Determination of the capacitance of solid-state potentiometric sensors: An electrochemical time-of-flight method.

Abstract

A dual microelectrode electrochemical time-of-flight technique in which diffusion flux of Ag+, Cl-, or H+ ions electrochemically produced at a generator electrode is measured by recording potential-time transients with Ag, Ag/AgCl, or iridium oxide potentiometric microsensors, respectively, is developed. The generator and microsensor electrodes are typically spaced by 50-100 microm and are incorporated in the lithographically fabricated thin-layer-type devices. Under conditions of moderate rates of the ion electrogeneration, the potential-time (E-t) transients recorded with the three microsensors show excellent agreement with theory involving linear diffusion equations and the experimentally determined Nernstian slopes of the microsensors. However, when the generator current, or the initial concentration of the primary ion of interest is low, appreciable delays in the recorded E-t transients are observed due to the finite capacitance of the micropotentiometric sensors. The recorded delay in the E-t transients can be quantitatively accounted for by including the sensor capacitance (C) in the theoretical description of the transients. Direct comparison between the theoretical and the experimental E-t transients yields the sensor's capacitance. This capability of our new technique is unique in that it allows determination of the capacitance of a potentiometric sensor at open circuit. In the cases of silver electrodes, this method results in C = 31 +/- 2 microF/cm2, a value that is in agreement with those obtained by other methods. The results for silver chloride sensors yield a C in the range of 100-140 +/- 10 microF/cm2. The specific values depend on sensor preparation and the resulting roughness of the Ag/AgCl interface. Iridium oxide sensors show a capacitance that linearly depends on the thickness of the film. Specific capacitance of these microporous films was determined to be 59 +/- 6 F/cm3.

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Determination of the Capacitance of Solid-State
Potentiometric Sensors: An Electrochemical
Time-of-Flight Method
Heather A. Elsen, Katarzyna Slowinska,†Ewa Hull,‡and Marcin Majda*
Department of Chemistry, University of California, Berkeley, Berkeley, California 94720-1460
A dual microelectrode electrochemical time-of-flight tech-
nique in which diffusion flux of Ag+, Cl-, or H+ions
electrochemically produced at a generator electrode is
measured by recording potential-time transients with Ag,
Ag/AgCl, or iridium oxide potentiometric microsensors,
respectively, is developed. The generator and microsensor
electrodes are typically spaced by 50-100 µm and are
incorporated in the lithographically fabricated thin-layer-
type devices. Under conditions of moderate rates of the
ion electrogeneration, the potential-time (E-t) transients
recorded with the three microsensors show excellent
agreement with theory involving linear diffusion equations
and the experimentally determined Nernstian slopes of
the microsensors. However, when the generator current,
or the initial concentration of the primary ion of interest
is low, appreciable delays in the recorded E-t transients
are observed due to the finite capacitance of the micro-
potentiometric sensors. The recorded delay in the E-t
transients can be quantitatively accounted for by including
the sensor capacitance (C) in the theoretical description
of the transients. Direct comparison between the theoreti-
cal and the experimental E-t transients yields the sen-
sor’s capacitance. This capability of our new technique is
unique in that it allows determination of the capacitance
of a potentiometric sensor at open circuit. In the cases of
silver electrodes, this method results in C ) 31 ( 2 µF/
cm2, a value that is in agreement with those obtained by
other methods. The results for silver chloride sensors
yield a C in the range of 100-140 ( 10 µF/cm2. The
specific values depend on sensor preparation and the
resulting roughness of the Ag/AgCl interface. Iridium
oxide sensors show a capacitance that linearly depends
on the thickness of the film. Specific capacitance of these
microporous films was determined to be 59 ( 6 F/cm3.
