Stripe Domain Phase of a Thin Nematic Film and theK13Divergence Term

To verify the status of the divergence $K_{13}$ term in the elastic theory of liquid crystals we study submicron films placed onto an isotropic fluid substrate in the Langmuir trough (Langmuir liquid crystal, LLC). The upper and lower surfaces favor normal and tangential molecular orientation, respectively. The periodic domain phase is observed in a nematic LLC. The dependence of the periodicity $L$ of the domains vs film thickness $h$ can be explained only if the elastic energy is accompanied by divergence terms with nonzero constants $K_{13}$ and $K_{24}$. It is found that for 5CB $K_{13}\approx -0.2\mathrm{}{K}_{11}$.