Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal.

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, Beff could differ substantially from the typical value of similar to 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 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.