Effect of chirality on active elastomers and solids in three dimensions

Abstract

We examine the effect of chiral activity on nematic and polar uniaxial elastomers and solids by constructing the general hydrodynamic equations for these phases. We start with the elastomer, which is not only invariant under rigid rotations but also under an independent rotation of the uniaxial direction, and show that this higher symmetry strongly constrains the effects of chiral activity. We then break the elastomeric symmetry by adding a symmetry-breaking term to the free energy but still retain invariance under rigid rotations. The resulting state has the symmetry of a uniaxial solid, and we show that in a fixed background medium chiral activity generically destabilises it. The force density responsible for this {instability} vanishes as the field that breaks the elastomeric symmetry goes to zero. Further, the presence of the symmetry-breaking field also allows for an additional odd elastic force density that generically destabilises momentum-conserved chiral and uniaxial solids in the inertial regime.