Predicting Elastic Properties of Liquid Crystals from Molecular Simulation

The elastic behavior of liquid crystalline materials plays an important role in the design of responsive electrical, mechanical, and optical devices. This dissertation focuses on developing, extending, and implementing sampling methods to predict the elastic properties of liquid crystals from molecular simulation. The utility of molecular simulation in predicting elastic properties of liquid crystals has historically been limited due to the immense time and length scales needed to generate accurate estimates of quantities such as the bulk elastic moduli. A recently proposed free energy perturbation method was shown to overcome many of these limitations and produce reliable estimates of the elastic constants. However, there remained a number of challenges to be addressed which would eliminate the use of approximations and extend the technique to molecular systems.

We begin by introducing uniaxial nematic liquid crystals and Frank elastic theory. Next, a series of studies of increasing complexity investigating the elastic properties of liquid crystal systems are presented. First, we perform comprehensive study of binary liquid crystal mixtures represented by the multicomponent Lebwohl-Lasher lattice model. Then we use density-of-states simulations to systematically study the elastic properties of four common Gay--Berne nematogenic models. The third study investigates the elastic and thermodynamic properties of chromonic liquid crystals which exhibit a unique self--assembly process. Finally, we present the first direct simulations of the bulk and surface-like elastic constants for molecular 4-5-alkyl-4'-cyanobiphenyl which challenge indirect experimental observations that suggest spontaneous elastic curvature in certain geometries.