Elastic Constants of a Disc-Like Nematic Liquid Crystal: Pseudo-Molecular Approach

Abstract

The pseudo-molecular method is employed to obtain analytical expressions for the elastic constants of an ensemble of anisotropic particles, in both disc-like and rod-like geometries. These particles interact via a phenomenological pair potential constructed from the non-spherical correction to the dispersion forces between two identical molecules. The molecular shape appears in the calculations of the elastic constants in two different cases. The first case considers a molecular volume of ellipsoidal shape continuously deformed from a positive (prolate spheroid, rod-like molecule) to large negative (oblate spheroid, disc-like molecule) values of a parameter describing some kind of eccentricity. The second one considers a molecular volume shape continuously deformed from a cylinder (calamitic molecule) to a plane disc by changing the ratio between the diameter of the cylinder and its long axis. The particular cases of Maier-Saupe and Nehring-Saupe interactions are obtained as simple limiting cases of the general pair potential interaction. These general results may be helpful to understand the limits of the pseudo-molecular method, and to understand the origin of elastic constants in discotic liquid crystals from a molecular perspective.

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Notes

  1. 1.

    It is assumed L = 0 in the nematic phase. In this case, there is no deformation in the ground state. L would be nonzero only in the cholesteric phase [1].

  2. 2.

    The value of C 1 will not be shown here, because when it is replaced in C i j k l , it yelds a vanishing contribution. In the following, we show that the elastic constants do not depend on C 1.

  3. 3.

    In ref. [28], Bates calls HLR potential a similar potential to (5), used in computational simulations. As (5) appears in [18], and there is a reference to it in the paper from Humphries, Luckhurst and Romano [19], it is convenient to call (5) HLR potential, too.

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Acknowledgments

The authors would like to thank L. R. Evangelista and R. T. Teixeira-Souza for comments and suggestions to improve the work, and the anonymous referee for suggesting a better redaction.

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Simonário, P.S., de Andrade, T.M. & Freire, F.C.M. Elastic Constants of a Disc-Like Nematic Liquid Crystal: Pseudo-Molecular Approach. Braz J Phys 46, 26–34 (2016). https://doi.org/10.1007/s13538-015-0375-2

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Keywords

  • Elastic constants
  • Liquid crystals
  • Lattice models
  • Pseudo-molecular method