Nonlinear Elasticity, Fluctuations and Heterogeneity of Nematic Elastomers
arXiv:0709.3665 · doi:10.1016/j.aop.2007.10.009
Abstract
Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These {\em solid} liquid crystal amalgams, quite similarly to their (conventional, fluid) liquid crystal counterparts, can spontaneously partially break translational and/or orientational symmetries, accompanied by novel soft Goldstone modes. As a consequence, these materials can exhibit unconventional elasticity characterized by symmetry-enforced vanishing of some elastic moduli. Thus, a proper description of such solids requires an essential modification of the classical elasticity theory. In this work, we develop a {\em rotationally invariant}, {\em nonlinear} theory of elasticity for the nematic phase of ideal liquid crystal elastomers. We show that it is characterized by soft modes, corresponding to a combination of long wavelength shear deformations of the solid network and rotations of the nematic director field. We study thermal fluctuations of these soft modes in the presence of network heterogeneities and show that they lead to a large variety of anomalous elastic properties, such as singular length-scale dependent shear elastic moduli, a divergent elastic constant for splay distortion of the nematic director, long-scale incompressibility, universal Poisson ratios and a nonlinear stress-strain relation fo arbitrary small strains. These long-scale elastic properties are {\em universal}, controlled by a nontrivial zero-temperature fixed point and constitute a qualitative breakdown of the classical elasticity theory in nematic elastomers. Thus, nematic elastomers realize a stable ``critical phase'', characterized by universal power-law correlations, akin to a critical point of a continuous phase transition, but extending over an entire phase.
61 pages, 24 eps pages, submitted to Annals of Physics
References in corpus (18)
- Algebraic spin liquid as the mother of many competing orders
- Nonaffine Correlations in Random Elastic Media
- Smectic Liquid Crystals in Random Environments
- Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
- Isotropic-Nematic Transition in Liquid-Crystalline Elastomers
- Symmetries and Elasticity of Nematic Gels
- Semi-soft Nematic Elastomers and Nematics in Crossed Electric and Magnetic Fields
- Dirt Softens Soap: Anomalous Elasticity of Disordered Smectics
- Universal Elasticity and Fluctuations of Nematic Gels
- Anomalous elasticity of nematic elastomers
- Networks of helix-forming polymers
- Thermal Fluctuations and Rubber Elasticity
- Thermal fluctuations and anomalous elasticity of homogeneous nematic elastomers
- "Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors
- Anomalous elasticity of nematic and critically soft elastomers
- A Discotic Disguised as a Smectic: A Hybrid Columnar Bragg Glass
- Elastic heterogeneity of soft random solids
- Elasticity, fluctuations and vortex pinning in ferromagnetic superconductors: A "columnar elastic glass"
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