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) K24 and K13 terms on stability of the uniform ground state of a nematic phase. It is shown that the K13 term can effectively boost the action of the K24 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, K11 and K24 are the standard Nehring-Saupe elastic constants, and K*13 is the effective elastic constant of the layer.