Beyond the Rigid Static Models for Liquid Crystals: Flexible or Active Particles

In the present work we study the dynamics of non-rigid or of active particles dispersed in liquid crystals. This is important to develop the theoretical tools needed to interpret experimental data from a variety of techniques, such as fluorescence depolarization and magnetic resonance. In the first part of the thesis the dynamics of non-rigid particles is studied in the roto-diffusional framework, where the particle movements are described by a random walk in an anisotropic medium. The interaction between the solvated particles and the liquid crystal host is handled through an effective field potential, which is, in turn, shape dependent. This treatment allowed us to develop expressions to calculate any time correlation function related to changes in shape and/or orientation. We expect that the availability of this framework will provide an incentive for the development of experimental techniques in this field. In the second part of the thesis, a study of active particles suspended in a liquid crystal host, formed from normal non active mesogens, was performed using molecular dynamics simulations. We modeled both type of particles as uniaxial ellipsoids interacting with a Gay-Berne potential. The distinction between active and passive particles is done by adding a propelling non conservative force to the equation of motion of the former. We found that the long range order of the liquid crystals host can induce the self assembly of active particles in lanes , clusters of particles flowing in the same direction. We also showed that the thermal energy added by the active particles increases the sample temperature, which in turn reduce the orientational order of the host. In particular no laning is obtained from active particles in an isotropic host.