All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals.

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.