Modeling, Computation, and Analysis of Complex Liquid Crystal Systems and Transitions

Kent State University, Kent OH

Investigators

Abstract

Gartland DMS-0608670 The investigator carries out numerical modeling of problems in two important new areas of the physics of liquid crystals: (1) mean-field theories for phases of biaxial and bent-core liquid-crystal materials, and (2) numerical solution of macroscopic models for the dynamics and statics of point defects in liquid-crystal systems (in the absence or presence of fluid flow). The investigator uses techniques from modern numerical bifurcation analysis together with the theories of singularities and bifurcations in the presence of symmetry to study the full bifurcation and phase behavior of recent mean-field models for biaxial materials, along with models that he and collaborators are developing for the important new class of bent-core materials. The investigator adapts and extends methods from computational fluids with moving and deforming bodies ("moving overset grid methods") to provide effective techniques to accurately model challenging problems involving the dynamics and statics of point defects in macroscopic liquid-crystal director models, with application to surprising recent physical experiments on defect-pair annihilation in capillaries filled with a liquid-crystal material. Liquid crystals are complex fluids that possess partial molecular orientational order. They can be used to control light, and this feature underlies many of their significant technological applications. In recent years, new liquid-crystal molecules have been synthesized that exhibit certain special phases. These new phases are termed "biaxial," because they have secondary ordering properties in addition to those of the more common "uniaxial" materials. The liquid-crystal community has high hopes for potential new applications of these new materials. The theoretical and experimental study of biaxial liquid crystals is at a relatively early stage. In this project the investigator analyzes a mathematical model for such materials that characterizes the bulk equilibrium state of the system and associated transitions, as a function of control parameters such as temperature. This study requires both mathematical and numerical techniques. In addition, the investigator and collaborators develop new models for the special sub-class of "bent core" liquid crystals, which are of high current interest. The merits of this work are two-fold: (1) validation of the models and (2) the development of predictive tools to aid in the design of experiments and in the identification of parameter ranges for technological applications. The second main topic of the project concerns the numerical modeling of the dynamics of defects in liquid crystals (isolated singularities in the fields that characterize the orientational properties of the medium). Defects are ubiquitous in liquid-crystal systems, and they cause considerable difficulty both from mathematical and numerical points of view. The investigator and co-workers apply numerical procedures from other areas of computational fluid dynamics, both to model numerically a target problem involving the annihilation of a pair of point defects in a capillary tube filled with liquid crystal and to compare these numerical results to recently published experimental data. These techniques (new to the area of liquid crystals) should open the door to a number of other numerical-modeling problems involving defects that have previously been hampered by unphysical numerical artifacts.