Steady states and dynamics of 2-D nematic polymers driven by an imposed weak shear
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We study the 2-D Smoluchowski equation governing the evolution of orientational distribution of rodlike molecules under an imposed weak shear. We first recover the well-known isotropic-to-nematic phase transition result [G. Marrucci and P.L. Maffettone, Description of the liquid-crystalline phase of rodlike polymeres at high shear rates, Macromolecules, 22, 4446-4451, 1989]; in the absence of flow the isotropic-nematic phase transition occurs at U = 2 where U is the normalized polymer concentration, representing the intensity of the Maier-Saupe interaction potential. The we show that in the presence of an imposed weak shear there is a threshold (U-0 approximate to 2.41144646) for U: When U U-0, the angular velocity of the director is always positive and the orientational distribution will not reach a steady state. Finally, the effect of weak shear on the phase diagram is investigated. It is found that the phase relation under weak shear can be obtained from the pure nematic phase relation through a simple algebraic transformation.
The article of record as published may be located at http://www.intlpress.com/CMS/p/2007/issue5-1/CMS_5_1_113-132.pdf
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