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A unified continuum theory of liquid crystals

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ARI - An International Journal for Physical and Engineering Sciences

Abstract

A unified continuum theory is proposed governing physical behavior of all liquid crystals whose molecules are modelled with rigid directors. Balance laws and constitutive equations are given and thermodynamic restrictions are obtained. Chiral and nonchiral liquid crystals are shown to differ only in their symmetry groups and smectic liquid crystals in a constraint on twist elasticities. Dynamic constitutive equations include translation and gyration viscosities coupled with heat conduction. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.

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References

  • de Gennes PG, Prost J (1993) The physics of liquid crystals (2nd edn) Oxford University Press, New York

    Google Scholar 

  • Edelen DGB (1972) A nonlinear Onsager theory of irreversibility. Int J Eng Sci 10:481–490

    Article  Google Scholar 

  • Eringen AC (1964) Simple microfluids. Int J Eng Sci 2:205–217

    Article  Google Scholar 

  • Eringen AC (1966) Theory of micropolar fluids J Math Mech 16:1–18

    Google Scholar 

  • Eringen AC (1970) Foundation of micropolar thermoelasticity. Springer, Vienna

    Book  Google Scholar 

  • Eringen AC (1978) Micropolar theory of liquid crystals. In: Liquid crystals and ordered fluids Vol 3. Plenum Press, New York, 443–473

    Google Scholar 

  • Eringen AC (1980) Mechanics of continua (2nd edn) Krieger, Huntington, New York

    Google Scholar 

  • Eringen AC (1993) An assessment of director and micropolar theories of liquid crystals, Int J Eng Sci 31: 605–616

    Article  Google Scholar 

  • Eringen AC, Kafadar CB (1976) Polar Field theories. In: Eringen AC (ed) Continuum physics Vol 4. Academic Press, New York, pp 2–71

    Google Scholar 

  • Frank FC (1958) On the theory of liquid crystals. Discuss Faraday Soc 25: 19–28

    Article  Google Scholar 

  • Leslie FM, Stewart IW, Nakagawa M (1991) A continuum theory for smectic C liquid crystals. Mol Cryst Liq Cryst 198: 443–454

    Article  Google Scholar 

  • Oseen CW (1933) The theory of liquid crystals. Trans Faraday Soc 29: 883–899

    Article  Google Scholar 

  • Rymarz CZ (1990) More about the relations between the Ericksen-Leslie-Parodi and Eringen-Lee theories of nematic liquid crystal. Int J Eng Sci 28: 11–21

    Article  Google Scholar 

  • Stephen MJ and Strahley JP (1974) Physics of liquid crystals. Rev Mod Phys 46: 617–704

    Article  Google Scholar 

  • Synge JL (1960) Classical dynamics. In: Flügge S (ed) Handbuch der Physik III/1. Springer, Berlin Heidelberg New York, p 18.

    Google Scholar 

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Authors and Affiliations

  1. 15 Red Tail Drive, Littleton, CO, 80126-5001, USA

    A. C. Eringen

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  1. A. C. Eringen
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Eringen, A.C. A unified continuum theory of liquid crystals. ARI 50, 73–84 (1997). https://doi.org/10.1007/s007770050001

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  • DOI: https://doi.org/10.1007/s007770050001

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