• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
10.11606/D.54.1983.tde-04032015-210940
Document
Author
Full name
Giomal Aparecido Antonio
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1983
Supervisor
Committee
Hipolito, Oscar (President)
Chaba, Amar Nath
Mokross, Bernhard Joachim
Title in Portuguese
Propriedades estáticas e dinâmicas de um cristal dipolar
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Foi observado experimentalmente que esferas poliestireno ( ≈ 2500 Å) adsorvidas na interface água-ar formam um cristal bidimensional de estrutura hexagonal. Supondo um potencial de interação dipolar nós calculamos, empregando métodos analíticos para acelerara convergência das somas, a energia estática de interação para todos os tipos de rede de Bravais em duas dimensões e mostramos que a estrutura hexagonal é aquela que tem a menor energia. Usando a aproximação harmônica encontramos a matriz dinâmica do sistema e obtivemos a relação de dispersão dos modos normais de vibração para vetores de onda ao longo das direções de simetria da primeira zona de Brillouin da rede hexagonal. No limite de longos comprimentos de onda os dois ramos vão linearmente a zero, dando velocidades transversal e longitudinal, cT and cL, com as quais, através da teoria da fusão de Kosterlitz e Thouless estimamos o valor do parâmetro T para a fusão, TM=40,6. T é o parâmetro adimensional definido como a razão entre a energia potencial média e a energia cinética (KBT). Nossos resultados são comparados com os resultados da simulação deste sistema realizada em computador, através de dinâmica molecular.
Title in English
Not available
Keywords in English
Not available
Abstract in English
It was experimentally observed that polysturene spheres (≈ 2500 Å in diameter) trapped at the water-air interface form a two-dimensional hexagonal lattice. Assuming a dipolar interaction potential between spheres we have calculated, by using analytical methods to acelerating the convergence, the static energy for all two-dimensional Bravais lattice and we showed that tje hexagonal lattice has the lowest energy. Using the harmonic approximation we found the dynamical matrix for the system and obtained the dispersion relation of the vibrational normal modes for wave vectors along the symmetry directions in the hexagonal first Brillouin zone. In the long-wavelenght limit the two branches vanish linearlly, giving transversal and longitudinal velocities (cT and cL with which, through the Kosterlitz-Touless theory of melting we estimated the melting parameter, TM=40,6 . T is the dimensionless parameter defined as the ratio between the potential and kinetic energies. Our results are compared with those recently obtained by computer simulations through the molecular dynamics method
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Publishing Date
2015-03-05
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2019. All rights reserved.