a part of fundamentals.of.electrochemistry book :
When alternating current is used for the measurements, a transient state arises at the
electrode during each half-period, and the state attained in any half-period changes
to the opposite state during the next half-period. These changes are repeated according
to the ac frequency, and the system will be quasisteady on the whole (i.e., its
average state is time invariant).
For measurements, an ac component IIm sin ωt with the amplitude Im and angular
frequency ω (ω2πf, where f is the ac frequency) is passed through the electrode
(alone or in addition to a direct current). Alternating potential (polarization) changesΔE having the same frequency and an amplitude ΔEm are the response. Sometimes
alternating potential components are applied, and the resulting alternating current component
is measured. In all cases the potential changes are small in amplitude (10 mV).
For an electrode behaving like a pure (ohmic) resistance R, the relation between
the instantaneous values of current and the changes in potential at all times would be
ΔE/IΔEm /ImR. This is actually not found in real electrodes, but instead, a
phase shift α analoguous to that observed in electric circuits containing reactive elements
appears between alternating current and alternating polarization. In electrochemical
systems the potential changes always lag the current changes: ΔEΔEm
sin(ωtα), which corresponds to an electric circuit with capacitive elements. Thus,
the ac behavior of an electrode cannot be described in terms of a simple polarization
resistance R (even if variable) but only in terms of an impedance Z characterized by
two parameters: the modulus of impedance ZΔEm/Im and the phase shift α. The
reciprocal of impedance, Y1/Z, is known as admittance or ac conductance.
A model for the ac response of real electrodes is the simple electric equivalent circuit
consisting of a resistance Rs and capacitance Cs connected in series (Fig. 12.12a).
It follows from the rules for ac circuits that for this combination