Dependence of the reliability of electrochemical quartz-crystal nanobalance mass responses on the calibration constant, Cf: Analysis of three procedures for its determination

Article abstract of DOI:10.1016/S0013-4686(03)00083-5

The acquisition of accurate results in use of the electrochemical quartz-crystal nanobalance (EQCN) for surface-electrochemical studies depends on reliability of the value of the calibration constant relating changes of the crystal oscillator frequency to the specific surface mass change resulting from some chemisorption or electrosorption process. Three electrochemical methods are employed comparatively to determine the calibration constant for use of an EQCN. In the present paper, study of electrodeposition/electrodissolution of silver on Pt(poly) electrode surfaces provides a means of determining values of the calibration constant for the EQCN response using cyclic voltammetry, chronopotentiometry and chronoamperometry. The experimentally determined value of the calibration constant (C_f) is found to depend on the electrochemical methodology and technique used for its measurement as well as the thickness of the Ag deposit. Use of these three complementary procedures applied under well-defined conditions provides a basis for adoption of a preferred and reliable procedure for determination of the calibration constant; the resulting mean value is precise and very reproducible.

Full text of DOI:10.1016/S0013-4686(03)00083-5

Electrochimica Acta 48 (2003) 1613Á1622
/
www.elsevier.com/locate/electacta
Dependence of the reliability of electrochemical quartz-crystal
nanobalance mass responses on the calibration constant, Cf : analysis
of three procedures for its determination
G. Vatankhah a, J. Lessard a, G. Jerkiewicz b,*,1, A. Zolfaghari c, B.E. Conway c
a De´partement de Chimie, Universite´ de Sherbrooke, 2500, boul. de l’Universite´, Sherbrooke, Que´bec, Canada J1K 2R1
b Department of Chemistry, Queen’s University, Kingston, Ont., Canada K7L 3N6
c Chemistry Department, University of Ottawa, 10 Marie Curie Street, Ottawa, Ont., Canada K1N 6N5
Received 14 January 2003; received in revised form 20 January 2003
Abstract
The acquisition of accurate results in use of the electrochemical quartz-crystal nanobalance (EQCN) for surface-electrochemical
studies depends on reliability of the value of the calibration constant relating changes of the crystal oscillator frequency to the
specific surface mass change resulting from some chemisorption or electrosorption process. Three electrochemical methods are
employed comparatively to determine the calibration constant for use of an EQCN. In the present paper, study of electrodeposition/
electrodissolution of silver on Pt(poly) electrode surfaces provides a means of determining values of the calibration constant for the
EQCN response using cyclic voltammetry, chronopotentiometry and chronoamperometry. The experimentally determined value of
the calibration constant (Cf) is found to depend on the electrochemical methodology and technique used for its measurement as well
as the thickness of the Ag deposit. Use of these three complementary procedures applied under well-defined conditions provides a
basis for adoption of a preferred and reliable procedure for determination of the calibration constant; the resulting mean value is
precise and very reproducible.
# 2003 Elsevier Science Ltd. All rights reserved.
Keywords: EQCN; Calibration constant; Silver electrodeposition; Cyclic voltammetry; Chronopotentiometry; Chronoamperometry
1. Introduction
gram, mass changes were readily determinable. The
technique has now become a valuable procedure in
electrochemical surface science, complementary to
charge evaluation procedures such as cyclic voltamme-
try (CV) and chronoamperometry [2,3]. It should be
recognized that a combination of the charge and mass
changes can lead to in-situ determination of the
molecular weight of the species formed within certain
limitations that have already been discussed in the
Immersion of a quartz-crystal oscillator in an electro-
lyte solution, with simultaneous control of the applied
potential to the overlaying metallic film, marked a new
stage in the development of sensitive techniques for
study of interfacial electrochemistry [1]; it enables
simultaneous and in-situ determination of the mass
variation in relation to surface charge-density associated
with an electrosorption or electrodeposition process.
The instrument on which this technique is based became
known as the electrochemical quartz-crystal microba-
lance (EQCM) because microgram, and later, nano-
literature [4Á9].
/
As the electronic shielding and vibration isolation of
the electrochemical setup has become improved, the
mass-change detection limit has shifted from micro to
nanograms per cm2 of the electrode’s surface area [9Á
11]
/
hence the instrument has now become known as the
electrochemical quartz-crystal nanobalance (EQCN),
and the technique, ‘electrochemical nanogravimetry’.
