Resistor-Network Modeling of Ionic Conduction in Polymer Electrolytes

A general-purpose tool for modeling multifunctional thin porous media (POREnet): From pore network to effective property tensors

POREnet, a novel approach to model effective properties of thin porous media, TPM, is presented. The methodology allows the extraction of local effective property tensors by volume averaging from discrete pore networks, PNs, built on the tessellated continuum space of a TPM. The gradient theorem is used to describe 3D transport in bulk tessellated space, providing an appropriate metric to normalize network fluxes. Implemented effective transport properties include diffusivity, permeability, solid-phase conductivity, and entry capillary pressure and contact angle under two-phase conditions, considering multi-component materials with several solid phases and local contact resistances. Calculated property tensors can be saved on 3D image stacks, where interfacial and sub-CV scale features can be added before exporting data to CFD meshes for simulation. Overall, POREnet provides a general-purpose, versatile methodology for modeling TPM in an ample range of conditions within a single CFD framework. Among other advantages, coupling of PN and continuum models at TPM-channel interfaces is simplified, interfacial contact resistances can be included using robin boundary conditions, and transient multiphysics simulations can be implemented more easily using CFD. The code is tested against a miscellaneousness of examples extracted from electrochemical applications.

A Numerical Assessment of Mitigation Strategies to Reduce Local Oxygen and Proton Transport Resistances in Polymer Electrolyte Fuel Cells

The optimized design of the catalyst layer (CL) plays a vital role in improving the performance of polymer electrolyte membrane fuel cells (PEMFCs). The need to improve transport and catalyst activity is especially important at low Pt loading, where local oxygen and ionic transport resistances decrease the performance due to an inevitable reduction in active catalyst sites. In this work, local oxygen and ionic transport are analyzed using direct numerical simulation on virtually reconstructed microstructures. Four morphologies are examined: (i) heterogeneous, (ii) uniform, (iii) uniform vertically-aligned, and (iv) meso-porous ionomer distributions. The results show that the local oxygen transport resistance can be significantly reduced, while maintaining good ionic conductivity, through the design of high porosity CLs (ε≃ 0.6-0.7) with low agglomerated ionomer morphologies. Ionomer coalescence into thick films can be effectively mitigated by increasing the uniformity of thin films and reducing the tortuosity of ionomer distribution (e.g., good ionomer interconnection in supports with a vertical arrangement). The local oxygen resistance can be further decreased by the use of blended ionomers with enhanced oxygen permeability and meso-porous ionomers with oxygen transport routes in both water and ionomer. In summary, achieving high performance at low Pt loading in next-generation CLs must be accomplished through a combination of high porosity, uniform and low tortuosity ionomer distribution, and oxygen transport through activated water.

Humidity-Dependent Hydration and Proton Conductivity of PFSA Ionomer Thin Films at Fuel-Cell-Relevant Temperatures: Effect of Ionomer Equivalent Weight and Side-Chain Characteristics

Studies on the hydration properties, proton conductivity, and water content of perfluorinated ionomer thin films at temperatures relevant to fuel cell operation temperatures (around 80 °C) and the effect of ionomer chemistry are scarce. In this work, we report the water content and proton conductivity properties of thin-film ionomers (30 nm) at 80 °C over a wide range of relative humidity (0-90%) for seven different ionomers differing in the side-chain structure, including the number of protogenic groups, with the equivalent weight ranging from 620 to 1100 g/mol of sulfonic acid. The results show that the acid content or equivalent weight of the ionomer is the strongest determinant of both the swelling and the proton conductivity of ionomer films at a given relative humidity. The molar water content (λ) of ionomer films normalized to the molar protogenic group is observed to be equivalent-weight-dependent, implying that the affinity for water is acid-content-dependent. At high relative humidity conditions (>70%) pertinent to fuel cell operations, the proton conductivity of low-equivalent-weight ionomers was higher than that of higher-equivalent-weight ionomers. However, upon correlating the proton conductivity with molar water content (λ), the differences reduce dramatically, highlighting that water content is the controlling factor for proton conduction. Significantly higher values of both water content and proton conductivity are observed at 80 °C compared to those at 30 °C, implying that room temperature data are not reliable for estimating ionomer properties in the fuel cell catalyst layer.

Influence of Mesoscale Interactions on Proton, Water, and Electrokinetic Transport in Solvent-Filled Membranes: Theory and Simulation

Transport of protons and water through water-filled, phase-separated cation-exchange membranes occurs through a network of interconnected nanoscale hydrophilic aqueous domains. This paper uses numerical simulations and theory to explore the role of the mesoscale network on water, proton, and electrokinetic transport in perfluorinated sulfonic acid (PFSA) membranes, pertinent to electrochemical energy-conversion devices. Concentrated-solution theory describes microscale transport. Network simulations model mesoscale effects and ascertain macroscopic properties. An experimentally consistent 3D Voronoi-network topology characterizes the interconnected channels in the membrane. Measured water, proton, and electrokinetic transport properties from literature validate calculations of macroscopic properties from network simulations and from effective-medium theory. The results demonstrate that the hydrophilic domain size affects the various microscale, domain-level transport modes dissimilarly, resulting in different distributions of microscale coefficients for each mode of transport. As a result, the network mediates the transport of species nonuniformly with dissimilar calculated tortuosities for water, proton, and electrokinetic transport coefficients (i.e., 4.7, 3.0, and 6.1, respectively, at a water content of 8 H₂O molecules per polymer charge equivalent). The dominant water-transport pathways across the membrane are different than those taken by the proton cation. Finally, the distribution of transport properties across the network induces local electrokinetic flows that couple water and proton transport; specifically, local electrokinetic transport induces water chemical-potential gradients that decrease macroscopic conductivity by up to a factor of 3. Macroscopic proton, water, and electrokinetic transport coefficients depend on the collective microscale transport properties of all modes of transport and their distribution across the hydrophilic domain network.

Continuum Modeling of Porous Electrodes for Electrochemical Synthesis

Electrochemical synthesis possesses substantial promise to utilize renewable energy sources to power the conversion of abundant feedstocks to value-added commodity chemicals and fuels. Of the potential system architectures for these processes, only systems employing 3-D structured porous electrodes have the capacity to achieve the high rates of conversion necessary for industrial scale. However, the phenomena and environments in these systems are not well understood and are challenging to probe experimentally. Fortunately, continuum modeling is well-suited to rationalize the observed behavior in electrochemical synthesis, as well as to ultimately provide recommendations for guiding the design of next-generation devices and components. In this review, we begin by presenting an historical review of modeling of porous electrode systems, with the aim of showing how past knowledge of macroscale modeling can contribute to the rising challenge of electrochemical synthesis. We then present a detailed overview of the governing physics and assumptions required to simulate porous electrode systems for electrochemical synthesis. Leveraging the developed understanding of porous-electrode theory, we survey and discuss the present literature reports on simulating multiscale phenomena in porous electrodes in order to demonstrate their relevance to understanding and improving the performance of devices for electrochemical synthesis. Lastly, we provide our perspectives regarding future directions in the development of models that can most accurately describe and predict the performance of such devices and discuss the best potential applications of future models.

Characterization and Modeling of Free Volume and Ionic Conduction in Multiblock Copolymer Proton Exchange Membranes

Free volume plays a key role on transport in proton exchange membranes (PEMs), including ionic conduction, species permeation, and diffusion. Positron annihilation lifetime spectroscopy and electrochemical impedance spectroscopy are used to characterize the pore size distribution and ionic conductivity of synthesized PEMs from polysulfone/polyphenylsulfone multiblock copolymers with different degrees of sulfonation (SPES). The experimental data are combined with a bundle-of-tubes model at the cluster-network scale to examine water uptake and proton conduction. The results show that the free pore size changes little with temperature in agreement with the good thermo-mechanical properties of SPES. However, the free volume is significantly lower than that of Nafion®, leading to lower ionic conductivity. This is explained by the reduction of the bulk space available for proton transfer where the activation free energy is lower, as well as an increase in the tortuosity of the ionic network.

Random pore-network model for polymer electrolyte membranes

A random pore-network model for polymer electrolyte membranes (PEM) is presented that couples the flow of protons and water through cylindrical channels to the swelling of the membrane. While the flows are determined by closed-form solutions of the Poisson-Nernst-Planck-Stokes equations, the fluid-structure interaction is described by a pressure balance at the channel walls. Macroscopic membrane properties, such as the conductivity, permeability and electro-osmotic coefficient, are computed and compared to experimental data in the literature. In light of the model simplifications, the results compare favourably to data but they also point to the importance of describing proton diffusion in PEM nanopores accurately.

