A theory of viscoelastic nematodynamics

A nonlinear viscoelastic theory of nematodynamic type is developed for nematic liquid crystalline (LC) semi-flexible polymers. A measure of transient elastic strain due to the change in length of macromolecular strands under stress, and the director of unit length are employed in the theory as hidden variables. In the marked contrast to the common theoretical approaches to low molecular nematics, the effect of directors space gradient is neglected in the present theory. Nevertheless, the theory allows describing nonlinear anisotropic viscoelasticity and evolution equation for the director in flows of LC polymers. When LC macromolecules are relatively rigid or when they are soft but the flow is slow, a weakly nonlinear viscoelastic anisotropic behavior is described by few temperature dependent parameters. In the infinitesimal case the evolution equation for director reminds the Ericksens equation, but with an additional relaxation term. The present theory can also be applied for analyzing flows of concentrated polymer suspensions and nano-composites filled with uniaxially symmetric particles.