MICROSTRUCTURE CONSTITUTIVE EQUATION FOR DISCOTIC NEMATIC LIQUID-CRYSTALLINE MATERIALS PART I - SELECTION PROCEDURE AND SHEAR-FLOW PREDICTIONS

Four different microstructure constitutive equations (CEs) for discoti c nematic liquid crystals based on Doi's modified nematodynamics theor y are formulated. Their dynamic and steady state responses under simpl e shear flows are computed and analyzed in terms of the tensor order p arameter Q, the orientation director triad (n, m, 1), and the uniaxial S and biaxial P alignments. A unit sphere description of the director triad is used to characterize and classify the various predicted stab le orientation states, and to discuss and analyze their multistabiliti es as a function of dimensionles shear rate. Various attractors, stead y and periodic, are also identified and their stability is discussed i n detail for all the CEs. A validation procedure based on the predicte d microstructural response along with bifurcation diagrams of the indi vidual CE and representative experimental observations as well as theo retical results is implemented, and used to select the most appropriat e CE. The selected CE predicts, under shear; the simultaneous presence of stable in-plane (steady and periodic) states and out-of-plane stea dy state, and the classical transition among the in-plane periodic and steady states with increasing shear rate. The excellent performance o f the selected CE in shear flows strongly suggests that it is a reliab le contribution towards the formulation of a process model for mesopha se pitch spinning.