Transport in solid oxide porous electrodes: Effect of gas diffusion

We extend our previous treatment of a mixed ionic electronic conductor membrane, consisting of a porous cathode and anode separated by a thin non-porous layer, to the case where mass transport of molecules in the porous electrodes can be the rate-limiting step. The linearized transport equations for the ion-hole pairs in the solid and of the gas molecules in the pores are characterized by the length scales L_P = √L_d(1 ? φ)/Sτ_s and L_g = 2L_p√τ_sφ/τ(1 ? φ)]D_gc_g/D_IEc_i] respectively, where L_d = D_IE/K is the length scale that determines the transition from diffusion limited to surface exchange limited transport in the non-porous electrodes, K is the surface exchange coefficient, D_IE and D_g are the diffusion coefficients of the ion-hole pairs and of the molecules, c_i and c_g are the concentrations of the ions and molecules, S is the pore surface area per unit volume, φ the porosity and τ_s and τ the tortuosities of the solid and pore phases respectively. When L_g L_p, which is the case treated previously, the rate-limiting step in the transport is ionic diffusion and surface exchange. Enhancements in oxygen ion current of two orders in magnitude, over non-porous electrodes, are in principle achievable with porous perovskite MIEC having surface area s = 10⁶ cm^?1. When L_g L_p the rate-limiting step is mass transport in the pores and the enhancement in ion current is substantially reduced.