Page 325 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stack and System Modelling 301

depend not only on the materials forming the reaction interface but also on its
microstructure[l3,14].
The reasons for the importance of microstructure are twofold. Electrode
reactions are interfacial reactions, i.e., surface bound, and therefore intrinsically
slow compared with the reactions of gases. Moreover, in an SOFC they must take
place at particular locations on the electrode-electrolyte interface, namely at or
near a triple-phase boundary (TPB), where solid electrocatalyst, electrolyte, and
gaseous reactants or products meet. In a typical SOFC porous electrode, the TPB
is geometrically a serpentine line. The TPB by itself would form an extremely
limited ‘area’ available for electron transfer. However, in SOFC electrodes the
electron transfer step is only one of several steps in a reaction mechanism that
may be quite complicated (as discussed in Chapter 9 and further referred to in
Section 11.8). At the microscopic level, the active area of SOFC electrodes
appears to be a nm-to-pm-wide zone bordering the TPB where surface diffusion of
intermediate reactants or product species occurs. Nevertheless, the entire
internal area of a porous electrode usually is not active. Typically. SOFC
electrodes must have a reaction surface large enough to generate an internal
current density (usually called transfer current density and denoted]) that is two
to four orders of magnitude smaller than the projected (or external) current
density at the electrode. Thus, to reduce the activation losses at an SOFC
electrode, a large internal surface area is needed.
Therefore, in simplified continuum treatment of the electrochemical
performance, e.g., in the potential balance (Eq. (7)), the activation polarisation is
frequently calculated from Eq. (loa) by dividing the projected current density, i,
by a dimensionless quantity, a, which represents the ratio of active internal area
to external area:
j = i/a = io{exp[-azFq,/RT] - exp[(l - ~)ZF~~/RT]) (lob)

The parameter a is specific for a given electrode microstructure and may be
estimated from known or estimated microstructural parameters, physicochemical
surface area measurements (e.g., by the BET technique, yielding total pore
volume), or special-purpose electrochemical measurements (which yield the
product ioa). However, a is rarely known accurately and may vary significantly
with current load. Electrode-level models may be used to determine this variation
and calculate polarisation without recourse to Eq. (lob) (see Section 11.8).
In practice, the activation loss of the SOFC cathode is larger than that of
the anode: that is, the cathode reaction has a smaller ioa than the anode
reaction. In fact, greater kinetic limitation of oxygen reduction than of hydrogen
oxidation is common to all types of fuel cells at high (e.g. 1000cC) as ell as low
(ambient) temperatures.
The concentration polarisation is the voltage loss associated with the
resistance to transport of reactant species to and product species from
the reaction sites. This transport occurs by diffusion because convection is
negligible in the pores of SOFC electrodes. The concentration difference between
the bulk gas and the gas contacting the reaction site forms a concentration cell