, ion concentration
and composition may modify the capacitance, in which dielectric
constant is involved. However, dielectric constant is known to be
almost independent of ion concentration and composition as long
as concentration is lower than 1 M [17,44]. Therefore, ꢄ is expressed
by
Fig. 1. Admittance, Y, as a function of concentration for a comparison between the
nanoporous and flat electrode. Impedometric results of (a) alkali metal and (b) alka-
line earth metal ions. The admittances for K+ ion were measured up to 0.1 M due to
the limited solubility of KClO4. The frequency was 1 kHz which is a typical frequency
for conductometry. The dc offset potential and the amplitude of ac input signals were
−0.5 V (vs. Hg/Hg2SO4) and 10 mV, respectively. All measurements were repeated 5
times under identical condition and average values were plotted with error bars of
corresponding standard deviations.
ꢂ1˛−1 − ꢂ2˛−1
ꢂ1˛−1 + ꢂ2˛−1
ı|Ze|
ꢄ =
= 2
(10)
[|Ze|]
In ideal electrode system, ˛ equal to one so that Eq. (10) should
be zero. A value of Eq. (8) is always larger than that of Eq. (10)
because ˛ is usually in range 0.9–0.99. The geometric area (Ag) and
real area (Ar) of a flat electrode should be almost same. On the other
hand, porous electrodes in this study have fR values higher than
30. fR can be easily controlled by experimental parameters such
as electroplating time. Fig. 2 shows the theoretical (Eq. (7)) and
Fig. 2. Relationship between ı|Z|/[|Z|] and frequency for a variety of roughness factors. Theoretical (a) and experimental (b) results in 0.1 M NaClO4 and KClO4, respectively.
At lower frequency, larger fR provides better selectivity for recognizing metal ions. The dc offset potential and the amplitude of ac input signals were −0.5 V (vs. Hg/Hg2SO4)
and 10 mV, respectively.

J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
1951
Fig. 3. Bode plots from a L2-ePt in 0.1 M various alkali metal ions without correction (a) and with correction by the solution resistances (b). The data in (b) were fitted based
on Eq. (12) (solid line). Bode plots from a flat Pt in 0.1 M various alkali metal ions without correction (c) and with correction by the solution resistances (d). The dc offset
potential and the amplitude of ac input signals were −0.5 V (vs. Hg/Hg2SO4) and 10 mV, respectively.
experimental influences of fR in 0.1 M NaClO4 and KClO4 solutions.
ences observed in Fig. 2a and b. Nonetheless, the overall trend can
be compared and discussed between the theoretical and experi-
mental impedance spectra in Fig. 2, which is enough to probe the
effect of nanoporous electrode structure. At nanoporous Pt, the neg-
ative values of ꢄ appeared in low frequency region, indicating that
the electrode impedance for Na+ ion was lower than that for K+ ion.
This is interesting behavior in that the relative electrode impedance
for the two ions is opposite to that in solution resistance. Such an
impedance reversal contrary to ion mobility order is unusual phe-
nomenon that is observed only in extremely narrow nanopores. The
origin of the negative values of ꢄ in porous Pt has not been clearly
understood yet and the detailed study is in progress.
ꢉ
Solution conductivity, ꢂ, is expressed by ꢂ = F/1000
|zi|uiCi
i
where F is the Faraday constant (96,485 C mol−1), |zi| is a charge
of species i (1), ui is mobility of species i (Na+: 5.193 × 10−4, K+:
7.619 × 10−4, ClO4−: 7.05 × 10−4 (cm2 s−1 V−1)) and Ci is concen-
tration of species i (0.1 M). We set other parameters for theoretical
estimation as follows; L (1 cm), ˛ (0.95), εε0/d (10 ␮F cm−2), Ag
(0.00785 cm2) and Ar (fR × Ag). The experimental data of ꢄ were
converted from the impedance data that were obtained in respec-
tive NaClO4 and KClO4 solutions. The calculated results in Fig. 2a
show that the frequency where ꢄ undergoes transition from the
lower limit to upper plateau keeps shifting to lower region as fR
rises. This is consistent with what is expected. Larger fR brings about
more contribution of the solution resistance to the total impedance
through enlarged Ar. In this regard, the experimental results in
Fig. 2b are largely in accordance with theoretical prediction.
