Symmetries and Elasticity of Nematic Gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these novel materials.Comment: 21 pages, 4 eps figure

Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions

The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-\epsilon dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law < m(x) m(y) >\sim |x-y|^{-0.62\epsilon}. The magnetic susceptibility diverges at low fields as \chi \sim H^{-1+0.15\epsilon}. In the random field O(N) model the correlation radius is found to be finite at the arbitrarily weak disorder for any N>3. The random field case is studied with a new simple method, based on a rigorous inequality. This approach allows one to avoid the integration of the functional renormalization group equations.Comment: 12 pages, RevTeX; a minor change in the list of reference

Characterization and optimization of electrospun TiO2/PVP nanofibers using Taguchi design of experiment method

TiO2 nanofibers were prepared within polyvinylpyrrolidone (PVP) polymer using a combination of sol–gel and electrospinning techniques. Based on a Taguchi design of experiment (DoE) method, the effects of sol–gel and electrospinning on the TiO2/PVP nanofibers’ diameter, including titanium isopropoxide (TiP) concentration, flow rate, needle tip-to-collector distance, and applied voltage were evaluated. The analysis of DoE experiments for nanofiber diameters demonstrated that TiP concentration was the most significant factor. An optimum combination to obtain smallest diameters was also determined with a minimum variation for electrospun TiO2/PVP nanofibers. The optimum combination was determined to be a 60% TiP concentration, at a flow rate of 1 ml/h, with the needle tip-to-collector distance at 11 cm (position a), and the applied voltage of 18 kV. This combination was further validated by conducting a confirmation experiment that used two different needles to study the effect of needle size. The average nanofiber diameter was approximately the same for both needle sizes in good accordance with the optimum condition estimated by the Taguchi DoE method