Local distortion energy and coarse-grained elasticity of the twist-bend nematic phase.

The recently discovered twist-bend nematic phase of achiral bent-shaped molecules, NTB, has a doubly degenerate ground-state with a periodically modulated heliconical structure and unusual distortion elasticity, the theoretical description of which is still debated. We show that the NTB phase has the same macroscopic symmetry as another periodic mesophase, the chiral smectic-A, SmA*. Based on this NTB/SmA* analogy, we develop a coarse-grained elastic model for the NTB phase. Adopting one of the existing microscopic NTB elastic models, we calculate the coarse-grained elastic constants, coherence and penetration lengths in terms of a few Frank-like nematic elastic coefficients that can be measured in macroscopic experiments. The same coarse-grained approach, applied to different local elastic models, may provide an efficient experimental test of their validity. We show that the anisotropy of the NTB coarse-grained elasticity is opposite to that of the SmA*, leading probably to different configurations of some of the defects of the "layered" NTB structure. Moreover, we argue that the intrinsic chiral frustration of the NTB phase may be resolved by penetration of the twist field into the bulk through a network of screw dislocations of the NTB pseudo-layers, resulting in a twist-bend analogue of the twist grain boundary phase TGBA.