Rotational invariance and Goldstone modes in nematic elastomers and gels

(Received 13 April 1994, received in final form 19 July 1994, accepted 29 July 1994)

Abstract
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 which cost no elastic energy, when accompanied by a given rotation of the nematic director; this is a specific realization of a class of soft modes originally proposed, on symmetry arguments, by Golubovic and Lubensky [Phys. Rev. Lett. 63 (1989) 1082]. The corresponding elastic theory has a set of Goldstone modes which possesses singular fluctuations. We describe several experimental signatures of these ideas, and elucidate the physical picture of these soft modes.