Fluctuation modes of a twist-bend nematic liquid crystal

We report a dynamic light-scattering study of the fluctuation modes in a thermotropic liquid crystalline mixture of monomer and dimer compounds that exhibits the twist-bend nematic (NTB) phase. The results reveal a spectrum of overdamped fluctuations that includes two nonhydrodynamic modes and one hydrodynamic mode in the NTB phase, and a single nonhydrodynamic mode plus two hydrodynamic modes (the usual nematic optic axis or director fluctuations) in the higher temperature, uniaxial nematic phase. The properties of these fluctuations and the conditions for their observation are comprehensively explained by a Landau-de Gennes expansion of the free-energy density in terms of heliconical director and helical polarization fields that characterize the NTB structure, with the latter serving as the primary order parameter. A "coarse-graining" approximation simplifies the theoretical analysis and enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the mode relaxation rates.