Polydomain-monodomain transition in nematic elastomers

Director textures and alignment of polydomain nematic elastomers under uniaxial extension are described theoretically applying the concept of randomly quenched disorder introduced by network cross-links. Within this model, treated with the replica trick and Gaussian variational approximation, the polydomain-monodomain transition occurs in a critical fashion with a small jump and rapid increase of the macroscopic order parameter. The transition is characterized by a plateau on the stress-strain curve. The critical stress value at which the transition takes place is estimated as $\sim \mu Q_{\mathrm{ch}}$ with $\mu$ the rubber modulus of the elastomer and $Q_{\mathrm{ch}}$ the parameter of chain anisotropy. The aligning of polydomain texture occurs via rotation of domains rather than their growth, with domain size almost unchanged through and above the transition. Experimental data obtained by several groups for various nematic elastomers are analyzed, showing a qualitative agreement with model predictions.