An overview over the current state of research in the field of biaxial nematic liquid crystalline materials is given. After a short introduction, providing some general aspects and summarizing the classical approaches, the main part focuses on recent developments of new concepts for designing biaxial nematics. First, the major theoretical concepts are outlined, including the classification to different symmetries, the importance of cooperativity and cluster formation for the development of biaxial order and the conditions for the establishment of field induced and spontaneous biaxiality in nematic phases. These new concepts also require the re-evaluation of the tools used for the identification of phase biaxiality, which are discussed briefly. In the second part, recent progress in the design of potential biaxial nematic materials, especially focussing on bent-core molecules with nematic phases, is reported and, finally, comparisons with phase biaxiality as observed in smectic liquid crystals are made.

We study theoretically the molecular origins of the fascinating, and still debated, nematic–nematic phase transition exhibited by symmetric, statistically achiral, mesogenic dimers. A simple molecular model that mimics the key features and symmetry (C_2V) of this class of mesogens is presented. In the mean-field approximation, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase (N_X) has a local two-fold symmetry axis, which is also a direction of molecular polar ordering and is tightly twisted about a macroscopic phase axis. The onset of polar ordering generates spontaneous chiral symmetry breaking and the formation of chiral domains of opposite handedness, manifested primarily by the twisting of the polar director. Within these domains the statistical balance between the enantiomer conformations is slightly shifted and the principal axes of the ordering tensors of the molecular segments twist at constant tilt angles with the helical axis. Key experimental results on the N_X phase of liquid crystalline dimers are discussed in the light of the theoretical predictions of the model, which are also contrasted with the predictions of the twist-bend nematic model.

A theory of thermotropic nematic liquid crystals in which molecules form internally ordered clusters is presented. The formulation is based on the same molecular-field approximation and form of the anisotropic potential used in the Maier–Saupe theory. One uniaxial nematic and two macroscopically isotropic phases are predicted. The lower-temperature isotropic phase consists of thermodynamically stable clusters with internal orientational order. The transition from this phase to the nematic phase is characterised by the divergence of cluster size whilst the entropy and the order parameter change continuously.

A theoretical model of shape-anisometric particles embedded in a cubic lattice is formulated for binary mixtures combining rod-like, plate-like and spherical particles. The model aims at providing a tool for the prediction and interpretation of complex phase behavior in a variety of liquid crystalline colloids, biological and macromolecular systems. Introducing just repulsive interactions among the particles, a rich variety of phase structures and multiphasic equilibria is obtained, including isotropic, nematic, lamellar and columnar phases, demixing into phases of the same or different symmetries and structural microsegregation of the different species of the mixture within the same phase.

We present tractable molecular theory descriptions of liquid crystalline dendrimers based on clearly defined approximations and in terms of the dominant interactions underlying the self-organisation of these large and complex supermolecular entities. We formulate the configurational partition function for dendrimers, taking explicit account of their conformations and segmental interactions. Two approximate schemes are presented: the first is based on the effective interactions of the dendrimers as a whole while the second scheme is based on the interactions among the mesogenic units contained in the dendrimers. Results of lattice calculations for phase transitions in the context of the first scheme are presented and they show that the minimal inclusion of shape anisotropy and of sub-molecular partitioning into chemically distinct parts is sufficient to reproduce the variety of phases and phase sequences observed experimentally and provides insights into the conformational aspect of these transitions. In the second scheme, the description of the dendromesogenic system reduces to that of an ensemble of mesogenic dimers. This scheme can be readily extended to the description liquid crystalline oligomers and polymers consisting of mesogenic units connected by flexible spacers in various architectures. It thus provides a unified approach for treating mesomorphic phase transitions of supermolecular and macromolecular systems that can be built by connecting the same submolecular units in topologically different ways.

The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely “shrinks down” established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (N_X), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist–bend nematic (N_TB). We show that the N_X is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the N_X phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the N_X and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank–Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist–bend, splay–bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the N_X phase. The latter modulation derives from packing constraints associated with nonlinear molecules—a chiral, locally-polar structural organization indicative of a new type of nematic phase.