Abstract
This thesis focuses on the liquid crystal phase transitions of colloids with anisotropic shapes such as rods, boomerangs, and cuboids. Colloids are solute particles with dimensions in the range from several nanometers to a micrometer that are suspended in a solvent. These colloids experience Brownian motion due to collisions with
... read more
solvent particles, and so explore their configuration space. The colloids can form analogous phases to molecular systems, such as liquid and crystal phases as well as intermediate so-called liquid crystal phases. For example, a liquid crystal phase commonly formed by long rodlike colloids, the nematic phase has long-range orientational order but no positional order. The phase that the colloids form depends on the thermodynamic properties such as number density as well as the interactions between the colloids. We focus on repulsive colloidal interactions, namely "hard" interactions due to the fact that the colloids cannot overlap. The equilibrium phase behavior is calculated for a given system using the theoretical framework of density functional theory within the second or third virial approximation. In Chapter 2, we study the phase behavior of weakly and strongly charged hard rodlike colloids. Additionally, we investigate the stability of the nematic phase with respect to twist deformations. We then shift our focus to hard particles of various shapes less symmetric than rods. In Chapter 3, we study flexible "boomerangs," i.e., two rods joined at one end that can fluctuate around a certain preferred interarm angle. Here our focus is on biaxial nematic phases and how flexibility affects their stability. In Chapter 4, we investigate the homogeneous phases of rigid boomerangs as well as their limit of stability with respect to smectic phases by performing a bifurcation analysis. In Chapter 5, we study the prolate, oblate, and biaxial nematic phases of cuboids within second and third-virial theory, and compare our results to recent simulations. Then, in Chapter 6 we consider the sedimentation of a binary mixture of thick and thin rods, and build "stacking diagrams," which describe the sequences of phases that appear due to gravity. Finally, in Chapters 7 and 8, we study the percolation transitions of various shapes of colloidal particles in the isotropic phase. Specifically, in Chapter 7 we investigate the effect of kink and bend deformations on the percolation threshold of rodlike particles and in Chapter 8 we calculate the percolation thresholds of polygonal rods and platelet
show less
