Continuum Theory of Cholesteric Liquid Crystals

  • A. Cemal Eringen
  • James D. Lee


Based on the theory of micropolar viscoelasticity a continuum theory of cholesteric liquid crystals is presented. The balance laws of motion are given and a constitutive theory is derived and restricted by the second law of thermodynamics. Material symmetry restrictions are obtained by means of physical considerations. The theory includes thermomechanical effects of dissipation. The axis of ellipse and coefficient of optical activity are defined to characterize the helical structure of cholesteric liquid crystals. Analytically it is shown that in general the coefficient of optical activity depends on the temperature variations, deformation and mechanical stresses. Several special cases of practical importance are studied in detail. A coupling of longitudinal and twist waves along the axis of helix is investigated theoretically and corresponding experiments are suggested.


Liquid Crystal Continuum Theory Optical Activity Cholesteric Liquid Crystal Undeformed State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. S. Porter, E. M. Barrall II, and J. F. Johnson, J. Chem. Phys., V. 45, No. 5, 1452 (1966).CrossRefGoogle Scholar
  2. 2.
    G. Friedel, Ann. Physique 19, 273 (1922).Google Scholar
  3. 3.
    J. L. Fergason, Sci. Am. V. 211, No. 2, 77 (1964).CrossRefGoogle Scholar
  4. 4.
    G. H. Brown and W. G. Shaw, Chem. Rev., 57, 1049 (1957).CrossRefGoogle Scholar
  5. 5.
    R. S. Porter and J. F. Johnson, Rheology IV (New York): Academic Press, 1967, edited by F. R. Eirich), p. 317.Google Scholar
  6. 6.
    I. G. Chistyakov, Soviet Physics USPEKHI, V. 9, No. 4, 551 (1967).CrossRefGoogle Scholar
  7. 7.
    A. Saupe, Angew. Chem. International Edit. V. 7, No. 2, 97 (1968).CrossRefGoogle Scholar
  8. 8.
    P. G. DeGennes, Solid State Communications V. 6, 163 (1968).CrossRefGoogle Scholar
  9. 9.
    P. G. DeGennes, Molecular Crystals and Liquid Crystals, V. 7, 325 (1969).CrossRefGoogle Scholar
  10. 10.
    R. B. Meyer, Applied Phys. Lett., 12, 281 (1968).CrossRefGoogle Scholar
  11. 11.
    O. S. Selawry, H. S. Selawry, and J. F. Holland, Liquid Crystals (New York: Gordon and Breach, 1966, edited by Brown, Dienes, and Labes), p. 175.Google Scholar
  12. 12.
    F. M. Leslie, Proc. Roy. Soc. A., 307, 359 (1968).CrossRefGoogle Scholar
  13. 13.
    F. M. Leslie, Molecular Crystals and: Liquid Crystals, 7, 407 (1969).CrossRefGoogle Scholar
  14. 14.
    J. L. Ericksen, Trans. Soc. Rheol., 5, 23 (1961).CrossRefGoogle Scholar
  15. 15.
    A. C. Eringen and E. S. Suhubi, Int. J. Engng. Sci., 2, 189 (1964).CrossRefGoogle Scholar
  16. 16.
    A. C. Eringen, ¿. Math. & Mech., 15, 909 (1966).Google Scholar
  17. 17.
    A. C. Eringen, ¿. Math. & Mech.16, 1 (1966).Google Scholar
  18. 18.
    A. C. Eringen, Foundations of Micropolar Thermoelasticity, International Center for Mechanical Sciences, Udine, Italy, 1970.Google Scholar
  19. 19.
    J. D. Lee and A. C. Eringen, J. Chem. Phys., V. 54, No. 12, 5027 (1971).CrossRefGoogle Scholar
  20. 20.
    A. C. Eringen, Mechanics of Continua (New York: John Wiley & Sons, 1967).Google Scholar
  21. 21.
    A. C. Eringen, Int. J.. Engng., Sci., 5, 191 (1967).CrossRefGoogle Scholar
  22. 22.
    A. C. Eringen, Proceedings of the Eleventh International Congress of the Eleventh International Congress of Applied Mechanics (held in 1964, Munich, Germany), edited by H. Gortler, Springer-Verlag (1966) 131–138.Google Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • A. Cemal Eringen
    • 1
    • 2
  • James D. Lee
    • 1
    • 2
  1. 1.Princeton UniversityPrincetonUSA
  2. 2.George Washington UniversityUSA

Personalised recommendations