Lebwohl-Lasher model: Difference between revisions

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The '''Lebwohl-Lasher model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase | nematic liquid crystal]]. The Lebwohl-Lasher model consists of a cubic lattice with the [[Intermolecular pair potential | pair potential]]  
The '''Lebwohl-Lasher model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase | nematic liquid crystal]]. The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial [[nematogens|nematogenic]] particles with the [[Intermolecular pair potential | pair potential]]  


:<math>\Phi_{ij} = -\epsilon_{ij} P_2 (\cos \beta_{ij}) </math>
:<math>\Phi_{ij} = -\epsilon_{ij} P_2 (\cos \beta_{ij}) </math>


where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials |Legendre polynomial]].
where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials |Legendre polynomial]].
==Isotropic-nematic transition==
==Isotropic-nematic transition==
(Ref. 3)
(Ref. 3)

Revision as of 15:14, 19 February 2009

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The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal. The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial nematogenic particles with the pair potential

where , is the angle between the axes of nearest neighbour particles and , and is a second order Legendre polynomial.

Isotropic-nematic transition

(Ref. 3)


Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition. (Mondal, Roy; Physics Letters A, 2003, 312, 397-410) (Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311)

Lattice Gas Lebwohl-Lasher model

This model is the lattice gas version of the Lebwohl-Lasher model. In this case the sites of the lattice can be occupied by particles or empty. The interaction between nearest-neighbor particles is that of the Lebwohl-Lasher model. This model has been studied in

Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702

References

  1. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
    1. Erratum, Physical Review A 7 p. 2222 (1973)
  2. U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 58 (1986)