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Jerry Ericksen: Liquid Crystal Pioneer

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Abstract

In the 1960s Jerry Ericksen made major contributions to the construction of the continuum theory of nematic liquid crystals. This paper gives a brief summary of his work and the consequent giant impact on the field.

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Notes

  1. The notation here corresponds to that of Selinger [77], rather than that of Frank [36].

  2. We have substituted the modern notation \(N\) for Ericksen’s contemporary \(\hat{n}\).

References

  1. Anzelius, A.: Über die Bewegung der anisotropen Flüssigkeiten (On motion in anisotropic fluids) (in German) PhD thesis, Uppsala University (1931)

  2. Atkin, R.: Poiseuille flow of liquid crystals of the nematic type. Arch. Ration. Mech. Anal. 38, 224–240 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  3. Atkin, R.J., Sluckin, T.J.: [Obituary of] Frank Matthews Leslie. Biogr. Mem. Fellows R. Soc. 49, 315–333 (2003)

    Article  Google Scholar 

  4. Becker, R., Feng, X., Prohl, A.: Finite element approximations of the Ericksen–Leslie model for nematic liquid crystal flow. SIAM J. Numer. Anal. 46, 1704–1731 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Beris, A.N., Edwards, B.J.: Thermodynamics of Flowing Systems with Internal Microstructure. Oxford University Press, Oxford (1994)

    Book  Google Scholar 

  6. Bethuel, F., Brezis, H., Coleman, B.D., Hélein, F.: Bifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders. Arch. Ration. Mech. Anal. 118, 149–168 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Brand, H.R., Cladis, P.E., Pleiner, H.: Macroscopic properties of smectic liquid crystals. Eur. Phys. J. B 6, 347–353 (1998)

    Article  Google Scholar 

  8. Brochard-Wyart, F.: [Obituary of] Pierre-Gilles de Gennes (1932–2007). Nature 448, 149 (2007)

    Article  Google Scholar 

  9. Carlsson, T., Leslie, F.M.: The development of theory for flow and dynamic effects for nematic liquid crystals. Liq. Cryst. 26(9), 1267–1280 (1999)

    Article  Google Scholar 

  10. Castellano, J.A.: Liquid Gold: The Story of Liquid Crystal Displays and the Creation of an Industry. World Scientific, Singapore (2005)

    Book  Google Scholar 

  11. Chandrasekhar, S.: Liquid Crystals, 1st edn. Cambridge University Press, Cambridge (1977). There was a second edition in 1992, which brings the reader up to date, but beginners can start with the first edition without being seriously disadvantaged

    Google Scholar 

  12. Cladis, P., Torza, S.: Stability of nematic liquid crystals in Couette flow. Phys. Rev. Lett. 35, 1283–1286 (1975)

    Article  Google Scholar 

  13. Cladis, P.E., Kléman, M.: Non-singular disclinations of strength \({S} = + 1\) in nematics. J. Phys. 33(5–6), 591–598 (1972)

    Article  Google Scholar 

  14. Cladis, P.E., Torza, S.: Flow instabilities in Couette flow in nematic liquid crystals. In: Kerker, M. (ed.) Hydrosols and Rheology, pp. 487–499. Academic Press, London (1976)

    Chapter  Google Scholar 

  15. Coleman, B.D., Noll, W.: On certain steady flows of general fluids. Arch. Ration. Mech. Anal. 3, 289–303 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dunmur, D., Sluckin, T.: Soap, Science, and Flat-Screen TVs: A History of Liquid Crystals. Oxford University Press, Oxford (2011)

    Google Scholar 

  17. de Gennes, P.G.: The Physics of Liquid Crystals 1st edn. Clarendon, Oxford (1974). There is also a second edition, published in 1993, jointly authored by Jacques Prost

    MATH  Google Scholar 

  18. Doostmohammadi, A., Ladoux, B.: Physics of liquid crystals in cell biology. Trends Cell Biol. 32, 40–50 (2022)

    Article  Google Scholar 

  19. Ericksen, J.L.: Anisotropic fluids. Arch. Ration. Mech. Anal. 4, 231–237 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ericksen, J.L.: Theory of anisotropic fluids. Trans. Soc. Rheol. 4, 29–39 (1960)

