Regimes of the lateral van der Waals force in the presence of dielectrics

TL;DR

This paper explores how the lateral van der Waals force regimes change when a neutral anisotropic particle interacts with a corrugated dielectric interface, revealing complex behaviors depending on dielectric permittivities.

Contribution

It extends previous work by analyzing the impact of two different dielectrics on the van der Waals force regimes, uncovering nontrivial behaviors for certain permittivity configurations.

Findings

Regimes are similar to vacuum case when ε2<ε1.

Unexpected nontrivial behaviors occur when ε2>ε1.

Classical polarized particles exhibit similar regime patterns.

Abstract

In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $\epsilon_{1}$ and $\epsilon_{2}$, separated by a corrugated interface. Specifically, we study the vdW interaction between a neutral anisotropic polarizable particle, embedded in the dielectric $\epsilon_{2}$, and the dielectric $\epsilon_{1}$. We show that when $\epsilon_{2}<\epsilon_{1}$ the peak, valley and intermediate regimes have, unless numerical factors, behaviors similar to those found for the situation where the particle is in vacuum and interacting with a conducting medium. For the case $\epsilon_{2}>\epsilon_{1}$, one might expect a mere permute between the peak and valley regimes, in comparison to the case $\epsilon_{2}<\epsilon_{1}$. Surprisingly, we find that when $\epsilon_{2}>\epsilon_{1}$ the regimes exhibit a very different and nontrivial behavior. Moreover, we show that similar regimes arise in the classical case involving a neutral polarized particle. The description of how the peak, valley and intermediate regimes are affected by the presence of dielectrics may be relevant for a better understanding of the interaction between anisotropic particles and corrugated surfaces.