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arXiv · cond-mat/0307686

Anomalous elasticity of nematic and critically soft elastomers

Olaf Stenull·T. C. Lubensky
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Abstract

Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C_5 describing the energy of shear strains in planes containing the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d less than or equal to 3, soft elastomers exhibit anomalous elasticity with certain length-scale dependent bending moduli that diverge and shear moduli that vanish at large length-scales. Using renormalized field theory at d = 3 and to first order in ε= 3 - d, we calculate critical exponents and other properties characterizing the anomalous elasticity of two soft systems: (i) nematic elastomers in which softness is a manifestation of a Goldstone mode induced by the spontaneous symmetry breaking associated with a transition from an isotropic state to a nematic state and (ii) a particular version of what we call a critically soft elastomer in which C_5 = 0 corresponds to a critical point terminating the stability regime of a uniaxial elastomer with C_5 > 0.

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Olaf Stenull, T. C. Lubensky. 2003-11-10. Anomalous elasticity of nematic and critically soft elastomers. https://doi.org/10.1103/physreve.69.021807

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