Study of strongly correlated colloidal systems

Abstract

This thesis presents the study of the structural and dynamical properties, as well as, melting of colloidal systems. Initially, we study the structure and phonon spectrum of a system of charged magnetic dipoles, organized in a bilayer structure and oriented perpendicular to the plane of the layers. This system can be tuned through six different crystalline phases by changing parameters such as the interlayer separation and/or the charge and/or dipole moment of the particles. The presence of the electric charge on the dipole particles is responsible for the nucleation of five staggered phases and a disordered phase which are not found in the magnetic dipole bilayer system previously presented in the literature. These extra phases are a consequence of the competition between the repulsive Coulomb and the attractive dipole interlayer interaction. The minimum energy structures are summarized in a phase diagram associated to the separation between the layers and to the relative importance between the magnetic and electric interactions. We determine the order of the structural phase transitions. The phonon spectrum of the system was calculated within the harmonic approximation. A non-monotonic behavior of the phonon spectrum is found as a function of the effective strength of the inter-particle interaction. The thermodynamic stability of the different phases is determined. Then, we study the bilayer system of charged magnetic dipoles for nonzero temperatures, investigating the melting behavior of the system through the modified Lindemann criterion, as a function of the parameters: (i) the distance between the layers η and (ii) the relative intensity of the magnetic interaction with respect to the electric interaction λ. For large enough λ, one of the phases (the matching hexagonal phase) exhibits a re-entrant melting behavior as a function of η. Since the charges and the magnetic dipole moment of the colloidal particles can be altered, for example, by changing the pH of the solution in which they are immersed or an external magnetic field, respectively, this system can be in principle verified experimentally. Last, a two-dimensional (2D) binary colloidal system consisting of interacting dipoles is investigated. Within the harmonic approximation, we obtained the phonon spectrum of the system as a function of the composition, dipole moment ratio and mass ratio between the small and big particles. Through a systematic analysis of the phonon spectra, we are able to determine the stability region of the different lattice structures of colloidal alloys. The gaps in the phonon frequency spectrum, the optical frequencies in the long-wavelength limit and the sound velocity are discussed as well. Using the modified Lindemann criterion and within the harmonic approximation, we estimated the melting temperature of the sub-lattice generated by the big particles.