Onsager's Real Cavity model near solid interfaces

TL;DR

The paper addresses how dispersion interactions between dissolved molecules and planar solid interfaces are modified by solvent screening and local-field effects within a dielectric continuum. It extends Onsager's real cavity to an open-cavity geometry using a Born-series Green-function approach, yielding a five-region decomposition that connects to the long-range medium-assisted $- ilde{C}_3/z^3$ behavior. Using experimental dielectric data for water, propanol, and PTFE and accurate molecular polarisabilities for O$_2$ and N$_2$, it computes the full distance-dependent CP potential for four combinations and shows how $R_1$, $R_2$, and the frequency-dependent response shape $U_{ m CP}(z)$. The results emphasize strong solvent screening in water, enhanced near-field strength in propanol, and a smooth crossover to the asymptotic regime, providing a principled baseline and outlining directions to incorporate finite-size and multipole effects for ultrashort separations.

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 a closed expression that arises when the molecule approaches a surface and connects them smoothly to the asymptotic medium-assisted interaction. Using experimentally established dielectric functions for water, propanol, and PTFE together with accurate molecular polarisabilities for O2 and N2, we compute the full distance-dependent potential for four molecule (O2 and N2)-liquid (water and propanol)-surface (PTFE) combinations. The results reveal how local-field screening inside the cavity, molecular polarisability, and liquid permittivity jointly determine the magnitude and shape of the interaction, including the characteristic transition from the open cavity (small separations) and closed cavity (large separations). The framework provides a transparent baseline for dispersion forces in liquids, while highlighting limitations associated with the point-dipole description, the absence of repulsive contributions, and the breakdown of the dipole approximation at ultrashort separations.

Figures (3)

• Figure 1: Cross-section through the considered system: a point-particle located at ${\bm{r}}$ embedded in a medium (grey area) with dielectric function $\varepsilon_{\rm L}(\omega)$ creates a vacuum bubble with radius $R_1$ surrounding it. Close to a dielectric interface $\varepsilon_{\rm S}(\omega)$ (hatched area) at a distance $z$, the particle will displace the surrounding media and open the cavity. The single medium particles occupy a spherical volume with a radius $R_2$, leading to the opened cavity illustrated in white, bounded by a profile (red line). To describe the profile mathematically, the centre of the circle of the medium particles is labelled with the coordinates $(z_2,x_2)$, and the touching points are in the plane $z=z_b$. The three-dimensional scenario is a body of rotation around the $z$-axis. To describe the Casimir--Polder interaction between the particle and the surrounding material, the van der Waals interaction must be integrated over the entire volume, split into five regions I--V.
• Figure 2: Dielectric function of water (solid blue line) from Ref. water, propanol (solid orange line) and polytetrafluoroethylene (PTFE) (dashed green line) from Ref. PhysRevA.81.062502 and the normalised polarisabilities for oxygen (dotted red line) and nitrogen (dash-dotted purple line) from Ref. doi:10.1021/acs.jpca.7b10159.
• Figure 3: Casimir--Polder potential between a in water or propanol dissolved oxygen or nitrogen molecule near a PTFE surface. The impact of the potentials within the regions I+II (dash-dotted lines) and III (dash-double-dotted lines) is negligible in water, where as the contribution from region III dominates potential very short separations in propanol. The dominant parts region IV (dashed lines) and V (long dashed-dotted lines) dominate the total potential (solid grey lines). Particle-surface separations, leading to a closing of the cavity, $z\ge z_{\rm C}$ (vertical dotted lines) continue into the medium-assisted Casimir--Polder potential (solid black lines).