As micropotentiometric sensors find an increasing range of
applications in biological sciences and medicine and as compo-
nents of modern analytical measurement techniques,1-7it is
necessary to fully characterize all their operating parameters. Most
studies explore the sensitivity and selectivity. Some, in addition,
determine sensor response time.8-15However, it becomes increas-
ingly important to also characterize capacitance in order to
optimize the microsensor’s performance. In applications involving
very small sample volumes, such as those relying on microfluidic
devices, or involving low analyte concentrations, sensor capaci-
tance can be performance-limiting.16-18
When dealing with characterization of potentiometric sensors,
the effect of capacitance is not one commonly considered.
Although the importance of both ion selectivity and sensitivity
are widely understood, the effect of sensor capacitance is not. In
the process of sensor equilibration in an analyte solution involving
a change of sensor’s potential, some of the ions generating a
sensor’s selective response are consumed (or generated). De-
pending on the type of potentiometric sensor, this may involve
either an electron transfer or an ion-exchange reaction at the
sensor surface. For example, an increase in silver ion activity near
a silver potentiometric sensor results, at open circuit, in a net
reduction of silver ions at the sensor surface, thus leading to an
increase in the sensor potential. Likewise, an increase in a
solution’s proton activity, provoking an increase in the potential
of a pH sensor immersed in that solution is a direct result of a
shift of the proton exchange equilibrium at the sensor surface
that reduces proton activity on the solution side of the interface.
Regardless of the nature of the equilibration reaction, the relation-
ship between the sensor potential and activity of the primary ion
* Corresponding author. Fax: (510) 642-0269. E-mail: majda@berkeley.edu.
†Permanent address: Department of Chemistry and Biochemistry, California
State University, Long Beach, CA 90840.
‡Permanent address:Department of Materials Science and Ceramics,
University of Science and Technology, 30-059 Krakow, Poland.
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Published on Web 08/12/2006
© xxxx American Chemical Society
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is governed by the Nernst equation. In turn, the differential
quantity of ions involved in such equilibria is proportional to the
sensor capacitance. Therefore, as we document below, the very
equilibrium leading to the establishment of the sensor potential
may alter the concentration of the analyte one intends to measure.
In cases in which potentiometric sensors are used to monitor
changes in the activity of a particular ion, the phenomena outlined
above may also lead to an apparent delay in the sensor’s response
even if the sensor intrinsic response kinetics are very fast.15,19We
discuss this at a greater length below.
We take advantage of these phenomena to develop a new
technique capable, for the first time, of determining the capaci-
tance of a potentiometric sensor at open circuit. The method relies
on a controlled perturbation of the activity of the primary ion in
a small volume adjacent to the sensor surface. The observed delay
in a sensor response relative to the predictions based on an
assumption of negligible surface capacitance is then interpreted
to yield the sensor’s capacitance. It is important to stress that
unlike classical methods of measuring interfacial capacitance that
rely on the application of a potential or current perturbation to an
electrode of interest, our method is unique in that it involves,
instead, open circuit potential measurements of an electrode of
interest in response to a controlled perturbation of the activity of
its primary ion.
P-ETOF, potentiometric electrochemical time-of-flight is a new
method in which potential-time (E-t) transients of a solid-state
microsensor are recorded in response to an increasing concentra-
tion of the primary ions using a lithographically fabricated dual-
microelectrode device shown schematically in Figure 1. The two
microband electrodes are situated in close proximity (50-100 µm).
