Dipolar Liquids and Their Mixtures: Equilibrium and Nonequilibrium Properties with Field-Theoretic Approaches

Liquid is a state of matter that is intermediate between the gas state and the solid state. Though it is an ordinary state of matter, the application of statistical mechanics for understanding its properties is far from complete. Compared to the solid state, the liquid state has molecules that can move around freely, and yet, unlike that in the gas state, the intermolecular correlations are significant in the liquid state. Therefore, the distance dependent correlations in a liquid need to be taken into account to properly describe a liquid. In particular, all molecules are polarizable. The polarizable nature allows the molecules to induce polarization in surrounding molecules, giving rise to van der Waals interactions that have important consequences on the properties of a liquid. In addition to polarizability, many molecules are intrinsically polar. The long-ranged dipole-dipole correlations contribute to the complexity of interactions and lead to a myriad of interesting properties special to a liquid. In recent years, field-theoretic technique has emerged as a convenient and systematic tool for deriving coarse-grained theories for a wide range of complex-fluid and soft-matter systems while preserving the essential physics. In this thesis, we present the application of field-theoretic approaches to two problems of liquids and their mixtures. The first problem is to describe the dielectric properties of an ordinary liquid or liquid mixture under equilibrium condition, where current field-theoretic methods are inadequate. In this problem, we apply a variational field-theoretic approach to develop a statistical field theory of the liquid, and predict the dielectric constant and the miscibility of liquids using the variational free energies derived. The second problem involves the nonequilibrium solvent composition and orientational polarization surrounding some charged solute in the context of electron transfer reactions. Using a self-consistent-field theory with constrained coarse-grained fields, we derive expressions for the nonequilibrium solvation energy, and apply it to compute the reorganization energy of electron transfer reactions. The theories presented in this thesis lead to simple analytical expressions for the equilibrium and the nonequilibrium free energies, making it possible to theoretically survey a wide range of liquids. In addition, our models involve only a few readily-available molecular parameters and avoid the use of any adjustable parameters, allowing one to make a priori predictions on the properties of liquids and their mixtures. </p

Combined Theoretical and Experimental Study of Refractive Indices of Water–Acetonitrile–Salt Systems

We propose a simple theoretical formula for describing the refractive indices in binary liquid mixtures containing salt ions. Our theory is based on the Clausius–Mossotti equation; it gives the refractive index of the mixture in terms of the refractive indices of the pure liquids and the polarizability of the ionic species, by properly accounting for the volume change upon mixing. The theoretical predictions are tested by extensive experimental measurements of the refractive indices for water–acetonitrile-salt systems for several liquid compositions, different salt species, and a range of salt concentrations. Excellent agreement is obtained in all cases, especially at low salt concentrations, with no fitting parameters. A simplified expression of the refractive index for low salt concentration is also given, which can be the theoretical basis for determination of salt concentration using refractive index measurements

Salt-Induced Liquid–Liquid Phase Separation: Combined Experimental and Theoretical Investigation of Water–Acetonitrile–Salt Mixtures

Salt-induced liquid–liquid phase separation in liquid mixtures is a common phenomenon in nature and in various applications, such as in separation and extraction of chemicals. Here, we present results of a systematic investigation of the phase behaviors in water–acetonitrile–salt mixtures using a combination of experiment and theory. We obtain complete ternary phase diagrams for nine representative salts in water–acetonitrile mixtures by cloud point and component analysis. We construct a thermodynamic free energy model by accounting for the nonideal mixing of the liquids, ion hydration, electrostatic interactions, and Born energy. Our theory yields phase diagrams in good agreement with the experimental data. By comparing the contributions due to the electrostatic interaction, Born energy, and hydration, we find that hydration is the main driving force for the liquid–liquid separation and is a major contributor to the specific ion effects. Our theory highlights the important role of entropy in the hydration driving force. We discuss the implications of our findings in the context of salting-out assisted liquid–liquid extraction and make suggestions for selecting salt ions to optimize the separation performance

Accurate Determination of Ion Polarizabilities in Aqueous Solutions

We present a novel method for obtaining salt polarizabilities in aqueous solutions based on our recent theory for the refractive index of salt solutions, which predicts a linear relationship between the refractive index and the salt concentration at low concentrations, with a slope determined by the intrinsic values of the salt polarizability and the density of the solution. Here we apply this theory to determine the polarizabilities of 32 strong electrolyte salts in aqueous solutions from refractive index and density measurements. Setting Li^+ as the standard ion, we then determine the polarizabilities of seven cations (Na^+, K^+, Rb^+, Cs^+, Ca^(2+), Ba^(2+), and Sr^(2+)) and seven anions (F^–, Cl^–, Br^–, I^–, ClO_4^–, NO_3^–, and SO_4^(2–)), which can be used as important reference data. We investigate the effect of temperature on salt polarizabilities, which decreases slightly with increasing temperature. The ion polarizability is found to be proportional to the cube of bare ionic radius (r_(bare)^3) for univalent ions, but the relationship does not hold for multivalent ions. Contrary to findings of Krishnamurti, we find no significant linear relationship between ion polarizability and the square of the atomic number (N^2) for smaller ions

Small-Network Approximations for Geometrically Frustrated Ising Systems

The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths in frustrated Ising systems, we develop a method for obtaining first approximations to the energetic properties of frustrated two-dimensional Ising systems using small networks of less than 30 spins. These small networks allow much faster numerical simulations, and more importantly, analytical evaluations of their properties are numerically tractable. We choose Ising systems on the triangular lattice, the kagome lattice, and the triangular kagome lattice as prototype systems and find small systems that can serve as good approximations to these prototype systems. Through comparisons between the properties of extended models and small systems, we develop a set of criteria for constructing small networks to approximate general infinite two-dimensional frustrated Ising systems. This method of using small networks provides a different and efficient way to obtain a first approximation to the properties of frustrated spin systems