Normal stress difference crystal polymers

Magda, J.J. Back, S.G. DeVries, K.L. Larson, R.G. Shear flows of liquid crystal polymers measurements of the second normal stress difference and the Doi molecular theory. Macromolecules 1991, 24, 4460-4468. 

Despite the numerous confirmations of the negative phenomenon, it has still been widely stated that the flow of all polymer systems exhibits only positive primary normal forces (i.e. a positive Nj, the first normal stress difference) [8, 9]. Even subsequent reviews and research papers on the specific subject of lyotropic main chain liquid crystal polymers have not mentioned the confirmed negative effect [10], and even equivalent shear measurements on the identical solutions did not report the negative effect [11]. 

One of the distinctive phenomena observed in the flow of liquid crystal polymers in the nematic state is that of a negative steady-state first normal stress difference, Ni, in shear flow over a range of shear rates. Ni is zero or positive for isotropic fluids at rest over all shear rates, which means that the force developed due to the normal stresses, tends to push apart the two surfaces between which the material is sheared. In liquid crystalline solutions, positive normal stress differences are found at low and high shear rates, with negative values occurring at intermediate shear rates (Kiss G. and Porter R. S. 1978). 

Alderman N, Mackley M (1985) Optical textures observed during the shearing of thermotropic liquid-crystal polymers. Faraday Discuss Chem Soc 79 149-160 Antoun S, Lenz RW, Jin I (1981) Liquid crystal polymers. IV. Thermotropic polyesters with flexible spacers in the main chain. J Polym Sci Polym Chem Ed 19 1901-1920 Baek SG, Magda JJ, Cementwala S (1993) Normal stress differences in liquid crystalline hydroxypropyl cellulose solutions. J Rheol 37 935-945 Barnes HA (2003) A review of the rheology of filled viscoelastic systems. In The British Society of Rheology, pp 1-36... 

Orthorhombic crystals have three mutually perpendicular principal symmetry axes. Since a 180° rotation about each principal axis results in no change, there can be no linear relations between shear stresses and normal strains or between shear stresses and shear strains with different subscripts. This can be proved immediately by observing that, if this were not so, the stated symmetry would not be present. This establishes that in such materials only nine independent elastic compliances (or constants) remain, namely sn, S22, 33, 12, 13, 23, 44, 55, and See- Many technologically important materials, such as rolled metal plates, unidir-ectionally produced polymer films and paper, composite sheet materials, and even wood, have such symmetry, which is referred to as orthotropic symmetry, when it relates to materials rather than crystals. 

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