  A general physics-based model is developed for heterogeneous electrocatalysis
in porous electrodes and used to predict and interpret the impedance of solid
oxide fuel cells. This model describes the coupled processes of oxygen gas
dissociative adsorption and surface diffusion of the oxygen intermediate to the
triple phase boundary, where charge transfer occurs. The model accurately
captures the Gerischer-like frequency dependence and the oxygen partial
pressure dependence of the impedance of symmetric cathode cells. Digital image
analysis of the microstructure of the cathode functional layer in four
different cells directly confirms the predicted connection between geometrical
properties and the impedance response. As in classical catalysis, the
electrocatalytic activity is controlled by an effective Thiele modulus, which
is the ratio of the surface diffusion length (mean distance from an adsorption
site to the triple phase boundary) to the surface boundary layer length (square
root of surface diffusivity divided by the adsorption rate constant). The
Thiele modulus must be larger than one in order to maintain high surface
coverage of reaction intermediates, but care must be taken in order to
guarantee a sufficient triple phase boundary density. The model also predicts
the Sabatier volcano plot with the maximum catalytic activity corresponding to
the proper equilibrium surface fraction of adsorbed oxygen adatoms. These
results provide basic principles and simple analytical tools to optimize porous
microstructures for efficient electrocatalysis.