One electrode is used to electrochemically generate species of
interest, such as Ag+, Cl-, or H+. The generator electrode operates
under galvanostatic or constant rate conditions. The other mi-
croband electrode is the potentiometric microsensor exhibiting a
Nernstian response with respect to the generated ions. We used
Ag, Ag/AgCl, and IrO2as the microsensors. The method outlined
here is analogous to the original amperometric time-of-flight
technique introduced by Feldman et al.23and used by others to
measure diffusion constants of redox species.21-25However, unlike
the amperometric time-of-flight technique, P-ETOF uses the
constant current generation and potentiometric sensing first
described in our previous reports.15,19
As shown in Figure 1, the two microband electrodes are
confined to a narrow channel of ∼3 µm between the device surface
and a second glass cover slip. Au counter and Ag reference
electrodes are also confined to the narrow channel but not shown
in this schematic. Since the thickness of the narrow channel in
this sandwich device is far smaller than the interelectrode gap
(g), the diffusion of the electrogenerated ions in the channel
between the generator and sensor microelectrodes obeys linear
diffusion equations. Specifically, we can solve Fick’s diffusion
equations to obtain the following expression for the time-
dependent concentration of the diffusing ions at the sensor
microelectrode, C(g,t),26
nFAD{2(
where Cinand D are the initial, background concentration of the
ions in the channel and their diffusion constant, F is Faraday’s
constant, and i is the value of the constant current applied to
generate the ions (50% value of the applied current is used, since
the symmetric design of the device results in just 50% of the
generated ions diffusing toward one of the microsensors elec-
trodes). A, the effective surface area of the generator microelec-
trode is taken as the cross-sectional area of the narrow channel
equal to the product of the length (l) of the microband electrodes
and the height (h) of the channel. The linear diffusion approxima-
tion mentioned above allows us to treat the generator electrode
as if it were occupying the entire cross-sectional area of the narrow
channel, as shown in Figure 1. The height of the narrow channel
is established by the polymeric spacers (see the Experimental
Section). Equation 1, combined with the Nernst equation and the
value of the experimentally determined Nernstian slope, is used
to predict the shapes of the E-t transients recorded in the P-ETOF
experiments. We show that the comparison of the predicted and
recorded E-t transients can be used to obtain the capacitance of
the microsensors.
In this report, we first describe the functioning of our P-ETOF
method using silver and Ag/AgCl microband electrodes both to
generate and potentiometrically to sense silver and chloride ions,
respectively. Next, we outline conditions under which a delay in
the rise of the sensor’s potential can be observed relative to the
theoretical expectations. The delay in the E-t transients is used
(19) Slowinska, K.; Feldberg, S. W.; Majda, M. J. Electroanal. Chem. 2003, 554-
555, 61.
(20) Feldman, B. J.; Feldberg, S. W.; Murray, R. W. J. Phys. Chem. 1987, 91,
6558.
(21) Licht, S.; Cammarata, V.; Wrighton, M. S. Science 1989, 243, 1176.
(22) Cammarata, V.; Talham, D. R.; Crooks, R. M.; Wrighton, M. S. J. Phys. Chem.
1996, 94, 2680.
(23) Licht, S.; Cammarata, V.; Wrighton, M. S. J. Phys. Chem. 1990, 94, 6133.
(24) Tatistcheff, H. B.; Fritsch-Faules, I.; Wrighton, M. S. J. Phys. Chem. 1993,
97, 2732.
(25) Wittek, M.; Mo ¨ller, G.; Johnson, M. J.; Majda, M. Anal. Chem. 2001, 73,
870.
(26) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and
Applications, 2nd ed.; J. Wiley & Sons: New York, 2001; Chapter 8, pp 305-
310.
Figure 1. A schematic drawing of the main components of a narrow-
channel, electrochemical time-of-flight device. The generator electrode
(G) and the two symmetrically positioned sensor electrodes (S) are
lithographically fabricated on a glass slide. A second, parallel glass
slide is located at a distance, h, of ∼2-4 µm from the electrode
assembly. Typical spacing between the generator and the sensor is
g of 50-100 µm.
C(g,t) ) Cin+
i
Dt
π)
1/2exp(-g2
4Dt)-
g × erfc[
g
2(Dt)1/2]}(1)
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to determine the sensor’s capacitance. Using this approach, we
then measure the capacitance of the Ag, Ag/AgCl, and IrO2
microsensors. Whereas in the case of the silver sensor, the
capacitance can be measured using standard electrochemical
methods, in the other two cases, this is far less straightforward.
In fact, data presented below offer new insight into the properties
of these microsensors. Specifically, in the case of the IrO2sensors,
we show that the capacitance is proportional to their volume,
confirming the existence of appreciable porosity and internal
structure of the oxide film. We also demonstrate that proton
transport within the oxide film is slow and leads to a further delay
in the microsensor response to pH changes.
