Molecular structure and elastic properties of thermotropic liquid crystals: integrated molecular...

The connection between the molecular structure of liquid crystals and their elastic properties, which control the director deformations relevant for electro-optic applications, remains a challenging objective for theories and computations. Here, we compare two methods that have been proposed to this purpose, both characterized by a detailed molecular level description. One is an integrated molecular dynamics-statistical mechanical approach, where the bulk elastic constants of nematics are calculated from the direct correlation function (DCFs) and the single molecule orientational distribution function [D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1973)]. The latter is obtained from atomistic molecular dynamics trajectories, together with the radial distribution function, from which the DCF is then determined by solving the Ornstein-Zernike equation. The other approach is based on a molecular field theory, where the potential of mean torque experienced by a mesogen in the liquid crystal phase is parameterized according to its molecular surface. In this case, the calculation of elastic constants is combined with the Monte Carlo sampling of single molecule conformations. Using these different approaches, but the same description, at the level of molecular geometry and torsional potentials, we have investigated the elastic properties of the nematic phase of two typical mesogens, 4'-n-pentyloxy-4-cyanobiphenyl and 4'-n-heptyloxy-4-cyanobiphenyl. Both methods yield K3(bend) >K1 (splay) >K2 (twist), although there are some discrepancies in the average elastic constants and in their anisotropy. These are interpreted in terms of the different approximations and the different ways of accounting for the structural properties of molecules in the two approaches. In general, the results point to the role of the molecular shape, which is modulated by the conformational freedom and cannot be fully accounted for by a single descriptor such as the aspect ratio.