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Nematic elastomers consist of networks of cross-linked polymeric chains in which the peculiar properties of nematic liquid crystals manifest themselves within a solid phase. The nematic mesogens are rigid rod-like molecules attached to the polymeric backbone. They are randomly oriented at high temperature, but upon cooling through the isotropic-nematic transition temperature they align along a common direction described by the nematic director n. With the establishment of nematic order, the underlying polymer network experiences spontaneous elastic distortions, as sketched in the figure.

Given the isotropy of the high-temperature phase, the system is free to choose an arbitrary direction of alignment, so that different parts of the sample may spontaneously deform in different ways, giving rise to spatially modulated equilibrium configurations. Their typical appearance is that of stripe domains, which are highly mobile under the influence of external forces.

The prediction that isotropic gels prepared by cross-linking polymers with a nearby nematic phase could exhibit a transition to an anisotropic phase characterized by the coupling of elastic deformations to the alignement of the nematic director was first formulated by Golubovic and Lubensky (1989). A material exhibiting this behavior was synthesized by a two-step cross-linking process by Küpfer and Finkelmann (1991). Stripe-domain configurations were experimentally observed by Kundler and Finkelmann (1995). In each domain, the stretch is one of the minimizers of the energy density, while domain structures are mixtures of pure states. By combining zero-energy states with different orientations in different parts of the sample, states of average deformation characterized by smaller stretches can be accomodated at almost zero energy. In a loading experiment where uniaxial homogeneous deformations are imposed, one expects a window of strains for which the stress is essentially zero (``liquid phase''), and a standard rubber-like response (``solid phase'') for strains larger than the critical one corresponding to the pure phase aligned with the externally imposed stretch. These deformation processes are accompanied by a reorientation of the nematic director which, in the final pure phase, is aligned with the external stretch.

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