EXPERIMENTAL SECTION
Reagents. Nanopure water was obtained using a three-
cartridge Millipore purification system. Silver electrodeposition
was carried out using a silver plating solution from Transene Co..
Potassium chloride, sulfuric acid (reagent grade), hydrogen
peroxide (30%), perchloric acid (70%), acetone (reagent grade),
and potassium carbonate were supplied by EM Science. Lithium
perchlorate (99.99%), oxalic acid (99%), and silver nitrate were
supplied by Aldrich. Iridium (IV) chloride (99.95%) was supplied
by Alfa Aesar. Negative photoresist, SU-8 2 was supplied by
MicroChem. All chemicals were used as received.
Device Design, Fabrication and Assembly. Figure 2 shows
a schematic of the device design. There are six electrodes on a
typical device. The far left contact pad, labeled R, leads to a large
silver-plated reference electrode. The two counter electrodes (C)
are externally shorted to ensure a symmetric current distribution
and, thus, ion flux on both sides of the generator electrode (G).
There are two identical sensor electrodes (S) flanking the
generator electrode. In each experiment, the potential of only one
of these electrodes is monitored. The P-ETOF devices were
fabricated utilizing photolithographic patterning and physical vapor
deposition techniques (lift-off technology). Lithographic micro-
fabrication involves standard, chromic acid-cleaned, 1-in. × 3-in.
× 1-mm glass microscope slides. These are spin-coated with
Shipley 1818 photoresist and then exposed to pattern the elec-
trodes. After developing and drying, 8-10 nm of chromium and
then ∼100 nm of gold are deposited via resistive heating evapora-
tion in a vacuum. The slides are then placed in an acetone bath
that removes the remaining photoresist and gold, leaving only
the electrode assembly behind. A layer of epoxy-based photoresist
polymer (SU-8 2) is spun, baked, and exposed to create an
insulating layer that separates the working electrode area from
the contacts, as shown in Figure 2 by the shaded rectangle over
the electrodes. This defines the length of microband electrodes
and protects the contact area from further chemical modification.
The active electrode length (l) was 2.0 mm. It was selected to be
large relative to the width of the interelectrode gap in order to
render radial diffusion contribution to the total ion flux at the tip
of the generator microelectrode negligible. The area outlined by
the dotted line indicates the approximate area confined by the
cover slip used as the upper barrier of the thin layer cell shown
in Figure 1. The cell height is controlled with the polymeric
spacers deposited in the corners of the cover slip.
After device fabrication, the electrodes were chemically modi-
fied for use as specific ion generator and sensor pairs. For the
Ag+/Ag system, silver is electroplated from a commercial silver-
plating solution on both the G and S microelectrodes. A typical
thickness of the silver layer, measured with a stylus profilometer,
is ∼0.7 µm on the generator and tens of nanometers on the sensor.
Chloride P-ETOF experiments required Ag/AgCl electrodes.
These were made by oxidizing silver in 0.1 M KCl solutions. The
generator electrode is formed by applying a constant anodic
current of 1 µA for a period of time sufficient to oxidize
approximately three-quarters of the 1.5-2.5 µm thick silver film
to AgCl. The preparation of the Ag/AgCl sensors is discussed in
the Results and Discussion Section. In the case of proton P-ETOF,
the Au generator electrode is left unmodified, and an iridium (IV)
oxide layer of 40-250 nm is formed by electrochemically induced
precipitation from an alkaline solution containing an iridium
oxalate complex following the procedures of Yamanaka.27The
latter solution was 4 mM IrCl4with a 10-fold excess of oxalic acid.
