Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Effective theories for liquid crystals and the Maier-Saupe phase transition

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      We discuss effective theories for thermotropic nematic liquid crystals. In the first part of this article, we rigorously carry out two physically different scaling limits of the fundamental statistical mechanical model of a system of \(N\) rod-like particles as \(N\to\infty\), which we call the mean-field and the Gross-Pitaevskii limit. Each of them yields an effective `one-body' free energy functional. In the second part, we study the associated Euler-Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier-Saupe potential, that the system converges to perfect nematic order.

      Related collections

      Most cited references 22

      • Record: found
      • Abstract: not found
      • Article: not found

      I. Liquid crystals. On the theory of liquid crystals

       F. Frank (1958)
        Bookmark
        • Record: found
        • Abstract: not found
        • Article: not found

        The theory of liquid crystals

         C. W. Oseen (1933)
          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          Bifurcation from simple eigenvalues

            Bookmark

            Author and article information

            Journal
            2015-08-20
            2016-10-28
            1508.05025

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            abstract modified; references added; discussion of connection with literature expanded
            math-ph cond-mat.stat-mech math.AP math.MP

            Comments

            Comment on this article