3.4 Surface Stress Versus Surface Charge Density or Potential …
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t:
ε = ε o sin(ωt),
(3.10)
where ω is the angular frequency and ε o is the amplitude of ε. In the case of an
ideally polarizable electrode without Faraday process under open-circuit condition,
the concomitant potential variation is formulated as follows [42]:
E = E o sin(ωt) = ε o
ζ E,ε
sin(ωt),
(3.11)
where
ζ E,ε
is the absolute value of ζ E,ε . Therefore,
ζ E,ε
can be obtained as the
amplitude ratio of E to ε, i.e.,
E o
ε o
.
If ε is changed sinusoidally at constant potential under the assumption that ε is
small and a linear relationship between q and ε holds, the small change of q will be
represented by
δq =
∂q
∂ε
E
δε.
(3.12)
In addition,
∂q
∂ε
E
can be divided into the two terms:
∂q
∂ε
E
= −
∂q
∂ E
ε
∂ E
∂ε
q
= −cζ E,ε ,
(3.13)
where
∂q
∂ E
ε
= c and
∂ E
∂ε
q
= ζ E,ε . Consequently, the change of q due to cyclic
small strain at equilibrium is given by [42]:
δq = −c
ζ E,ε
ε o sin(ωt).
(3.14)
The corresponding variation of current density i is [42]:
i =
dq
dt
= i o cos(ωt),
(3.15)
and
i o = −c
ζ E,ε
ε o ω,
(3.16)
or equivalently in the case where the electrode surface area is unknown:
I =
dQ
dt
= I o cos(ωt),
(3.17)
and