The pH of the solution was adjusted to 10.5 with K2CO3. The
resulting solution was allowed to stabilize over 2 days at room
temperature. The electrochemically induced deposition was car-
ried out galvanostatically with i ) 35 mA/cm2. In all cases, the
values of the Nernstian slopes of the microsensors were deter-
mined experimentally. All experiments were carried out in 1 M
lithium perchlorate electrolyte. This high concentration of the
supporting electrolyte is used to eliminate ohmic potential drop
within the narrow channel. The effects of a potential field gradient
and migration on the E-t transients were discussed in an earlier
report.19Initial concentration of the primary ion of interest was
set with standard solutions of silver nitrate, potassium chloride,
and perchloric or sulfuric acid. A typical P-ETOF experiment
involves rinsing and air-drying the electrode assembly, then
dropping a few hundred microliters of a desired electrolyte
(27) Yamanaka, K. Jpn. J. Appl. Phys. 1989, 28, 632.
Figure 2. A schematic drawing of the entire narrow-channel time-
of-flight device electrode assembly (left) and a cross section of the
generator and sensor pair (right). The reference electrode (R) is silver-
plated in all experiments. The two counter electrodes (C) are
externally shorted. Alhough the generator electrode (G) is flanked
by two sensor electrodes (S), only one of those is used in each
experiment. An ∼1-µm-thick layer of an inert polymer, shown as the
shaded area, is used to isolate the working section of the electrodes
from their contact area. The polymer film also defines the length (l )
2.0 mm) of the generator and sensor electrodes. The dotted line
outlines the size and the position of the top glass slide used to form
the narrow channel filled with electrolyte solution above the electrode
assembly plate. Four small polymeric spacers (not shown in the figure)
are deposited in each corner of the top glass slide to define the
thickness of the narrow channel.
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solution and closing the cell with the upper cover slip. A small
mechanical brace is then used to squeeze the device, immobilize
the cover slip, and adjust the thickness of the thin-layer channel.
Reproducibility of this step is discussed in the Results and
Discussion Section.
Instrumentation. Electrochemical experiments were carried
out using a CH Instruments model 660B electrochemical analyzer.
Recording of P-ETOF transients is made possible through dual-
channel recording during chronopotentiometric experiments. The
generator is directly controlled and the open circuit potential is
monitored at the sensor electrode. This instrument has a 1-kHz
sampling rate and better than 0.5 mV resolution.
Computations. The theoretical E-t transients corresponding
to those obtained in the P-ETOF experiments were computed (eq
1) using a Matlab software package (version 6.1.0.450 by The
MathWorks Inc.).
RESULTS AND DISCUSSION
P-ETOF Device Performance. The shape of the potential-
vs-time transients can be computed using eq 1 together with the
Nernst equation. The knowledge of the experimentally determined
value of the Nernstian slope of the microsensors and the critical
dimensions of the P-ETOF devices are also required. The
subsequent comparison between the computed and experimental
transients was used to assess the performance of the P-ETOF
devices. The interelectrode gap (g, taken as the center-to-center
distance between the 10-µm-wide microband electrodes), the
electrode length, and the thickness of the narrow channel obtained
by measuring the thickness of the polymeric spacers (see the
Experimental Section) were measured with ca. (2% precision.
Literature values of the diffusion coefficients were corrected for
the particular ionic strength of the electrolyte solutions used in
the P-ETOF experiments.19The general agreement between the
theoretical expectations and the experimental data was excellent
and typically reflected the (2% precision of the measurements of
the device dimensions. For example, Figure 3 shows the com-
parison between the computed and recorded E-t transients in a
silver ion P-ETOF experiment. In Figure 4, we compare a set of
three Cl-P-ETOF transients recorded with the same device
assembled and opened three consecutive times to test the
reproducibility of the device channel thickness. The two runs
exhibiting small deviations from the theoretical E-t transient
computed with a channel thickness of 3.30 µm could be fit with
channel thicknesses of 3.25 and 3.35 µm. This corresponds to a
(1.5% error, likely resulting from the changes in the thickness of
the polymeric spacers due to solvent swelling or simple wear
following multiple uses. The agreement of the experimental E-t
transients with the theory shows that the linear diffusion ap-
proximation outlined in the Introduction is appropriate. It also
shows that, under these conditions, it is reasonable to neglect
the finite size of the microsensor electrode. However, the latter
assumption does not hold under the conditions of low generator
current or low background concentration of the electrogenerated
ions. We address this in the next section.
