Theory for the Rheology of LCPs

1 Theory for Rigid Rodlike Macromolecules with Monodomains 

we present the molecular theory of Doi and coworkers (Doi 1981, 1983 Doi and Edwards 1978a, 1978b Kuzuu and Doi 1980, 1983, 1984) for predicting the rheological behavior of concentrated solutions of monodomains consisting of rigid rodlike macromolecules. 

While considering the shear flow of a concentrated solution of rigid rods, let us restrict our attention to the nematic phase, where the orientation of a rod is determined by 

The difference between Eq. (9.1) and the analogous equation for flexible homopolymers (Eq. (4.69)) is in the orientation-dependent rotary diffusivity D. which depends on the anisotropy of the system, as expressed by (Doi and Edwards 1978a, 1978b)  

Note that on the microscopic level, nematics are characterized by the fact that the equilibrium orientation distribution function /(u) for the molecules in the directions u is not isotropic. The anisotropy is represented by the order parameter tensor S defined as 

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