These improvements have led researchers to apply this
technique not only to polycrystalline electrodes but also,
* Corresponding author. Fax: ꢀ1-613-533-6669.
E-mail address: gregoryj@chem.queensu.ca (G. Jerkiewicz).
1
The experimental part of this work was carried out in the
Laboratory of G. Jerkiewicz while still at the Universite´ de
Sherbrooke.
/
0013-4686/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0013-4686(03)00083-5

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G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á1622
/
in some cases, to single-crystal electrode interfaces such
as Au(111) [12Á14] ]and to epitaxial growth of Pd and Pt
effects have been studied theoretically and experimen-
tally, they are not yet well understood so that a standard
experimental procedure for calibration of the EQCN is
necessary to enable an accurately determined mass
change to be precisely assigned to the electrochemical
processes under investigation.
Two decades after the introduction of in-situ applica-
tion of the piezoelectric quartz crystal to research on
electrochemical systems by Nomura and Iijima [1], use
of the EQCN has become a well established technique
for investigation of mass changes associated with
electrochemical surface processes, e.g. electrosorption,
underpotential deposition, anion adsorption, oxide film
growth, electropolymerization and ion insertion
[5,20,21]. However, in spite of publication of numerous
/
layers [15]. These achievements have shown that the
EQCN is a useful and quantitative tool for monitoring
atomic-level processes at well-defined electrode surfaces.
With these increases in sensitivity, there arises, however,
the necessity for reliable and accurate evaluation of the
calibration constant (Cf) which is required for quantita-
tively relating measured frequency (f) changes to mass
changes (Dm) at the electrode surface. The conversion of
frequency changes (Df) to mass changes during electro-
deposition or dissolution experiments is possible
through the Sauerbrey equation [16]:
ꢀ
ꢁ
ꢀ
ꢁ
pffiffiffiffiffiffiffiffiffiffi
rqmq
2nfo2
Nrq
fo2
Dmꢁꢂ
Df ꢁꢂ
Df ꢁꢂCf Df
(1)
papers and review articles [4,5,10,22Á24] on the EQCN,
/
a well-defined and standard procedure, and its basis for
the determination of the required calibration constant of
the system, is missing in the electrochemical literature.
In the first paper on EQCM by Nomura and Iijima,
silver electrodeposition was used, amongst other metal
electrodeposition processes, to demonstrate the quanti-
tative analytical potentiality of the procedure. They used
metal ions the concentrations of which were in the nano-
molar range and the electrolyte’s pH from 7.5 to 11, and
obtained good empirical calibration curves in terms of
the relation of measured frequency changes to metal-ion
concentrations, but did not use or discuss any relation
between the frequency changes and the deposited mass,
which for surface electrochemistry, is the desired depen-
dence. Bruckenstein and Swathirajan [25] reported a
procedure for calibrating the EQCM employing galva-
nostatic electrodeposition of Ag from acidic solution
using a current of 10 mA. They calculated the calibration
constant from the slope of the observed linear relation
of Dm to Df at the above-mentioned current but without
any further discussion concerning the effect of the
magnitude of the applied current and duration of its
application, thus the number of Ag monolayers depos-
ited.
where fo is the resonant frequency of the quartz-crystal
resonator (in our case ꢀ8.9 MHz in air), rq the density
of quartz (2.648 g cmꢂ3), mq the shear modulus of
quartz (2.947ꢃ
1011 g cmꢂ1 sꢂ2), n a harmonic number
(for the first harmonic, nꢁ1), N is a frequency
parameter (1670 kHz mm) characteristic of the crystal,
and Cf is the sensitivity factor (ng Hzꢂ1 cmꢂ2) of the
crystal (referred to as the calibration constant when it is
determined through a calibration procedure). It has to
be recognized that the Sauerbrey equation is valid for a
quartz-crystal immersed in a fluid phase, whether
gaseous or liquid [5,17,18]. However, as the density
and viscosity of the fluid increase, the fundamental
frequency, fo, drops [19]. For instance, upon transfer of
a quartz-crystal resonator from a gaseous medium (air)
to a liquid (aqueous solution), the value of fo drops to a
/
/
/
new (lower), yet stable, value characteristic of the solidÁ
/
liquid interactions [17,18].
In electrochemical systems, the frequency changes are
associated with the electrochemical process that takes
place at the electrode surface (electrodeposition or
electrosorption) and also with modification of other
physico-chemical parameters such as pressure of the
fluid in contact with the electrode (pressure effect),
viscosity of the medium, and the surface roughness.
