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

We investigate ionization at a solid-water interface in an applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density Γ0, where the degree of dissociation α is determined by the proton density in water close to the film. We show how α depends on the density n0 of NaOH in water and the surface charge density σm on the electrode. For σm > 0, the protons are expelled away from the film, leading to an increase in α. In particular, in the range 0 < σm < eΓ0, self-regulation occurs to realize α ≅ σm/eΓ0 for n0 ≪ nc, where nc is 0.01 mol/L for silica surfaces and is 2 × 10(-5) mol/L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness H below the Debye length κ(-1), where a crossover occurs at the Gouy-Chapman length. In particular, when σm ∼ eΓ0 and H ≪ κ(-1), the surface charges remain only partially screened by ions, leading to a nonvanishing electric field in the interior.