In gas evolving systems, such as water electrolysis, the surface reactions on the electrode produces gas which is dissolved in the liquid surrounding the electrode. The continuous surface reaction leads to supersaturation of the liquid. In order to recover thermodynamic equilibrium, a fraction of the dissolved gas phase separates to form a bubble, a phenomena denoted as nucleation. Apart from electrochemical systems, this process is also observed during opening of a carbonated beverage, boiling and cavitation.

In a seminal paper by Jones et al., four types of nucleation mechanisms in supersaturated systems are described [1]. Type 1 or homogeneous nucleation occurs in the liquid bulk at high levels of supersaturation, while type 2, or heterogeneous nucleation, happens at surface imperfections like pits and cavities at slightly lower levels of supersaturation compared to Type 1. Type 3, or pseudo-classical nucleation, utilizes pre-existing gas cavities that have radius smaller than the critical radius predicted by the classical theory ( r^c =−2 γ /ΔG_v , where γ is surface tension between the liquid and gas phase and ΔG_v is the Gibbs free energy required to form a gas bubble). This mechanism still requires to overcome an energy barrier to form the interface, albeit lower than types 1 and 2. Type 4, or non-classical nucleation, occurs at pre-existing gas cavities whose radius of curvature is larger than the critical radius, effectively reducing the energy barrier to zero.

All of the modes of nucleation have been used to explain experimental observations in saturated systems [1-3]. Considering modeling of electrochemical systems, the main proposed approach appears to be based on Type 4 nucleation as the energy barrier for nucleation is seldom considered [4,5]. In the current work, we describe the thermodynamics of the different types of nucleation, aiming to provide a theoretical framework to describe gas evolution on electrodes.

The framework to explain nucleation is developed using a Helmholtz energy description of the gas-liquid solution, the interface and bubble. The interface is assumed to be diffused across a thickness and the associated free energy is calculated based on gradient theory [6]. The scenarios corresponding to Type 1, 2 ,3 and 4 nucleation are analyzed such that the change in free energy of the system is analyzed based on the difference in free energies before and after nucleation. The main assumptions used in the analysis are that the spatial distribution of molecules in both solution and gas bubble is always uniform (no gradient in concentration and other properties). Secondly, the number of molecules that gets converted into gaseous state is the same in all scenarios. Finally, the addition of a gaseous molecules into the pre-existing bubble does not alter its volume or morphology (for Type 4 nucleation).

The bubble’s behavior (nucleation, growth and detachment) on the electrode effects its current distribution and exposure of the surface to electrolyte which are critical in electrochemical processes like electrowinning, chlor-alkali process, etc. The bubble behavior has also been shown to adversely effect the electrode by removing the catalyst coatings [7]. Understanding the nucleation process provides insight into the plausible sites on electrode where the bubbles subsequently grow
and detach, which is crucial in designing durable and efficient electrodes. This paper provides a thermodynamic and physical reasoning to explain the different nucleation energy requirement in each mechanism, corresponding to those predicted by Jones et al. [1] under certain reasonable approximations.

References:
1. Jones S.F., Evans G.M., Galvin K.P., Bubble nucleation from gas cavities - a review, Advances in Colloid and Interface Science, Vol. 80 (1), 1999, pp 27-50
2. German S.R., Edwards M.A., Chen Q., Liu Y., Luo L., White H.S., Electrochemistry of single nanobubbles. Estimating the critical size of bubble-forming nuclei for gas-evolving electrode reactions, Faraday Discussions, Vol 193, 2016, 223-240
3. Novak B.R., Maginn E.J., McCready M.J., Comparison of heterogeneous and homogeneous bubble nucleation using molecular simulations, Physical Review B, Vol 75, 2007, 085413
4. Lubetkin S.D., Why Is It Much Easier To Nucleate Gas Bubbles than Theory Predicts?, Langmuir, Vol 19 (7), 2003, 2575-2587
5. Maciel P., Nierhaus T., Van Damme S., Van Parys H., Deconinck J., Hubin A., New model for gas evolving electrodes based on supersaturation, Electrochemistry Communications, Vol. 11 (4), 2009, pp 875-877
6. Cahn J.W., Hilliard J.E., Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics, Vol 28 (2), 1958, pp 258-267
7. Kibsgaard J., Gorlin Y., Chen Z., Jaramillo T.F., Meso-Structured Platinum Thin Films: Active and Stable Electrocatalysts for the Oxygen Reduction Reaction, Journal of the American Chemical Society, Vol. 134 (18), 2012, pp 7758-7765