These factors have been discussed by Bruckenstein and
Shay [19] and Tsionsky et al. [6], and recently reviewed
by Hepel [5] who considered the following equation to
illustrate the participation of various factors determin-
ing the overall variation in frequency:
Gabrielli et al. [26] also employed galvanostatic silver
electrodeposition using chronopotentiometry for cali-
bration of their EQCM system by application of various
constant current-densities of 5, 50, 250, and 500 mA
cmꢂ2 at gold-plated quartz electrodes having various
radii (Rꢁ1.5, 2.5 and 4.5 mm). They concluded that
/
values of the calibration constant vary with radius of the
electrode but attained the value calculated from the
Sauerbrey equation when the radius was sufficiently
large. However, they did not observe any effect of the
extent of charge passed, i.e. the amount of the electro-
deposit, on the value of calibration constant.
Some researchers have used electrodeposition of other
metals to calibrate their systems, just assuming the
deposition efficiency to be very close to 100%. For
example, Soares [27] electrodeposited Ni to evaluate the
Df ꢁDfm ꢀDfv ꢀDfp ꢀDfT ꢀDfs ꢀDfr
(2)
where Dfm is the mass-change effect discussed by
Sauerbrey [16], Dfv the viscosity effect, Dfp the pressure
effect, DfT the temperature effect, Dfs the stress effect
and Dfr is the roughness effect. Additional, more subtle
effects can arise depending on the extent to which the
diffuse double-layer distribution of ions is coupled to the
lateral motions of the crystal’s surface [6]. Though these

G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á
/1622
1615
sensitivity of his home-made microbalance while Noel
¨
The Pt surface roughness factor, R, was found
through determination of the charge-density associated
with underpotential deposition of H (UPD H) and
anion adsorption, compared with the standard reference
value of 220 mC cmꢂ2 [29], allowing for double-layer
charging. The resulting value of R was 1.68 (the real
and Topart [28] electrodeposited both silver and copper
in their evaluation of the impedance behavior of the
quartz microbalance. They demonstrated a wider dy-
namic range by measuring admittance leading to a linear
calibration curve suitable for quantitative analytical
work.
surface area was Arꢁ
/
0.3389
0.003 cm2). All the CV
features were exactly as for a regular, annealed poly-
crystalline Pt wire or sheet.
/
Examination of the previous procedures and publica-
tions on calibration of EQCN mass responses, as
outlined above, indicates divergences of results. This
situation indicates the desirability of evaluating the Cf
for a given metal surface, e.g. Pt, independently by
several electrochemical methods in the same laboratory.
In the present paper, we have therefore, examined
electrodeposition of silver comparatively by means of
three principal, but different, electrochemical techni-
ques: CV, chronopotentiometry and chronoamperome-
try, in order to derive, comparatively, values of the
calibration constant. A careful analysis of the resulting
relations between the electrochemical and frequency-
response results enabled us to obtain a consistent value
for the calibration constant from each of the three
techniques.
A reversible hydrogen electrode (RHE) was used as
the reference electrode and a Pt sheet (Aesar, 99.99%) as
the counter-electrode.
2.3. Experimental methodology
Prior to commencement of silver electrodeposition for
calibration purposes, CV (i vs. E) and frequency
response (Df vs. E) measurements were conducted in
0.5 M aqueous H2SO4 prepared from BDHTM Aristar
grade H2SO4 and ‘Nanopure’ water of 18 MV (Barn-
stead). All measurements were carried out at 298 K.
Ultra-high purity Ar or N2 was passed through the
working electrode compartment to sustain an inert-gas
environment. Each new Pt electrode was cycled 1000
times between 0.05 and 1.50 V, RHE, in order to release
any stress from the near-surface region. The quality of
the Pt deposit and the cleanliness of electrolyte were
2. Experimental
2.1. Electrochemical instrumentation
EQCN measurements were conducted using a Seiko-
EG&G (presently AMETEK) quartz crystal analyzer
(model QCM 917), an EG&G potentiostat (model
263A), a home-built Faraday cage and M270 Electro-
chemical Software.
