Universal Elasticity and Fluctuations of Nematic Gels

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local hetergeneities down to d_lc < 3.Comment: 4 RevTeX pgs, submitted to PR

Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

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

Anomalous elasticity of nematic elastomers

We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic elastomers. Performing a diagrammatic low temperature expansion, we analyze the fluctuations of the displacement fields at and below the upper critical dimension 3. Our analysis reveals an anomaly of certain elastic moduli in the sense that they depend on the length scale. In $d = 3$ this dependence is logarithmic and below $d=3$ it is of power law type with anomalous scaling exponents. One of the 4 relevant shear moduli vanishes at long length scales whereas the only relevant bending modulus diverges.Comment: 4 page

Continuous Spatial Tuning of Laser Emissions in a Full Visible Spectral Range

In order to achieve a continuous tuning of laser emission, the authors designed and fabricated three types of cholesteric liquid crystal cells with pitch gradient, a wedge cell with positive slope, a wedge cell with negative slope, and a parallel cell. The length of the cholesteric liquid crystal pitch could be elongated up to 10 nm, allowing the lasing behavior of continuous or discontinuous spatial tuning determined by the boundary conditions of the cholesteric liquid crystal cell. In the wedge cell with positive slope, the authors demonstrated a continuous spatial laser tuning in the near full visible spectral range, with a tuning resolution less than 1 nm by pumping with only a single 355 nm laser beam. This continuous tuning behavior is due to the fact that the concentration of pitch gradient matches the fixed helical pitch determined by the cell thickness. This characteristic continuous spatial laser tuning could be confirmed again by pumping with a 532 nm laser beam, over 90 nm in the visible spectral range. The scheme of the spatial laser tuning in the wedge cell bearing a pitch gradient enabled a route to designing small-sized optical devices that allow for a wide tunability of single-mode laser emissions

Thermal and mechanical properties of new main-chain liquid-crystalline elastomers

New Main-Chain Liquid-Crystalline Elastomers (MCLCEs) were synthesised based on reacting vinyloxy-terminated mesogens under hydrosilylation conditions with a flexible crosslinker. These main-chain systems showed smectic and nematic mesophases and their anisotropic properties were mechanically and thermally analysed as function of the crosslinking density. Due to the suitable chemistry used in this work low crosslinking densities have been achieved (2.5 mol-%) with low soluble content (5%). For the first time, the degree of crosslinking could be adjusted and nematic or smectic MCLCEs with tuneable thermal and mechanical properties were obtained

An optically activated cantilever using photomechanical effects in dye-doped polymer fibers

We report on what we believe is the first demonstration of an optically activated cantilever due to photomechanical effects in a dye-doped polymer optical fiber. The fiber is observed to bend when light is launched off-axis. The displacement angle monotonically increases as a function of the distance between the illumination point and the fiber axis, and is consistent with differential light-induced length changes. The photothermal and photo-reorientation mechanisms, each with its own distinct response time, are proposed to explain the observed time dependence. The measured degree of bending is consistent with a model that we have proposed which includes coupling between photoisomerization and heating. Most importantly, we have discovered that at high light intensity, a cooperative release of stress results in cis-to-trans isomerization that yields a large and abrupt length change.Comment: 13 pages, 16 figure

Uniaxial and shear deformations in smectic-C main-chain liquid-crystalline elastomers

ABSTRACT: A novel cross-linked smectic-C main-chain liquid-crystalline elastomer has been synthesized by polycondensation of vinyloxy-terminated mesogens, tetramethyldisiloxane and pentamethylpentaoxapentasilecane. The introduction of the functional vinyloxy group allows the synthesis of well-defined networks having low soluble content and good mechanical properties due to elimination of side reactions as in the case of vinyl groups. Networks having a macroscopic uniformly ordered director and a conical distribution of the smectic layer normal with respect to the director are mechanically deformed by uniaxial and shear deformations. Under uniaxial deformations two processes were observed: parallel to the director the mechanical field directly couples to the smectic tilt angle while perpendicular to the director a reorientation process takes place. A shear deformation parallel and perpendicular to the director causes a uniform layer orientation and the network exhibits a smectic-C monodomain phase having a macroscopic uniform director and layer orientation. This process is reversible for shear deformation perpendicular and irreversible by applying the shear force parallel to the director