Determining the Dielectric Constant of Solid/Liquid Interfaces

The dielectric constant (${\epsilon }^{\mathrm{\prime }}$) 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 ${\epsilon }^{\mathrm{\prime }}$ of a buried interface using the slab model for a half-solvated sphere: ${\epsilon }^{\mathrm{\prime }}={\epsilon }_1{\epsilon }_2({\epsilon }_2-{\epsilon }_1+6)\mathrm{/}2(2{\epsilon }_2+{\epsilon }_1)$, where ${\epsilon }_1$ and ${\epsilon }_2$ 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 (${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$) and acetonitrile. This fills an important knowledge gap in the description of the dielectric constant of interfaces.