# Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson--Nernst--Planck equations involving ionization in a weak electrolyte

## TL;DR

This study explores how the Kuramoto length influences ion concentration and charge density profiles in weak electrolytes during photo-catalytic water splitting, using Poisson--Nernst--Planck equations without assuming charge neutrality.

## Contribution

The paper introduces analytical expressions linking ionization, ion association, and length scales like Kuramoto and Debye lengths in weak electrolytes.

## Key findings

- Ion concentration profiles depend on ion transport and ionization.
- Kuramoto length characterizes the ion density gradient.
- Charge density gradient is described by the Debye length.

## Abstract

We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson--Nernst--Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the total ion density gradient was given by the Kuramoto length which characterized the distance over which an ion diffuses before association. The charge density gradient is characterized by the Debye length for 1:1 weak electrolytes. We discuss the role of these length scales for efficient water splitting reactions using photo-electrocatalytic electrodes.