Determining the Dielectric Constant of Solid-Liquid Interfaces

The dielectric constant 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 the interfacial dielectric constant of a buried interface using the slab model for a half-solvated sphere: ϵ^{'}=ϵ_{1}ϵ_{2}(ϵ_{2}-ϵ_{1}+6)/2(2ϵ_{2}+ϵ_{1}), where ϵ_{1} and ϵ_{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 neutral alumina with water (H_{2}O and D_{2}O) and CH_{3}CN. This fills an important knowledge gap in the description of the dielectric constant of interfaces.