Statistical thermodynamics of charge-stabilized colloids

Abstract

This thesis is a theoretical study of equilibrium statistical thermodynamic properties of colloidal systems in which electrostatic interactions play a dominant role, namely, charge-stabilized colloidal suspensions. Such systems are fluids consisting of a mixture of a large number of mesoscopic particles and microscopic ions which interact via the Coulomb force, suspended in a molecular fluid. Quantum statistical mechanics is essential to fully understand the properties and stability of such systems. A less fundamental but for many purposes, sufficient description, is provided by classical statistical mechanics. In such approximation the system is considered as composed of a great number of charged classical particles with additional hard-core repulsions. The kinetic energy or momentum integrals become independent Gaussians, and hence their contribution to the free energy can be trivially evaluated. The contribution of the potential energy to the free energy on the other hand, depends upon the configuration of all the particles and becomes highly non-trivial due to the long-range character of the Coulomb force and the extremely different length scales involved in the problem. Using the microscopic model described above, we focus on the calculation of equilibrium thermodynamic properties (response functions), correlations (structure factors), and mechanical properties (forces and stresses), which can be measured in experiments and computed by Monte Carlo simulations. This thesis is divided into three parts. In part I, comprising chapters 2 and 3, we focus on finite-thickness effects in colloidal platelets and rigid planar membranes. In chapter 2 we study electrolyte-mediated interactions between two of such colloidal objects. Several aspects of these interactions are considered including the nature (attractive or repulsive) of the force between the objects, the osmotic properties for different types of surfaces and image charge effects. In part II, which includes chapters 4 and 5, we consider colloidal mixtures. In chapter 4 we propose a generalization of the cell model which allows the calculation of osmotic properties of polydisperse systems. In chapter 5 we consider volume terms for colloidal mixtures. We calculate explicitly the effective interaction potential for a colloidal mixture that results after tracing out the ionic degrees of freedom. In part III, namely chapters 6 and 7, we study colloidal dispersions in external fields. In chapter 6 we focus on sedimentation of charge-stabilized colloids. We calculate sedimentation profiles by using a one-component model, which effectively treats the degrees of freedom associated with the ions, and compare the results with Monte Carlo simulations of the primitive model, which treats the ions explicitly. In chapter 7 we consider sedimentation of polydisperse systems. In particular we exploit the effective interaction potential calculated in chapter 5 to study the colloidal Brazil nut effect.