Theory of Liquid Crystals and Soft Materials

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This award supports theoretical research and education the area of soft condensed matter. Research will be carried out on layered structures, nematic liquid crystals, twist grain boundary phases, nematic elastomers, and granular matter.The PI has demonstrated that layered structures, such as free standing smectic-C films, lyotropic smectics with dissolved proteins that form 2D lattices within their bilayer membranes, or DNA-lipid complexes with DNA intercalated between lipid bilayers can exhibit remarkable new "sliding phases" of matter. These phases are characterized by 2D power law behavior of correlations in spite of nonvanishing interlayer couplings. Many properties of these phases both in stacks of 2D classical systems and in arrays of 1D quantum wires are unexplored or incompletely understood and will be investigated by the PI.Nematic liquid crystals exhibit both line disclination and point hedgehog defects. Disclination loops can produce far-field director configurations equivalent to those of point hedgehogs and can carry hedgehog charge. The topology and homotopy group of these charge carrying loops is well understood. The distribution of hedgehog charge along a disclination loop is, however, largely unexplored. The PI will develop ways of quantifying hedgehog density, explore its energetic consequences, and study its effect on coarsening of defect patterns after a quench into the nematic phase from the isotropic phase. Twist-grain boundary (TGB) phases are liquid-crystal analogs of the Abrikosov vortex lattice phase of superconductors. At least three distinct TGBC phases in addition to the original TGBA phase have now been predicted or observed experimentally. Investigations of the energetic differences among these phases and the parameters that determine their stability, which are poorly understood, form an important part of the proposed program. Nematic elastomers, formed by crosslinking nematic polymers, combine the properties of rubber elasticity and orientational order of nematic liquid crystals. They have unusual elastic properties that have a number of potential applications, most notably as artificial muscles. A major part of the proposed program will be devoted to the study of the static and dynamic properties of nematic elastomers, including nematic elastomeric membranes and lyotropic nematic elastomers formed by dispersing colloidial rods in a swollen gel. When subjected to sufficiently strong shear stresses, granular matter becomes partially fluidized and exhibits flow properties that differ from those of a Newtonian fluid. The PI will investigate the flow of granular materials in various flow geometries using a generalization of the Chapman-Ensgog kinetic hydrodynamical equations with inelastic collisions in which effects of particle corrrelations are modeled near random close packing by a viscosity that diverges more rapidly with density than other transport coefficients. %%%This award supports research and education in the area of soft condensed matter. The term "soft materials" encompasses a wide spectrum of materials that includes complex fluids and liquid crystals and that are important to industry, as well as most biological matter. The PI will use these materials as an arena to explore fundamental concepts in condensed matter physics, such as broken symmetry, topological defects, and fluctuation destruction of long-range order in low-dimensional systems. This work helps improve our fundamental understanding of soft materials, and involves novel new phases of matter, "sliding phases," that occur in layered 'soft matter,' topological defects that occur in nematic liquid crystals, twist-grain boundary phases that occur in liquid crystals, nematic elastomers, and complex fluids. ***