外加电场中固体-水界面的电离：电荷调节
Ionization at a solid-water interface in an applied electric field: Charge regulation
摘要：
本文研究了外加电场作用下固体-水界面的电离。我们将电极连接到带有面密度为$Γ_0$的硅烷醇或羧基的介电膜上，其中解离度$Γ_0$由靠近膜的水中的质子密度确定。我们展示了$α$如何依赖于NaOH在水中的密度$n_0$和电极上的表面电荷密度$σ_m$。对于$σ_m>0$，质子从膜中排出，导致$α$增加。特别地，在$0<σ_m<eΓ_0$的范围内，发生自调节以实现对于$n_0\ll n_c$的$α\cong σ_m/eΓ_0 $，其中对于二氧化硅表面，$n_c$是$0.01$ mol $/$ L，对于带有羧基的表面，$n_c$是$2\times 10^{-5}$ mol $/$ L。我们还研究了电荷调节与降低细胞厚度$H$低于德拜长度$κ^{-1}$，其中交叉发生在Gouy-Chapman长度。特别地，当$σ_m \sim eΓ_0$和$H\ll κ^{-1}$时，表面电荷保持仅部分地被离子屏蔽，导致内部的电场。
英文摘要：
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 $Γ_0$, 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 $n_0$ of NaOH in water and the surface charge density $σ_m$ on the electrode. For $σ_m>0$, the protons are expelled away from the film, leading to an increase in $α$. In particular, in the range $0<σ_m<eΓ_0$, self-regulation occurs to realize $α\cong σ_m/eΓ_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 $κ^{-1}$, where a crossover occurs at the Gouy-Chapman length. In particular, when $σ_m \sim eΓ_0$ and $H\ll κ^{-1}$, the surface charges remain only partially screened by ions, leading to an electric field in the interior.
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