Abstract
A weakly nonlinear viscoelastic theory is developed for nematic liquid crystalline (LC) polymers. A small transient elastic strain due to the change in length of macromolecular strands under stress and a director of unit length are employed in the theory as hidden variables. The theory allows describing anisotropic viscoelasticity and the evolution equation for the director in flows of relatively rigid LC polymers or in slow flows of LC polymers with flexible spacers. As shown, omitting the director gradient does not affect macroscopic predictions of the theory. In the infinitesimal case, the evolution equation for the director looks like the Ericksen equation, but with an additional relaxation term. Although the present theory is mostly applicable for thermotropic LC polymers it can also be used for concentrated lyotropic LC systems, as well as for analyzing flows of concentrated polymer suspensions and nano‐composites filled with uniaxially symmetric particles.
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REFERENCES
E. T. Samulski, Phys. Today, 35, 40–46 (1982).
M. Doi, J. Pol. Sci.: Pol. Phys. Ed., 19, 229–243 (1981).
M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford (1986).
G. Marrucci and F. Greco, Adv. Chem. Phys., 86, 331–403 (1993).
R. G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, Oxford (1998).
J. J. Feng, G. Sgalari, and L. G. Leal, J. Rheol., 44, 1085–1101 (2000).
B. J. Edwards, A. N. Beris, and M. Grmela, Mol. Liq. Cryst., 201, 51–86 (1991).
A. N. Beris and B. J. Edwards, Thermodynamics of Flowing Systems, Oxford University Press, Oxford (1999).
I. E. Dzyaloshinskii and G. E. Volovick, Ann. Phys., 125, 67–97 (1980).
P. G. De Gennes, The Physics of Liquid Crystals, Oxford University Press, New York (1974).
L. G. Larson and D. W. Mead, J. Rheol., 33, 85–206 (1989).
P. G. De Gennes, in: W. Helfrich and G. Kleppke (eds.), Liquid Crystals in One-and Two-Dimensional Order, Springer, Berlin (1980), pp. 231–237.
M. Warner, Mech. Phys. Solids, 47, 1355–1377 (1999).
V. S. Volkov and V. G. Kulichikhin, J. Rheol., 34, 281–293 (1990).
V. S. Volkov, in: I. Emri (ed.), Proc. 5th Eur. Rheology Conf. "Progress and Trends in Rheology," Ljubljana, Slovenia (1998), pp. 240–241.
V. S. Volkov and V. G. Kulichikhin, Rheol. Acta, 39, 360–370 (2000).
R. S. Porter and J. F. Johnson, in: F. R. Eirich (ed.), Rheology, Vol. 4, Academic Press, New York (1967), pp. 317–345.
H. Pleiner and H. R. Brand, Mol. Cryst. Liq. Cryst., 199, 407–418 (1991).
H. Pleiner and H. R. Brand, Macromolecules, 25, 895–901 (1992).
A. D. Rey, Rheol. Acta, 34, 119–131 (1995).
A. D. Rey, J. Non-Newt. Fluid. Mech., 58, 131–160 (1995).
D. Long and D. C. Morse, J. Rheol., 46, 49–92 (2002).
A. I. Leonov and V. S. Volkov, ArXiv.org e-Print archive: http://xyz.lanl.gov/pdf/cond-mat/0202275
J. L. Ericksen, Lect. Notes Math., 1063, 27–36 (1984).
I. Prigogine, Etude Thermodynamique des Phenomenes Irreversible, Liege (1947).
S. R. DeGroot and P. Mazur, Non-Equilibrium Thermodynamics, North-Holland, Amsterdam (1962).
A. I. Leonov and A. N. Prokunin, Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids, Chapman & Hall, New York (1994).
A. I. Leonov, in: D. A. Siginer, D. De Kee, and R. P. Chhabra (eds.), Advances in the Flow and Rheology of Non-Newtonian Fluids, Elsevier, New York (1999), pp. 519--575.
A. I. Leonov and V. S. Volkov, ArXiv.org e-Print archive: http://arxiv.org/ftp/cond-mat/papers/0203/ 0203265.pdf.
I. Gyarmati, Non-Equilibrium Thermodynamics (Field Theory and Variational Principles), Springer, New York (1970).
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Leonov, A.I., Volkov, V.S. Weakly Nonlinear Viscoelastic Nematodynamics. Journal of Engineering Physics and Thermophysics 76, 498–506 (2003). https://doi.org/10.1023/A:1024744224923
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DOI: https://doi.org/10.1023/A:1024744224923