Lebwohl-Lasher model: Difference between revisions

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==Confined systems==
==Confined systems==
The Lebwohl-Lasher model has been used to study the effect of confinement in the phase
The Lebwohl-Lasher model has been used to study the effect of [[Confined systems |confinement]] in the phase
behavior of [[Nematic phase |nematogens]] <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and  Michael P. Allen, " Computer simulation of liquid crystal films",  Molecular Physics '''80''' pp 253-276 (1993) ]</ref>
behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and  Michael P. Allen, " Computer simulation of liquid crystal films",  Molecular Physics '''80''' pp 253-276 (1993) ]</ref>


==Planar Lebwohl–Lasher model ==
==Planar Lebwohl–Lasher model ==

Revision as of 13:45, 15 April 2009

The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal [1][2]. 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

Fabbri and Zannoni estimated the transition temperature [3] via a Monte Carlo simulation:

More recently N. V. Priezjev and Robert A. Pelcovits [4] used a Monte Carlo cluster algorithm and obtained:

See also the paper by Zhang et al. [5].

Confined systems

The Lebwohl-Lasher model has been used to study the effect of confinement in the phase behavior of nematogens [6]

Planar Lebwohl–Lasher model

The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a continuous transition. The ascription of such a transition to the Kosterlitz-Touless type is still under discussion [7] [8] [9] [10].

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-neighbour particles is that of the Lebwohl-Lasher model. This model has been studied in [11].

References

  1. P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
  2. Erratum, Physical Review A 7 p. 2222 (1973)
  3. 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)
  4. N. V. Priezjev and Robert A. Pelcovits Cluster Monte Carlo simulations of the nematic-isotropic transition Phys. Rev. E 63, 062702 (2001) [4 pages]
  5. Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters 69 pp. 2803-2806 (1992)
  6. Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics 80 pp 253-276 (1993)
  7. Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A 312 pp. 397-410 (2003)
  8. C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model", Physica A 148 pp. 298-311 (1988)
  9. H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B 46, 662-673 (1992)
  10. Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)
  11. Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E 64 051702 (2001)