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Geometrical content of Leslie coefficients

M. Simões* and J. L. Correia da Silva

  • Departamento de Física, Universidade Estadual de Londrina, Campus Universitário, 86051-990 Londrina, Paraná, Brazil

  • *simoes@uel.br
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Phys. Rev. E 83, 051702 – Published 10 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051702

Abstract

In this work, we will study how the effective geometry acquired by nematic molecules under thermal vibration contribute to the determination of the Leslie coefficients. To do this, we will divide this work in two sections. In the first section, we present the geometrical fundamentals of the so-called Hess-Baalss (HB) approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] where we show that its basic assumptions can be understood as a geometrical interpretation of de Gennes’ passage from the microscopic to the macroscopic order parameter. In the second section, we use an extended version of the HB approach [M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. E 80, 061701 (2009)] to obtain the geometrical contribution to each Leslie coefficient. Our results will be compared with experimental data, and we will show that the Miesowicz’s coefficients are connected as long as the ratio α3/α4 between these Leslie coefficients can be considered small.

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      References (39)

      1. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, Oxford, 1993).
      2. M. Miesowicz, Nature (London) 17, 261 (1935).
      3. M. Miesowicz, Bull. Acad. Pol. Sci. A 228 (1936).
      4. J. L. Ericksen, Arch. Ration. Mech. Anal. 4, 231 (1960); 9, 371 (1962).
      5. F. M. Leslie, Q. J. Mech. Appl. Math. 19, 357 (1966).
      6. O. Parodi, J. Phys. (France) 31, 581 (1970).
      7. D. Foster, T. Lubensky, P. Martin, J. Swift, and P. Pershan, Phys. Lett. 26, 1016 (1971).
      8. P. C. Martin, O. Parodi, and P. Pershan, Phys. Rev. A 6, 2401 (1972).
      9. P. C. Martin, P. J. Pershan, and J. Swift, Phys. Rev. Lett. 25, 844 (1970).
      10. H. Tseng and B. A. Finlayson, Mol. Cryst. Liq. Cryst. 116, 265 (1985).
      11. C. H. Gahwiller, Mol. Cryst. Liq. Cryst. 20, 301 (1972).
      12. H. Kneppe, F. Schneider, and N. K. Sharma, Ber. Bunsenges. Phys. Chem. 85, 784 (1981).
      13. H. Kneppe, F. Schneider, and N. K. Sharma, J. Chem. Phys. 77, 3203 (1982).
      14. S. Meiboom and R. C. Hewitt, Phys. Rev. Lett. 30, 261 (1973).
      15. M. Simões and S. M. Domiciano, Phys. Rev. E 66, 061703 (2002).
      16. M. Simões and S. M. Domiciano, Phys. Rev. E 68, 011705 (2003).
      17. M. Simões, A. de Campos, and D. Barbato, Phys. Rev. E 75, 061710 (2007).
      18. M. Doi, J. Polymer. Sci., Polym. Phys. Ed. 19, 229 (1981).
      19. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).
      20. M. Doi and S. F. Edwards, J. Chem. Soc. Faraday Trans. 2 74, 560 (1978); 74, 918 (1978).
      21. N. Kuzuu and M. Doi, J. Phys. Soc. Jpn. 52, 3486 (1983); 53, 1031 (1984).
      22. M. A. Osipov and E. M. Terentjev, Z. Naturforsch., A: Phys. Sci. 44, 785 (1989); Mol. Cryst. Liq. Cryst. 198, 429 (1991); Nuovo Cimento 12, 1223 (1990).
      23. R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, Oxford, 1999).
      24. D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986).
      25. D. Baalss and S. Hess, Z. Naturforsch. Teil A 43, 662 (1988).
      26. H. Sollich, D. Baalss, and S. Hess, Mol. Cryst. Liq. Cryst. 168, 189 (1989).
      27. S. Hess, J. F. Scwarz, and D. Baalss, J. Phys.: Condens. Matter 2, SA279 (1990).
      28. H. Ehrentraut and S. Hess, Phys. Rev. E 51, 2203 (1995).
      29. G. W. Gray, The Molecular Physics of Liquid Crystals, Chap. 1 (Academic, London, 1979).
      30. L. Onsager, Phys. Rev. 37, 405 (1931); 38, 2265 (1931).
      31. M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. E 80, 061701 (2009).
      32. M. Simões, A. J. Palangana, A. Steudel, N. M. Kimura, and S. L. Gomez, Phys. Rev. E 77, 041709 (2008).
      33. M. Simões, M. Pazetti, S. M. Domiciano, D. A. Oliveira, and A. J. Palangana, Phys. Rev. E 78, 022702 (2008).
      34. M. Simões and A. de Campos, Liq. Cryst. 34, 719 (2007).
      35. M. Simões and A. de Campos, Phys. Lett. A 370, 173 (2007).
      36. M. Simões and D. S. Simeão, Phys. Rev. E 73, 062702 (2006).
      37. M. Simões and D. S. Simeão, Phys. Rev. E 74, 051701 (2006).
      38. M. Simões and M. Pazetti, Europhys. Lett. 92, 14001 (2010).
      39. R. K. Pathria, Statistical Mechanics (Butterworth Heinemann, Oxford, 1996).

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      Phys. Rev. E 83, 051702– Published 10 May, 2011
      • Received 23 October 2010

      ©2011 American Physical Society

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