Free-energy analysis of bubble nucleation on electrocatalytic surfaces

Bubble nucleation at catalyst surfaces plays a critical role in the operation of electrolyzers. However, achieving controlled bubble nucleation remains challenging due to limited understanding of the underlying mechanisms. Here, we present a free-energy model that quantitatively predicts both the activation energy and critical nucleus size of bubbles at given supersaturation, temperature, pressure, and surface wettability. We find that the activation energy ΔG_max decreases with increasing supersaturation ζ, following a power-law scaling of ΔG_max ∼ ζ^-2, while the critical nucleus radius R_c scales as R_c ∼ ζ^-1. Our theoretical predictions for the critical nucleus radius of hydrogen, oxygen and nitrogen bubbles are in quantitative agreement with experimental measurements. Finally, we present a simple model that couples gas diffusion and electrochemical reaction kinetics to determine the maximum gas supersaturation at a given current density. Our results advance the fundamental understanding of bubble nucleation at catalyst surfaces and provide practical guidelines for catalyst layer design to improve the performance of electrolyzers.