2.2. Electrodes
Planar AT-cut quartz crystals having a resonant
frequency of ꢀ
/
8.9 MHz in air (it drops to ꢀ8.8
/
MHz when the crystal is in contact with an aqueous
medium) were used as the working electrodes after
deposition of Pt on each side of the crystal (to a
thickness of ca. 300 nm) on top of a sputtered Ti deposit
(30 nm in thickness). These electrodes had a flat surface,
little roughness and exhibited no effect associated with
the cell geometry that could affect the crystal response,
e.g. for vertical compared with horizontal orientation
[10]. The lack of any effect associated with the cell
design allows us to deduce that were there any hydro-
dynamic effect, it was either absent or negligible in the
experiments described below [5]. The Pt working elec-
trode was mounted in a specifically designed TeflonTM
holder. The electrochemical cell and quartz-crystal
holder were described in detail in a previous publication
[10].
Fig. 1. CV profile (A) and corresponding quartz-crystal response (B)
for Pt electrode in 0.5 M aqueous H2SO4 recorded at a scan rate of 50
mV sꢂ1 at Tꢁ
298 K.
/

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G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á1622
/
verified by recording CV profiles over the 0.05Á
/
1.40 V,
3.1. Calibration constant from cyclic voltammetry
experiments
RHE, range (Fig. 1) and finding them closely compar-
able with the now standard ones representative of an
impurity-free system and a relaxed Pt surface, following
In order to find a potential window for the following
CV studies, a potential scan was performed from 0.425
to 0.775 V versus RHE, at a Pt(poly) electrode in 0.5 M
annealing [30Á
/
32]].
The silver electrodepositionÁ
/
electrodissolution pro-
cesses were investigated by (i) CV; (ii) chronopotentio-
metry; and (iii) chronoamperometry [2,3]. All the
electrochemical experiments were conducted in 0.5 M
aqueous H2SO4 solution containing 1.5 mM concentra-
tion of analytical grade Ag2SO4 (Fisher Scientific) at
aqueous H2SO4ꢀ1.5 mM Ag2SO4 solution at a scan
/
rate of 1 mV sꢂ1. Fig. 2A shows the characteristic CV
profile and the corresponding frequency response (Fig.
2B) for silver deposition and stripping at the Pt(poly)
electrode surface from the Agꢀ solution in 0.5 M
H2SO4. The cathodic and anodic charge densities are
T $
CV profiles for Ag deposition and stripping were
recorded in the potential range 0.425Á0.750 V versus
/298 K.
almost identical (3.809
0.02 mC cmꢂ2). As the potential
/
/
is swept from 0.775 V towards lower values, the
response current is very low (0.5 mA cmꢂ2) but starts
to increase cathodically at about 0.65 V, RHE, reaching
RHE, and at various scan rates (s) between 0.5 and 15
mV sꢂ1. The chronopotentiometry experiments were
a peak of ꢂ
diminish and, at the sweep-reversal potential of 0.425 V,
it remains cathodic (its current density being ca. ꢂ
/
58 mA cmꢂ2 at 0.615 V. It then starts to
performed by applying different current-densities of 5Á
/
100 mA cmꢂ2, using a step-time (Dt) of 60 s. The
chrono-amperometry measurements were conducted by
applying potential steps from an initial potential (Ei) of
/
31 mA
cmꢂ2) while following reversal of the sweep, it decreases
and reaches zero at 0.613 V, and then becomes an
anodic current. This current then appreciably increases,
reaching a maximum of 322 mA cmꢂ2 at 0.695 V.
The features of the CV profiles indicate that the silver
deposition is under diffusion control (on account of the
low concentration of Agꢀ), therefore, the cathodic
0.775 V to final potentials (Ef) of 0.520Á/0.580 V versus
RHE, at 0.01 V intervals with Dtꢁ60 s. In each of these
/
three sets of experiments, frequency-response changes
were recorded simultaneously with the electrochemical
responses over the same respective potential ranges.
3. Results and discussion
The electrochemical reaction involved in the silver
electrodissolution is simply:
electrodepositionÁ
/
Agꢀ ꢀeꢂ l Ag
(3)
where Agꢀ is a hydrated ion. Using Faraday’s second
law:
Dm
MAg
Dqꢁ
F
(4)
where Dq in coulombs cmꢂ2 is the charge measured
from the electrochemical response; Dm in grams cmꢂ2
corresponds to the mass change of silver during the
electrodissolution, and MAg and F
,
electrodepositionÁ
/
are the atomic weight of silver (108 g molꢂ1) and the
Faraday constant, respectively. By combining the
Sauerbrey equation [16] (Eq. 1) with the above formula,
we obtain the following relation that is used in the
experimental determination of the calibration constant
for the EQCN:
MAg Dq
zF Df
Cf ꢁ
(5)
Fig. 2. CV profile (A) and corresponding quartz-crystal response (B)
for Ag deposition on and stripping from Pt electrode in 0.5 M aqueous
where z is the number of electrons transferred in the
electrochemical reaction (Eq. 3) and in the case of Ag
H2SO4ꢀ
/
1.5 mM Ag2SO4 solution at a scan rate of 1 mV sꢂ1 at Tꢁ
/
deposition zꢁ1.
