Higher-order surface free energy in azimuthal nematic anchoring on nanopatterned grooves

The higher-order component in liquid crystal (LC) surface free energy beyond the Rapini–Papoular anchoring potential was examined for azimuthal anchoring by analyzing nematic LC alignment on nanogrooved surfaces treated by rubbing or photoalignment. We confirmed that the surface anchoring energy for large director deviations cannot be properly described with the Rapini–Papoular form and should include higher order contributions in a power series of $sin2ϕ$⁠, as $∑n=12Wnsin2nϕ$⁠, with $ϕ$ being the azimuthal angular deviation. Based on the corrected Berreman’s theory, we obtained the anchoring ratio between the first and second order terms, $W2/W1≈−1/4$⁠, and the surface elastic constant, $K24≈−0.846K22$⁠, for 4-n-pentyl-$4′$-cyanobiphenyl.