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, N-TB, 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 N-TB phase has the same macroscopic symmetry as another periodic mesophase, the chiral smectic-A, SmA*. Based on this N-TB/SmA* analogy, we develop a coarse-grained elastic model for the N-TB phase. Adopting one of the existing microscopic N-TB 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 N-TB coarse-grained elasticity is opposite to that of the SmA*, leading probably to different configurations of some of the defects of the layered N-TB structure. Moreover, we argue that the intrinsic chiral frustration of the N-TB phase may be resolved by penetration of the twist field into the bulk through a network of screw dislocations of the N-TB pseudo-layers, resulting in a twist-bend analogue of the twist grain boundary phase TGBA.