Viscosity and Rheology of Liquid Crystalline Polymers

The phenomenological hydrodynamics for small molecular mass liquid crystals which were developed in analog to conventional fluids was, at the early stage, addressed by Ericksen (I960) and Leslie (1966, 1968). The hydrodynamics of the conventional fluids deals with the profile of the velocity field of fluid v(xi) = y(i = f, 2,3). The distortion of velocity field results in 

There is an orientational order in the liquid crystals which are anisotropic fluids. The director field n(r) or its components n affect the hydrodynamic behavior, so that is dependent on the distortion of the director field as well. For convenience, we designate a vector N for the angular velocity of liquid crystal directors with respect to the background fluid, 

The viscous stress of liquid crystals is defined as the Ericksen-Leslie stress tensor and is related to A, n and w or IV  

Parodi obtained the following relation (1970) according to the Onsager reciprocal relation 

Consequently only five independent coefficients actually exist in the nematic liquid crystals. The viscosity tensor is no longer symmetrical and hence a viscous moment appears 

---