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Sharp-Interface Nematic–Isotropic Phase Transitions without Flow

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Abstract.

We derive a supplemental evolution equation for an interface between the nematic and isotropic phases of a liquid crystal when flow is neglected. Our approach is based on the notion of configurational force. As an application, we study the behavior of a spherical isotropic drop surrounded by a radially oriented nematic phase: our supplemental evolution equation then reduces to a simple ordinary differential equation admitting a closed-form solution. In addition to describing many features of isotropic-to-nematic phase transitions, this simplified model yields insight concerning the occurrence and stability of isotropic cores for hedgehog defects in liquid crystals.

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Acknowledgments.

P.C. was supported by the Italian M.I.U.R. project “Modelli matematici per la scienza dei materiali” during the completion of this work. E.F. and M.E.G. were supported by the National Science Foundation and the Department of Energy.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Paolo Cermelli

  2. Department of Mechanical and Aerospace Engineering, University of Washington in St. Louis, St. Louis, MO, 63130-4899, USA

    Eliot Fried

  3. Department of Mathematical Sciences, Carnegie Mellon University Pittsburgh, PA, 15213-3190, USA

    Morton E. Gurtin

Authors
  1. Paolo Cermelli
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  2. Eliot Fried
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  3. Morton E. Gurtin
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Correspondence to Morton E. Gurtin.

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Cermelli, P., Fried, E. & Gurtin, M. Sharp-Interface Nematic–Isotropic Phase Transitions without Flow. Arch. Rational Mech. Anal. 174, 151–178 (2004). https://doi.org/10.1007/s00205-004-0334-5

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