Arvinder P. Singh Alejandro D. Rey Microstructure constitutive equation for discotic nematic liquid crystalline materials Part I: Selection procedure and shear flow predictions Received: 8 May 1997 Accepted: 15 September 1997 A.P. Singh · A.D. Rey ( ✉ ) Department of Chemical Engineering McGill University 3610 University Street Montreal, Quebec, H3A 2B2 Canada e-mail: alex@chemeng.lan.mcgill.ca Abstract Four different microstruc- ture constitutive equations (CEs) for discotic nematic liquid crystals based on Doi’s modified nematody- namics theory are formulated. Their dynamic and steady state responses under simple shear flows are com- puted and analyzed in terms of the tensor order parameter Q, the orien- tation director triad (n, m, l), and the uniaxial S and biaxial P align- ments. A unit sphere description of the director triad is used to charac- terize and classify the various pre- dicted stable orientation states, and to discuss and analyze their multi- stabilities as a function of dimen- sionles shear rate. Various attractors, steady and periodic, are also identi- fied and their stability is discussed in detail for all the CEs. A valida- tion procedure based on the pre- dicted microstructural response along with bifurcation diagrams of the individual CE and representative experimental observations as well as theoretical results is implemented, and used to select the most appro- priate CE. The selected CE predicts, under shear, the simultaneous pres- ence of stable in-plane (steady and periodic) states and out-of-plane steady state, and the classical transi- tion among the in-plane periodic and steady states with increasing shear rate. The excellent perfor- mance of the selected CE in shear flows strongly suggests that it is a reliable contribution towards the for- mulation of a process model for me- sophase pitch spinning. Key words Mesophase pitches – discotic nematic liquid crystals – simple shear flow of nematics – constitutive equations for discotic nematic liquid crystals – mesophase carbon fibers Introduction Carbonaceous mesophases or mesophase pitches are ob- tained from natural (petroleum or coal tar pitches) or synthetic feed stock (naphthalene), and are used in the manufacture of high-performance mesophase pitch- based carbon fibers (Zimmer and White, 1982; Singer, 1985; McHugh and Edie, 1996). The mesophase carbon fibers show outstanding stiffness and thermal transport properties due to their ability to develop extended gra- phitic structures. The physical properties of high perfor- mance fibers are mainly due to the molecular orienta- tion developed during the spinning process (McHugh, 1994). These precursor mesophase pitches consist of flat poly-aromatic molecules that adopt a uniaxial thermo- tropic discotic nematic liquid crystalline phase (Chan- drasekhar, 1981; Destrade et al., 1981). The flat disc- like molecules orient more or less along a common di- rection (see Fig. 1), represented by the (uniaxial) direc- tor n; in what follows we use n and uniaxial orientation interchangeably (deGennes, 1975). The average degree of alignment of unit normals to the discs along the di- rector n is defined by the (uniaxial) scalar order param- Rheol Acta 37:30–45 (1998) © Steinkopff Verlag 1998 ORIGINAL CONTRIBUTION RA 866