An analytical model of hydrogen evolution and oxidation reactions on electrodes partially covered with a catalyst.

Our previous theoretical study on the performance limits of the platinum (Pt) nanoparticle catalyst for the hydrogen evolution reaction (HER) had shown that the mass transport losses at a partially catalyst-covered planar electrode are independent of the catalyst loading. This suggests that the two-dimensional (2D) numerical model used could be simplified to a one-dimensional (1D) model to provide an easier but equally accurate description of the operation of these HER electrodes. In this article, we derive an analytical 1D model and show that it indeed gives results that are practically identical to the 2D numerical simulations.