326 research outputs found
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 this dependence
is logarithmic and below 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
Stereo-selective swelling of imprinted cholesteric networks
Molecular chirality, and the chiral symmetry breaking of resulting
macroscopic phases, can be topologically imprinted and manipulated by
crosslinking and swelling of polymer networks. We present a new experimental
approach to stereo-specific separation of chiral isomers by using a cholesteric
elastomer in which a helical director distribution has been topological
imprinted by crosslinking. This makes the material unusual in that is has a
strong phase chirality, but no molecular chirality at all; we study the nature
and parameters controlling the twist-untwist transition. Adding a racemic
mixture to the imprinted network results in selective swelling by only the
component of ``correct'' handedness. We investigate the capacity of demixing in
a racemic environment, which depends on network parameters and the underlying
nematic order
Photonic band structure of highly deformable, self-assembling systems
We calculate the photonic band structure at normal incidence of highly
deformable, self-assembling systems - cholesteric elastomers subjected to
external stress. Cholesterics display brilliant reflection and lasing owing to
gaps in their photonic band structure. The band structure of cholesteric
elastomers varies sensitively with strain, showing new gaps opening up and
shifting in frequency. A novel prediction of a total band gap is made, and is
expected to occur in the vicinity of the previously observed de Vries bandgap,
which is only for one polarisation
Untwisting of a cholesteric elastomer by a mechanical field
A mechanical strain field applied to a monodomain cholesteric elastomer will
unwind the helical director distribution. There is an analogy with the
classical problem of an electric field applied to a cholesteric liquid crystal,
but with important differences. Frank elasticity is of minor importance unless
the gel is very weak. The interplay is between director anchoring to the rubber
elastic matrix and the external mechanical field. Stretching perpendicular to
the helix axis induces the uniform unwound state via the elimination of sharp,
pinned twist walls above a critical strain. Unwinding through conical director
states occurs when the elastomer is stretched along the helical axis.Comment: 4 pages, RevTeX 3 style, 3 EPS figure
Electro-Mechanical Fredericks Effects in Nematic Gels
The solid nematic equivalent of the Fredericks transition is found to depend
on a critical field rather than a critical voltage as in the classical case.
This arises because director anchoring is principally to the solid rubbery
matrix of the nematic gel rather than to the sample surfaces. Moreover, above
the threshold field, we find a competition between quartic (soft) and
conventional harmonic elasticity which dictates the director response. By
including a small degree of initial director misorientation, the calculated
field variation of optical anisotropy agrees well with the conoscopy
measurements of Chang et al (Phys.Rev.E56, 595, 1997) of the electro-optical
response of nematic gels.Comment: Latex (revtex style), 5 EPS figures, submitted to PRE, corrections to
discussion of fig.3, cosmetic change
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