Page 259 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

236 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

measurable parameters, analytical expressions for cathodic concentration
polarisation have been derived which allow its explicit determination as a
function of a number of parameters. As with the anode, one of the important
parameters is the cathode-limiting current density, which is the current density
at which the partial pressure of the oxidant, e.g. 02, at the cathode/electrolyte
interface is near zero such that the cell is starved of oxidant. Depending upon the
contributions of the other terms, such a condition may not be realised in cell
operation. However, if this condition is realised during operation, then the
voltage precipitously drops to near zero. This cathode-limiting current density,
i,, has the following form [6]

The effective cathode diffusivity contains the binary diffusivity of the relevant
species, Do2-~*, the volume fraction of porosity in the cathode, Vv(c), and
tortuosity, t,. In terms of the current density, i, and the cathode limiting current
density, ics, cathodic concentration polarisation can be given by [6]
rlconc --g+-;)
-

For comparable cathode and anode thicknesses and microstructures, the
anodic concentration polarisation is usually much lower than cathodic
concentration polarisation for two reasons: (1) The binary diffusivity of H2-H20,
DH~-H~o is about four to five times greater than the binary diffusivity of 02-N2,
2,
Do2-~2, due to the lower molecular weight of H2 compared to the other species:
(2) Typical partial pressure of hydrogen in the fuel, pg2, is much larger than the
typical partial pressure of oxygen in the oxidant,fO2. Thus, for comparable anode
and cathode thicknesses and microstructures, the anode-limiting current
density is much greater than the cathode-limiting current density, i.e., i,, >> its.
In practice, one of the electrodes is thicker than the other in an electrode-
supported design. In anode-supported design, the anode thickness is much
greater than the cathode thickness, i.e., 1, >> l,, and in such a case, often
i,, =- ias. However, even in anode-supported design, often cathode concentration
polarisation can be comparable to anode concentration polarisation. Figure 9.2
shows the estimated cathodic concentration polarisation as a function of current
density for a 50 micron thick cathode with different amounts of carbon added to
generate various amounts of porosities [8]. The relevant effective diffusivities
through porous cathodes required for the estimation of concentration
poIarisation were experimentally measured.
Similar anode concentration polarisation curves can be generated using
equation (1 0) for various anode effective diffusivities. In practice, the fuel almost
always is a reformed (at least partially) hydrocarbon. In such a case, internal

Or for that matter that of H2-CO (DH~-co and H2-02 (DH*-C~)
)