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The nematic surface violates the translational symmetry of unrestricted medium and induces novel elastic effects. An ideal surface, where the nematic order parameter and density vanish abruptly, induces the surface elastic term that cancels out the Nehring-Saupe divergenceterm. A more realistic, nonideal surface is represented by a thin layer where the order parameter and density smoothly vary from their bulk values to zero. This surface is shown to induce additional contributions to the effective surface elasticandterms. These terms are no longer total divergences which is employed to incorporate them in the elastic theory. It is shown how the higher order elasticity and the finite surface layer provide the lower free energy bound both for nonzeroterm and forterm violating Ericksen’s stability condition for the uniform director ground state. The effective boundary condition and procedure of the free energy minimisation for arbitraryandare derived. It is shown how Ericksen’s condition is modified by the presence of theterm, anchoring, and spatial boundedness. An example of the surfacelike-elasticity-induced spontaneous modulations of the uniform director ground state is presented.

Continuum theory of a nematic liquid crystal with a nonideal physical surface and the surfacelike elasticity