Smecticlike rheology and pseudolayer compression elastic constant of a twist-bend nematic liquid crystal

Abstract

In twist-bend nematic (${N}_{\mathrm{TB}}$) liquid crystals (LCs), the director (mean molecular orientation) exhibits heliconical structure with nanoscale periodicity. On the mesoscopic scale, ${N}_{\mathrm{TB}}$ resembles layered systems (like smectics) without a true mass density wave, where the helical pitch is equivalent to a ``pseudolayer.'' We study rheological properties of a ${N}_{\mathrm{TB}}$ phase and compare the results with those of a usual smectic-$A$ phase. Analyzing the shear response and adapting a simplified physical model for the rheology of defect-mediated lamellar systems, we measure the pseudolayer compression elastic constant ${B}_{\mathrm{eff}}$ of the ${N}_{\mathrm{TB}}$ phase from the measurements of the dynamic modulus ${G}^{*}(\ensuremath{\omega})$. It is found that ${B}_{\mathrm{eff}}$ of the ${N}_{\mathrm{TB}}$ phase is in the range of ${10}^{3}$--${10}^{6}$ Pa and it follows a temperature dependence, ${B}_{\mathrm{eff}}\ensuremath{\sim}{({T}_{\mathrm{TB}}\ensuremath{-}T)}^{2}$, as predicted by the recent coarse-grained elastic theory. Our results show that the structural rheology of ${N}_{\mathrm{TB}}$ LCs is strikingly similar to that of the usual smectic LCs, although the temperature dependence of ${B}_{\mathrm{eff}}$ is much faster than that of smectic LCs as predicted by the coarse-grained models.