Voltammetric Determination of the Stochastic Formation Rate and Geometry of Individual H_2, N₂, and O₂ Bubble Nuclei

Herein, we report a general voltammetric method to characterize the electrochemical nucleation rate and nuclei of single nanobubbles. Bubble nucleation is indicated by a sharp peak in the current in the voltammetry of gas-evolving reactions. In contrast to expectations based on the stochastic nature of nucleation events, the peak current signifying a stable nucleus is extremely reproducible over hundreds of cycles (∼3% deviation). By applying classical nucleation theory, this seemingly deterministic behavior can be not only understood but also used to quantify the nucleation rate and size of bubble nuclei. A statistical model is developed whereby properties of single critical nuclei (contact angle, the radius of curvature, activation energy, and Arrhenius pre-exponential factor) can be readily measured from the narrow distribution of peak currents (mean, standard deviation) from hundreds of voltammetric cycles at a nanoelectrode. Single nanobubbles formed from gas-evolving reactions (H₂ from H⁺ reduction, N₂ from N₂H₄ oxidation, O₂ from H₂O₂ oxidation) are analyzed to find that their critical nuclei have contact angles of ∼150, ∼160, and ∼154° for H₂, N₂, and O₂, respectively, corresponding to ∼50, ∼40, and ∼90 gas molecules in each nucleus. The energy barriers for heterogeneous nucleation of H₂, N₂, and O₂ bubbles are, respectively, 2, 0.4, and 0.7% of those required for homogeneous nucleation under the same supersaturation.