Spontaneous deformations of the uniform director ground state induced by the surfacelike elastic terms in a thin planar nematic layer

We study the effect of the divergence (surfacelike) K-24 and K-13 terms on stability of the uniform ground state of a nematic phase. It is shown that the K-13 term can effectively boost the action of the K-24 term. As a result, even if the two Ericksen stability conditions are satisfied, spontaneous deformations can occur in geometries with a sufficiently small volume-to-surface ratio. For a specific example, we show that this mechanism can destabilize the uniform planar director field in a thin nematic layer with planar anchoring and produce spontaneous periodic director modulation. The critical thickness below which the predicted modulated phase occurs is found to be h(c) = - 2L(a)[1 -(1 - 2K(24)/K-11)(2) + K-13*/K-11], where L-a is the polar anchoring extrapolation length, K-11 and K-24 are the standard Nehring-Saupe elastic constants, and K-13* is the effective elastic constant of the layer.