Anomalous elasticity of nematic and critically soft elastomers

Details Anomalous elasticity of nematic and critically soft elastomers Anomalous elasticity of nematic and critically soft elastomers

2003-07-28

arxiv.org/abs/cond-mat/0307686v2

Phys. Rev. E 69, 021807 (2004)

Physics

Condensed Matter

Soft Condensed Matter

24 pages, 3 figures, version to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.69.021807

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 \epsilon = 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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