Parametric Study and Mathematical Modeling of the Hydrogen Evolution Reaction: Application to Mildly Acidic Environments Containing Acetic Acid on a Gold Surface
Authors: Kahyarian Aria , Nesic Srdjan 
Published: February 2020

The present study utilizes a computational parametric study and a continuum scale mathematical model to investigate the mechanism and the kinetics of the hydrogen evolution reaction in the mildly acidic environments in the presence of acetic acid (HAc). Such environmental condition is of great interest in the metallic corrosion field of study where a comprehensive knowledge of the mechanism and kinetics of the underlying electrochemical reactions are essential for development of accurate predictive models.
The metallic corrosion in aqueous acidic solutions consists of two dominant electrochemical reactions, the metal dissolution reaction, which results in deterioration of the structure, and the hydrogen evolution reaction (HER) which provides the necessary electron sink for the former reaction to spontaneously progress. In the context of metallic corrosion, for example, the inner pipeline corrosion of oil and gas transmission lines, the hydrogen evolution reaction is not limited to the hydrogen ion (H+) reduction. In this case, the weak acids such as acetic acid are also commonly assumed to be reduced at the metal surface, although its significanec has been debated [1]. This reaction can also be categorized as a hydrogen evolving reaction, where 2HAc+2e-→H2+2Ac- . Additionally, as a weak acid the concentration of the undissociated acetic acid in the solution is defined by the chemical equilibrium, HAc↔ H++Ac-. Therefore, HAc can act as an additional source for H+ at the surface and hence, increase the rate of cathodic currents [2]. Considering this system of electrochemical and chemical reactions, the following mechanistic aspects needs to be determined: a) the mechanism of the HER from H+ based on the elementary Volmer, Tafel, Heyrovsky, and surface diffusion step. b) The significance of HAc reduction, where either a CE (HAc dissociation followed by H+reduction) or an EC (HAc reduction followed by HAc association) mechanism could be expected. C) If HAc reduction was significant, the mechanism of HAc reduction based on the elementary steps.
A computational parametric study for HER reaction, based on the known elementary steps was developed similar to that introduced in an earlier publication [3]. Considering the experimentally obtained apparent Tafel slope and reaction order on a rotating disk gold electrode in perchlorate solutions in the pH range from 3 to 5 and HAc concentrations up to 1000 ppm, the mechanism of the HER from H+ was discussed. The results suggest that the rate of HER from H+ was limited by the surface diffusion step at low current densities, and by the Heyrovsky desorption step at the high current densities. A comprehensive mathematical model was used to analyze the experimental polarization curves and to obtain the kinetic rate constants of the elementary steps HER from H+. This model accounts for the mass transfer by molecular diffusion, electro migration and conceive flow as well as the chemical equilibria of water and HAc. The boundary conditions at the electrode surface account for the elementary reactions associated with the HER and also the coverage by the intermediate adsorbed hydrogen atoms. This same model was then used to analyze the experimental results in the presence of HAc. The results suggest that HAc is not significantly reduced during the cathodic polarizations, implying that a CE mechanism governs this system.
This study demonstrated the application of a parametric study and mathematical modeling to investigate the mechanism and the kinetic of the HER reaction. This same theoretical framework can be used in future studies to provide valuable information on the mechanism of cathodic reactions on other surfaces and also in the solutions containing other weak acids such as carbonic acid and hydrogen sulfide.

References

[1] A. Kahyarian, M. Singer, S. Nesic, Modeling of Uniform CO2Corrosion of Mild Steel in Gas Transportation Systems: a Review, J. Nat. Gas Sci. Eng. 29 (2016) 530–549. doi:10.1016/j.jngse.2015.12.052.
[2] A. Kahyarian, B. Brown, S. Nesic, Mechanism of Cathodic Reactions in Acetic Acid Corrosion of Iron and Mild Steel, Corrosion. 72 (2016) 1539–1546. doi:http://dx.doi.org/10.5006/2177.
[3] A. Kahyarian, B. Brown, S. Nesic, Mechanism of the Hydrogen Evolution Reaction in Mildly Acidic Environments on Gold, J. Electrochem. Soc. 164 (2017) 365–374. doi:10.1149/2.1061706jes.