Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

It is generally accepted that the transition into the twist–bend nematic phase (NTB) is driven by an elastic instability related to the reduction of the bend elastic constant. Here we use a molecular–statistical theory to show that sufficiently strong polar interactions between bent–shaped molecules may lead to experimentally observed reduction of the bend elastic constant in the nematic phase even if electrostatic dipole-dipole interactions are not taken into account. We propose a simple model of bent–core particles and derive explicit analytical expressions which enable one to understand how polar molecular shape affects the elastic constants, and, in particular, the important role of the bend angle. Numerical graphs showing temperature variations of all elastic constants are also presented including the variation of the bend and splay elastic constants before and after the renormalization determined by local polar order of molecular steric dipoles and the corresponding polar correction to the one–particle distribution function.