Estudo de sistemas bidimensionais de partículas clássicas

Abstract

This thesis is dedicated to the study of the structural, dynamical and thermal properties of finite two-dimensional systems of classical particles. In its first part, we study the structures and the vibrational properties of particles of confined systems in the zero temperature case. Specifically, the ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures, like chains and Y-shaped configurations, when a magnetic field is applied parallel to the plane of the particles. Besides, we analyze the dynamic of particles through the study of the normal-mode spectrum. It is studied as a function of the magnetic field and the strength of the dipole moment of the particles. The translational and rotational components of the normal mode spectrum are obtained and investigated in details. As a function of the number of particles, we found different ordered configurations for different values of the dipole moment and the external magnetic field. We also study numerically the structure and the normal mode spectrum of a two vertically coupled finite-size two-dimensional system, composed of interacting classical charged particles confined by a nonuniform distribution of background charge. The structural and dynamical properties of the system are analyzed as a function of the separation between the planes of charges, and as a function of the strength of the confinement potential. We find different asymmetrical ground-state configurations, as well as structural phase transitions induced by the unbinding of particles, which were not present in previous models with a parabolic confinement potential. Depending on the order of the structural transition the normal-mode frequencies exhibit a discontinuity or a softening. In the second part of the thesis, we study the structural dependence of the twodimensional systems on the temperature. Specifically, we systematically investigate the melting of a finite size binary system consisting of two types of particles having different charges and/or masses, confined in a two-dimensional parabolic trap. The melting temperature is obtained for different values of the ratio between the charges and/or masses of the two types of particles. It is found that two types of particles melt at different temperatures; e.g., particles with smaller charge melt first. The importance of the commensurate/incommensurate configurations, and the different normal modes to the melting phenomenon, is also studied. When the ground state consists of a nonsymmetric arrangement of particles, new thermally induced structural phase transitions are found. In addition, a remarkable temperature induced spatial separation of the two types of particles is observed. We also study the melting of a competing interacting potential system of classical particles confined in a circular parabolic trap. The particles interact through a short-range attractive, and long-range repulsive, potential. Different behaviors of the melting temperature are found depending on the strength of the attractive part of the interparticle potential. The melting of a system consisting of small bubbles takes place through a two-step melting process. A reentrant behavior and a thermally induced structural phase transition are observed in a small region of a space diagram of the main parameters of the system. A hysteresis effect in the configuration of the particles is observed as a function of temperature. This is a consequence from the presence of a potential barrier between different configurations of the system.