2003/07/31 by Olaf Stenull, T. C. Lubensky · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Advanced Materials and Mechanics #Liquid Crystal Research Advancements #Structural Analysis and Optimization #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.021807
published as Phys. Rev. E 69, 021807 (2004) · 24 pages, 3 figures, version to appear in Phys. Rev. E
arxiv created 2003/11/10 · openalex publication_date 2004/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C5 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 C5>0.