Nontouching Nanoparticle Diclusters Bound by Repulsive and Attractive Casimir Forces

We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a molecular two-sphere dicluster geometry consisting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay between material and geometric dispersion, and this is exemplified by the qualitatively different stability behavior observed in planar versus spherical geometries.

Figure 1

Schemes for stable suspension of fluid-separated objects, involving: (a) enclosed geometries; (b) gravity countering Casimir repulsion; and (c) material dispersion producing repulsive and attractive Casimir forces (here).

Figure 2

(Top): Plot of the dielectric permittivity $\epsilon (i\xi )$ of various materials evaluated at imaginary frequency $\xi$ (units of $c/\mu \mathrm{m}$). (Bottom): Casimir force between a semi-infinite slab and a sphere (dots) and Casimir pressure between semifinite slabs (lines), normalized by the corresponding perfect-metal PFA force $F_{\mathrm{PFA}}=\hslash c{\pi }^3/360d^3$ (slab-sphere) and pressure $F_{\mathrm{PFA}}=\hslash c{\pi }^2/240d^4$ (slab-slab). The normalized force is plotted for various material configurations, described in the text.

Figure 3

Equilibrium separation $d_c$ vs sphere-radius ($R$) or slab-thickness ($t$) for various slab-sphere (dots) and slab-slab (lines) configurations. Dashed lines correspond to slab-slab geometries with materials swapped (semi-infinite silicon slab).

Figure 4

(Top:) Plot of the stable equilibrium center-surface ($L_c$) and surface-surface ($h_c$) separation between either a Teflon (red) or silicon (blue) sphere and a semi-infinite gold slab (depicted schematically on the left inset), as a function of sphere-radius $R$. The black lines also show the presence of an unstable equilibrium in the silicon-sphere case. (Bottom:) Plot of the force $F_{SS}$ between two Teflon and silicon spheres of radii $R_T$ and $R_S$ , showing the existence of a stable equilibrium.