Chebyshev–Gauss–Lobatto Collocation Method for 1D Diffusion in Holby–Morgan Model of Platinum Degradation

Electrokinetic mechanisms of platinum catalyst degradation in polymer electrolyte membrane fuel cells are represented by platinum ion dissolution and platinum oxide formation. The other primary mechanism of degradation is the diffusion of platinum particles. The governing one-dimensional Holby–Morgan model across the catalyst thickness is described by nonlinear reaction–diffusion equations with Butler–Volmer reaction rates. To approximate properly spatial diffusion, the Chebyshev–Gauss–Lobatto pseudo-spectral collocation method is introduced and tested numerically within implicit–explicit time discretization. The accurate approximation makes it possible to simulate the nonlinear degradation of a platinum catalyst over a long cyclic voltammetry test until it loses its operational capacity.