A Molecular Theory of the Nematic-Nematic Phase Transitions in Mesogenic Dimers

We present a simplified molecular model of mesogenic dimers consisting of two identical uniaxial mesogenic cores separated by a fixed-length spacer and allowed to assume only two, statistically equivalent, conformations which are non-planar and of opposite handedness. In the mean-field approximation, with additive interactions among the mesogenic cores, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase ($\mathrm{N_X}$) 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, manifested primarily by the twisting of the polar director and the formation of chiral domains of opposite handedness. Within these domains the statistical balance between the two enantiomer conformations is shifted and the principal axes of the ordering tensors of the molecular segments twist at constant tilt angles with the helix axis. Key experimental results on the $\mathrm{N_X}$ 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.