Molecular simulation and theory of liquid crystals: chiral parameters, flexoelectric coefficients, and elastic constants

We present an overview of the simulation methods available to calculate the phenomenological coefficients which appear in the Frank free energy of nematic liquid crystals: the elastic constants, helicity parameter, and flexoelectric coefficients. We concentrate on approaches which are based on measuring and correlating molecular orientational stresses, as these have not received much attention previously, and their statistical mechanical basis seems not to be widely understood. We relate methods which rely on applying external fields or distortions to methods which rely on static equilibrium correlations, highlighting some of the unresolved problems, and presenting some new results and perspectives.