Anomalous elasticity of nematic and critically soft elastomers

TL;DR

This paper investigates the anomalous elasticity behavior of soft nematic and critically soft elastomers in three dimensions, revealing diverging bending moduli and vanishing shear moduli at large scales through renormalized field theory.

Contribution

It provides the first analytical calculation of critical exponents for the anomalous elasticity in nematic and critically soft elastomers using renormalized field theory.

Findings

Diverging bending moduli at large scales.

Vanishing shear moduli at large scales.

Critical exponents characterizing the anomalous elasticity.

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 \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.