    Article  MathSciNet  Google Scholar 

  21. Ericksen, J.L.: Transversely isotropic fluids. Kolloid-Z. 173, 117–122 (1960)

    Article  Google Scholar 

  22. Ericksen, J.L.: A vorticity effect in anisotropic fluids. J. Polym. Sci. 47, 231–237 (1960)

    Article  MATH  Google Scholar 

  23. Ericksen, J.L.: Conservation laws for liquid crystals. Trans. Soc. Rheol. 5, 23–34 (1961)

    Article  MathSciNet  Google Scholar 

  24. Ericksen, J.L.: Poiseuille flow of certain anisotropic fluids. Arch. Ration. Mech. Anal. 4, 1–8 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  25. Ericksen, J.L.: Hydrostatic theory of liquid crystals. Arch. Ration. Mech. Anal. 59, 371–378 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  26. Ericksen, J.L.: Nilpotent energies in liquid crystal theory. Arch. Ration. Mech. Anal. 10, 189–196 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ericksen, J.L.: Inequalities in liquid crystal theory. Phys. Fluids 9, 1205–1207 (1966)

    Article  Google Scholar 

  28. Ericksen, J.L.: Instability of Couette flow of anisotropic fluids. Q. J. Mech. Appl. Math. 19, 455–459 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ericksen, J.L.: Some magnetohydrodynamic effects in liquid crystals. Arch. Ration. Mech. Anal. 23, 266–275 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ericksen, J.L.: A boundary layer effect in viscometry of liquid crystals. Trans. Soc. Rheol. 13, 9–15 (1969)

    Article  Google Scholar 

  31. Ericksen, J.L.: J.L. Ericksen’s autobiography. In: Beatty, M.F., Hayes, M.A. (eds.) Mechanics and Mathematics of Crystals: Selected Papers of J.L. Ericksen, pp. xiii–xxv. World Scientific, Singapore (2005)

    Google Scholar 

  32. Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  33. Eringen, A.C.: Micropolar theory of liquid crystals. In: Liquid Crystals and Ordered Fluids, pp. 443–474. Plenum Press, New York (1978)

    Chapter  Google Scholar 

  34. Eringen, A.C.: An assessment of director and micropolar theories of liquid crystals. Int. J. Eng. Sci. 31, 605–616 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  35. Fisher, J., Fredrickson, A.G.: Interfacial effects on the viscosity of a nematic mesophase. Mol. Cryst. 8, 267–284 (1969)

    Article  Google Scholar 

  36. Frank, F.C.: On the theory of liquid crystals. Discuss. Faraday Soc. 25, 19–28 (1958)

    Article  Google Scholar 

  37. Fréedericksz, V., Zolina, V.: On the use of a magnetic field in the measurement of the forces tending to orient an anisotropic liquid in a thin homogeneous layer. Trans. Am. Electrochem. Soc. 55, 85–96 (1929). Reprinted in [80], pp. 222–233

    Google Scholar 

  38. Friedel, G.: Les états mésomorphes de la matière (The mesomorphic states of matter). Ann. Phys. 9, 273–474 (1922). (in French) This famous article is partly translated into English in ref. [80], pp. 162–210

    Article  Google Scholar 

  39. Green, A.E., Rivlin, R.S.: The mechanics of non-linear materials with memory. Arch. Ration. Mech. Anal. 1, 1–21 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gross, B.: The TVs of Tomorrow: How RCA’s Flat-Screen Dreams Led to the First LCDs. University of Chicago, Chicago (2018)

    Book  Google Scholar 

  41. Hardt, R., Kinderlehrer, D., Lin, F.-H.: Existence and partial regularity of static liquid crystal configurations. Commun. Math. Phys. 105, 547–570 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  42. Kelker, H.: History of liquid crystals. Mol. Cryst. Liq. Cryst. 21, 1–48 (1973)

    Article  Google Scholar 

  43. Kelker, H.: Flüssige Kristalle und die Theorien des Lebens: 100 Jahre Flüssigkristallforschung. Nat.wiss. Rundsch. 39, 239–247 (1986)

    Google Scholar 

  44. Kelker, H.: An important detail from the history of liquid crystals. Wiss. Beitr. Martin-Luther-Univ. Halle-Wittenb. 52, 193–215 (1986)

    Google Scholar 

  45. Kelker, H.: Survey of the early history of liquid crystals. Mol. Cryst. Liq. Cryst. 165(1), 1–43 (1988)

    Google Scholar 

  46. Knoll, P.M., Kelker, H.: Otto Lehmann. BoD–Books on Demand, Norderstedt (2010)

    Google Scholar 

  47. Lagerwall, S.T.: On some important chapters in the history of liquid crystals. Liq. Cryst. 40(12), 1698–1729 (2013)

    Article  Google Scholar 

  48. Lee, J.D., Eringen, A.C.: Boundary effects of orientation of nematic liquid crystals. J. Chem. Phys. 55, 4509–4512 (1971)

