Estudo das propriedades estruturais e dinâmicas de um sistema binário quasi-unidimensional - Oliveira, Paulo Willyam Simão de (2007)
The aim of this work is to study the structural and dynamical properties of a classical binary system of charged particles confined in a two dimensional channel. Such a system is described in the literature as quasi-unidimensional, and its relevance is supported by the possibility of technological applications, shown recently in the scientific literature, and also the interest and understanding of properties in condensed matter physics. Although the theoretical and numerical character of the present work, several experimental systems can be described by the present model. The summary of the contents of this work is presented in each chapter. In chapter 1, a general overview is given. The concept of Wigner crystallization is introduced, and examples of experimental systems, which exhibit such an ordered phase under proper conditions are given. We discuss the physics of complex plasmas, colloidal suspensions and applications in biological systems. A description of the simulation method is given in chapter 2. Scale transformations are introduced in order to construct a general model, i.e. no longer depending on particular features of the system, but only on relevant parameters of a general model. The Molecular Dynamics simulation technique (MD) is presented, focusing on the Langevin Dynamics. The competition between the inter-particle interaction, in the form of the electrostatic repulsion, and the external confinement, which is assumed to be parabolic and act only in one direction, generates a chain-like strutural pattern. A description of the model, the harmonic approach used in the analytical calculations of the normal modes spectrum, and the analytical calculation of the energy per particle of the different chain-configutations are given in chapter 3. The ground state configurations, the structural phase transitions and normal modes of the present chain-like binary system are presented in Chapter 4. In the low density regime particles crystallize in a single chain. When the density is increased a zig-zag transition occurs and the single chain splits into two chains. Such a transition is characterized by a spontaneous symmetry breaking. With the increase of the density the system changes to the four-chains configuration (case 1) (particles not aligned vertically), where the two -> four chains (case 1) transition occurs through a zig-zag transition accompanied by a shift along the chain direction. A further increase of the density will lead the system to a new ground state configuration with four chains (case 2) (particles aligned vertically). The dynamical properties are related to the phonon spectrum, in which the number of normal modes is two times the number particle in the unit cell. The conclusions and perspectives are presented in chapter 5.