Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques

Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director n. The nematic director field n(r) of a chiral twist-bend nematic (NTB) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in NTB phases, and find that the predilection of curved rods to diffuse in the direction of the twisting n(r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the NTB phase thereby connecting its structural and dynamical properties.