Page 277 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

2 54 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

The concentration of adsorbed oxygen [O,,] and the corresponding surface
vacancy concentration [SI depend on the oxygen partial pressure in the gas
phase p(Oz) for given rate constants kads, k,,, kdes and kred. Their actual values
depend on the microstructural properties of the cathode surface and the
interface and on temperature while the oxygen concentration [Oox] and
the oxygen vacancy concentration [Vo**] in the electrolyte are given by the
compositions of the materials. The reaction rate constants kred and k,, consist of
a potential-dependent and a part given by the activation potential AG:of the
form

where B is the symmetry factor of the interface and the other constants have
their usual meanings. Therefore, the net Faradaic current ip that passes through
the interface depends exponentially on the overvoltage q (Butler Volmer-type
behavior [26]).
In the model, the quantity x = [o,d]/No denotes the oxygen surface coverage.
No = [s] + toad] is the concentration of active oxygen sites on the LSM surface. Its
value is given by the rates of surface exchange and charge transfer at the
interface and depends on the operating conditions and on the materials
parameters. By combining equations (29) and (30), the mass and charge
balances for oxygen in the TPB-region can be expressed as

where F is the Faraday constant, I,, is the TPB-length of the electrode/
electrolyte/gas phase and w is the lateral extension of the TPB-region. Usually,
the magnitude of w is not known, but can still be included as a parameter. For a
given equilibrium potential difference, AQe, and known rate constants, the
equilibrium surface coverage x is determined using the above relations.
According to this model, the static characteristic ip(q) obeys Butler-Volmer
behavior not too far from equilibrium. Under high polarisation, the current is
limited by the surface adsorption process. Models of this type are discussed in
greater detail in references [ 16,481 and literature referenced there in.
The evaluation of the non-linear iF(q)-characteristics given by equation (33) is
mathematically difficult. Therefore, the static polarisation curves are usually
linearised and subjected to Fourier transformation that yields an expression of
the Faradaic impedance Z, of the interface for the given operating point.