Elasticlike Contribution of Electric Origin to the Distortion Free Energy of Nematics

Ions dissolved in nematics screen the flexoelectric polarization induced by distortions. I show that for long-range distortions (long compared to the Debye length), the free energy associated with these effects varies as the fourth power of the distortion wave vector. This free energy has a magnitude at least 10⁵ times larger than elastic energy of identical order. The equilibrium equations involve, besides a modified stress tensor, a new tensor representing the force conjugated to the second gradients of the deformation.