Onsager's Real Cavity model near solid interfaces

Abstract

We develop an extended Onsager real-cavity framework to describe the Casimir--Polder interaction of small molecules dissolved in dielectric liquids near planar interfaces. By analytically resolving the geometry of the cavity opening, we derive closed-form expressions that capture the modification of the interaction as the molecule approaches a surface and connect smoothly to the asymptotic medium-assisted limit. Using experimentally established dielectric functions for water, propanol, and PTFE together with accurate molecular polarisabilities for O$_2$ and N$_2$, we compute the full distance-dependent potential for representative molecule--liquid--surface combinations. The results reveal how local-field screening, cavity geometry, and material response jointly determine both the magnitude and shape of the interaction, including the characteristic transition between open-cavity ($z\lesssim z_{\rm C}$) and closed-cavity ($z\gtrsim z_{\rm C}$) regimes. Beyond providing quantitative predictions, the framework offers an analytically transparent decomposition of dispersion forces in liquids, enabling a direct identification of the underlying physical contributions and an efficient exploration of parameter dependencies across different systems. The approach thus provides a useful baseline for interpreting dispersion interactions in complex environments within a continuum, local-field corrected description.