Casimir-Lifshitz interaction between ZnO and SiO${}_2$ nanorods in bromobenzene turns repulsive at intermediate separations due to retardation effects

We consider the interaction between a ZnO nanorod and a SiO${}_2$ nanorod in bromobenzene. Using optical data for the interacting objects and ambient we calculate the force (from short-range attractive van der Waals force to intermediate-range repulsive Casimir-Lifshitz force to long-range entropically driven attraction). The nonretarded van der Waals interaction is attractive at all separations. We demonstrate a retardation-driven repulsion at intermediate separations. At short separations (in the nonretarded limit) and at large separations (in the classical limit) the interaction is attractive. These effects can be understood from an analysis of multiple crossings of the dielectric functions of the three media as functions of imaginary frequencies.

Figure 1

The dielectric function at imaginary frequencies for SiO${}_2$ (silica) [41], Bb (bromobenzene) [9], and ZnO (zinc oxide).

Figure 2

The Casimir-Lifshitz interaction energy per unit length between ZnO and SiO${}_2$ nanorods (each with 2-nm diameter) in bromobenzene. The fully retarded free energy is attractive in regions I and III, but turns repulsive in region II. The nonretarded energy and the $n=0$ contribution are both attractive and they decay $\propto R^{-5}$.

Figure 3

The absolute value of the ratio between the retarded and nonretarded interaction free energy per unit length (the nonretarded energy is attractive and $\propto R^{-5}$). The fully retarded free energy is attractive in regions I and III, but turns repulsive in region II.