A stochastic geometry based model for total triple phase boundary length in composite cathodes for solid oxide fuel cells

An analytical equation is derived for total triple phase boundary length per unit volume (LTPB) in an isotropic uniform random microstructure of LSM/YSZ composite cathode. The equation is applicable to YSZ and LSM particles of any convex shapes and size distributions. The equation explicitly relates LTPB to the shapes, mean sizes, coefficient of variation (a measure of the spread in a size distribution) and skewness of YSZ and LSM particle populations, and volume fractions of YSZ, LSM, and porosity. The equation is verified using available experimental data, and compared with the results of earlier simulations and models. The parametric analysis reveals that (1) non-equiaxed plate-like, flake-like, and needle-like YSZ and LSM particle shapes can yield substantially higher LTPB; (2) mono-sized YSZ and LSM powders lead to higher LTPB as compared to the powders having size distributions with large coefficient of variation; (3) LTPB is inversely proportional to the mean sizes of YSZ and LSM particles; (4) high value of LTPB is obtained at the lowest porosity volume fraction that permits sufficient connectivity of the pores for gas permeability; and (5) LTPB is not sensitive to the relative proportion of YSZ and LSM phases in the regime of interest in composite cathode applications.