However, the ꢄ values at the low frequency region significantly
deviate from the calculated. And the transition frequencies of the
experimental curves were found in notably higher frequency region
than theoretical prediction. This behavior is not surprising but what
was expected. First of all, the parameters employed for calculation
were not exactly relevant to the experimental system. For example,
the ui value is the information assuming infinitely diluted aque-
ous solution at 25 ◦C. More significantly, the electrochemical cell
employed in this study is a conventional three electrode system
that has a working electrode with the small area and a counter
electrode with the excessively wide area. This is appropriate for
examination of what is happening at the nanoporous electrode, but
provides ill-defined cross sectional area of the solution that should
be substituted for the area in the term for solution resistance. The
experimental cross sectional area of the solution is predicted to
be much larger than the working electrode, resulting in the differ-
4.3. Geometric effect of porous electrodes
The nanopore effect on selective ion detection was investigated
by electrochemical impedance spectroscopy (EIS). Transmission
line model for the porous electrode was previously applied to
nanoporous Pt electrode [45,46]. According to this work, the elec-
trode impedance of the porous electrode is expressed by
ꢅ
ꢊ
r
Ze
=
coth(l rQ(jw)˛)
(11)
Q(jw)˛
where r is electrolyte resistance per unit length in the pores, l is
the film thickness, Q and ˛ are the same as the notations in the
present report. In high frequency region, real and imaginary parts
are merged into a line with a slope of −˛. Approximate expression
of Eq. (11) in the low frequency region is as follows:
ꢁ
ꢂ
ꢁ
ꢂ
lr
1
˛ꢀ
j
˛ꢀ
Ze
=
+
cos
−
sin
(12)
3
Qw˛
2
Qw˛
2
Although this equation results from approximation in low fre-
quency limit, a short plateau due to pore resistance as the constant

1952
J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
Fig. 4. Relationship between ı|Z|/[|Z|] and frequency as a function of concentration for Na+ and K+ ions with ClO4−. Theoretical (a) and experimental (b) results were obtained
from a porous Pt (squares) and a flat Pt (triangle). Arrows indicate the parallel shifts as the concentration augments ten times (from 0.1 M to 1 M for theoretical analysis and
from 0.01 M to 0.1 M for experimental data). The dc offset potential and the amplitude of ac input signals were −0.5 V (vs. Hg/Hg2SO4) and 10 mV, respectively.
term, lr/3 appears in the intermediate frequency region. In the low
frequency range, the real and imaginary curves are in parallel with
a slope of −˛ and separated by log(tan(˛ꢀ/2)). In Eq. (12), solution
resistance is omitted so that measured impedance including the
solution resistance can be written as
employing nanoporous electrode. This is interesting in that con-
ductometric ion detection in high ionic strength at low frequency
suggests the way to monitor instantaneous change in ion con-
centration and composition in non-destructive manner in natural
environments such as physiological fluids and cell media. For extra-
cellular monitoringpropagation ofaxon potential, forinstance, very
small electrode is required to be placed as closely the ion channels
as possible and to quickly detect composition reversal of Na+ and
K+ ions. Smaller geometric area of the electrode makes larger con-
tribution of the electrode impedance to the total impedance, which
becomes less sensitive to the local change in ion composition near
the electrode surface. Nanoporous electrode provides huge sur-
face area that remarkably reduces the total impedance. The pore
resistance helps further us to discriminate the ions. As a result, it
is expected that even very small nanoporous electrode would be
available for conductometric ion detection at a sufficiently low fre-
quency that corresponds to typical range of frequency adopted in
conventional measurements. Importantly, patterned and miniatur-
ized electrode array on a chip must be thin and relatively wide area
of insulating cover layer that may give rise to serious problems such
as imperfect insulation of passivated electrode [21] and cross-talk
in a cellular medium when a high frequency is applied. Considering
the recent trend that electrodes are ceaselessly miniaturized and
integrated on a chip for biological process and analysis, this issue is
increasingly crucial. Therefore, nanoporous electrode, which allows
conductometry at substantially lower frequency, proposes new
exciting applications based on conventional conductometry by just
switching the electrode material.
ꢁ
ꢂ
ꢁ
ꢂ
lr
1
Qw˛
˛ꢀ
j
˛ꢀ
Z = Rs +
+
cos
−
sin
(13)
3
2
Qw˛
2
Fig. 3a and b shows the Bode plots obtained from L2-ePt for a
series of alkali metal cations. Regardless of the sort of metal ions,
the curves in the Bode plots exhibit similar behavior, which are
a plateau in intermediate frequency region and two parallel lines
between log Zre and log Zim with −˛ slope in the low frequency
regime. The short plateau in Fig. 3b is characteristic aspect that
is observed at nanoporous electrodes [45,46]. The corrected Zre
by subtracting Rs, that is Zre,e, corresponds to the component of
constant phase element (CPE) and resistance independent of fre-
quency in the Zre, real part of the electrode impedance. Unlike the
nanoporous electrode, the plateau of log Zre is even shorter at the
flat electrode due to large electrode impedance as shown in Fig. 3c.
