The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or pseudo-layers, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining layer compression and bending ought to be characterized by an effective layer compression elastic constant $B_{eff}$ and average director splay constant $K_1^{eff}$. The magnitude of $K_1^{eff}$ is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, $B_{eff}$ could differ substantially from the typical value of $sim 10^6$ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the pseudo-layer structure of the TB phase with $B_{eff}$ in the range $sim 10^3-10^4$ Pa. We show additionally that the temperature dependence of $B_{eff}$ at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director.
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