Sign of the Casimir-Polder interaction between atoms and oil-water interfaces: Subtle dependence on dielectric properties

We demonstrate that Casimir-Polder energies between noble gas atoms (dissolved in water) and oil-water interfaces are highly surface specific. Both repulsion (e.g., hexane) and attraction (e.g., glycerine and cyclodecane) is found with different oils. For several intermediate oils (e.g., hexadecane, decane, and cyclohexane) both attraction and repulsion can be found in the same system. Near these oil-water interfaces the interaction is repulsive in the nonretarded limit and turns attractive at larger distances as retardation becomes important. These highly surface specific interactions may have a role to play in biological systems where the surface may be more or less accessible to dissolved atoms.

Figure 1

Geometry considered: an atom immersed in water near an interface with an oil.

Figure 2

Dielectric functions of water  [6], hexane, decane, cyclohexane, cyclodecane, and glycerine  [13] for imaginary frequencies. Near the quasistatic limit the permittivity of water rises to $77.9$, whereas the same limit for glycerine is substantially lower.

Figure 3

Excess polarizability of dissolved noble gas atoms in water at imaginary frequencies. The static excess polarizabilities do not fit neatly on the graph. Because the static dielectric function of water is so large it gives negative values for the static excess polarizability. The results (in Å${}^3$) for He, Ne, Ar, and Kr are $-0.1375$, $-0.2655$, $-1.0045$, and $-1.7351$, respectively.

Figure 4

Retarded Casimir-Polder energy between noble gas atoms dissolved in water near a water-hexadecane interface.

Figure 5

Retarded and nonretarded Casimir-Polder energy between krypton atoms dissolved in water near different water-oil interfaces. We study in this figure the following oils: hexane, hexadecane, and glycerine.

Figure 6

Retarded Casimir-Polder energy between krypton atoms dissolved in water near different water-oil interfaces. We study in this figure the following oils: hexane, decane, cyclohexane, and cyclodecane.