522
N. Yadav and R. Dhar
1.3 Limitations of IS
The demerits of IS are related to the ambiguities which come up during the interpretation of the measured data. A major complex analysis based on an equivalent
circuit as used by Bauerle [15] is that ideal lumped constant features are represented by ordinary ideal elements of the circuit. But all electrolytic cells and their
microscopic characteristics are certainly distributed in space independently. Under
these circumstances, ideal elements of the circuit may not be sufficient to explain the
obtained electrical results. So, it is mostly found that the impedance deduced from
experiment cannot be accurately approximated by the equivalent circuit impedance
which involves only a small number of ordinary elements. The method of fitting the
experimental impedance data for a system having distributed properties is assisted by
using equivalent circuit with distributed impedance elements such as elements with
constant phase. Equivalent circuit analysis poses several other important problems
such as: choosing a specific equivalent circuit out of infinite possibilities [16]. These
circuits are mostly not unique. Same value of impedance can be obtained even if
circuit elements are rearranged in an equivalent circuit. But there is an ambiguity
here because for different connections, value of elements used in circuit should also
be different in order to get same value of impedance.
Bulk and interface parameters show an anomalous dependence on frequency. This
again is one of the limitations of IS. Capacitance of interface and conductivity are
considered to be not dependent on frequency whereas in reality, significant aberrations from this behavior are often observed. Further, the assumption that IS deals
with a small linear signal causes certain irregularity. Impedance is expected to not
depend on amplitude of applied signal or reaches a finite limit with the lowering of
the amplitude of the signal. But, electrochemical systems can be highly non-linear
which need rectification and generation of higher harmonics.
2 Techniques for Impedance Measurement
There are variety of standard techniques which are used for the measurement of
impedance and its related functions of a system. While using any of the techniques, a
very small perturbation must be applied so that a linear response is obtained. Theoretical considerations decide the linearity condition [17–20]. But practically, linearity
can be achieved by increasing the input signal to maximum. At the maximum, the
response becomes independent of the amplitude of the stimulus. The methods of
impedance measurement can be broadly classified into: (1) frequency domain and
(2) time domain methods.
N. Yadav and R. Dhar
1.3 Limitations of IS
The demerits of IS are related to the ambiguities which come up during the interpretation of the measured data. A major complex analysis based on an equivalent
circuit as used by Bauerle [15] is that ideal lumped constant features are represented by ordinary ideal elements of the circuit. But all electrolytic cells and their
microscopic characteristics are certainly distributed in space independently. Under
these circumstances, ideal elements of the circuit may not be sufficient to explain the
obtained electrical results. So, it is mostly found that the impedance deduced from
experiment cannot be accurately approximated by the equivalent circuit impedance
which involves only a small number of ordinary elements. The method of fitting the
experimental impedance data for a system having distributed properties is assisted by
using equivalent circuit with distributed impedance elements such as elements with
constant phase. Equivalent circuit analysis poses several other important problems
such as: choosing a specific equivalent circuit out of infinite possibilities [16]. These
circuits are mostly not unique. Same value of impedance can be obtained even if
circuit elements are rearranged in an equivalent circuit. But there is an ambiguity
here because for different connections, value of elements used in circuit should also
be different in order to get same value of impedance.
Bulk and interface parameters show an anomalous dependence on frequency. This
again is one of the limitations of IS. Capacitance of interface and conductivity are
considered to be not dependent on frequency whereas in reality, significant aberrations from this behavior are often observed. Further, the assumption that IS deals
with a small linear signal causes certain irregularity. Impedance is expected to not
depend on amplitude of applied signal or reaches a finite limit with the lowering of
the amplitude of the signal. But, electrochemical systems can be highly non-linear
which need rectification and generation of higher harmonics.
2 Techniques for Impedance Measurement
There are variety of standard techniques which are used for the measurement of
impedance and its related functions of a system. While using any of the techniques, a
very small perturbation must be applied so that a linear response is obtained. Theoretical considerations decide the linearity condition [17–20]. But practically, linearity
can be achieved by increasing the input signal to maximum. At the maximum, the
response becomes independent of the amplitude of the stimulus. The methods of
impedance measurement can be broadly classified into: (1) frequency domain and
(2) time domain methods.