Electrochemistry of single nanobubbles. Estimating the critical size of bubble-forming nuclei for gas-evolving electrode reactions

In this article, we address the fundamental question: What is the critical size of a single cluster of gas molecules that grows and becomes a stable (or continuously growing) gas bubble during gas evolving reactions? Electrochemical reactions that produce dissolved gas molecules are ubiquitous in electrochemical technologies, e.g., water electrolysis, photoelectrochemistry, chlorine production, corrosion, and often lead to the formation of gaseous bubbles. Herein, we demonstrate that electrochemical measurements of the dissolved gas concentration, at the instant prior to nucleation of an individual nanobubble of H-2, N-2, or O-2 at a Pt nanodisk electrode, can be analyzed using classical thermodynamic relationships (Henry's law and the Young-Laplace equation - including non-ideal corrections) to provide an estimate of the size of the gas bubble nucleus that grows into a stable bubble. We further demonstrate that this critical nucleus size is independent of the radius of the Pt nanodisk employed (<100 nm radius), and weakly dependent on the nature of the gas. For example, the measured critical surface concentration of H-2 of similar to 0.23 M at the instant of bubble formation corresponds to a critical H-2 nucleus that has a radius of similar to 3.6 nm, an internal pressure of similar to 350 atm, and contains similar to 1700 H-2 molecules. The data are consistent with stochastic fluctuations in the density of dissolved gas, at or near the Pt/solution interface, controlling the rate of bubble nucleation. We discuss the growth of the nucleus as a diffusion-limited process and how that process is affected by proximity to an electrode producing similar to 1011 gas molecules per second. Our study demonstrates the advantages of studying a single-entity, i.e., an individual nanobubble, in understanding and quantifying complex physicochemical phenomena.