Liquid-crystalline ordering in two-dimensional systems with discrete symmetry
✍ Scribed by Mercurieva, Anna A. ;Birshtein, Tatyana M.
- Publisher
- Wiley (John Wiley & Sons)
- Year
- 1992
- Weight
- 518 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1018-5054
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The mean‐field theories of liquid‐crystalline (nematic) ordering developed for three‐dimensional systems are applied to describe two‐dimensional systems of both geometrically anisotropic and anisotropically interacting particles. Systems with discrete symmetry (lattice models) for which long‐range order is possible are considered on the base of the Landau free‐energy expansion. It is shown that the Hamiltonian describing the energy of intermolecular interactions may be written in a common form for lyotropic and thermotropic systems. The mean‐field theory gives a continuous phase transition (second‐order phase transition) for a square lattice, whereas for a triangular lattice it gives a phase transition with latent heat (first‐order phase transition) like for three‐dimensional systems. These results are compared with results of the exact theories (two‐dimensional Ising and Potts models). It is concluded that for realistic two‐dimensional models the orientational in‐plane ordering is not sharper than a second‐order phase transition.