Determining the Dielectric Constant of Solid/Liquid Interfaces

TL;DR

This paper derives and experimentally validates a formula for the dielectric constant of solid/liquid interfaces, addressing a key challenge in interfacial water characterization and providing a generalized expression.

Contribution

The authors introduce a new formula for the dielectric constant of buried interfaces and validate it experimentally, filling a gap in interfacial dielectric characterization.

Findings

Derived a formula for interfacial dielectric constant using the slab model.

Validated the formula with vibrational sum frequency generation experiments.

Provided a generalized expression applicable to various solid/liquid interfaces.

Abstract

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_2\left(\varepsilon_2-\varepsilon_1+6\right) / 2\left(2 \varepsilon_2+\varepsilon_1\right)$, 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.