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

ABSTRACT

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 divergence $K_{13}$ term. 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 elastic $K_{13}$ and $K_{24}$ terms. 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 nonzero $K_{13}$ term and for $K_{24}$ term violating Ericksen’s stability condition for the uniform director ground state. The effective boundary condition and procedure of the free energy minimisation for arbitrary $K_{13}$ and $K_{24}$ are derived. It is shown how Ericksen’s condition is modified by the presence of the $K_{13}$ term, anchoring, and spatial boundedness. An example of the surfacelike-elasticity-induced spontaneous modulations of the uniform director ground state is presented.

GRAPHICAL ABSTRACT

KEYWORDS:

• Nematic free energy
• surfacelike elasticity
• spontaneous distortions
• boundary conditions

Acknowledgments

The author is grateful for financial support via (Polish) National Science Center Grant No. 2019/34/E/ST2/00289 and hospitality of the Polish Academy of Sciences and the Center for Theoretical Physics PAS.

Disclosure statement

No potential conflict of interest was reported by the author.