Emergence of Nanoscale Modulation in Liquid Crystals from Short-Range Order Parameter Condensation

Nanoscale-modulated nematic phases formed by bent-core and dimeric molecules raise the question of how a new periodic structure can emerge within an already orientationally ordered nematic state. In this note we discuss a Landau phenomenological interpretation in which a short-range orientational order parameter condenses at a finite wave vector. The resulting state is a helicoidal, nanoscale-modulated nematic associated here with the polar-twisted nematic (NPT), rather than with the macroscopic twist–bend nematic (NTB) proposed by the late R. B. Meyer. The distinction is essential: Meyer’s NTB is an elasticity-based modulation of the apolar nematic director on macroscopic length scales, whereas NPT describes molecular-scale modulation of a locally polar order parameter. The central idea is that condensation of the additional short-range order parameter, rather than softening of the conventional Frank elasticity itself, provides the primary mechanism for the transition to the nanoscale-modulated state. The resulting finite-wave-vector ordering is analogous in spirit to the de Gennes description of the nematic–smectic-A transition. We further discuss fluctuation effects and the associated Goldstone mode, and indicate how the same finite-wave-vector condensation framework may also be viewed as a phenomenological route toward the theoretically predicted macroscopic NTB state, provided that the relevant order parameter and length scale are changed.