Smectic-like rheology and pseudo-layer compression elastic constant of a twist-bend nematic liquid crystal

In twist-bend nematic (N\textsubscript{TB}) liquid crystals (LCs), the mean molecular orientation exhibits heliconical structure with nanoscale periodicity. On the mesoscopic scale, N\textsubscript{TB} resembles layered systems (like smectics), where the helical pitch is equivalent to "pseudo-layers" without a true mass density wave. We study rheological properties of a N\textsubscript{TB} phase and compare the results with those of an usual SmA phase. Analysing the shear response and adapting a simplified physical model for rheology of defect mediated lamellar systems we measure the pseudo-layer compression elastic constant $B_{eff}$ of N\textsubscript{TB} phase from the measurements of dynamic modulus $G^{*}(\omega)$. We find that $B_{eff}$ of the N\textsubscript{TB} phase is in the range of $10^{3}-10^{6}$ Pa and it follows a temperature dependence, $B_{eff}\sim (T_{TB}-T)^{2}$ as predicted by the recent coarse-grained elastic theory. Our results show that the structural rheology of N\textsubscript{TB} is strikingly similar to that of the usual smectic LCs although the temperature dependence of $B_{eff}$ is much faster than smectic LCs as predicted by the coarse-grained models.