Free-Energy Analysis of Bubble Nucleation on Electrocatalytic Surfaces

Abstract

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 $ΔG_{max} \sim ζ^{-2}$, while the critical nucleus radius $R_c$ scales as $R_c\sim ζ^{-1}$. 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.

Figures (4)

• Figure 1: Sketch of a system with a mixture of gas molecules and water without a bubble (a) and with a bubble (b). The red dots represent the gas molecules, the blue area represents water, and the white area denotes the bubble. The solution is in contact with a gas phase, depicted in grey. The contact angle, radius, and height of the bubble are denoted as $\theta$, $R$, and $h$, respectively.
• Figure 2: (a) Energy difference $\Delta G$ as a function of bubble radius $R$ at supersaturation $\zeta=100$ for different contact angles $\theta=0^{\circ}$ (blue), $\theta=60^{\circ}$ (orange), $\theta=120^{\circ}$ (green), $\theta=160^{\circ}$ (red). (b) Activation energy as a function of the contact angle $\theta$ (symbols). The solid line represents the function $\Delta G_{max} = C_0(2+3\cos \theta-\cos^3\theta)$, where $C_0=\Delta G_{max}^{\theta=0^{\circ}}$ is the activation energy at contact angle $\theta=0^{\circ}$.
• Figure 3: (a) Energy difference $\Delta G$ as a function of bubble radius at contact angle $\theta=85^{\circ}$ for different supersaturations $\zeta=5$ (blue), $\zeta=10$ (orange), $\zeta=100$ (green), $\zeta=1000$ (red). (b) Activation energy $\Delta G_{max}$ and (c) critical nucleus size $R_c$ as a function of the supersaturation $\zeta$.
• Figure 4: a) Schematic illustration of the anode side of PEMWE. The gas (red circles) diffuses away through the catalyst layer (light green) and the porous transport layer (dark blue) to a water channel (light blue). The bottom part (light grey) represents the membrane. The side and the top parts (dark grey) denote the bipolar plates. b) Sketch of bubble formation and gas transport in a catalyst layer. Bubbles (white) preferentially nucleate in the larger pores and at the CL–PTL interface, while in smaller pores, gas is generated and diffuses toward larger pores and the CL–PTL interface.