Delayed Response of Microsensors. Consider again the
P-ETOF device shown schematically in Figures 1 and 2. Confine-
ment of the microsensor electrode to a small volume of the narrow
channel may lead to a situation in which the change of the sensor
potential in response to an increase in the concentration of the
primary ion diffusing in the channel requires a nonnegligible
decrease in the ion concentration in the volume directly above
the sensor surface. This then results in a slower increase of the
sensor potential relative to a theoretical expectation, or a delay in
the E-t transient. Two such cases featuring Ag+P-ETOF experi-
ments carried out in the devices with 3.0- and 1.0-mm thick
channels are shown in Figure 5. In these experiments, unlike in
the Ag+P-ETOF experiment of Figure 3, the generator current
is significantly lower. This results in a delayed response of the
microsensor (circles) relative to the theoretical expectations
(continuous line). Furthermore, the delay observed in the 1-µm
channel device is greater than that in the 3-µm-thick channel
device. Clearly, in the process of reaching equilibrium, some Ag+
ions must be reduced at the microsensor surface. This causes
their concentration in the small volume of solution in the vicinity
Figure 3. A comparison of the experimental (small dots) and the
calculated (open circles) E-t transients of a Ag+ETOF experiment
obtained under the following experimental conditions: igen) 1.0 ×
10-5A, [Ag+]init) 1.0 × 10-5M, h ) 2.7 µm, g ) 100 µm, and DAg+
) 1.2 × 10-5cm2/s.
Figure 4. Three E-t transients obtained in the Cl-ETOF experi-
ments carried out with the same device testing reproducibility of the
device assembly process. Open circles represent the theoretical
prediction obtained for igen) 1.0 × 10-6A, [Cl-]init) 1.0 × 10-4, h
) 3.3 µm, g ) 50 µm, and DCl-) 1.2 × 10-5cm2/s. The transient
obtained in the first, second, and third runs are marked with dots,
open squares, and black diamonds, respectively.
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of the sensor to be actually smaller than expected when only the
rate of their diffusive transport is considered (eq 1) and results
in a slower increase of the sensor potential.
To quantify this effect, it is necessary to relate the differential
mole quantity of the reduced silver ions (dN) to the differential
change of sensor potential (dE), its specific capacitance (Cdl) and
its surface area (A).19
In general, delays due to the finite size and capacitance of
potentiometric sensors must be expected when the supply of the
ions participating in a sensor equilibrium reaction is small relative
to the demand for their reduction. Indeed, the analogy to the
market supply and demand equilibrium is quite appropriate. In
the present example, the supply of silver ions can be expressed
by the instantaneous flux of electrochemically generated Ag+ions
at the sensor. In view of eq 1, it is primarily determined by the
rate of their generation (igen). It also inversely depends on the
interelectrode gap. Demand refers to the number of moles of silver
ions, N, that must be reduced to increase the sensor potential by
a certain value, as shown by eq 2. Capacitance is the proportional-
ity constant in this equation. It is important to note that, in view
of the Nernst equation, the magnitude of the sensor potential
change per decade change of the concentration of the primary
ion is constant. Thus, for a given flux of silver ions in the device,
the change of the sensor potential and, thus, the demand depends
on the initial (background) Ag+concentration. When the latter is
low, even a small flux of silver ions may require a large change
of sensor’s potential. This is when demand is likely to exceed
supply and a delay in the sensor’s response is to be expected.