On the Conductivity of Proton-Exchange Membranes Based on Multiblock Copolymers of Sulfonated Polysulfone and Polyphenylsulfone: An Experimental and Modeling Study

The effect of relative humidity (RH) and degree of sulfonation (DS) on the ionic conductivity and water uptake of proton-exchange membranes based on sulfonated multiblock copolymers composed of polysulfone (PSU) and polyphenylsulfone (PPSU) is examined experimentally and numerically. Three membranes with a different DS and ion-exchange capacity are analyzed. The heterogeneous structure of the membranes shows a random distribution of sulfonated (hydrophilic) and non-sulfonated (hydrophobic) domains, whose proton conductivity is modeled based on percolation theory. The mesoscopic model solves simplified Nernst-Planck and charge conservation equations on a random cubic network. Good agreement is found between the measured ionic conductivity and water uptake and the model predictions. The ionic conductivity increases with RH due to both the growth of the hydrated volume available for conduction and the decrease of the tortuosity of ionic transport pathways. Moreover, the results show that the ionic conductivity increases nonlinearly with DS, experiencing a strong rise when the DS is varied from 0.45 to 0.70, even though the water uptake of the membranes remains nearly the same. In contrast, the increase of the ionic conductivity between DS=0.70 and DS=0.79 is significantly lower, but the water uptake increases sharply. This is explained by the lack of microphase separation of both copolymer blocks when the DS is exceedingly high. Encouragingly, the copolymer membranes demonstrate a similar performance to Nafion under well hydrated conditions, which can be further optimized by a combination of numerical modeling and experimental characterization to develop new-generation membranes with better properties.

Interesting Facets of Surface, Interfacial, and Bulk Characteristics of Perfluorinated Ionomer Films

Ion-containing perfluorinated polymers possess unique viscoelastic properties, excellent proton conductivity, and nanophase-segregated structure all arising from the clustering of hydrophilic sulfonic acid groups within a matrix of hydrophobic fluorocarbons. When these ionomers are confined to nanothin films, a broad swathe of structural organization imparting a rich variety of surface, interfacial, and bulk characteristics can be expected. However, our understanding of perfluorinated ionomer thin film behavior is still in a rudimentary stage, and much of the research focus to date has been on its hydration-related structure and properties pertinent to electrochemical applications. Thus, many hidden gems-their interesting surface and interfacial properties-have been overlooked. In this Invited Feature Article, which is a summary of the key contributions by the author's group, including several collaborative publications on ionomer thin films, we unravel many of these facets. In addition, the article attempts to integrate knowledge acquired from a variety of investigations of different aspects of the ionomer thin films to refine and develop a consistent picture of their structure and behavior. First, we focus on the self-assembly of ionomers and show that dispersion media and hydrophobicity/hydrophilicity of the substrate can result in partial or even no coverage of substrates, shedding light on the complexity of polymer-substrate, polymer-solvent, and polymer-polymer interactions, an insight completely obscured when the spin-coating method is adopted for film creation. We demonstrate that the same ionomer can be used to create a variety of surfaces ranging from superhydrophilic to highly hydrophobic by controlling the film thickness or through the choice of substrate material. The ultrathin, hydrophilic surfaces of self-assembled Nafion ionomer films exhibit wettability switching behavior which opens the door to creating stimuli-responsive smart surfaces. The thermoresponsive behavior of the films is discussed in the context of surface (wettability) and bulk (thermal expansion) characteristics as well as a newly discovered vibrational mode. The substrate- and film thickness-dependent thermal expansion coefficients reinforce the importance of interfacial interactions and confinement on the structure/properties of these films. They also open up the potential of tuning ionomer bulk properties via substrate chemistry. The discovery of a vibrational mode that becomes thermally activated at high temperature has provided new insights into the origins of the molecular motions responsible for the α-relaxation of the Nafion ionomer as well as the underlying reason for wettability switching. Our recent neutron reflectometry study of different ionomers varying in side-chain composition/length on a platinum substrate shows that the interfacial hydration level is correlated to the side-chain length, which opens up the possibility of the controlling the interfacial electrochemistry. Finally, a systematic analysis of factors affecting proton conduction is presented to elucidate the yet-unresolved origins of the suppressed conduction of nanothin ionomer films compared to that of the bulk membrane. By revealing these interesting yet poorly understood facets of ionomer thin films, the article aims to stimulate further scientific pursuit on this topic.

