Theory of Multiscale and Multicomponent Transport and Thermodynamics in Water-Filled Phase-Separated Cation-Exchange Membranes

Phase-separated water-swollen cation-exchange membranes are an important component in numerous energy-conversion devices. These materials make possible more established technologies such as low-temperature fuel cells, water electrolyzers, and the chlor-alkali process. Solvent-swollen membranes also play a key role in burgeoning energy-storage devices, such as redox-flow batteries (RFB), as well as processes geared towards electrifying the chemical industry, such as artificial photosynthesis and electrochemical ammonia production. The membrane is central to these technologies.To understand the role that these membranes play in energy-conversion devices, this work initially considers a RFB as a case study. This dissertation examines the effect that membrane properties, such as conductivity and ion permeability, have on cell performance and efficiency. There is typically a tradeoff between membranes with high conductivity and low ion permeability. Given specific operational constraints, we quantitatively map when this tradeoff should be made. Thermodynamic and transport properties of the membrane fundamentally influence process performance. These water-swollen membranes contain concentrated electrolyte solutions, often with multiple ionic species. The multicomponent and concentrated nature of these materials invalidates classic theoretical treatments of the material that invoke ideal dilute-solution approximations. To promote improved material design and process optimization, this dissertation develops mathematical models of the concentrated-solution thermodynamic and transport phenomena in these membranes. Perfluorinated sulfonic-acid (PFSA) ionomers (e.g., Nafion® developed by DuPont de Nemours, Inc.) is the quintessential phase-separated, solvent-swollen, cation-exchange membrane material. PFSAs consist of a hydrophobic polytetrafluoroethylene (PTFE) backbone with side chains terminating in hydrophilic sulfonate groups. The sulfonate groups are negatively charged and balanced by positively charged aqueous protons or other cations. In aqueous solutions or humid vapor, water absorbs into the membrane, hydrating the sulfonate groups. The hydrophilicity difference between the polymer backbone and hydrated ions drives nanophase separation and the formation of a bicontinuous structure with sulfonate groups imbedded at the hydrophobic/hydrophilic domain interface. The hydrophilic phase forms a network of connected aqueous water-filled channels that facilitate transport of ions and solvent across the membrane. The transport and thermodynamic phenomena occur across multiple length scales. Molecular interactions dictate the microscale behavior of species in the channels. The hydrophilic-phase network introduces mesoscale effects. Macroscopic membrane properties are a function of both the microscale and mesoscale. To first quantify the important molecular interactions and the role of the microscale on membrane properties, this dissertation develops a microcontinuum mathematical model of a representative water-filled channel. Negatively charged sulfonate groups are immobilized at the channel walls and mobile cations are distributed across the channel. The model calculates the potential of mean force and distribution functions of the cations. The model considers solvation energy, electrostatic interactions, image charges, finite-size effects, and dispersion forces. Bulk-electrolyte cation mobility is modified by electrohydrodynamic and confinement effects. Model predictions show that the portion of mobile cations is governed by a competition between solvation energy that promotes cation dissociation from the sulfonate groups and electrostatic interactions that induce ion-pair formation. The hydrophilic-phase tortuosity upscales the microscale transport model, specifying macroscopic conductivity. Tortuosity is fit to data using one adjustable parameter. Membrane conductivity is governed by the tortuosity of the hydrophilic channels and the microscale interactions inside the channels. These contributions vary with water content and membrane chemistry.Having identified the key microscale phenomena, this work develops molecular thermodynamic and transport models for the multicomponent membrane system. The thermodynamic model proposes a free energy that includes excess contributions proposed in the microcontinuum model (electrostatic interactions and solvation effects) as well as ion-pair formation, swelling forces, and confinement along with semi-empirical non-electrostatic specific-ion interactions,. Bulk-electrolyte solution properties parameterize most of the free-energy contributions. The thermodynamic model calculates ion and water partitioning into the membrane from dilute and concentrated aqueous solutions and water uptake from water vapor. The model calculations compare favorably to experimental measurements.Having established a thermodynamic framework, this work develops a multicomponent concentrated-solution model of transport that fully calculates macroscopic ion and solvent-transport properties of the membrane. The model uses a Stefan-Maxwell formalism describing frictional interactions between species. Bulk-electrolyte solution properties specify ion/ion and ion/solvent friction coefficients inside the water-filled channels. A classic electrokinetic treatment determines ion/membrane and solvent/membrane friction coefficients. Channel tortuosity upscales the microscale friction coefficients. The model predicts macroscopic conductivity, water permanence, ion-transference numbers, and electro-osmotic coefficients that agree with experiments of membranes in dilute and concentrated aqueous electrolyte solutions.As a case study, this dissertation uses the multicomponent thermodynamic and transport models to understand the performance of membranes in a vanadium RFB. The model reveals that concentration gradients of various species each drive transport of other species. This coupling is both thermodynamic in nature – with concentration gradients inducing chemical potential gradients in other species – and frictional – with molecular interactions among species influencing the transport of one another. This new model provides structure-function-performance relationships for RFB membranes and rationalizes how RFB performance results from the collective interactions between all of the species present. The proposed transport models invoke a ubiquitous assumption from literature that tortuosity of water-filled channels uniformly upscales microscale transport properties. This dissertation examines the usefulness of this approach using network simulations and theory. The models explore the role of the mesoscale on water, proton, and electrokinetic transport properties in PFSA membranes. Network simulations account for the size distribution of channels throughout the membrane to calculate macroscopic properties. An experimentally consistent 3D Voronoi network tessellation characterizes the topology of the membrane hydrophilic phase. Experimental water, proton, and electrokinetic transport properties validate model calculations. We show that the network does not uniformly upscale microscale transport properties. The simulations predict dissimilar tortuosities arising for water, proton, and electrokinetic transport coefficients. The pathways that water travels across the membrane are different than those taken by protons due to their intrinsic microscale interactions within a hydrophilic channel combined with a wide distribution of channel sizes. The distribution of transport properties across the network induces local electrokinetic gradients that couple water and proton transport. As a result, the macroscopic proton transport coefficient is a function of the microscale water and electrokinetic transport properties. This work provides a holistic approach to connect experiments and theory of microscale to macroscale properties.The fundamental analysis of transport and thermodynamic phenomena provided here informs design of improved solvent-filled ion-exchange membranes. Moreover, this work provides engineering models that facilitate optimization of energy-conversion devices