90
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
I o = −C
ζ E,ε
ε o ω,
(3.18)
where I , Q, and C are net current, net charge, and net capacity of the electrode,
respectively.
The experiment for the potential variation due to surface elastic strain needs a
sufficiently high strain frequency to avoid the participation of Faraday loss current in
q. However, the strain cycles at such high frequency bring phase shifts of the potential
and current responses due to the slow transport process of the electrolyte or due to
the slow adsorption process of electrolyte anions [42]. At the high-frequency strain
cycles, Eq. (3.11) will be modified to
E = ε o
ζ E,ε
sin(ωt − φ),
(3.19)
where φ is the phase angle relative to the cyclic elastic strain. The potential amplitude
E o in Eq. (3.19) is given by ε o
ζ E,ε
. Equation (3.17) will be also modified to
I = I o cos(ωt − φ − ψ),
(3.20)
where ψ is the phase angle relative to the cyclic potential variation.
Since in conventional electrochemical impedance spectroscopy (EIS), potential
and current are correlated by the complex electrochemical impedance Z e = Z re −
j Z im , I o and ψ in Eq. (3.20) are given by [42]:
I o =
ε o
ζ E,ε
|Z e |
,
(3.21)
and
tan ψ =
Z im
Z re
,
(3.22)
where |Z e |, Z re , and Z im are the absolute value, real component, and imaginary
component of Z e , respectively. In the case where the equivalent circuit in electric
double-layer region simplifies to a series RC circuit, Z e can be expressed by [42]:
Z e = r sol −
j
ωc dl
,
(3.23)
where r sol is the solution resistance and c dl is the differential capacity of the electric
double layer. In DECMA, the potential variation is imposed by the cyclic elastic
strain, and the concomitant current response is controlled by Z e . Since E o = I o |Z e |,
ζ E,ε
is given by
ζ E,ε
=
E o
ε o
=
I o |Z e |
ε o
.
(3.24)
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
I o = −C
ζ E,ε
ε o ω,
(3.18)
where I , Q, and C are net current, net charge, and net capacity of the electrode,
respectively.
The experiment for the potential variation due to surface elastic strain needs a
sufficiently high strain frequency to avoid the participation of Faraday loss current in
q. However, the strain cycles at such high frequency bring phase shifts of the potential
and current responses due to the slow transport process of the electrolyte or due to
the slow adsorption process of electrolyte anions [42]. At the high-frequency strain
cycles, Eq. (3.11) will be modified to
E = ε o
ζ E,ε
sin(ωt − φ),
(3.19)
where φ is the phase angle relative to the cyclic elastic strain. The potential amplitude
E o in Eq. (3.19) is given by ε o
ζ E,ε
. Equation (3.17) will be also modified to
I = I o cos(ωt − φ − ψ),
(3.20)
where ψ is the phase angle relative to the cyclic potential variation.
Since in conventional electrochemical impedance spectroscopy (EIS), potential
and current are correlated by the complex electrochemical impedance Z e = Z re −
j Z im , I o and ψ in Eq. (3.20) are given by [42]:
I o =
ε o
ζ E,ε
|Z e |
,
(3.21)
and
tan ψ =
Z im
Z re
,
(3.22)
where |Z e |, Z re , and Z im are the absolute value, real component, and imaginary
component of Z e , respectively. In the case where the equivalent circuit in electric
double-layer region simplifies to a series RC circuit, Z e can be expressed by [42]:
Z e = r sol −
j
ωc dl
,
(3.23)
where r sol is the solution resistance and c dl is the differential capacity of the electric
double layer. In DECMA, the potential variation is imposed by the cyclic elastic
strain, and the concomitant current response is controlled by Z e . Since E o = I o |Z e |,
ζ E,ε
is given by
ζ E,ε
=
E o
ε o
=
I o |Z e |
ε o
.
(3.24)