Liquid crystals and their defects

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.Comment: CIME lecture course, Cetraro, 201

Coincident molecular auxeticity and negative order parameter in a liquid crystal elastomer

Auxetic materials have negative Poisson's ratios and so expand rather than contract in one or several direction(s) perpendicular to applied extensions. The auxetics community has long sought synthetic molecular auxetics - non-porous, inherently auxetic materials which are simple to fabricate and avoid porosity-related weakening. Here, we report, synthetic molecular auxeticity for a non-porous liquid crystal elastomer. For strains above ~0.8 applied perpendicular to the liquid crystal director, the liquid crystal elastomer becomes auxetic with the maximum negative Poisson's ratio measured to date being -0.74 ± 0.03 - larger than most values seen in naturally occurring molecular auxetics. The emergence of auxeticity coincides with the liquid crystal elastomer backbone adopting a negative order parameter, QB = -0.41 ± 0.01 - further implying negative liquid crystal ordering. The reported behaviours consistently agree with theoretical predictions from Warner and Terentjev liquid crystal elastomer theory. Our results open the door for the design of synthetic molecular auxetics

Critical Stripe-Domain Instability of Nematic Elastomers

We present an experimental and theoretical investigation of the critical formation of stripe domains in monodomain nematic elastomers. Domains with alternating sense of director rotation are formed when the material is stretched perpendicular to the initial director alignment. A wide range of differing samples are shown to have a singular onset to director rotation at a threshold deformation and a second singular point at the end of the stripe domain region. All the data collapses onto a master plot revealing a universal behaviour. We analyse theoretically the threshold properties of the stripe phase. The analysis of free energy yields a first order transition into a fully-coarsened texture without any intermediate state of sinusoidal modulation

Elastic energies for nematic elastomers

We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence