Page 342 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

3 18 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

where f3 is the CTE, E is the Young’s modulus, v is the Poisson’s ratio, and d is
the half-thickness of the plate. Assuming that the lattice expansion-induced
strain can be treated the same way as the thermal strain, PT, Eq. (32) can be
recast into a stress-isothermal strain relation. The experimental data for the
isothermal expansion characteristics can then be used to obtain the
nonstoichiometry-induced strain. Consequently, the isothermal stress due to
nonstoichiometry can be determined. Delamination will occur if the elastic
energy release rate by crack formation exceeds a critical value where the
critical value is an interface property and must be determined experimentally.
Alternatively, mechanical failure occurs if the thermal stress exceeds a
certain value.

11.8 Electrochemical Models at the Electrode level
Electrode-level models describe the performance of SOFC electrodes in detail.
They take into account the distribution of species concentrations, electric
potential, current, and even temperature in the electrode. Their purpose is to (i)
interpret the performance (polarisation curve) of electrodes in terms of rate-
limiting resistances such as kinetic (activation), mass transfer, and ohmic
resistance: and (ii) predict the local polarisation in full-scale cell and stack
models.
To predict the local polarisation in a full-scale cell or stack at any point, its
dependence on composition, pressure, and temperature of the gas flowing in the
gas channel contacting the electrode must be known. In a large cell, these bulk
gas properties vary from one point to the next. Electrode polarisation or
overpotential - the difference between the local potential of the electrode under
load and the potential at open circuit (equilibrium potential) - is also a local
quantity because it depends not only on the bulk gas composition but also on the
current density. In a large cell the current is usually distributed nonuniformly,
as discussed in Sections 11.2-11.5. Similar to Eq. 7, one can express the local
cell voltage under load, i.e., when current is passed, as the thermodynamic cell
potential minus three loss terms: the ohmic loss, the cathode polarisation, and
the anode polarisation:

V(i) = E,, - iRi - qc - g~ (33)

As discussed in Section 11.2, the total polarisation of each electrode consists of
two contributions, activation polarisation (due to electrode kinetic resistance)
and concentration polarisation (due to mass transfer resistance), so

VC = VCa + VCc and VA VAa + VAc (34)

For cell- and stack-level modelling it is necessary to have reliable values of the
total polarisation of cathode, qc, and anode, qA, as a function of local bulk gas
composition, pressure, and temperature, as well as the local current density.