Some Topics in Interfacial and Solution Thermodynamics

Abstract

Elements from Gibbsian composite-system thermodynamics, classical nucleation theory, combinatorics, and statistical mechanics were used to provide insights into and develop models for some equilibrium systems of practical importance. This thesis consists of two parts. In part one, three problems were considered in which complex interfacial geometries dictate the stability of configurations and phase change properties of the system: (i) interacting drop–drop and drop–bubble systems in an immiscible medium, (ii) vapor nucleation from a liquid¬¬–gas solution inside a cylindrical nanopore, and (iii) solid nucleation from a pure liquid inside and out of cylindrical nanopores. Regarding the first problem, contributions were made to the calculation of equilibrium configurations and system behavior at the nanoscale. Regarding the second problem, a nonideal model was derived for liquid–vapor equilibrium across an arbitrarily curved interface, and its predictive capability was demonstrated when used with a constant-value line tension correction. Regarding the third problem, equilibrium shapes of the new-phase nucleus near a liquid meniscus and equilibrium shapes for the growth of the new phase out of a collection of cylindrical pores were analyzed; the roles of these calculated geometries on the ease of nucleation and growth were quantified. In part two of this thesis, contributions were made to the development and application of the multisolute osmotic virial equation and its combining rules. It was shown that a similar model to that which was proposed by Elliott et al. earlier using the regular solution model can be derived in a more general solution theory framework with less restrictive assumptions. The derived model has a corrected combining rule for the cubic terms and new combining rules for higher order terms. This model was then extended to dissociating solutes by utilizing a previously used technique and was then applied to predict freezing points of ternary salt solutions yielding accurate predictions using binary data only as the input. Overall, the findings of this thesis can help further our understanding of the role of interfacial geometry in small systems and of multisolute mixtures, valuable in applications such as atmospheric physics, nanoscience, biology, and energy storage, among others.