A DEFORMATION TENSOR MODEL OF LIQUID-CRYSTALLINE POLYMERS

A new approach is described to obtain dynamical equations for the conf ormation of a liquid crystalline polymer (LCP). The starting point is kinetic theory, which yields an unwieldy evolution equation for the or ientation distribution of molecules associated with a material point o f the liquid crystal. The usual approach is to average this integro-pa rtial-differential evolution equation for the distribution function an d to make use of moment closure approximations in order to obtain a di rect moment tenser evolution equation. In the approach proposed herein , the evolution equation for the orientation distribution function is specialized to a particular class of deformations of the LCP. The resu lting ordinary differential equation for the remaining degrees of free dom of the deformation is self consistent, in the sense that deformati ons remain in the designated class. This deformation tenser model is c arefully constructed to yield physically sensible dynamics in any flow ; however, in tests of the model particular emphasis is placed on the behavior in shear flow. The model displays the complex dynamics of flo w aligning, tumbling, log rolling, wagging, etc. that are observed in experiments. Moreover, the model captures the subtle distinctions betw een flow aligning and tumbling dynamics based on molecular aspect rati o. (C) 1995 Society of Rheology