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Soft Matter and Biological Physics

Eur. Phys. J. E 4, 343-353

Linear hydrodynamics and viscoelasticity of nematic elastomers

E.M. Terentjev and M. Warner

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

(Received 16 October 2000 and Received in final form 10 December 2000)

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors.

61.30.-v - Liquid crystals..
61.41.+e - Polymers, elastomers and plastics.
83.50.Fc - Linear viscoelasticity.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001