Nematic phases with spontaneous splay-bend deformation: standard elastic description

Recently, possible deformed states in nematic liquid crystals have been discussed assuming that Frank's bend elastic constant is negative. The presence of a stable deformed state has been justified by introducing in the elastic energy density a term proportional to the second derivative square of the deformation parameter. This term, widely used in field theory, has been introduced in the elastic theory of liquid crystals mainly to investigate the effect of the splay-bend term in the nematic deformation in confined samples. Nevertheless, in the analysis of bulk properties this term is questionable. An alternative justification of possible spontaneous distortions in nematic liquid crystals is proposed. Our description of the elastic properties is based on an elastic energy density expanded to the fourth order in the deformation parameter. In this framework, we show that a stable nematic state characterised by a uniform deformation, related to a position-independent elastic energy density, is possible