Abstract
The local pH value at an electrochemical interface (pHs) inevitably changes during redox reactions involving the transfer of H+ or OH− ions. It is important to quantitatively estimate pHs during polarization, as this parameter has a significant impact on the activity and selectivity of electrochemical reactions. Numerical simulation is an effective means of estimating pHs because it is not subject to experimental constraints. As demonstrated in a number of studies, pHs can be estimated by solving partial differential equations that describe diffusion process. In the present work, we propose a method to consider the process by using ordinary differential equations (ODEs), which can significantly reduce the computational resources required for estimating pHs values. In the ODE-based model, the description of the diffusion process was achieved by considering the reaction plane in the diffusion layer over which the H+ and OH− concentrations are balanced while assuming that the concentration profiles in the layer are in a steady state. The resulting model successfully reproduces experimental voltammograms characterized by local pH changes in association with the hydrogen evolution and hydrogen peroxide reduction reactions.
Highlights
Electrochemical interfaces are regions in which electrical energy is directly converted to chemical energy or vice versa
The present work successfully developed an ordinary differential equations (ODEs) model that can generate simulated pHs values for various electrochemical reactions
Numerical calculations employing this model were able to predict increases in pHs during the hydrogen evolution reaction (HER) at a Pt electrode in H2SO4 solutions. This process suitably reproduced the experimental results, including the appearance of a current plateau originating from the limited diffusion of H+ ions and the occurrence of direct water reduction at low potentials (−1.8 V or lower). Our model has another significant advantage in that it is generally applicable to various reactions by replacing the reaction term, rH (Eq 16)
Summary
Electrochemical interfaces are regions in which electrical energy is directly converted to chemical energy or vice versa. Mayrhofer’s group established the fundamental physicochemical relationship between current density and the total diffusive flux of ions within a diffusion layer (Auinger et al., 2011; Katsounaros et al, 2011) In this prior work, increases in pHs during the hydrogen evolution reaction (HER) were estimated from the current density, and the electrode potential was calculated by substituting the calculated pHs values into the Nernst equation. Increases in pHs during the hydrogen evolution reaction (HER) were estimated from the current density, and the electrode potential was calculated by substituting the calculated pHs values into the Nernst equation This same study calculated ion distributions in the diffusion layer. We anticipate that the ODE model developed in the present work will provide valuable insights into dynamic changes of pHs during electrocatalytic reactions
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