Determining the Dielectric Constant of Solid/Liquid Interfaces

The dielectric constant ($varepsilon^{prime}$) of interfacial water is an important parameter, but its measurement has posed challenges, and no consensus has been reached on a generalized expression. We derived a formula for $varepsilon^{prime}$ of a buried interface using the slab model for a half-solvated sphere: $ varepsilon^{prime}=varepsilon_1 varepsilon_2left(varepsilon_2-varepsilon_1+6 ight) / 2left(2 varepsilon_2+varepsilon_1 ight)$, where $varepsilon_1$ and $varepsilon_2$ are the dielectric constants of the solid and liquid phases, respectively. We experimentally validated this expression using vibrational sum frequency generation and Fresnel factor calculations for interfaces of alumina with water ($ mathrm{H_2O} $ and $ mathrm{D_2O} $) and acetonitrile. This fills an important knowledge gap in the description of the dielectric constant of interfaces.

界面水的介电常数（$\varepsilon^{prime}$）是一个重要参数，但其测量具有挑战性，并且对于一个通用表达式尚未达成共识。我们使用半溶剂化球体的平板模型推导出了一个埋藏界面的$\varepsilon^{prime}$公式：$\varepsilon^{prime}=\varepsilon_1\varepsilon_2(\varepsilon_2 - \varepsilon_1 + 6) / 2(2\varepsilon_2 + \varepsilon_1)$，其中$\varepsilon_1$和$\varepsilon_2$分别是固相和液相的介电常数。我们通过振动和频产生以及菲涅耳因子计算，对氧化铝与水（$H_2O$和$D_2O$）以及乙腈的界面进行了实验验证。这填补了界面介电常数描述中的一个重要知识空白。