Implicit Nucleation and Competitive Dynamics of Electrogenerated Hydrogen Nanobubbles

TL;DR

The paper addresses the poorly understood nucleation and early evolution of electrogenerated hydrogen nanobubbles and their impact on electrochemical efficiency. It introduces a thermodynamically consistent phase-field framework that unifies dissolved-gas transport, interfacial thermodynamics, and implicit nucleation in a gap-averaged Hele–Shaw geometry. Key findings show that nucleation occurs at about $300\\times$ the equilibrium solubility, growth is diffusion-limited with curvature effects, and in multi-catalyst systems nanobubble interactions produce Ostwald ripening and selective persistence, with survival depending on spatial arrangement. These insights enable electrode designs that create nucleation hubs and feeder sites to minimize transport losses and preserve active area, reframing nanobubbles as controllable features rather than parasitic byproducts.

Abstract

Electrogenerated gas nanobubbles strongly influence the performance of electrochemical energy-conversion systems, yet their nucleation and early evolution remain poorly understood due to limitations of existing experimental and computational approaches. Operando imaging lacks the temporal resolution required to capture nucleation events, while molecular dynamics simulations are restricted to nanometer-scale domains containing at most a few bubbles. Here, we develop a thermodynamically consistent phase-field framework that unifies dissolved gas transport, curvature dependent interfacial thermodynamics, and implicit bubble nucleation within a single continuum description. Using hydrogen nanobubble formation during electrocatalysis as a canonical test case, the model captures nucleation without prescribing nuclei, resolves diffusion-controlled growth under curvature effects, and remains computationally tractable despite hydrogen's extremely low solubility. Simulations reveal how nanobubble nucleation occurs once a local supersaturation threshold is exceeded, triggering a reorganization of the chemical-potential field that focuses dissolved gas toward the nascent bubble. In multi-catalyst systems, overlapping diffusion fields lead to strong bubble-bubble interactions, including competitive growth, Ostwald ripening, and source occlusion. Extending the framework to dispersed catalyst populations shows that nanobubble survival is governed not only by catalyst size but also by spatial arrangement and diffusive competition, such that only a subset of bubbles persist while others dissolve and act as feeders. These results reframe electrogenerated nanobubbles as emergent, spatially organized features rather than unavoidable parasitic byproducts, and point toward electrode designs that deliberately control where bubbles nucleate and grow to preserve active area and mitigate transport losses.

Figures (5)

• Figure 1: Implicit nucleation of a hydrogen nanobubble on a single hydrogen-producing catalyst. (a) Snapshots of the hydrogen mole fraction $c$ (top), gas volume fraction $\phi$ (middle), and variational chemical potential $\psi$ (bottom) at initial, pre-nucleation, and post-nucleation times. The dashed circle denotes the 15 nm catalyst footprint. After nucleation, $\psi$ reorganizes and its gradient reverses relative to the pre-nucleation state, drawing dissolved hydrogen toward the newly formed gas-liquid interface. Consequently, the $c$ field develops a distinct halo surrounding the bubble, delineating the diffusion zone that feeds its growth. (b) Evolution of the area-averaged hydrogen mole fraction $\langle c \rangle_\text{ref}$ for catalyst radii $r_\text{cat}=10,15,30$ nm. Nucleation (asterisks) occurs at a heterogeneous supersaturation threshold of order $300\times$ the equilibrium solubility and is effectively independent of catalyst size. (c) Evolution of the area-averaged gas volume fraction $\langle \phi \rangle_\text{ref}$ for the same catalyst sizes. Larger catalysts nucleate earlier, consistent with their higher hydrogen production rates and faster local buildup of dissolved gas.
• Figure 2: Nanobubble nucleation and growth on a pair of catalysts. (a) Snapshots of the hydrogen mole fraction $c$ (top), gas volume fraction $\phi$ (middle), and variational chemical potential $\psi$ (bottom). The dashed circles denotes the 15 nm (left) and 15.5 nm (right) catalyst footprints. Prior to nucleation, both catalysts generate dissolved H$_2$, which diffuses into the surrounding domain. Nucleation occurs first on the larger catalyst, followed by the smaller one. As the bubbles grow and fully occlude their respective footprints, hydrogen production ceases at both sites. Ostwald ripening then governs the evolution: dissolved hydrgen flows from the smaller, higher-curvature bubble to the larger one until the smaller bubble completely dissoves. Once this occurs, the left catalyst becomes re-exposed to the electrolyte and resumes hydrogen production, which is subsequently captured by the larger bubble, sustaining its continued growth. (b) Bubble radius $R$ provides quantitative signatures of this process, with insets highlighting differences between the two catalysts sites at the moment of nucleation. (c) Phase diagram delineating single- and double-nucleation regimes as a function of percentage size difference $\Delta{r_\text{cat}}$ and imposed areal hydrogen production rate $\dot{n}_g$.
• Figure 3: Nanobubble nucleation and growth in a dispersed catalyst population. (a) Interference reflection microscopy experiments on electrochemically activated Pt nanoparticles reported by Lemineur et al.lemineur2021imaging. Left: nanoparticle positions before (black circles) and after (red circles) electrochemical activation. Right: nanoparticle positions (crosses) and hydrogen nanobubble locations (red circles) following electrochemical activation. Motivated by these observations, we investigate the role of catalyst size polydispersity on nanobubble nucleation and persistence by fixing the mean catalyst footprint radius at 15 nm and considering three levels of size dispersion, corresponding to standard deviations of (b) 0%, (c) 1.3%, and (d) 13%. For each case, the left panels show the spatiotemporal evolution of the hydrogen mole fraction $c$ and gas volume fraction $\phi$, while the right panels show the corresponding bubble radius evolution. Persistent nanobubbles are indicated by solid lines, whereas transient nanobubbles are denoted by dashed lines.
• Figure 4: Bulk excess free-energy densities for the pure liquid (water) phase, $f_l(c)$ (black), and the pure gas (hydrogen) phase, $f_g(c)$ (red), as functions of the hydrogen mole fraction $c$. The common-tangent construction (blue) identifies the equilibrium coexistence compositions in the liquid and gas phases (orange circles). The inset highlights the vicinity of the intersection $f_l(c)=f_g(c)$, which marks the composition at which the global bulk free-energy minimum shifts from liquid-dominated to gas-dominated, providing an estimate of the thermodynamic crossover relevant to nucleation.
• Figure 5: Diffusion-controlled growth of H$_2$ nanobubbles with initial radii of 10, 20, and 40 nm in a large, uniformly supersaturated aqueous bath ($S \approx 300$). Phase-field predictions (solid lines with symbols) show excellent agreement with the Epstein–Plesset analytical solution (gray dashed line) within its regime of validity, corresponding to early times $\tau = 4Dt/R_{0}^{2} \ll 1$.