Microphase segregation and twisting transitions in liquid crystal polymers.

摘要

This dissertation is a collection of five related journal articles, each exploring some aspect of the theory of polymers and liquid crystal polymers. In the first article, Lamellar Ordering in Symmetric Diblock Copolymers, the lamellar period and interphase thickness of an incompressible melt of symmetric diblock copolymers are calculated numerically, from the weak segregation limit to the strong segregation limit. An analytic expression for the lamellar period, valid in the neighborhood of the weak segregation limit, is also derived. In the second article, Nematic Ordering and Microphase Segregation in a Diblock Polymer-Liquid Crystal Polymer, a theory of nematic ordering and microphase segregation in an incompressible melt of AB diblock copolymers is developed, for the case when the A block is a polymer composed of isotropic monomers, and the B block is a main chain liquid crystal polymer composed of freely-jointed rod-like nematogens. Various segregation morphologies are considered, and a phase diagram--revealing both morphological and isotropic-nematic transitions--is presented. In the third article, Twisting Transition in a Capillary Filled with Chiral Smectic-C Liquid Crystal Polymer, a capillary filled with the chiral smectic-C phase of a main chain liquid crystal polymer is considered. Due to steric constraints, a line disclination appears along the capillary axis. The tendency for chiral twisting competes with boundary conditions at the capillary wall, and the disclination line can shift away from the axis and twist into a helix. The fourth article, Twisting Transition in a Fiber Composed of Chiral Smectic-C Liquid Crystal Polymer, is similar to the third, but considers the transformation of a free-standing fiber from a cylinder to a helix. In the fifth article, Fluctuations and Light Scattering in a Liquid Crystal Polymer Fiber, the spatial correlation function is calculated for thermal fluctuations of the liquid crystal director field in the core of an optical fiber composed of main chain liquid crystal polymer in the smectic-C phase. The correlation function is used to estimate the scattering distribution and attenuation of the fiber.