We stress that the observed capacitive delay in the response of
the silver microsensor is not at all related to the intrinsic kinetics
of this sensor response. In our earlier report, the latter was
estimated to be >80 V/s, a value far exceeding the theoretically
expected rate of the Ag sensor potential change (continuous lines
in Figure 5).15
The transient delay phenomenon can be used to deduce the
capacitance of the sensor. This is done by fitting the recorded
E-t curves using eq 1 and taking into account the finite size and
the capacitance of the microsensor. Briefly, the numeric routine
developed for this purpose calculates the increments of Ag+
concentration, ∆C, in the small volume of the solution, v, above
the microsensor (v ) wlh; see Figures 1 and 2) occurring over
the arbitrarily small time increments, ∆t, using eq 1. We then
assume that the silver ions contained in the volume of the solution
directly above the microsensor are in the Nernstian equilibrium
with the sensor. This requires an iterative computation of the true
equilibrium concentration of silver ions and the corresponding
sensor potential that takes into account the fact that some quantity
of silver ions (N) must be reduced to adjust the sensor potential
to the true equilibrium value, as dictated by eq 2. Clearly, the
true equilibrium Ag+concentration is smaller than that obtained
when only diffusion is considered. Likewise, the true equilibrium
potential of the sensor is also smaller and rises less rapidly. The
sensor’s intrinsic capacitance is the only adjustable parameter. It
is assumed to be constant over the range of the sensor potentials
recorded in a transient. Two such fits are shown in Figure 5 as
heavy continuous lines. The value of Cdlobtained in this way for
several different Ag+P-ETOF devices operated under different
conditions, 31 ( 2 µF/cm2, is in excellent agreement with the
capacitance found for the same silver microelectrodes using fast
scan cyclic voltammetry in a 0.1 M KNO3solution. In the data
analysis procedure outlined here, Cdl was a single adjustable
parameter. We knew the diffusion constant of silver ions. If the
latter were not available, it would be, in fact, possible to
simultaneously determine both D and Cdlby relying on a nonlinear
least-squares analysis; however, this approach is less precise than
an alternative scheme in which D is determined first in an
experiment run under conditions of a negligible capacitive delay
(high generation rate and high initial concentration of the primary
ion). Knowing D, one can then more precisely determine Cdlof a
sensor, as shown in Figure 5. We also point out that the
assumption of Nernstian equilibrium adopted in that case may
not hold for all potentiometric microsensors. As shown below, an
iridium oxide pH sensor is one such case.
Capacitance of the Silver/Silver Chloride Microsensors.
Next, the same approach was used to measure the capacitance of
the Ag/AgCl microsensors. AC impedance investigations of the
interfacial properties of the Ag/AgCl in chloride electrolytes have
been reported, for example, by Buck and co-workers.28The
response of this system to an ac perturbation is rather complex
and requires a multicomponent equivalent circuit to interpret the
data. In fact, Buck’s analysis of the impedance data does not yield
a parameter that is equivalent to the interfacial capacitance, which
we could then compare to our measurements reported below.
In the Cl-P-ETOF experiments, both the generator and sensor
microelectrodes were produced by first electroplating gold sub-
strates with silver, followed by its partial oxidation in a 0.1 KCl
electrolyte, as described in the Experimental Section. The thick-
ness of the silver films deposited on generator microelectrodes
was large, 1.5-2.5 µm. Following its oxidation to silver chloride,
(28) Rhodes, R. K.; Buck, R. P. Anal. Chim. Acta 1980, 113, 55-66.
Figure 5. Two experimental Ag+ETOF E-t transients (black dots)
recorded with the h ) 1.0 µm (A) and h ) 3.0 µm (B) devices. The
other experimental conditions were igen) 1.0 × 10-6A, [Ag+]init)
1.0 × 10-5, g ) 50 µm, and DAg+) 1.2 × 10-5cm2/s. The transients
obtained on the basis of eq 1 are shown by a thin, continuous line.
The transients marked with open circles were obtained by taking into
consideration the finite value of the capacitance of the microsensors
of 30 (A) and 31 µF/cm2(B).
dN )Cdl(E)A dE
nF
(2)
Analytical Chemistry
E