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

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.

1D Mathematical Modelling of Non-Stationary Ion Transfer in the Diffusion Layer Adjacent to an Ion-Exchange Membrane in Galvanostatic Mode

“…The boundary-value problems involving these equations are mathematically complicated, since a small parameter is present in the Poisson equation (in its dimensionless form) [ 1 ]. The most models are developed for the potentiostatic mode, where electric regime is set through the potential difference between two equipotential planes enveloping an electrode/membrane and parallel to it [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. The relationship between the local electric potential and ion concentrations is given by the Poisson equation.…”

“…The study was based on the numerical solution of the NPP equations with a boundary condition, which allowed setting the total current density as the parameter governing the electric regime in the system. Unlike potentiostatic (potentiodynamic) models [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ], where the potential difference was set, in Reference [ 27 ] the time derivative of the electric potential gradient at the outer edge of the diffusion layer was specified as an explicit function of the current density.…”