Microscopic modelling of nematic elastic constants beyond Straley theory

Recent findings on various classes of nematics, whose microscopic structure differs from the prototypical rod-like shape, evidence unusual elastic properties, which challenge existing theories. Here we develop a theoretical and numerical methodology for the calculation of Frank elastic constants, accounting for the coupling between the molecular shape and each specific deformation mode. This is done in the framework of Onsager-Straley's second-virial theory, using a non-local form of the orientational distribution function. The comparison between two benchmark systems, a straight and a bent rod, allows us to illustrate the distinct features of this approach, which include additional order parameters induced by the deformation and, related to this, an ideal contribution to the deformation free energy. Then, using a simple system that can be seen as a minimalist model of liquid crystal trimers, we discuss the impact of different molecular conformations on elastic constants.

Automated summary

This study introduces a theoretical and numerical methodology for calculating Frank elastic constants by considering the coupling between molecular shape and specific deformation modes. A comparison between two benchmark systems highlights the distinct features of this approach, including additional order parameters and ideal contribution to deformation free energy. The impact of different molecular conformations on elastic constants is discussed using a simple system that serves as a minimalist model of liquid crystal trimers.