Complex materials often exhibit a hierarchical structure with an intriguing mechanism responsible for the ‘propagation’ of order from the molecular to the nano- or micro-scale level. In particular, the chirality of biological molecules such as nucleic acids and amino acids is responsible for the helical structure of DNA and proteins, which in turn leads to the lack of mirror symmetry of macro-bio-objects. To fully understand mechanisms of cross-level order transfer there is an intensive search for simpler artificial structures exhibiting hierarchical arrangement. Here we present complex systems built of achiral molecules that show four levels of structural chirality: layer chirality, helicity of a basic repeating unit, mesoscopic helix and helical filaments. The structures are identified by a combination of hard and soft x-ray diffraction measurements, optical studies and theoretical modelling. Similarly to many biological systems, the studied materials exhibit a coupling between chirality at different levels.

In recent years there are several reports showing that bent-core mesogenic molecules are able to form biaxial nematic phase in which molecular rotation around the long molecular axis is strongly hindered. The x-ray pattern with azimuthally split signals at low angle region of diffraction is usually given as evidence for the biaxial nematic phase. We show experimentally and theoretically that such x-ray pattern is due to the local smectic-$C$ fluctuations (“cybotactic” groups) in the uniaxial nematic phase.

Periodic structures of phases with orientational order of molecules but homogenous electron density distribution: short pitch cholesteric phase, blue phase and twist-bend nematic phase, were probed by resonant soft X-ray scattering (RSoXS) at the carbon K-edge.

We studied the dielectric properties of a polar nematic phase (N_F) sandwiched between two gold or ITO electrodes, serving as a cell surface. In bulk, N_F is expected to exhibit a Goldstone mode (phason), because polarisation can uniformly rotate with no energy cost. However, because the coupling between the direction of nematic director and polarisation is finite, and the confinement, even in the absence of the aligning surface layer, induces some energy cost for a reorientation of polarisation, the relaxation frequency of the phason mode is measured in a kHz regime. The phason mode is easily quenched by a bias electric field, which enables fluctuations in the magnitude of polarisation to be followed in both the ferroelectric and paraelectric nematic phases. This amplitude (soft) mode is also influenced by boundary conditions. A theory describing the phase and amplitude fluctuations in the N_F phase shows that the free energy of the system and, consequently, the dielectric response are dominated by polarisation-related terms with the flexoelectricity being relevant only at a very weak surface anchoring. Contributions due to the nematic elastic terms are always negligible. The model relates the observed low-frequency mode to the director fluctuations weakly coupled to polarisation fluctuations. GRAPHICAL ABSTRACT