On the Origin of Negative Normal Stresses in Sheared or Lyotropic Liquid Crystals

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Abstract
In steady shear flow, sustained negative primary normal-stress differences have been reported for several liquid crystalline systems, in most detail for m-cresol solutions of helicoidal polypeptides and for copolyesters. A theoretical model is herewith proposed in which “dumbbell” molecules are constrained from rotating freely in the shear flow by the intermolecular potential that produces liquid crystalline order. In steady state, the molecules are imperfectly aligned, corresponding to a shortening or buckling of molecular layers. The tendency for the layers to straighten toward perfect order causes a compressive force along the streamlines, corresponding to a negative normal stress. For this actually to occur, a dimensionless group (containing the molecular axial ratio, shear rate, solute volume fraction and intermolecular potential) is predicted to be within a restricted range. The experimentally observed range for the polypeptide solutions is wider, probably because of polydispersity (imperfect monodispersity), and the theory underestimates the magnitude of observed negative normal stress. Although the copolyesters must be characterized by different independent variables, again one can identify a dimensionless group such that all the negative normal stresses occur within a restricted range. This simple model identifies dimensionless variables that will be important in any detailed microrheological theory based on calculating the distribution of molecular orientations.

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