/
298 K.

G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á
/1622
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current is smaller than the anodic one. The frequency
change has negative values (as expected upon mass
addition) as Ag becomes electrodeposited on Pt and its
decrease is almost linear down to the sweep-reversal
potential (0.425 V). Following the sweep reversal, the
frequency continues to decrease because Agꢀ deposition
continues up to the potential of 0.613 V (Fig. 2B).
Beyond this potential (Fig. 2A), the current-density
becomes anodic (stripping) and the frequency begins to
increase and eventually reaches its previous initial value
at the beginning of the next cycle (i.e. with no silver now
remaining on the Pt surface, as evidenced by the analysis
of the cathodic and anodic charge-densities that balance
to within 0.02 mC cmꢂ2).
A series of experiments conducted at a succession of
scan rates of 0.5, 1, 2, . . ., 15 mV sꢂ1 was performed and
their electrochemical responses and corresponding var-
iations in frequency response were recorded (Fig. 3A,
B). There is no new feature in the CV profiles upon
increasing the scan rate but there is a slight shift in the
anodic peak potential. As expected, the current rises as
the scan rate increases, and the absolute frequency
change declines with rising scan rate because the
duration of the sweep is shorter at higher sweep rates,
so that less mass of Ag is deposited. Upon plotting the
Fig. 4. Plot of the peak current densities vs. square root of the scan
rate for the cathodic (deposition) and anodic (stripping) CV profiles
shown in Fig. 3.
cathodic and anodic peak current densities (ip) versus
square-root of the scan rate (s1/2), an excellent linear
relationship resulted (Fig. 4; in both cases, the correla-
tion coefficient is over 0.999). Integration of the CV
profiles (Fig. 3A), gave the charge-densities for the
range of scan rates, which were subsequently plotted
versus the respective frequency changes. In Fig. 5, we
show two charge-density (q) versus frequency change
(Df) plots for sꢁ
/
0.5 and 15 mV sꢂ1, that are
representative of the overall tendency. An analysis of
the results demonstrates that the negative and positive-
going scans do not follow exactly each other, thus
revealing a hysteresis behavior.
Values of the apparent calibration constant (Cf) were
determined for the various scan rates using Eq. 5 giving
a complete set of data, samples of which are presented in
Fig. 5 (the values of Cf are determined on the basis of
Fig. 3. Series of CV profiles and corresponding quartz-crystal
frequency changes at for Ag deposition on and stripping from Pt
electrode in 0.5 M aqueous H2SO4ꢀ
298 K at different scan rate, sꢁ
2, 5, 10, 15 mV sꢂ1; arrows indicate
changes brought about by the scan rate increase.
/
1.5 mM Ag2SO4 solution at Tꢁ
/
Fig. 5. Charge density vs. frequency change plots for Ag deposition on
/
and stripping from Pt electrode in 0.5 M aqueous H2SO4ꢀ
/
1.5 mM
298 K and two scan rates, 0.5 and 15 mV sꢂ1
Ag2SO4 solution at Tꢁ
/
.

1618
G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á1622
/
both the respective negative and positive-going charge-
density versus frequency change plots, Dq vs. Df). Such
derived values of the calibration constant are plotted
versus square-root of the scan rate (s1/2) in Fig. 6. The
results demonstrate that Cf tends to decrease from ꢀ
to lower values as the scan rate decreases. A linear fit of
the results (correlation coefficient ꢀ0.80) shows that Cf
reaches 4.27 as the scan rate is extrapolated to 0 (s 00).
/
6
/
/
It was mentioned above that an apparent hysteresis is
observed in the relation of charge-density versus fre-
quency change (q vs. Df, Fig. 5), plotted for positive and
negative-going sweeps. The magnitude of the hysteresis
(the area inside the loop, qDf, in mC Hz cmꢂ2) was
calculated for each sweep and subsequently plotted
versus scan rate, s (Fig. 7). The hysteresis effect shows
a diminution with increasing scan rate, reaching a steady
value at sufficiently high scan rates. These results may
be interpreted as follows: in an ideal situation, there
should be no ‘hysteresis’ effect and in such a case the
values of Cf would be exactly the same for each scan
rate, i.e. if the apparent hysteresis were kinetic in origin.
