Variational models of network formation and ion transport: applications to polyelectrolyte membranes
CIG grant 2018620
This project focuses on the development, analysis, and simulation of continuum models, which characterize material morphological development (e.g., network formation) coupled to ion transport. Examples include nano-structure formation in room-temperature ionic liquids and water network formation in polyelectrolyte membrane fuel cells.
Ionic liquids (namely, liquids composed only of ions) have become the subject of an increasing number of investigations due to their advantages in numerous technological applications, including batteries, supercapacitors, dye-sensitized solar cells, lubricants and nanoparticle syntheses. In contrast to typical electrolyte solutions, ionic liquids often exhibit bulk nanostructure. The development of the nanostructure is tightly coupled to the electrokinetic behavior of the ionic liquid – charge transfer can change the structure of the ionic liquid and the structure, in turn, effects charge transfer via the ionic liquid.
From a theoretical point of view, essentially all research on morphology evolution focused on the self-assembly process of the morphology at static conditions. Mutual feedback between morphology and electrokinetics is beyond the classical theoretical description. The current proposal focused on the development of a novel theoretical framework that couples morphological changes to Coulombic interactions utilizing gradient flows and asymptotic methods. Specifically, the project objectives are two-fold:
* Development of a combined model of morphology evolution and electrokinetics.
* Modelling of electrokinetic phenomena of concentrated solution in confined regions such as water nano-pores.
In pursue of these goals, I have developed an Onsager system that couples morphology development and electrostatics in ionic liquids and later in concentrated electrolytes. Significantly, the system describes morphology evolution in a self–consistent way while satisfying the second law of Thermodynamics. At a basic configuration, this system reduces to the (symmetric) Ohta-Kawasaki equation – a nonlocal Cahn-Hilliard type model that arises from the Ohta and Kawasaki density functional theory for diblock copolymers (DCP) mixtures. The Ohta-Kawasaki equation, therefore, serves as a prototype model for morphology evolution driven by competing short-range and long-range Coulombic interactions. I have conducted a systematic analysis of the asymmetric Ohta-Kawasaki equation – a variant that accounts for asymmetric short-range and long-range interactions that arise, for example, due to a dielectric difference between the phases.
Study of this model in the context of ionic liquids showed how bulk and inter-facial nanostructure influences electrochemical properties of the system, demonstrated both type-I and type-II morphological phase changes, and showed that the coupling between electrokinetics and morphology evolution gives rise to ultra-slow relaxation times.
In parallel, I have studied electrokinetic models of concentrated electrolytes in aim to incorporate them into the morphology model. This study gave rise to the steric PNP-Cahn-Hilliard model which accounts for high-order steric effects and allows to connect relevant parameters in the ionic liquid model to Lennard-Jones iteraction parameters between the ionic species.
The efficiency of novel clean-energy devices such as organic photovoltaic cells and capacitors based on room-temperature ionic liquids critically depends on the interplay between morphology evolution and electrokinetics. The modeling framework developed in this study is readily suited to analyze such systems. Thus, I expect that foundations gained through this project will open many new technological vistas.