Curvature elasticity of nematic liquid crystals: simply a matter of molecular shape? Insights from atomistic modeling

The elastic moduli of low-molar-mass thermotropic liquid crystals (LCs) exhibit an intriguing dependence on the molecular structure of the constituents, which can be very important for applications. We have recently developed a molecular field theory, wherein the elastic constants of nematics are expressed in terms of integrals over the molecular surface. This theory, combined with molecular geometry optimization, allows us to connect mesoscale deformations in liquid crystals to atomic-scale details. Here we investigate typical mesogenic systems, i.e. para-azoxyanisole (PAA) and 4-n-alkyl,-4'-cyanobiphenyls (nCBs), whose elastic properties exhibit clear differences. We show that these can be traced back to differences in molecular shape. Our calculations also highlight the importance of the flexibility of mesogens, which was generally ignored by previous theories: in view of their different shape, conformers are shown to give different contributions to the elastic constants. The key role of deviations from a rod-like shape, which is generally assumed by models of mesogens, emerges from our calculations. The bend elastic constant is shown to be particularly sensitive to this feature; for a given compound, rod-like conformers give a high contribution to the bending stiffness, whereas the contribution of bent conformers is low or even negative. The possible implications of these findings are discussed, with special reference to the behavior of bent-core mesogens. Finally, we predict the temperature dependence of the surface-like elastic constants, whose experimental determination is still controversial; we find that these are generally smaller than the bulk moduli and even more sensitive to changes in the molecular shape.