ROTATIONAL INVARIANCE AND GOLDSTONE MODES IN NEMATIC ELASTOMERS AND GELS

We investigate the symmetries of elastomers and gels cross-linked in a nematic state. The coupling between the local nematic order parameter and an applied deformation leads to a class of uniform deformations w hich cost no elastic energy, when accompanied by a given rotation of t he nematic director; this is a specific realization of a class of soft modes originally proposed, on symmetry arguments, by Golubovic and Lu bensky [Phys. Rev, Lett. 63 (1989) 1082]. The corresponding elastic th eory has a set of Goldstone modes which possesses singular fluctuation s. We describe several experimental signatures of these ideas, and elu cidate the physical picture of these soft modes.