Page 268 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Electrode Polarisations 245

(02, N2 in the cathode: H2, HzO in the anode) transport through the porous
interstices, which are contiguous, to or away from reaction sites. (2) In the case
of two phase MIEC materials, electrons (or holes) transport through the
electronically conducting (contiguous) phase, oxygen ions transport through
the ionically conducting (contiguous) phase, and the charge transfer reaction
occurs at or near a TPB. In single phase MIEC, both electrons (and/or holes) and
oxygen ions transport through the single-phase MIEC, and the charge transfer5
reaction occurs along the surface of the porous MIEC. In this manner, whether
the electrode is two-phase or single-phase, the electrochemical reaction of
charge transfer is spread from the electrolyte/electrode interface over some
distance into the electrode. (3) The region over which this spreading occurs
depends upon the microstructure as well as the transport properties of the
electrode. Usually, the finer the microstructure, the smaller is the region over
which the reaction zone is spread out. (4) Very close to the electrolyte, the
current is predominantly ionic, and outside the critical thickness into
the electrode, the current is predominantly electronic. Over the critical or the
threshold thickness, the current varies from ionic (near the electrolyte) to
electronic (towards the current collector). Thus, the electrode should exhibit
MIEC characteristics at least over this critical or the threshold distance.
Typically, this critical thickness is on the order of a few, to few tens of microns.
This layer has been variably referred to as the electroactive layer, the
electrocatalytic layer, or the interlayer. As the microstructure in this region
must be he, which enhances the rate of electrochemical reaction (lowers
activation polarisation), also unfortunately impedes gas transport (increases
concentration polarisation) due to the Knudsen diffusion effects, as well as due
possibly to adsorption/desorption effects. The existence of a critical thickness
fortunately implies that the electrode microstructure need not be fine
throughout the electrode. Thus, the overall polarisation can be minimised by
grading the electrode microstructure such that near the electrolyte/electrode
interface, the electrode has a fine microstructure and exhibits MIEC properties;
and away from the interface, the electrode has a coarse microstructure with a
large pore size, and exhibits essentially electronic conduction.
While the general features of several of the models are similar, the particular
analytical expressions, wherever available, vary widely depending upon the
details of a given model. In what follows, some of the equations from the work of
Tanner et a1 for composite cathodes are given to illustrate the role of various
parameters [2 71. In the low current density limit, over which the Butler-Volmer
equation can be linearised, the effective charge transfer or the polarisation
resistance (activation polarisation only) for cathode interlayer thickness greater
than the critical thickness can be given by [22]

In the case of a single phase MIEC, the reaction may be regarded as that of oxygen incorporation (or
removal) rather than that of charge transfer.