    Article  Google Scholar 

  49. Lee, J.D., Eringen, A.C.: Wave propagation in nematic liquid crystals. J. Chem. Phys. 54, 5027–5034 (1971)

    Article  Google Scholar 

  50. Lee, J.D., Eringen, A.C.: Relations of two continuum theories of liquid crystals. In: Liquid Crystals and Ordered Fluids, pp. 315–330. Plenum, New York (1974)

    Chapter  Google Scholar 

  51. Lehmann, O.: Flüssige Kristalle sowie Plastizität von Kristallen im allgemeinen, molekulare Umlagerung und Aggregatzustandsänderungen (...Liquid Crystals...). Engelmann, Leipzig (1904) (in German)

    Google Scholar 

  52. Leslie, F.M.: Some constitutive equations for anisotropic fluids. Q. J. Mech. Appl. Math. 19(3), 357–370 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  53. Leslie, F.M.: Some constitutive equations for liquid crystals. Arch. Ration. Mech. Anal. 28(4), 265–283 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  54. Leslie, F.M.: Theory of flow phenomena in liquid crystals. Adv. Liq. Cryst. 4, 1–81 (1979)

    Article  Google Scholar 

  55. Lin, F.-H., Liu, C.: Nonparabolic dissipative systems modeling the flow of liquid crystals. Commun. Pure Appl. Math. 48, 501–537 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  56. Lin, F.-H., Liu, C.: Existence of solutions for the Ericksen-Leslie system. Arch. Ration. Mech. Anal. 154, 135–156 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  57. Martin, P.C., Parodi, O., Pershan, P.S.: Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. Phys. Rev. A 6, 2401–2420 (1972)

    Article  Google Scholar 

  58. Meyer, R.B.: On the existence of even indexed disclinations in nematic liquid crystals. Philos. Mag. 27(2), 405–424 (1973).

    Article  Google Scholar 

  59. Miȩsowicz, M.: Influence of a magnetic field on the viscosity of para-azoxyanisol. Nature 136(3433), 261 (1935)

    Article  Google Scholar 

  60. Miȩsowicz, M.: The three coefficients of viscosity of anisotropic liquids. Nature 158(4001), 27 (1946)

    Article  Google Scholar 

  61. Nabarro, F.R.N., Nye, J.F.: [Obituary of] Sir (Frederick) Charles Frank. Biogr. Mem. Fellows R. Soc. Lond. 46, 177–196 (2000)

    Article  Google Scholar 

  62. Noll, W.: On the continuity of the solid and fluid states. Arch. Ration. Mech. Anal. 4, 3–81 (1955)

    MathSciNet  MATH  Google Scholar 

  63. Oldroyd, J.G.: On the formulation of rheological equations of state. Proc. R. Soc. A. 200, 523–541 (1950)

    MathSciNet  MATH  Google Scholar 

  64. Olmsted, P.D., Goldbart, P.: Theory of the nonequilibrium phase transition for nematic liquid crystals under shear flow. Phys. Rev. A 41, 4578–4581 (1990)

    Article  Google Scholar 

  65. Olmsted, P.D., Goldbart, P.: Isotropic-nematic transition in shear flow: state selection, coexistence, phase transitions, and critical behavior. Phys. Rev. A 46, 4966–4993 (1992)

    Article  Google Scholar 

  66. Olver, P.J.: Introduction to Partial Differential Equations. Undergraduate Texts in Mathematics. Springer, New York (2014)

    Book  MATH  Google Scholar 

  67. Olver, P.J., Sivaloganathan, J.: The classification of null Lagrangians. Nonlinearity 1, 389–398 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  68. Oseen, C.W.: Beiträge zur Theorie der anisotropen Flüssigkeiten 5 (Contributions to the Theory of Anisotropic Fluids 5). Ark. Mat. Astron. Fys. 18, 1–8 (1924) (in German)

    Google Scholar 

  69. Oseen, C.W.: Die anisotropen Flüssigkeiten: Tatsachen und Theorien (Anisotropic Fluids: Facts and Theories). Gebrüder Borntraeger, Berlin (1929) (in German)

    Google Scholar 

  70. Oseen, C.W.: Probleme für die Theorie der anisotropen Flüssigkeiten (Problems in the Theory of Anisotropic Fluids). Z. Kristallogr. 79, 173–185 (1931). (in German) Some extracts from the discussion associated with this issue are reprinted in Ref. [80]

