Intermolecular Casimir-Polder forces in water and near surfaces

The Casimir-Polder force is an important long-range interaction involved in adsorption and desorption of molecules in fluids. We explore Casimir-Polder interactions between methane molecules in water, and between a molecule in water near ${\mathrm{SiO}}_2$ and hexane surfaces. Inclusion of the finite molecular size in the expression for the Casimir-Polder energy leads to estimates of the dispersion contribution to the binding energies between molecules and between one molecule and a planar surface.

Figure 1

Polarizabilities of methane in units of Å${}^3$ in water and in vacuum. Note that the polarizability of methane is to a large degree isotropic and we show therefore only the mean average. The polarizabilities corresponding to $n=0$ are shown on the $y$ axis. Also shown are the dielectric functions of hexane and ${\mathrm{SiO}}_2$.

Figure 2

Comparing the series-expanded and the nonexpanded theories of interaction of two methane molecules in water. The interaction energy is in units of $k_{B}T$.

Figure 3

Casimir-Polder energy of methane in units of $k_{B}T$ near water-${\mathrm{SiO}}_2$ interface with and without finite-size effects. Note that including the effects of finite size removes the divergence at zero separation distance.

Figure 4

Comparing the Casimir-Polder energy of finite-sized methane in water near different surfaces. ${\mathrm{SiO}}_2$ surface attracts the methane molecule while hexane and air surfaces repulse it.

Figure 5

Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole contributions to the interaction between two methane molecules in vacuum.