Elastic deformations in ferroelectric nematic liquid crystals analyzed in terms of a large effective splay elastic constant

The recent discovery of ferroelectric nematic liquid crystals has sparked intense research activities, both with the goal of understanding of the mechanisms behind the formation of the ferroelectric nematic phase and exploring its possible technological potential. A key characteristic of these materials is that the large value of spontaneous electric polarization makes electrostatic contributions to the free energy match, or even dominate over, the elastic contributions. In sample cells that combine one circularly rubbed surface with one linearly aligning surface, ferroelectric nematics form complex domain configurations. In a first approximation these domains can be predicted by assuming in-plane polar anchoring conditions with minimization of the local twist. However, this simple model is insufficient to fully describe the director field close to the center of circular rubbing. Here we also include the impact from splay and bend deformations, as well as from electrostatic contributions to the free energy. In particular we introduce a large effective splay elastic constant to deal with electrostatic avoidance of splay, and we also allow for a non-negligible surface pretilt. Our simulations agree well with previously published experimental results. The electrostatic stiffening (ESS) model might facilitate a simplified, although powerful, strategy for understanding and development of various ferroelectric nematic device cells.