J. Phys. II France
Volume 6, Numéro 7, July 1996
Page(s) 1049 - 1060
DOI: 10.1051/jp2:1996115
J. Phys. II France 6 (1996) 1049-1060

Non-Uniform Deformations in Liquid Crystalline Elastomers

E.M. Terentjev, M. Warner and G.C. Verwey

Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, UK

(Received 20 September 1995, received in final form 6 March 1996, accepted 22 March 1996)

We develop a molecular model of non-uniform deformations within the framework of liquid crystal rubber elasticity. The result of this work is the general expression for the free energy of deformations which combines the effects of large non-symmetric affine strains in the rubbery network and gradients of curvature deformations of the director field, $F\sim \lambda^{\rm T}\{\nabla{\bf n}\}^2\lambda$. We derive the molecular expressions for the elastic constants governing non-uniform directors in the presence of elastic strains. These constants depend on the polymer step length anisotropy $\ell_{\vert\vert}/\ell_\perp$ and - most strikingly - have an overall negative sense. We therefore predict that in some circumstances, especially at large elastic deformations $\lambda$, these new terms may overpower the usual, positive Frank elastic moduli of the underlying nematic structure, and also in some cases the coupling of uniform relative rotations of the director to the elastic matrix. In this event highly distorted polydomain textures n(r) would be favoured.

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