Role of the linear elastic term in the spatial derivatives of the nematic director in a 1D geometry

The role of the linear elastic term in the spatial derivatives of the nematic director on the director field is analysed. We consider a nematic sample in the shape of a slab, confined by two surfaces treated to induce homeotropic alignment. It is shown that this term can be responsible for spontaneous Fréedericksz transitions. The connection between the linear term and the flexoelectric contribution, associated with a surface field, to the bulk energy density, is discussed. The importance of dielectric anisotropy on the spontaneous Fréedericksz transition is also investigated.