Subtracting Rs yields the curves in Fig. 3d, in which the plateau
completely disappears. This critical difference comes from the pore
resistance in the nanoporous electrode.
The pore resistance and ˛ were determined by fitting the exper-
imental data on the basis of the transmission line model. The
solution resistance was obtained from the extrapolation in the high
frequency data of flat Pt. Table 1 presents that pore resistance of
nanoporous electrode is another factor for ion discrimination, in
addition to solution resistance. Li+, Na+, and K+ ions exhibit char-
acteristic pore resistances in decreasing order. This tendency is
consistent with the ion mobilities in the bulk solution, and thus in
good accordance with the solution resistance. Alkaline earth metal
ions exhibit the same trend.
Fig. 4 shows theoretical and experimental data of the difference
in total impedance, ı|Z|/[|Z|], as the concentrations of Na+ and K+
−
ions with ClO4 were increased to ten times (from 0.1 M to 1 M
for theoretical analysis and from 0.01 M to 0.1 M for experimental
data). As expected from the general behavior in conventional con-
ductometry, the transition to saturated maximum plateau shifted
to higher frequency range when the concentrations of Na+ and K+
ions were augmented. This means that higher frequency is needed
to detect any change in fractional ratio of Na+ and K+ ions at higher
concentrations.
As we have seen through ı|Z|/[|Z|], the difference in the total
impedance successfully allows us to discriminate Na+ and K+ ions
of the same concentration. This result indicates that the total
impedance would be sensitive to the fractional ratio of Na+ and
K+ ions under the condition of a constant total concentration of the
two ions (the sum of the ions is maintained to be constant). We
checked if changes in the ratio of Na+ to K+ ions in a mixed solu-
tion at the same ionic strength can be detected. The results in Fig. 5
were obtained from mixed solutions of 0.1 M NaClO4 and 0.01 M
4.4. Effect of ion concentration and mixed solutions
From the hitherto study, we got the lesson that alkali and
alkaline earth metal ions at high concentration (>0.1 M) can
be selectively detected by conductometry at low frequency by
Table 1
Impedometric parameters measured from L2-ePt.
Li+
Na+
K+
Mg2+
Ca2+
Solution resistance, Rs (ꢅ cm2)
Pore resistance (ꢅ cm2)
CPE exponent (˛)
4.22
0.21
0.94
3.99
0.19
0.94
3.16
0.11
0.95
2.38
0.12
0.91
1.99
0.09
0.94

J.H. Bae, T.D. Chung / Electrochimica Acta 56 (2011) 1947–1954
1953
iting electrode impedance imposed by nanoporous Pt suggests an
opportunity to miniaturize electrode array sufficiently, even down
to the nano scale, for non-destructive real time monitoring of extra-
cellular neuronal signals. Fabrication and biological applications of
nanoporous Pt nano array for in situ extracellular monitoring of
action potential in a living neuronal system are in due course.
Acknowledgements
This work was supported by the Converging Research Center
Program through the Ministry of Education, Science and Tech-
nology (2010K001297), by the grant from the Industrial Source
Technology Development Program (10033657) of the Ministry of
Knowledge Economy (MKE) of Korea, and by the Nano/Bio Science
& Technology Program (M10536090001-05N3609-00110) of the
Ministry of Education, Science and Technology (MEST). J.H. Bae was
supported by the Brain Korea 21 fellowship. Dr. Sejin Park (Noma-
dien Corporation, Seoul, Korea) is gratefully acknowledged for the
suggestion of transmission line model. Ms. Youn Joo Song (Noma-
dien Corporation, Seoul, Korea) and Ji-Hyung Han (Department of
Chemistry, Seoul National University, Seoul, Korea) are gratefully
acknowledged for the support in the fabrication of L2-ePt.
Fig. 5. Admittance, Y, that detected the changes in the ratio of Na+ to K+ ions in the
mixed solution at the same ionic strength. The dc offset potential, the frequency, and
the amplitude of ac input signals were −0.5 V (vs. Hg/Hg2SO4), 1 kHz, and 10 mV,
respectively. K+:Na+ = 1:10 means the mixed solution composed of KClO4 0.01 M and
NaClO4 0.1 M. Unlike bare electrode, L2-ePt sensitively detected a change in the ion
composition. All measurements were repeated 5 times under identical condition and
average values were plotted with error bars of corresponding standard deviations.
KClO4 or 0.01 M NaClO4 and 0.1 M KClO4. At a typical frequency
for conductometry (1 kHz), L2-ePt sensitively detects change of
the ion composition while flat Pt cannot does. This sensitivity of
nanoporous Pt to fractional ratio of ions benefits from enlarged
surface area and pore resistance as discussed above.
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