UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A statistical mechanical theory for the crystallization of alkali halides from aqueous solution Ursenbach, Charles


The crystallization transitions and physical stability of model aqueous alkali halide solutions are investigated. A second-order density functional theory is developed for molecules of general symmetry, and is applied to the crystallization of anhydrous alkali halides, ice Ih, sodium chloride dihydrate, and lithium iodide trihydrate from the appropriate solutions. Thermodynamic stability theory is clarified and then applied, using Kirkwood-Buff methods, to ionic solutions and a simple binary liquid mixture. The liquid correlation functions are obtained for two liquid models. In the first, ions are modelled as charged hard spheres, and the solvent as a polarizable multipolar hard sphere. The second is similar but involves a modification to the hard repulsive core of the ion-ion potential, and this is found to have a strong influence on solution properties and crystallization transitions. The density functional theory presented is the first such theory for nonlinear molecules based on generalized spherical harmonic expansions. It is also the first molecular theory with the density given in direct lattice vectors instead of reciprocal lattice vectors. Because of the long-range correlations in ionic solutions, a technique involving Ewald sums is developed to aid the convergence of sums over direct lattice vectors. The resulting theory is shown to be superior for these models to a reciprocal lattice vector method. In its final form, the theory for molecules such as H20 requires a number of one-dimensional integrals to be performed numerically. When applied, the density functional theory yields minima for nearly all systems, showing the possibility of a phase transition. In many of these systems, liquid-solid coexistence is predicted as well. Model dependence is shown to be important in determining whether the equilibrium is under conditions similar to those of real systems, and whether the crystal parameters are similar to those of real solids. The theory predicts reasonable values for the oscillation widths about average orientations. In applying stability concepts, it is important to distinguish between the strictest criteria of stability, a set of conditions which are collectively necessary and sufficient for thermodynamic stability, and the weaker criteria, which are necessary but not sufficient conditions. We use this to clarify some misconceptions in the literature, and then give its nontrivial application to electrolytes. The results indicate that salts with only large ions, such as Csl, and those with a small ion, such as Na+ or K+, behave differently near the absolute stability limit. The former act hydrophobically, and appear to undergo demixing from the solvent, while the latter, which bind the solvent more tightly, do not show clear signs of any such demixing, but do appear to become mechanically unstable.

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.