It must be noted that a hysteresis phenomenon strictly
arises when the backward pathway of a process is
microscopically not identical with the pathway in the
forward direction, even at very slow scan rates, i.e. when
the hysteresis arises for non-kinetic reasons (see the
Fig. 7. Graph of the hysteresis area (q ꢃDf) vs. scan rate determined
for the entire set of charge density vs. frequency change plots (see Fig.
5 for two samples of such plots).
/
conceivable that the hysteresis effect arises for mechan-
istic reasons, namely the molecular-level mechanism of
silver stripping is not the reverse of that for its
deposition. The results demonstrate that when Cf is
determined by Ag deposition and stripping using CV, its
apparent values are a function of the scan rate because
the process is under diffusion control. Therefore, this
methodology, as such, should not be applied to deter-
mine Cf unless experiments are conducted over a range
of different scan rates with subsequent extrapolation of
the values of Cf to zero scan rate (Cf(s 00)). Later, we
show that Cf(s 00), thus determined, agrees well with
values of Cf determined by means of chronopotentio-
metry and chronoamperometry measurements, which
show the self-consistency of the electrochemical mea-
surements.
treatment of Everett et al. [33Á35]. In general, the
/
hysteresis effect depends on the duration of the exter-
nally applied stimulus and becomes more pronounced
when the latter lasts long and vice versa. Therefore, our
results, which demonstrate that the hysteresis effect is
negligible at higher scan rates and substantial at lower
ones (Fig. 7), confirm that it is not kinetic in origin. In
surface electrochemistry, for instance, the underpoten-
tial deposition of H or metals reveals a pronounced
hysteresis effect that increases with scan rate, as
illustrated by the simulated CV profiles of Srinivasan
and Gileadi [36] based on kinetic calculations. It is
3.2. Calibration constant from chronopotentiometry
This procedure is based on the application of a
constant current-density (i) pulse with recording of the
resulting potential and frequency changes versus time
(t). Constant current-densities, having values varied
from 5 to 100 mA cmꢂ2 were applied for a period of
60 s and the corresponding frequency responses were
recorded as a function of time (Fig. 8). The resulting
frequency change versus time (Df vs. t) relations are
linear with no significant deviations, as seen in Fig. 8. In
other words, the observed frequency response, that is
linearly proportional to extent of addition of mass, is
proportional to the charge-density that passes across the
system.
Equation 5 was applicable to the experimental charge
density (Dqꢁ
/
i ꢃt) and frequency change (Df) values,
/
enabling the value of the calibration constant to be
evaluated for each current-density. In Fig. 9, these
values of the calibration constant (Cf) are plotted versus
the current-density and illustrate the extent of Ag
Fig. 6. Graph of the calibration constant vs. square root of the scan
rate determined for the entire set of charge density vs. frequency
change relations (see Fig. 5 for two samples of such plots).

G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á
/1622
1619
averaged for different current-densities giving a mean
value of the calibration constant as Cfꢁ4.1990.02 ng
Hzꢂ1 cmꢂ2 (Fig. 9).
/
/
The observed variation of Cf may be explained as
follows. In the case of Ag deposition at low current-
densities, corresponding to an Ag surface coverage of
less than 1 ML, the electrodeposition is localized, i.e.
homogeneous coverage is not attained at the electrode
surface due to formation of nuclei that are subsequently
growing; hence the frequency-response is representative
of localized changes of mass [26,37,38]. After the
completion of 1 ML of silver, the surface of the
electrode is in a transitional state from that of Pt to
Ag which might give rise to stress of the electrode’s near-
surface region that affects the frequency response and
consequently the derived value of Cf.
Fig. 8. Frequency change vs. time responses for Ag deposition on Pt
electrode in 0.5 M aqueous H2SO4ꢀ1.5 mM Ag2SO4 solution at
various constant current densities, iꢁ
5, 25, 50, 75, and 100 mA cmꢂ2
/
/
.
