Patterns and Defects in Nematic Elastomers

Nematic elastomers are materials that combine the orientational properties of nematic liquid crystals with the elastic properties of rubber. Ideal nematic elastomers, formed via a spontaneous symmetry breaking transition from the isotropic rubber state, exhibit soft elasticity in which one of the five elastic moduli of a uniaxial elastic medium vanishes. Monodomain samples crosslinked under imposed strain exhibit semi-soft elasticity in which that elastic modulus is small but nonzero. Applying linear stability analysis to the semi-soft elastic energy, we investigate two phenomena observed in experiments on nematic elastomers: (1) the formation, in experiments by Bob Meyer at Brandeis, of periodic modulations of the nematic director and elastic displacement (stripes) in cells subjected to a normal electric field in which the direction of stripe normals is at an oblique angle to the original nematic director and (2) the formation of +1 disclination defects at the surface of nanotube gel films [Islam, M. F., Nobili, M., Ye, Fangfu , Lubensky, T. C. and Yodh, A. G. , \textit{Phys. Rev. Lett }. \textbf{95}, 148301/1-4 (2005)].