Page 324 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

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

denoted by E", is therefore called the standard cell potential or standard emf.
It depends only on temperature. In the second term on the right-hand side of
Eq. (Sa), pO2 is an abbreviation of p02,c for notational simplicity. The quantities
PH2 and PH2o are, respectively, the H2 and H20 partial pressures in the anode
fuel channel.
In the most general way, one can express the thermodynamic cell potential of
an SOFC as the cell potential of an oxygen concentration cell using the Nernst
equation:

Eeq = (RT/4F)ln(Po2,c/Po2,a) (Sb)

In Eq (Sb), p02,c and pO2,, represent the oxygen partial pressures in the cathode
air channel and anode fuel channel, respectively. Notice from Eq. (Sb) that air
leakage reduces the open-circuit voltage and is detrimental to cell operation.
Good sealing technology is required to minimise the leakage.
In Eq. (7), Ri represents the total area specific ohmic resistance. Ri is the sum of
the cathode, electrolyte, anode, interconnect, and contact ohmic resistances
expressed in Q m2. Typically, Ri is dominated by the electrolyte resistance and
decreases with increasing operating temperature. To account for any electronic
conductivity in the electrolyte, the effective ohmic resistance should be used in
Eq. (7). The effective conductivity depends on the applied voltage and can be
expressed as a correction to the ionic conductivity, qon, by a term involving the
electronic conductivity, oe as follows [l 1,121:
geff = gion - ce/[exp(2eV/kT) - 1]/[1-exp(-2e(Eo - V)/kT)]} (9)

The final terms in Eq. (7). qc,, qcC, q~, and q~~, cathode activation,
the
are
cathode concentration, anode activation, and anode concentration
polarisations, respectively. In general, their dependence on the current density is
nonlinear, although at low polarisation they may be approximated by linear
relationships.
The activation polarisation terms are controlled by the electrode reaction
kinetics of the respective electrodes. They represent the voltage loss incurred due
to the activation necessary for charge transfer. The activation polarisation, qa, is
usually related to the current density by the phenomenological Butler-Volmer
equation [ 131:

i = io{exp[-azFq,/RT] - exp[(l - a)zFq,/RT]} (104

is
In this equation, io the exchange current density, a is the anodic transfer
coefficient (0 < a < l), and z is the number of electrons participating in the
electrode reaction. The exchange current density corresponds to the dynamic
electron transfer rate at equilibrium, which is thermally activated. Therefore, the
exchange current density can be expressed as io = P, exp(-E,,,/RT), where
the prefactor, P,, and the activation energy, EaCt, are properties specific for the
electrode-electrolyte interface in question. The kinetic properties (io, a, z, P,, E,,,)