ARRESTED TUMBLING IN SHEARING FLOWS OF LIQUID-CRYSTAL POLYMERS

The Doi equation for the three-dimensional time-dependent orientation-distribution function for rodlike polymers in the nematic liquid crystalline state in the presence of shearing flow is solved by anexpansion in spherical harmonic functions. The excluded-volume interactions between the molecules are accounted for with the Onsager potential. The results confirm two-dimensional calculations with the Maier-Saupe potential by Marrucci and Maffettone, who showed that a regime of steady-state negative first normal stress difference N1 exists at shear rates high enough to frustrate the tumbling of the average molecular orientation that occurs at lower shear rates. We find in addition that the second normal stress difference N2 usually is of sign opposite that of N1 and is therefore positive when N1 is negative. Between the tumbling and the steady regimes we find a regime of shear rate in which there is a wagging of the direction of average molecular orientation. Finally, we show that shear-induced transitions from the isotropic to the nematic state are not expected to occur for lyotropic systems unless the biphasic concentration regime can be made narrower than that predicted by the Onsager theory. © 1990, American Chemical Society. All rights reserved.