Phase behavior of charged colloids : many-body effects, charge renormalization and charge regulation

The main topic of this thesis is Poisson–Boltzmann theory for suspensions of charged colloids in two of its approximations: cell-type approximations that explicitly take into account non-linear effects near the colloidal surfaces, such as charge renormalization, at the expense of neglecting any explicit multi-body interactions; and (ii) linear approximations that do take into account explicit multi-body interactions but neglect any non-linear effects. These approximations give contradictory results with regards to the existence of spinodal instabilities at low salinity. Firstly, we review Poisson–Boltzmann theory and its cell approximation, and derive a complete description of the linear approximation in a semi-grand canonical framework; we show that this theory gives rise to so-called volume terms, which drive spinodal instabilities at low salinity, and which also give important contributions to the osmotic pressure of such colloidal suspensions. We then construct a novel theory by combining the cell-type and the linear approximations. Taking the strong points of each, the newly constructed theory takes into account both the non-linear behavior near the colloidal surfaces and the explicit multi-body interactions between the colloids. Using this theory, we calculate phase-diagrams as a function of the salt concentration and the colloidal density for many values of the charge Z and the radius over Bjerrum-length ratio λ B / a . We find that spinodal instabilities occur for systems with Z λ B / a ≥ 25 , and that these instabilities for large charges Z are connected to the gas–liquid instability of the primitive model with small (Z=1–10) valencies, suggesting that both instabilities have the same physical origin. Furthermore, we study charge regulation, which describes the chemical equilibrium between ions bound to the colloidal surfaces and free ions. We first study this effect in the Poisson–Boltzmann cell model, and calculate the net charge of the colloids as a function of the particle size, the dissociation constant, the colloid density and the salt concentration. We scanned a large part of parameter space for spinodal instabilities, but find no such instabilities within this model. Finally, we include the charge regulation effects into the newly developed multi-centered non-linear Poisson–Boltzmann theory. For silica particles, we calculate the charge Z as a function of the colloid density and the salt concentration, and we find that, for almost all systems examined, the coupling parameter Z λ B / a ≤ 10 . We thus conclude that, in this model with charge regulation, the coupling parameter is too small for spinodal instabilities to occur. We explicitly calculated phase-diagrams for a large number of colloidal charges and radii, and indeed find no instabilities. Therefore, we conclude that the spinodal instabilities that were found in the model with fixed colloidal charge are probably hard to reach in experimental setups with silica particles.