    Article  MATH  Google Scholar 

  71. Oseen, C.W.: The theory of liquid crystals. Trans. Faraday Soc. 29(140), 883–899 (1933). Reprinted in Ref. [80]

    Article  MATH  Google Scholar 

  72. Oswald, P., Pieranski, P.: Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments. CRC Press, Boca Raton (2005)

    Book  Google Scholar 

  73. Parodi, O.: Stress tensor for a nematic liquid crystal. J. Phys. (Paris) 31, 581–584 (1970)

    Article  Google Scholar 

  74. Poniewierski, A., Stecki, J.: Statistical theory of the elastic constants of nematic liquid crystals. Mol. Phys. 38, 1931–1940 (1979)

    Article  Google Scholar 

  75. Rymarz, C.Z.: More about the relations between the Ericksen-Leslie-Parodi and Eringen-Lee theories of nematic liquid crystals. Int. J. Eng. Sci. 28, 11–21 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  76. Schenck, R.: Kristallinische Flüssigkeiten und flüssige Kristalle (Crystalline Fluids and Liquid Crystals). Engelmann, Leipzig (1905). (in German)

    Google Scholar 

  77. Selinger, J.V.: Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals. Liq. Cryst. Rev. 6, 129–142 (2018)

    Article  Google Scholar 

  78. Sluckin, T.J.: [Obituary of] Pierre-Gilles de Gennes (1932–2007). Liq. Cryst. 36(10–11), 1019–1022 (2009)

    Article  Google Scholar 

  79. Sluckin, T.J.: Some reflections on defects in liquid crystals: from Amerio to Zannoni and beyond. Liq. Cryst. 45(13–15), 1894–1912 (2018)

    Article  Google Scholar 

  80. Sluckin, T.J., Dunmur, D.A., Stegemeyer, H.: Crystals That Flow: Classic Papers from the History of Liquid Crystals. Taylor & Francis, London (2004)

    Book  Google Scholar 

  81. Sonin, A.S.: A Road Reaching Back a Century: On the History of Liquid Crystal Science. Nauka, Moscow (1995) (in Russian)

    Google Scholar 

  82. Sonin, A.S., Frenkel, V.Ya.: Vsevolod Konstantinovich Frederiks. Nauka, Moscow (1995) (in Russian)

    Google Scholar 

  83. Srigengan, S., Nagaraj, M., et al.: Anomalously low twist and bend elastic constants in an oxadiazole-based bent-core nematic liquid crystal and its mixtures; contributions of spontaneous chirality and polarity. J. Mater. Chem. C 6, 980–988 (2018)

    Article  Google Scholar 

  84. Stark, H., Lubensky, T.C.: Poisson-bracket approach to the dynamics of nematic liquid crystals. Phys. Rev. E 67, 061709 (2003)

    Article  MathSciNet  Google Scholar 

  85. Stewart, I.W.: The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction. CRC Press, Boca Raton (2004)

    Google Scholar 

  86. Sluckin, T: Professor Sir Charles Frank (1911–1998): historical perspectives on the development of liquid crystal continuum theory. Liq. Cryst. Today 8(3), 1–5 (1998)

    Article  Google Scholar 

  87. Tsvetkov, V.N.: Motion of anisotropic liquids in a rotating magnetic field. Zh. Eksp. Teor. Fiz. 9, 603–615 (1939). (in Russian). A German equivalent paper was published in Acta Phys. URSS 10, 555–578 (1939)

    Google Scholar 

  88. Vertogen, G.: The equations of motion for nematics. Z. Naturforsch. A 38, 1273–1275 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  89. Vorländer, D.: Kristalllinisch-flüssige Substanzen (Crystalline-Fluid Substances). Enke, Stuttgart (1908) (in German)

    Google Scholar 

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Acknowledgements

The authors are grateful to Mrs Ellen Leslie for providing the photograph Fig. 1, and to the editors of the issue for the invitation to contribute an article. TJS is grateful to the late Frank Leslie for relating some personal recollections of his time at Johns Hopkins. MCC acknowledges many conversations with the late Jerry Ericksen which provided some of the deeper human and intellectual background to this article.

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TJS prepared the first draft of the manuscript. MCC added extra material. Both authors reviewed the final manuscript.

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Correspondence to Timothy J. Sluckin.

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Pioneering ideas, formulations, and techniques in modern continuum mechanics – in memory of Jerald Laverne Ericksen

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Sluckin, T.J., Carme Calderer, M. Jerry Ericksen: Liquid Crystal Pioneer. J Elast (2022). https://doi.org/10.1007/s10659-022-09955-8

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