2.2 Piezoelectric Detection of Differential Surface Stress
43
is synchronously detected at the same frequency as that of superimposed potential
modulation by using a lock-in amplifier. A simultaneous recording or data acquisition with a personal computer is performed for measuring the cyclic voltammogram
and piezoelectric signal curve (amplitude |A| vs. phase angle ϕ) in the course of
cyclic potential scan. In principle, the amplitude |A| is proportional to
∂g
∂E
and the
phase angle ϕ involves the component of the change in sign of
∂g
∂E
. The components
resulting from the instruments and the mechanical properties of the electrode system
are included in ϕ. Nevertheless, if the contribution of the additional components to ϕ
is kept constant during experiments, the change in sign of
∂g
∂E
can be evaluated from
the relative change of ϕ by 180°.
Figure 2.4 shows (a) the cyclic voltammogram and (b) the corresponding piezoelectric signal curve (|A| vs. E and ϕ vs. E) for a polycrystalline Au foil electrode
in 0.5 M H 2 SO 4 solution [10]. The cyclic voltammetry was performed at a potential
scan rate of 33.3 mV s
−1 , and simultaneously a sinusoidal signal of 5 mV at 200 Hz
was superimposed on the linear potential scan. The minima of |A| with the change of
ϕ by 180° are observed at about—0.05 V (SHE) in the cathodic potential scan and
at about 0.15 V (SHE) in the anodic potential scan, respectively, which correspond
to the maxima of surface stress. The potentials of the surface stress maximum E max ,
despite the hysteresis of about 0.2 V in the anodic and cathodic potential scans, are
close to those obtained by scrape [12] and ribbon extension [13] methods. The value
of E max is independent of pH in acidic and neutral sulfate solutions, while at pH
higher than 8, E max shifts toward negative direction, indicating that adsorption of
OH
− ions on Au proceeds in alkaline solutions [10]. The relationship between g
and |A| can be given by
g = ∫
∂g
∂E
dE = K ∫|A|dE,
(2.2)
where K is the conversion coefficient from |A| to
∂g
∂E
. It is difficult to determine
K accurately because the mechanical coupling of the piezoelectric electrode is
complicated.
Figure 2.5 shows the g versus E curve obtained from the graphical integration
of |A| with respect to E in the anodic potential scan in Fig. 2.4b by taking the signreversal of
dg
dE
at about 0.2 V (SHE) into account. Seo et al. [10] neglected the second
term of the Gokhshtein equation, i.e.,
∂q
∂ε
, and determined K = 0.35 C m
−2 per µV
from the linear relationship between |A| and q in the potential range of E > E max .
However, as pointed out by Valincius [5, 6], the term of
∂q
∂ε
as compared to q cannot
be neglected and the potential of the surface stress maximum E max is not equal to the
potential of zero charge E pzc . Valincius [5] proposed two procedures to calibrate the
conversion coefficient K. Figure 2.6 illustrates the calibration procedures of K from
two-coupled |A| vs. E and q vs. E (a, b and a
, b) curves in the vicinity of E pzc for
two electrolyte solutions with different concentrations. In the limiting case where
∂q
∂ε
43
is synchronously detected at the same frequency as that of superimposed potential
modulation by using a lock-in amplifier. A simultaneous recording or data acquisition with a personal computer is performed for measuring the cyclic voltammogram
and piezoelectric signal curve (amplitude |A| vs. phase angle ϕ) in the course of
cyclic potential scan. In principle, the amplitude |A| is proportional to
∂g
∂E
and the
phase angle ϕ involves the component of the change in sign of
∂g
∂E
. The components
resulting from the instruments and the mechanical properties of the electrode system
are included in ϕ. Nevertheless, if the contribution of the additional components to ϕ
is kept constant during experiments, the change in sign of
∂g
∂E
can be evaluated from
the relative change of ϕ by 180°.
Figure 2.4 shows (a) the cyclic voltammogram and (b) the corresponding piezoelectric signal curve (|A| vs. E and ϕ vs. E) for a polycrystalline Au foil electrode
in 0.5 M H 2 SO 4 solution [10]. The cyclic voltammetry was performed at a potential
scan rate of 33.3 mV s
−1 , and simultaneously a sinusoidal signal of 5 mV at 200 Hz
was superimposed on the linear potential scan. The minima of |A| with the change of
ϕ by 180° are observed at about—0.05 V (SHE) in the cathodic potential scan and
at about 0.15 V (SHE) in the anodic potential scan, respectively, which correspond
to the maxima of surface stress. The potentials of the surface stress maximum E max ,
despite the hysteresis of about 0.2 V in the anodic and cathodic potential scans, are
close to those obtained by scrape [12] and ribbon extension [13] methods. The value
of E max is independent of pH in acidic and neutral sulfate solutions, while at pH
higher than 8, E max shifts toward negative direction, indicating that adsorption of
OH
− ions on Au proceeds in alkaline solutions [10]. The relationship between g
and |A| can be given by
g = ∫
∂g
∂E
dE = K ∫|A|dE,
(2.2)
where K is the conversion coefficient from |A| to
∂g
∂E
. It is difficult to determine
K accurately because the mechanical coupling of the piezoelectric electrode is
complicated.
Figure 2.5 shows the g versus E curve obtained from the graphical integration
of |A| with respect to E in the anodic potential scan in Fig. 2.4b by taking the signreversal of
dg
dE
at about 0.2 V (SHE) into account. Seo et al. [10] neglected the second
term of the Gokhshtein equation, i.e.,
∂q
∂ε
, and determined K = 0.35 C m
−2 per µV
from the linear relationship between |A| and q in the potential range of E > E max .
However, as pointed out by Valincius [5, 6], the term of
∂q
∂ε
as compared to q cannot
be neglected and the potential of the surface stress maximum E max is not equal to the
potential of zero charge E pzc . Valincius [5] proposed two procedures to calibrate the
conversion coefficient K. Figure 2.6 illustrates the calibration procedures of K from
two-coupled |A| vs. E and q vs. E (a, b and a
, b) curves in the vicinity of E pzc for
two electrolyte solutions with different concentrations. In the limiting case where
∂q
∂ε