Poly(bis-arylimidazoliums) possessing high hydroxide ion exchange capacity and high alkaline stability

Solid polymer electrolyte electrochemical energy conversion devices that operate under highly alkaline conditions afford faster reaction kinetics and the deployment of inexpensive electrocatalysts compared with their acidic counterparts. The hydroxide anion exchange polymer is a key component of any solid polymer electrolyte device that operates under alkaline conditions. However, durable hydroxide-conducting polymer electrolytes in highly caustic media have proved elusive, because polymers bearing cations are inherently unstable under highly caustic conditions. Here we report a systematic investigation of novel arylimidazolium and bis-arylimidazolium compounds that lead to the rationale design of robust, sterically protected poly(arylimidazolium) hydroxide anion exchange polymers that possess a combination of high ion-exchange capacity and exceptional stability.

Nafion® Tubing Humidification System for Polymer Electrolyte Membrane Fuel Cells

Humidity and temperature have an essential influence on PEM fuel cell system performance. The water content within the polymeric membrane is important for enhancing proton conduction and achieving high efficiency of the system. The combination of non-stationary operation requests and the variability of environment conditions poses an important challenge to maintaining optimal membrane hydration. This paper presents a humidification and thermal control system, to prevent the membrane from drying. The main characteristics of such a device are small size and weight, compactness and robustness, easy implementation on commercial fuel cell, and low power consumption. In particular, the NTHS method was studied in a theoretical approach, tested and optimized in a laboratory and finally applied to a PEMFC of 1 kW that supplied energy for the prototype vehicle IDRA at the Shell Eco-Marathon competition. Using a specific electronic board, which controls several variables and decides the optimal reaction air flow rate, the NTHS was managed. Furthermore, the effects of membrane drying and electrode flooding were presented.

Imaging Channel Connectivity in Nafion Using Electrostatic Force Microscopy

Channel connectivity is an important material property that is considered in making higher-performance proton-exchange membranes. Our group has previously demonstrated that nearly 50% of the aqueous surface domains in Nafion films do not have a connected path to the opposite side of the membrane. These so-called "dead-end" channels lead to a loss in the conductance efficiency of the membrane. Understanding the structure of these dead-end channels is an important step in improving the conductance of the membrane. Although conductive atomic force microscopy is able to provide insight into the connected channels, it does directly report on the dead-end channels. To address this, we use electrostatic force microscopy (EFM) to probe channel connectivity in a Nafion thin film (100-300 nm) under ambient conditions. EFM provided an image of the capacitive phase shift, which is influenced by surface charge, dielectric permittivity, and tip-sample geometry. We studied several individual channels and measured the quadratic dependence of the EFM signal with the bias voltage. Applying a simple parallel plate model allowed us to assign differences in the EFM signal to particular channel shapes: connected cylindrical channels, dead-end cylinder channels, and bottleneck channels.

New Insights into Perfluorinated Sulfonic-Acid Ionomers

In this comprehensive review, recent progress and developments on perfluorinated sulfonic-acid (PFSA) membranes have been summarized on many key topics. Although quite well investigated for decades, PFSA ionomers' complex behavior, along with their key role in many emerging technologies, have presented significant scientific challenges but also helped create a unique cross-disciplinary research field to overcome such challenges. Research and progress on PFSAs, especially when considered with their applications, are at the forefront of bridging electrochemistry and polymer (physics), which have also opened up development of state-of-the-art in situ characterization techniques as well as multiphysics computation models. Topics reviewed stem from correlating the various physical (e.g., mechanical) and transport properties with morphology and structure across time and length scales. In addition, topics of recent interest such as structure/transport correlations and modeling, composite PFSA membranes, degradation phenomena, and PFSA thin films are presented. Throughout, the impact of PFSA chemistry and side-chain is also discussed to present a broader perspective.