van der Waals contribution to the surface and anchoring energies of nematic liquid crystals

Abstract

Using a continuum theory, analytical expressions are derived for the van der Waals contribution to the surface and anchoring energies of nematic liquid crystals. The results depend on an effective molecular separation parameter $d$, whose experimental determination is critically discussed. For liquid crystals in contact with a solid of refractive index ${n}_{s}$, it is found that a planar alignment is favored for small ${n}_{s}$ and a hemeotropic alignment for large ${n}_{s}$. Between ${n}_{s}=1.35 \mathrm{and} 2.5$, the van der Waals contribution $\ensuremath{\Delta}\ensuremath{\gamma}$ to the anchoring energy changes by several erg/${\mathrm{cm}}^{2}$, which is of the same order as the total anchoring energy, so that the general trend is expected to survive in the presence of other than dispersive contributions. Around ${n}_{s}=1.5$, $\ensuremath{\Delta}\ensuremath{\gamma}$ is small, and other than dispersive contributions are likely to dominate the anchoring energy.