Critical Nuclei Size, Rate, and Activation Energy of H₂ Gas Nucleation

Abstract

Electrochemical measurements of the nucleation rate of individual H bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H nuclei leading to stable bubbles. Precise knowledge of the H concentration at the electrode surface, C, is obtained by controlled current reduction of H in a HSO solution. Induction times of single-bubble nucleation events are measured by stepping the current, to control C, while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s) over a very small relative change in C (0.21-0.26 M, corresponding to a ∼0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ∼150° with the electrode surface and contain between 35 and 55 H molecules.

Initial growth dynamics of 10 nm nanobubbles in the graphene liquid cell

“…The radius of first appeared nanobubbles are all similar and about 5-10 nm (denoted as arrows). This value is similar with the previous result ~ 5 nm obtained from the electrochemical measurement of the hydrogen nanobubble nuclei on the Pt nanoelectrode (German et al 2018). It implies that the first appearance of the nanobubble on the TEM window is related with the nucleation event.…”

The Nucleation Rate of Single O2 Nanobubbles at Pt Nanoelectrodes

“…Now we can measure the nucleation rate at different supersaturation levels, which are directly controlled by the applied current. 29 We chose to control current rather than voltage because the experiment is very sensitive to any drift in the voltage. For example, in the region very close to i nb p , a change of 20 mV generated a change of 8% in current, as can be seen in Figure 6 a, in which we plot a voltammogram for O 2 nanobubble nucleation.…”

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

“…The bulk component term is proportional to the bubble volume 4/3 3 and to the free energy difference between the gaseous and dissolved state in that volume, ΔGV, leading to: where ( ) = (1 + ) 2 (2 − )/4, θ being the contact angle (through the liquid phase) between the gas-liquid interface and the solid substrate. 54 We may define a critical radius for diffusive stability of a bubble in a supersaturated solution (not growing or shrinking), below which the bubble dissolves due to surface tension effects (i.e., the Laplace pressure, cf. Equation 3).…”