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Equilibrium of fluid membranes endowed with orientational order

Jaya Kumar Alageshan1, Buddhapriya Chakrabarti2,*, and Yashodhan Hatwalne1

  • 1Raman Research Institute, C.V. Raman Avenue, Bangalore 560 080, India
  • 2Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom

  • *Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK.
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Phys. Rev. E 95, 042806 – Published 28 April, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.042806

Abstract

Minimization of the low-temperature elastic free-energy functional of orientationlly ordered membranes involves independent variation of the membrane-shape, while keeping the orientational order on it (its texture) fixed. We propose an operational, coordinate-independent method for implementing such a variation. Using the Nelson-Peliti formulation of elasticity that emphasizes the interplay between geometry, topology, and thermal fluctuations of orientationally ordered membranes, we minimize the elastic free energy to obtain equations governing their equilibrium shape, together with associated free boundary conditions. Our results are essential for understanding and predicting equilibrium shapes as well as textures of membranes and vesicles; particularly under conditions in which shape deformations are large.

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Phys. Rev. E 95, 042806– Published 28 April, 2017
  • Received 17 June 2015
  • Revised 24 January 2017

©2017 American Physical Society

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