3.3. Calibration constant from chronoamperometry
In this series of experiments, the potential is stepped
from an initial value Eiꢁ0.775 V (where no Ag is on the
/
electrode) to the final one (Ef) between 0.520 and 0.580
V versus RHE with a potential interval (DE) of 0.010 V;
the duration (Dt) of the step is 60 s. A typical example of
the results, which is representative of the overall trend, is
shown in graphs A to D of Fig. 10. Fig. 10A shows a
plot of current (I) versus time (t) upon the potential step
from Eiꢁ
/
0.775 V to Efꢁ0.550 V. Corresponding
/
graphs of charge (Q) and dependence of frequency
(Df) on time are shown in Fig. 10B and C, respectively.
They show an increase in Q and a corresponding
frequency change decrease (Df) with time during the
deposition of Ag. It is interesting to observe that Q
versus t and Df versus t plots reveal the same features,
in other words they are correlated with each other. Each
plot exhibits a curvature at the beginning that becomes
Fig. 9. Graph of the calibration constant (determined by application
of Eq. 5 to the data shown in Fig. 8) vs. current density; the extent of
Ag deposition in the number of ML’s is shown for different values of
the current density.
transformed into a linear relation after ꢀ
polarization time. The initial 20 s of polarization results
in the deposition of ꢀ7 ML’s of Ag at the Pt substrate.
The slope of Q versus Df plot (Fig. 10D) allows a value
of the calibration constant to be calculated from the
experimental data by means of Eq. 5.
/
20 s of the
deposition through indications on the graph of the
number of Ag monolayers (ML). An inspection of Fig.
9, reveals that such determined Cf values are scattered
/
between ꢀ4.1 and 4.3, i.e. over a narrow range
/
(compare with the distribution of Cf values determined
by application of CV, Fig. 6). In the case of Ag
A careful examination of Fig. 10D shows that there is
a transition region in Q versus Df relation that is
deposition at low current-densities (i 5
and for tꢁ60 s, leading to films having up to 5 ML’s of
Ag, the Cf values are almost randomly scattered between
4.1 and 4.3. However, in the case of Ag deposition at
higher current-densities (255i 5
100 mA cmꢂ2) and for
tꢁ60 s, leading to films having thicknesses in the range
5Á16 ML’s, the Cf values are less scattered and
gradually increase from ꢀ4.25 to 4.3. Application of
/
25 mA cmꢂ2
)
/
manifested by a change of slope at Df $
/
550 Hz (this
corresponds to DQ $0.5 mC, equivalent to ꢀ
/
/7 ML’s of
ꢀ
/
Ag), which consequently gives rise to a different value of
Cf beyond this point. This modification of slope was
observed in each separate experiment and the inflection
/
/
/
/
point always appeared when DQ $
/
0.5 mC, i.e. when the
7 ML’s. The
/
thickness of the Ag deposit had reached ꢀ
/
higher current-densities was avoided because this would
lead to thick films that might have possessed uncontrol-
lable surface roughness, thus resulting in complications
due to additional hydrodynamic effects at the oscillating
crystal surface [5,6,10,19]. The entire set of Cf values was
Cf values for the two Q versus Df linear regions (Fig.
10D) were determined for each separate experiment. It
was observed that in the case of Ag deposits whose
thickness was up to 7 ML’s, Cf assumed high values, up
to ꢀ
6 ng Hzꢂ1 cmꢂ2 (not shown in a graphical form).
/

1620
G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á1622
/
Fig. 10. Chronoamperometric deposition of Ag on Pt electrode in 0.5 M aqueous H2SO4ꢀ
/
1.5 mM Ag2SO4 solution at Tꢁ/298 K; current vs. time
transient brought about by the potential step from the initial potential, Eiꢁ0.775 V, to the final one, Efꢁ
/
/0.550 V, vs. RHE (A); charge vs. time (B)
and frequency change vs. time (C) transients determined from data shown in (A); graph of the charge vs. frequency change (D) obtained by
combining the two previous plots (B and C).
Such values of Cf could be the result of interfacial
phenomena that arise as the Pt substrate becomes
covered by the Ag deposit, thus introducing interfacial
stress [5,10]. As the Ag deposits became thicker than 7
ML’s and more uniform [38], Cf assumed significantly
lower values, in the 4.1Á
4.3 ng Hzꢂ1 cmꢂ2 range. In
/
Fig. 11, are plotted Cf values versus the final potential
(Ef), determined from the second linear region of the Q
versus Df relations, in Fig. 10D, i.e. for Ag deposits
whose thickness was greater than 7 ML’s. These results
demonstrate that Cf gradually decreases as Ef increases,
i.e. as the deposit becomes thicker, the resulting average
value is 4.199
It was mentioned above that Cf can attain values as
high as ꢀ
6 ng Hzꢂ1 cmꢂ2 in the case of very thin Ag
4.2 ng Hzꢂ1
/
0.02 ng Hzꢂ1 cmꢂ2
.
