Page 274 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Electrode Polarisations 25 1

9.5 Measurement of Polarisation (By Electrochemical Impedance
Spectroscopy)
Impedance spectroscopy has emerged over the past several years as a powerful
technique for the electrical characterisation of electrochemical systems [ 51. The
strength of the method lies in the fact that by small-signal perturbation, it reveals
both the relaxation times and relaxation amplitudes of the various processes
present in a dynamic system over a wide range of frequencies.
Various polarisations exhibit different time dependence, due to different
origins of the kinetic processes involved. The response time for ohmic
polarisation is essentially zero, while the response time for concentration
polarisation is related to the relevant gas phase transport parameters: e.g.
diffusivity. In terms of an equivalent circuit, a Warburg-type element can be used
to describe gas transport through porous electrodes. Similarly, the time constant
for activation polarisation is related to details of the charge transfer process. In
the very simplest case, it can be represented by a time constant for a parallel R-C
circuit, provided the activation process can be described by a parallel R-C circuit.
This, however, is an oversimplification, and an R-C element rarely describes the
activation process accurately: it, nevertheless, allows some insight into the
nature of time constants involved. The experimental procedure thus involves
measuring impedance, Z(w), as a function of frequency over a wide range,
usually from as low as a few mHz to several hundred kHz. Often experimental
difficulties in separating relevant parameters arise due to overlapping semi-
circles, as well as inductive effects due to the testing setup at high frequencies.
In general, the occurrence of a muItitude of chemical and physical processes in
the system leads to a complicated, non-linear relationship between cell voltage
and cell current. Therefore, the definition of a unique polarisation resistance is
difficult, since it itself is usually a function of current density. There are two
methods that can be used to measure cell polarisation: an AC method, and a DC
method. The polarisation resistance determined from AC measurements can be
different from that determined from DC measurements. When the system is
perturbed by an AC input current signal, the AC voltage signal observed at the
terminals of the cell is phase-shifted with respect to the perturbation input. The
corresponding complex impedance can be determined from the current input
signal, and phase shifted voltage signal. In the DC method, electrode potentials
are measured with respect to suitably positioned reference electrodes, and the
measured voltage differences are corrected for ohmic contributions. These two
approaches are briefly described in what follows.
In the AC method, the cell is subjected to an AC source of variable frequency,
and the cell response is measured as a function of frequency. Graphical
representation involves a plot of negative of the imaginary part of the
impedance. - ImZ(o), on the y-axis and real part of impedance, ReZ(o), on the x-
axis; or alternatively a plot of the imaginary part of the admittance, B(o), on the
y-axis, and the real part, G(w), on the x-axis. The plots in the ideal case are a
series of semi-circles, quarter-circles, or distorted semi-circles and quarter-
circles. The intercepts with the x-axis are measures of resistive losses due to