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| Author(s): |
Eduardo do Carmo
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 2011-10-07 |
| Examining board members: |
Silvio Roberto de Azevedo Salinas;
Roberto Fernandes Silva Andrade;
Vera Bohomoletz Henriques;
Jürgen Fritz Stilck;
Carlos Seihiti Orii Yokoi
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| Advisor: | Silvio Roberto de Azevedo Salinas |
| Abstract | |
We consider the Maier-Saupe model with the Zwanzig restriction for the orientations of the liquid-crystalline molecules. This model describes the nematic-isotropic phase transition of the thermotropic liquid-crystals. In order to study an elusive biaxial structure on a binary mixture of rods and discs, we add new disordered shape variables. For a quenched distribution of shapes, the system displays a stable biaxial nematic phase. For a thermalized distribution of shapes, however, the biaxial structure is forbidden. These results are confirmed through a connection with the Landau-de Gennes theory. To gain confidence in the use of these techniques, we also studied a model for a binary mixture of Ising magnets on a lattice. In order to go beyond the mean-field calculations, we consider the discretized Maier- Saupe (-Zwanzig) model on a Bethe lattice. The analysis of the problem is performed by the iteration of some recurrence relations. The isotropic-nematic phase transition is determined through the free energy that comes from the Gujrati method. For the problem of a binary mixture of prolate and oblate molecules, using a formalism suitable for the fluidity of the nematic molecules, we show that both thermodynamic and dynamic analyses of stability preclude the existence of a nematic biaxial phase. (AU) | |