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 $\Delta G_{max}$ decreases with increasing supersaturation $\zeta$, following a power-law scaling of $\Delta G_{max} \sim \zeta^{-2}$, while the critical nucleus radius $R_c$ scales as $R_c\sim \zeta^{-1}$. 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.