2.2 Piezoelectric Detection of Differential Surface Stress
41
frequencies) of a solid electrode designed by Gokhshtein [2, 3]. A small alternating voltage superimposed on an applied DC potential of the metal electrode
induces an oscillatory variation of the surface stress, which leads to a mechanical oscillation in the entire electrode-piezoelectric element system. The potential
modulation in the range of 0.5–20 kHz is chosen to induce the mechanical resonances of the whole system in which the amplitude of oscillation of the piezoelectric
element becomes very large compared to non-resonance oscillations. The piezoelectric element converts the mechanical oscillations to alternating electric signals,
which can be sensitively detected by using an oscilloscope, a lock-in amplifier, or a
frequency response analyzer.
The oscillatory variation of the surface stress can also be induced by the application
of a small alternating current at a high frequency, in which the amplitude of the
surface charge density is kept constant. The amplitudes of the piezoelectric signals
generated by the potential and current modulations are proportional to the absolute
values
∂g
∂E
and
∂g
∂q
of the differentials of surface stress g with respect to electrode
potential E and with respect to surface charge density q, which are, respectively,
named “E-estance” and “q-estance” by Gokhshtein [2–4]. Furthermore, the phase
angles of the piezoelectric signals contain information of the changes in sign of
∂g
∂E
and
∂g
∂q
. The following relationship between
∂g
∂E
and
∂g
∂q
holds:
∂g
∂E
=
∂g
∂q
∂q
∂E
= c
∂g
∂q
,
(2.1)
where c is the differential capacity of the electrode. The
∂g
∂E
versus E or
∂g
∂q
versus
E curve has a minimum amplitude (nearly zero) of the piezoelectric signal with a
phase angle change of 180° at a certain potential, which corresponds to the surface
stress maximum. The potential at the surface stress maximum for a solid electrode is
not equal to the potential of zero charge E pzc (q = 0) since q = −
∂q
∂ε
= 0 holds at the
surface stress maximum as manifested by the Gokhshtein equation (see Eq. (1.119)
in Sect. 1.8 of Chap. 1). Valincius [5, 6] measured the q-estance
∂g
∂q
vs. E
curves
for a polycrystalline Au in HClO 4 solutions with different concentrations and found
the negative shift of the potential at the surface stress maximum for the Au electrode
with respect to E pzc determined from the differential capacity measurements. This
means that
∂q
∂ε
> 0 holds near E pzc for the polycrystalline Au electrode.
The device for the piezoelectric detection of differential surface stress was modified by several researchers [7–11]. Figure 2.2 shows the piezoelectric electrode modified by Seo et al. [9, 10], in which a metal foil plate (working electrode) is attached
via a thin polyimide film for electrical isolation to a piezoelectric ceramic plate with
strain gauge cement and then doubly coated with epoxy cement and silicon sealant
for electrical isolation from solution in the back side. The modified device combined
with piezoelectric element and working electrode can be used in electrolyte solutions. Seo et al. [9, 10] by using the piezoelectric electrode in Fig. 2.2 measured the
differential surface stress induced by a potential modulation for polycrystalline Pt
41
frequencies) of a solid electrode designed by Gokhshtein [2, 3]. A small alternating voltage superimposed on an applied DC potential of the metal electrode
induces an oscillatory variation of the surface stress, which leads to a mechanical oscillation in the entire electrode-piezoelectric element system. The potential
modulation in the range of 0.5–20 kHz is chosen to induce the mechanical resonances of the whole system in which the amplitude of oscillation of the piezoelectric
element becomes very large compared to non-resonance oscillations. The piezoelectric element converts the mechanical oscillations to alternating electric signals,
which can be sensitively detected by using an oscilloscope, a lock-in amplifier, or a
frequency response analyzer.
The oscillatory variation of the surface stress can also be induced by the application
of a small alternating current at a high frequency, in which the amplitude of the
surface charge density is kept constant. The amplitudes of the piezoelectric signals
generated by the potential and current modulations are proportional to the absolute
values
∂g
∂E
and
∂g
∂q
of the differentials of surface stress g with respect to electrode
potential E and with respect to surface charge density q, which are, respectively,
named “E-estance” and “q-estance” by Gokhshtein [2–4]. Furthermore, the phase
angles of the piezoelectric signals contain information of the changes in sign of
∂g
∂E
and
∂g
∂q
. The following relationship between
∂g
∂E
and
∂g
∂q
holds:
∂g
∂E
=
∂g
∂q
∂q
∂E
= c
∂g
∂q
,
(2.1)
where c is the differential capacity of the electrode. The
∂g
∂E
versus E or
∂g
∂q
versus
E curve has a minimum amplitude (nearly zero) of the piezoelectric signal with a
phase angle change of 180° at a certain potential, which corresponds to the surface
stress maximum. The potential at the surface stress maximum for a solid electrode is
not equal to the potential of zero charge E pzc (q = 0) since q = −
∂q
∂ε
= 0 holds at the
surface stress maximum as manifested by the Gokhshtein equation (see Eq. (1.119)
in Sect. 1.8 of Chap. 1). Valincius [5, 6] measured the q-estance
∂g
∂q
vs. E
curves
for a polycrystalline Au in HClO 4 solutions with different concentrations and found
the negative shift of the potential at the surface stress maximum for the Au electrode
with respect to E pzc determined from the differential capacity measurements. This
means that
∂q
∂ε
> 0 holds near E pzc for the polycrystalline Au electrode.
The device for the piezoelectric detection of differential surface stress was modified by several researchers [7–11]. Figure 2.2 shows the piezoelectric electrode modified by Seo et al. [9, 10], in which a metal foil plate (working electrode) is attached
via a thin polyimide film for electrical isolation to a piezoelectric ceramic plate with
strain gauge cement and then doubly coated with epoxy cement and silicon sealant
for electrical isolation from solution in the back side. The modified device combined
with piezoelectric element and working electrode can be used in electrolyte solutions. Seo et al. [9, 10] by using the piezoelectric electrode in Fig. 2.2 measured the
differential surface stress induced by a potential modulation for polycrystalline Pt