Ionization at a solid-water interface in an applied electric field: Charge regulation

TL;DR

This paper studies how ionization at a solid-water interface responds to applied electric fields, revealing charge regulation mechanisms and effects of cell thickness on surface charge screening.

Contribution

It introduces a model for ionization and charge regulation at solid-water interfaces under electric fields, considering surface chemistry and electrostatic effects.

Findings

Charge regulation depends on electrode surface charge and water pH.

Self-regulation occurs for certain surface charge densities and low ion concentrations.

Partial screening of surface charges leads to internal electric fields when cell thickness is small.

Abstract

We investigate ionization at a solid-water interface in applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density $\Gamma_0$, where the degree of dissociation $\alpha$ is determined by the proton density in water close to the film. We show how $\alpha$ depends on the density $n_0$ of NaOH in water and the surface charge density $\sigma_m$ on the electrode. For $\sigma_m>0$, the protons are expelled away from the film, leading to an increase in $\alpha$. In particular, in the range $0<\sigma_m<e\Gamma_0$, self-regulation occurs to realize $\alpha \cong \sigma_m/e\Gamma_0 $ for $n_0\ll n_c$, where $n_c$ is $0.01$ mol$/$L for silica surfaces and is $2\times 10^{-5}$ mol$/$L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness $H$ below the Debye length $\kappa^{-1}$, where a crossover occurs at the Gouy-Chapman length. In particular, when $\sigma_m \sim e\Gamma_0$ and $H\ll \kappa^{-1}$, the surface charges remain only partially screened by ions, leading to an electric field in the interior.