Modeling of Electric Double Layer to Analyze Reaction Kinetics
Authors: Shibata Masao Suzuki , Morimoto Yu , Zenyuk Iryna , Weber Adam Z. 
Published: August 2024

Electric double layers (EDLs) play a fundamental role in various electrochemical processes such as colloid dispersion, surface charging, and charge-transfer reactions. Increasingly, the role of EDLs on reaction kinetics is being studied (1). Despite the extensive history of EDL modeling, there remain challenges in accurate prediction of its structure. The characteristic length of EDL (nanometer scale) exceeds the grasp of typical ab-initio molecular-dynamic simulations in order to capture a whole picture of the statistical equilibrium. While continuum models offer a means to estimate the thermodynamic equilibrium of EDLs with substantially lower computational cost than molecular dynamics, state–of-the-art continuum models require parameter fitting(2) due to the lack of appropriate expressions for microscopic interactions.

Herein, we propose a predictive multiscale continuum model of EDL that eliminates the empirical fitting and relies more on physical relations. This model computes the distribution of the electrostatic potential, electron density, and species’ concentrations by minimizing the total grand potential of the system. The grand potential is calculated from entropic energy, electrostatic energy, electron energy, solute-solute interactions, and electrode-solute interactions. These energy expressions include not only the terms from previous work(2), but also the microscopic interactions that are newly introduced in this work: polarization of hydration shells, electrostatic interaction in parallel plane toward the electrode, and ion-size-dependent entropy. The parameters that identify the electrode and electrolyte materials are obtained from independent experiments such as vacuum work function, bulk modulus, X-ray diffraction, and concentration-dependent dielectric constant. The developed model reproduces the trends in the experimental differential capacitance with multiple electrode and electrolyte materials (Ag (111)-NaF, Ag (111)-NaClO4, and Hg-NaF), which verifies the accuracy and predictiveness of the model in a system without significant specific electrode-electrolyte interactions. The difference in the capacitance between mercury and silver electrode was attributed to the difference in the electron stability in the metal that is parameterized from the material’s bulk modulus. Finally, extension of the model to systems with specific electrode-electrolyte interactions (e.g., Pt (111)-NaClO4) and the analysis of reaction kinetics will be introduced. Overall, the model framework and findings will provide insights into the EDL structures and guidance on how to tailor electrode-electrolyte interface for improved reaction kinetics.

Acknowledgements:

This work was partially supported by the Hydrogen and Fuel Cell Technologies Office (HFTO), Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy (DOE) through the Million Mile Fuel Cell Truck (M2FCT) consortia, technology managers G. Kleen and D. Papageorgopoulos, under contract number DE-AC02- 05CH11231, as well as by a CRADA with Toyota Central R&D Labs., Inc. and by the Center for Ionomer-based Water Electrolysis (CIWE), a DOE Energy Earthshot Research Center.

Reference:

S. J. Shin, D. H. Kim, G. Bae, S. Ringe, H. Choi, H. K. Lim, C. H. Choi and H. Kim, Nat Commun, 13, 174 (2022).

J. Huang, J Chem Theory Comput, 19, 1003 (2023).