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Doctoral Thesis
DOI
10.11606/T.43.2011.tde-29092011-144333
Document
Author
Full name
Danilo Barbosa Liarte
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Yokoi, Carlos Seihiti Orii (President)
Arenzon, Jeferson Jacob
Figueiredo Neto, Antonio Martins
Henriques, Vera Bohomoletz
Stilck, Jürgen Fritz
Title in Portuguese
Modelos estatísticos de campo médio para vidros de spins e fluidos complexos
Keywords in Portuguese
Física teórica
Mecânica estatística
Mudança de fase
Abstract in Portuguese
Estudamos nesta tese três sistemas desordenados distintos das áreas de vidros de spins e fluidos complexos, por meio de modelos estatísticos no contexto da aproximação de campo médio. Analisamos os efeitos da inclusão de graus de liberdade elásticos sobre o diagrama de fases do modelo de Sherrington-Kirkpatrick, que é a versão de campo médio de um modelo popular de vidros de spins, paradigmas de sistemas com desordem temperada. Analisamos em seguida alguns problemas típicos da física dos fluidos complexos. Investigamos o diagrama de fases de um modelo de Maier-Saupe (MS), que é uma espécie de arquétipo das transições nemáticas, numa versão de rede muito simples, denominada modelo de Maier-Saupe-Zwanzig (MSZ), com a introdução de uma variável binária de desordem para representar uma mistura de discos e cilindros. Mostramos que o aparecimento de uma fase nemática biaxial, termodinamicamente estável, que tem sido intensamente procurada na literatura, depende da forma de tratamento das variáveis de desordem. Finalmente, utilizamos o modelo MSZ, na presença de termos elásticos não lineares e de elementos de desordem, a fim de reproduzir diversas características do comportamento termodinâmico dos elastômeros nemáticos, novos materiais poliméricos, com propriedades dos cristais líquidos nemáticos e das borrachas, tema de grande interesse na física da matéria mole.
Title in English
Mean-field statistical models for spin glasses and complex fluids
Keywords in English
Phase transition
Statistical mechanics
Theoretical Physics
Abstract in English
We study three distinct disordered systems in the areas of spin glasses and complex fluids, by means of mean-field statistical models. We first analyze the effects of compressibility on the phase diagram of the Sherrington-Kirkpatrick model, a mean-field version of a popular model of spin glasses, which are paradigmatic examples of systems with quenched disorder. We then analyze some typical problems in the area of physics of complex fluids. We investigate the phase diagram of a Maier-Saupe model (MS), which is a sort of archetype of nematic transitions, in a simple lattice version called Maier-Saupe-Zwanzig model (MSZ), with the introduction of a binary variable of disorder to mimic a mixture of rod-like and plate-like mesogens. We show that the emergence of a stable nematic biaxial phase, which has been intensely pursued in the literature, depends on the form of treatment of the disorder variables. Finally, we use the MSZ model, in the presence of non-linear elastic terms and elements of disorder, to reproduce several aspects of the thermodynamic behavior of nematic elastomers, new polymeric materials with the properties of liquid crystals and rubber, and of great importance in the area of soft-matter physics.
 
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tese_daniloliarte.pdf (2.76 Mbytes)
Publishing Date
2011-11-18
 
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