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Nonlocal model for nematic liquid-crystal elastomers.

R Ennis1, L C Malacarne, P Palffy-Muhoray

  • 1Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA and Pressco Technology, Solon, Ohio 44139, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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We developed a nonlocal model for nematic liquid-crystal elastomers, capturing dynamic behavior through free energy and dissipation functions. This model accurately describes their complex mechanical and orientational responses.

Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Soft Matter Physics

Background:

  • Nematic liquid-crystal elastomers (NLCEs) exhibit complex behaviors arising from the interplay between elastic and nematic properties.
  • Existing models often rely on gradient expansions, which may not fully capture nonlocal effects in NLCEs.

Purpose of the Study:

  • To develop a fully nonlocal model for describing the dynamic behavior of nematic liquid-crystal elastomers.
  • To incorporate both elastic and nematic contributions into a unified free energy framework.

Main Methods:

  • Developed a free energy functional dependent on displacement and orientational order parameter tensor.
  • Incorporated nonlocal interactions to account for spatial variations of order parameters.
  • Utilized a Lagrangian approach with the Rayleigh dissipation function to derive equations of motion.

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Main Results:

  • Derived equations of motion for displacement and orientational order in NLCEs.
  • Analyzed the free energy and equations of motion in the long-wavelength, small-amplitude limit.
  • Recovered standard viscoelastic theory for nematic liquid crystals when the scalar order parameter is fixed.

Conclusions:

  • The fully nonlocal model provides a comprehensive description of NLCE dynamics.
  • The model accounts for nonlocal interactions, offering advantages over gradient-based approaches.
  • This work advances the understanding of soft matter physics and materials science applications.