/
deposits and subsequently decreases to ꢀ
/
cmꢂ2 as the thickness of the Ag deposit exceeds some 7
ML’s. A qualitatively similar behavior is observed in the
case of the Cf values determined by application of
Fig. 11. Graph of the calibration constant vs. the final potential
determined for the entire set of chronoamperometry experiments (Fig.
10 shows a typical chronoamperometry experiment).

G. Vatankhah et al. / Electrochimica Acta 48 (2003) 1613Á
/1622
1621
chronopotentiometry (Fig. 9). It is interesting to observe
that the values of Cf evaluated through chronopotentio-
metric and chronoamperometric measurements are in
very good agreement leading to the same, well-defined
The understanding of the origin of this difference is
vital in quantitative research that utilizes the EQCN. It
should be recognized that the theoretical (calculated)
value, Cf,theor, corresponds to a vibrating crystal that is
placed in vacuum. When the crystal is put in contact
with a condensed medium, the latter couples to the
crystal surface and affects the shear mode that results in
a decrease of the fundamental vibrational frequency. In
addition, the crystal’s surface roughness and the electro-
chemical double layer play a significant yet not well
understood role and cause an additional decrease of the
fundamental vibrational frequency and a decrease of the
Cf value. Finally, it should be recognized that the
precision and reliability of the Cf value determination
are fundamental in any quantitative EQCN data analy-
sis and, in some cases, might call for a small but
significant rectification of interpretation of previously
published results, including our own.
average value, Cfꢁ
/
4.199 .
0.02 ng Hzꢂ1 cmꢂ2
/
4. Summary of comparative formal and theoretical values
of Cf
The values of Cf obtained by means of chronopoten-
tiometry and chronoamperometry are consistently in the
range 4.10Á
4.19 ng Hzꢂ1 cmꢂ2. In the case of CV, however, the
values of Cf fall in a wide range (4.4Á
6.1 ng Hzꢂ1 cmꢂ2
/
4.30 ng Hzꢂ1 cmꢂ2, the average value being
/
)
and such determined Cf values exhibit a strong depen-
dence on the scan rate. Extrapolation of the Cf versus
pffiffi
s relation to the zero scan rate, Cf(s 00), gives a value of
4.27 ng Hzꢂ1 cmꢂ2 that falls very close to those
determined on the basis of chronopotentiometry and
chronoamperometry measurements, i.e. they differ by
only 0.08 ng Hzꢂ1 cmꢂ2 (1.9%). The chronoampero-
metry data reveal a scatter when the thickness of the Ag
Acknowledgements
The senior authors (J.L., G.J. and B.E.C.) acknowl-
edge support of this work by the NSERC of Canada.
J.L. and G.J. gratefully acknowledge support from the
Fonds FCAR du Que´bec and MEQ (Research Chair).
We acknowledge scientific interaction with and support
from Princeton Applied Research and their Canadian
representative, Gamble Technologies. We acknowledge
Que´bec-Ontario Interprovincial Collaborative Research
Grants for the purpose of enhancing collaboration
between our respective electrochemistry research labora-
tories for training of graduate students.
deposit is in the 0Á
deposits having thicknesses in the range 7Á
values of Cf are less scattered, being in the 4.1Á
Hzꢂ1 cmꢂ2 range and thus leading to a well-defined
average value, 4.209
0.02 ng Hzꢂ1 cmꢂ2. Therefore, the
/
7 ML’s range. However, for Ag
16 ML’s, the
4.3 ng
/
/
/
preferred experimental procedure for determination of
the EQCN calibration constant should be based on
chronopotentiometry or chronoamperometry measure-
ments and the thickness of the Ag deposit should fall in
the range 7Á16 ML’s, when the procedure of Ag
/
deposition on smooth Pt is chosen as the basis for
calibration of quartz-crystal electrodes for the EQCN.
The determination of Cf by application of CV is more
troublesome and requires a careful data analysis
through determination of the scan-rate dependence of
Cf followed by its extrapolation to zero scan rate.
The theoretical value of the calibration constant can
be determined using the following formula that origi-
nates from the Sauerbrey equation (Eq. 1):
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