The Fréedericksz transition in liquid crystals: An undergraduate experiment for the advanced laboratory

American Journal of Physics

Volumn 66, Issue 1, 1998, Pages 49-56

  Moses, Thomas ^a   Jensen, Brian ^a  

^a KNOX COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032351821     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18807     Document Type: Article

References (28)

1. V. K. Fréedericksz and A. Repiewa, "Theoretisches und Experimentelles sur Frage nach der Natur der Anisotropen Flussigkeiten," Z. Phys. 42, 532-546 (1927).
2. Introduction to Liquid Crystals, edited by E. B. Priestley, P. J. Wojtowicz, and P. Sheng (Plenum, New York, 1974).
3. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).
4. A collection of recent papers and reviews, including papers in physics education-oriented journals may be found in R. J. Ondris-Crawford, G. P. Crawford, and J. W. Doane, "Resource letter: LC-1: Liquid crystals: Physics and applications," Am. J. Phys. 63 (9), 781-788 (1995).
5. P. J. Collings, "Liquid crystal displays," Am. J. Phys. 63 (11), 1044-1048 (1995).
6. We limit our attention in this paper to liquid crystals composed of rod-like molecules. Nematics composed of disk-like molecules are also known.
7. If the magnetic susceptibility tensor is positive uniaxial (the usual case), a liquid-crystal molecule reduces its potential energy by orienting with its long molecular axis along the magnetic field. Molecules with a negative uniaxial magnetic susceptibility tensor would tend to orient in a plane normal to the applied field. The cyanobiphenyl liquid crystals used in this study have a positive uniaxial susceptibility tensor.
8. Actually, the liquid-crystal molecules at the substrate surface are not perfectly rigidly anchored and may reorient to a small extent when an external field is applied. The effect is negligible for the measurements described in this paper.
9. H. Gruler, T. J. Scheffer, and G. Meier, "Elastic Constants of Nematic Liquid Crystals I. Theory of the Normal Deformation," Z. Naturforsch. Teil A 27, 966-976 (1972).
10. M. J. Bradshaw and E. P. Raynes, "The Frank constants of some nematic liquid crystals," J. Phys. (Paris) 46, 1513-1520 (1985).
11. χ in cgs-Gaussian units.
12. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960), pp. 126-130.
13. This form of the Euler-Lagrange equation is applicable when the integrand has no explicit dependence on the independent variable x. For a derivation, see J. B. Marion and S. T. Thornton, Classical Dynamics of Particles and Systems (Harcourt-Brace, New York 1995), 4th ed., pp. 222-223.
14. 2, respectively. For more details, see L. D. Landau and E. M. Lifshitz, Statistical Physics, Part I (Pergamon, New York, 1980), 3rd ed., Chap. 14.
15. W. H. de Jeu, W. A. P. Claassen, and A. M. J. Spruijt, "The Determination of the Elastic Constants of Nematic Liquid Crystals," Mol. Cryst. Liq. Cryst. 37, 269-280 (1976).
16. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), Chap. 17.
17. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), 6th ed., pp. 679-680.
18. We note that in order to measure the oscillations in the transmitted light intensity rather than just noting the intensity minima, one needs about a factor of 5 better resolution in the applied magnetic field. Since the first two intensity minima differ by a field of 30 G for a 2.2-mil sample, a resolution of 6 G or so is desirable.
19. Central Scientific Company, Franklin Park, IL sells magnet pole pieces with axial holes ($395). If one decides to fabricate poles, it is important to use a low-carbon steel with small magnetic hysteresis, such as 10-08 type steel with 0.08% carbon by weight. Gary Steel Co., Oakland, CA carries this alloy.
20. 20 5CB (catalog No. K15) and other cyanobiphenyl liquid crystals are available from EM Industries, Hawthorne, NY for $110 for 5 g.
21. P. P. Karat and N. V. Madhusudana, "Elastic and Optical Properties of Some 4′-n-Alkyl-4-Cyanobiphenyls," Mol. Cryst. Liq. Cryst. 36, 51-64 (1976).
22. N. V. Madhusudana and R. Pratibha, "Elasticity and Orientational Order in Some Cyanobiphenyls: Part IV. Reanalysis of the Data," Mol. Cryst. Liq. Cryst. 89, 249-257 (1982).
23. A. Buka and W. H. de Jeu, "Diamagnetism and orientational order of nematic liquid crystals," J. Phys. (Paris) 43, 361-367 (1982).
24. Mylar shim stock suitable for spacers may be obtained from Small Parts Inc., Miami Lakes, FL.
25. A better view of defects may be obtained if the sample is viewed in transmitted light when placed between crossed polarizers; ideally, a polarized microscope, or an ordinary microscope with crossed polaroids inserted in the light path, can be used.
26. A very complete list of surface preparation methods is given by J. Cognard, "Alignment of Nematic Liquid Crystals and Their Mixtures," Mol. Cryst. Liq. Cryst. 78, Suppl. 1, 1-77 (1982).
27. A more accurate measurement of the sample cell thickness may be made using a microscope, by focusing alternately on the two inner surfaces of the substrates and noting the differences in the readings of the calibrated fine-adjust micrometer.
28. F. Brochard, P. Pieranski, and E. Guyon, "Dynamics of the Orientation of a Nematic-Liquid-Crystal Film in a Variable Magnetic Field," Phys. Rev. Lett. 28 (26), 1681-1683 (1972).