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.
Highlights
The Poisson-Nernst-Planck (PNP) equations have been used to describe a wide range of transport phenomena from electrons and holes in semiconductors to ions in electrolytes. [1,2,3,4,5,6,7,8,9] The conservation of charge for each ion species and electrostatic interactions among charge carriers are treated by the PNP equations in a self-consistent manner
For certain cases, approximate analytical solutions have been obtained for strong electrolytes. [2, 3, 8,9,10,11,12,13] Using the PNP equations, it has been shown that the spatial dimensions of concentration gradient can be many orders of magnitude larger than the characteristic length scale of charge density profiles given by the Debye length in strong electrolytes. [1,2,3,4, 13]
We study charge transport induced by electrode reactions in weak electrolytes using the extended PNP (e-PNP) equations without assuming a priori charge neutrality
Summary
The Poisson-Nernst-Planck (PNP) equations have been used to describe a wide range of transport phenomena from electrons and holes in semiconductors to ions in electrolytes. [1,2,3,4,5,6,7,8,9] The conservation of charge for each ion species and electrostatic interactions among charge carriers are treated by the PNP equations in a self-consistent manner. [26,27,28,29,30,31] Our results indicate that the ion density gradients can be characterized by the Kuramoto length when both cations and anions are discharged at the electrode in binary monovalent weak electrolytes. For this case, ion density drop caused by electrode reactions is recovered by ion density fluctuations localized within the Kuramoto length. We discuss the overpotential related to a charge density gradient near the electrode and show that it can be reduced when both cations and anions are discharged at the electrode
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