Rism Variational Theories, AN Approach to Solvated Electrons and Colloidal Stability.

This thesis will describe how the RISM (reference interaction site model) theory can be used to model the interactions within a variational theory to calculate experimentally measurable quantities for two diverse problems: an excess electron dissolved in a solvent and polymeric stabilized colloidal solutions. First, the variational theory is used to calculate the nonuniform solvent density for an excess electron under the condition of ground state dominance. It is shown that this new variational theory, coupled with the RISM equation, is formally equivalent to the Polaron -RISM theory. The variational theory is then applied to the specific case of an excess electron in helium. Trapping of the electron within a helium "bubble" is shown to occur for helium excluded volumes greater than 0.15. Favorable comparisons are made with Monte Carlo simulations, while comparisons with the Polaron-RISM theory demonstrate that the new variational theory is more accurate for localized electrons at smaller solvent densities. A new theory is developed for the interactions of colloids with a dilute or semi-dilute solution of polymers. This theory is based on the Edwards' Hamiltonian, but models the polymer-colloid interaction as the direct correlation function of the RISM equation. This is the first theory to include the effects of the colloidal solution on the polymer using formally exact considerations. With the dilute polymer theory, it is shown how a free polymer can induce a metastable state, if the colloidal solution, as apposed to the solvent solution, is a poor solvent. The importance of including three-body terms is demonstrated, while scaling relations for the end-to-end polymer distance are discussed for several polymer conditions. For the first time, the polymer-colloid density-density correlation function is formally calculated. Finally, a theory for colloids interacting with a semi-dilute polymer solution is developed.