Quantum theory of chiral interactions in cholesteric liquid crystals

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 1, 1999, Pages 578-597

  Issaenko, S A ^a   Harris, A B ^a   Lubensky, T C ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MATRIX ALGEBRA; POLARIZATION; QUANTUM THEORY;

ATOMIC DIPOLE MOMENTS; CHIRAL INTERACTIONS; QUANTUM CHARGE FLUCTUATIONS;

CHOLESTERIC LIQUID CRYSTALS;

EID: 0032607668     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.60.578     Document Type: Article

References (39)

1. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, Oxford, 1993).
2. A. L. Tsykalo, Thermophysical Properties of Liquid Crystals (Gordon and Breach, New York, 1991).
3. S. Fraden, in Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids, edited by M. Baus, L. F. Rull, and J. P. Ryckaert (Kluwer, Dordrecht, 1995).
4. R. Podgornik et al., Proc. Natl. Acad. Sci. USA 93, 4261 (1996).
5. We introduce the chiral term with opposite sign to the one taken in Ref. [22], so that positive h corresponds to right-handed chirality.
6. D. P. Craig, in Optical Activity and Chiral Discrimination, edited by S. F. Mason (D. Reidel, New York, 1979).
7. J. P. Straley, Phys. Rev. A 14, 1835 (1976).
8. L. Onsager, Ann. (N.Y.) Acad. Sci. 51, 627 (1949).
9. D. Frenkel, in Phase Transitions in Liquid Crystals, edited by S. Martellucci and A. N. Chester (Plenum, New York, 1992).
10. G. T. Evans, Mol. Phys. 77, 969 (1992).
11. See, for example, J. P. Bareman, G. Cardini, and M. L. Klein, Phys. Rev. Lett. 60, 2152 (1988).
12. W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 12, 237 (1970).
13. B. W. Van der Meer, G. Vertogen, A. J. Dekker, and J. G. J. Ypma, J. Chem. Phys. 65, 3935 (1976).
14. E. I. Kats, Zh. Éksp. Teor. Fiz. 74, 2320 (1978) [Sov. Phys. JETP 47, 1205 (1978)].
15. E. I. Kats, Zh. Éksp. Teor. Fiz. 74, 2320 (1978) [Sov. Phys. JETP 47, 1205 (1978)].
16. B. J. Berne and P. Pechukas, J. Chem. Phys. 56, 4213 (1972).
17. A. L. Tsykalo, E. E. Nyankina, and A. D. Bagmet, Zh. Tekh. Fiz. 50, 2365 (1980) [Sov. Phys. Tech. Phys. 25, 1384 (1980)].
18. A. L. Tsykalo, E. E. Nyankina, and A. D. Bagmet, Zh. Tekh. Fiz. 50, 2365 (1980) [Sov. Phys. Tech. Phys. 25, 1384 (1980)].
19. H. Schroder, in The Molecular Physics of Liquid Crystals, edited by G. R. Luckhurst and G. W. Gray (Academic, New York, 1979).
20. R. A. Pelcovits, Liq. Cryst. 21, 361 (1996).
21. A. Ferrarini, G. J. Moro, and P. L. Nordio, Phys. Rev. E 53, 681 (1996); Mol. Phys. 87, 485 (1996).
22. A. Ferrarini, G. J. Moro, and P. L. Nordio, Phys. Rev. E 53, 681 (1996); Mol. Phys. 87, 485 (1996).
23. T. Odijk, J. Phys. Chem. 91, 6060 (1987).
24. W. Thomson, The Robert Boyle Lecture, Oxford University Junior Scientific Club, May 16, 1893, reprinted in Baltimore Lectures (C. J. Clay & Sons, London, 1904).
25. A. B. Harris, R. Kamien, and T. C. Lubensky, Phys. Rev. Lett. 78, 1476 (1997).
26. L. Salem, J. Am. Chem. Soc. 109, 2887 (1987).
27. Long polymeric molecules inevitably are nonuniform. For such a one-dimensional system, we expect the states to be strongly localized by disorder, in which case the bandwidth is no longer relevant.
28. S. A. Issaenko and A. B. Harris (unpublished).
29. W. Maier and A. Saupe, Z. Naturforsch. A 14A, 882 (1959).
30. z as the axis about which the molecule spins.
31. M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).
32. I.
33. -(p+1).
34. H. Hart, Organic Chemistry - A Short Course, 7th ed. (Houghton-Mifflin, Boston, 1987), p. 144.
35. In general, the handedness of a molecule consisting of discrete atoms is actually not a precise concept, although it may seem intuitively obvious for a helix. If the helix is continuous, then it is possible to unambiguously distinguish the handedness of the structure. This question is discussed in more detail in Ref. [22].
36. See D. V. Widder, Advanced Calculus (Prentice-Hall, New York, 1947), p. 78.
37. This fact can be seen by considering the packing of propellers (small q) as contrasted to that of screws (large q). M. Green (private communication).
38. S. Fraden, A. J. Hurd, R. B. Meyer, M. Cahoon, and D. L. D. Caspar, J. Phys. (Paris), Colloq. 46, C3-85 (1985).
39. S. A. Issaenko (unpublished).