Variational models of network formation and ion transport: applications to polyelectrolyte membranes
CIG grant 2018620
The main goal of this project is the development, analysis, and simulation of continuum models, which characterize amphiphilic network formation coupled to ion transport. Such systems arise in polyelectrolyte membrane fuel cells, and in particular in Nafion – the industry standard membrane for fuel cells. As Nafion absorbs water, a network of selective water nano-pores evolves in the membrane. The morphology of the network had been extensively studied as it has crucial influence on fuel cell efficiency.
From a theoretical point of view, essentially all research on network morphology focused on the self-assembly process of the pore network. The network morphology, however, is likely to evolve under operating conditions – namely, charge transferred via the pores may change the pore network morphology. Thus, the system involves mutual feedback between morphology and electrokinetics. Such feedback is beyond the available theoretical description. The current proposal aims to develop a novel theoretical framework that will allow understanding morphological changes coupled to Coulombic interactions utilizing gradient flows and asymptotic methods. Specifically, the project objectives are two-fold:
* Development of a combined model for morphology evolution and charge transfer.
* Modelling of electrokinetic phenomena of concentrated solution in confined regions such as the water nano-pores.
In pursue of these goals, I have developed an Onsager system that couples morphology development and electrostatics, as well as reactions. The system describes morphology evolution in a self–consistent way while satisfying the second law of Thermodynamics. At a basic configuration, this system reduce to the (symmetric) Ohta-Kawasaki equation – 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 interactions. My research included 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. The Ohta-Kawasaki framework, however, is insufficient to model network evolutions in membranes like Nafion. Therefore, I have extended the framework to explicitly incorporate electrokinetics and non-equilibrium chemical reactions which are required to model network morphology.
In parallel, I have studied electrokinetic models of concentrated electrolytes in aim to incorporate them into the network morphology model at a later phase. The common approach in the literature is to apply physical reasoning to derive a model, and then identify its region of validity by comparing it’s predictions with experimental data. I have taken a different approach, and recovered suitable models by systematic interpretation of experimental data. Specifically, by analyzing differential capacitance data we identified all non-ideality terms, within a class, that give rise to the prescribed data.
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 proposal will open many new technological vistas.