Polymer-electrolyte fuel cells are a promising energy-conversion technology. Over the last several decades significant progress has been made in increasing their performance and durability, of which continuum-level modeling of the transport processes has played an integral part. In this review, we examine the state-of-the-art modeling approaches, with a goal of elucidating the knowledge gaps and needs going forward in the field. In particular, the focus is on multiphase flow, especially in terms of understanding interactions at interfaces, and catalyst layers with a focus on the impacts of ionomer thin-films and multiscale phenomena. Overall, we highlight where there is consensus in terms of modeling approaches as well as opportunities for further improvement and clarification, including identification of several critical areas for future research. Fuel cells may become the energy-delivery devices of the 21 st century. Although there are many types of fuel cells, polymer-electrolyte fuel cells (PEFCs) are receiving the most attention for automotive and small stationary applications. In a PEFC, fuel and oxygen are combined electrochemically. If hydrogen is used as the fuel, it oxidizes at the anode releasing proton and electrons according toThe generated protons are transported across the membrane and the electrons across the external circuit. At the cathode catalyst layer, protons and electrons recombine with oxygen to generate waterAlthough the above electrode reactions are written in single step, multiple elementary reaction pathways are possible at each electrode. During the operation of a PEFC, many interrelated and complex phenomena occur. These processes include mass and heat transfer, electrochemical reactions, and ionic and electronic transport. * Electrochemical Society Active Member. z E-mail: azweber@lbl.govOver the last several decades significant progress has been made in increasing PEFC performance and durability. Such progress has been enabled by experiments and computation at multiple scales, with the bulk of the focus being on optimizing and discovering new materials for the membrane-electrode-assembly (MEA), composed of the proton-exchange membrane (PEM), catalyst layers, and diffusionmedia (DM) backing layers. In particular, continuum modeling has been invaluable in providing understanding and insight into processes and phenomena that cannot be resolved or uncoupled through experiments. While modeling of the transport and related phenomena has progressed greatly, there are still some critical areas that need attention. These areas include modeling the catalyst layer and multiphase phenomena in the PEFC porous media.While there have been various reviews over the years of PEFC modeling 1-7 and issues, [8][9][10][11][12][13][14] as well as numerous books and book chapters, there is a need to examine critically the field in terms of what has been done and what needs to be done. This review serves that purpose with a focus on transport modeling of PEFCs. This is not meant to be an exhaustive review...

Perfluorinated sulfonic acid (PFSA) ionomers are the most widely used solid electrolyte in electrochemical technologies due to their remarkable ionic conductivity with simultanous mechanical stability, imparted by their phase‐separated morphology. In this work, the morphology and swelling of PFSA ionomers (Nafion and 3M) as bulk membranes (>10 μm) and dispersion‐cast thin films (<100 nm) are investigated to identify the roles of equivalent weight (EW) and side‐chain length across lengthscales. Humidity‐dependent structural changes as well as different PFSA chemistries are explored in the thin‐film regime, allowing for the development of thickness‐EW phase diagrams. The ratio of macroscopic (thickness) to nanoscopic (domain spacing) swelling during hydration is found to be affine (1:1) in thin films, but increases as the thickness approaches bulk values, revealing the existence of a mesoscale organization governing the multiscale swelling in PFSAs. Ionomer chemistry, in particular EW, is found to play a key role in altering the confinement‐driven structural changes, including thin‐film anisotropy, with phase separation becoming weaker as the film thickness is reduced below 25 nm or as EW is increased. For the lower‐EW 3M PFSA ionomers, confinement appears to induce even stronger phase separation accompanied by domain alignment parallel to the substrate.

Two-photon confocal microscopy and back extraction with UV/Vis-absorption spectrophotometry quantify equilibrium partition coefficients, k, for six prototypical drugs in five soft-contact-lens-material hydrogels over a range of water contents from 40 to 92%. Partition coefficients were obtained for acetazolamide, caffeine, hydrocortisone, Oregon Green 488, sodium fluorescein, and theophylline in 2-hydroxyethyl methacrylate/methacrylic acid (HEMA/MAA, pKa≈5.2) copolymer hydrogels as functions of composition, aqueous pH (2 and 7.4), and salinity. At pH 2, the hydrogels are nonionic, whereas at pH 7.4, hydrogels are anionic due to MAA ionization. Solute adsorption on and nonspecific electrostatic interaction with the polymer matrix are pronounced. To express deviation from ideal partitioning, we define an enhancement or exclusion factor, E ≡ k/φ1, where φ1 is hydrogel water volume fraction. All solutes exhibit E > 1 in 100 wt % HEMA hydrogels owing to strong specific adsorption to HEMA strands. For all solutes, E significantly decreases upon incorporation of anionic MAA into the hydrogel due to lack of adsorption onto charged MAA moieties. For dianionic sodium fluorescein and Oregon Green 488, and partially ionized monoanionic acetazolamide at pH 7.4, however, the decrease in E is more severe than that for similar-sized nonionic solutes. Conversely, at pH 2, E generally increases with addition of the nonionic MAA copolymer due to strong preferential adsorption to the uncharged carboxylic-acid group of MAA. For all cases, we quantitatively predict enhancement factors for the six drugs using only independently obtained parameters. In dilute solution for solute i, Ei is conveniently expressed as a product of individual enhancement factors for size exclusion (Ei(ex)), electrostatic interaction (Ei(el)), and specific adsorption (Ei(ad)):Ei≡Ei(ex)Ei(el)Ei(ad). To obtain the individual enhancement factors, we employ an extended Ogston mesh-size distribution for Ei(ex); Donnan equilibrium for Ei(el); and Henry's law characterizing specific adsorption to the polymer chains for Ei(ad). Predicted enhancement factors are in excellent agreement with experiment.

Recent experiments have revealed that a variety of associative polymers with different architecture (linear and branched) and different nature of the associating interaction (associative protein domains and metal−ligand bonds) exhibit unexplained superdiffusive behavior. Here, Brownian dynamics simulations of unentangled coarse-grained associating starshaped polymers are used to establish a molecular picture of chain dynamics that explains this behavior. Polymers are conceptualized as particles with effective Rouse diffusivities that interact with a mean field background through attachments by stickers at the end of massless springs that represent the arms of the polymer. The simulations reveal three mechanisms of molecular diffusion at length scales much larger than the radius of gyration: hindered diffusion, walking diffusion, and molecular hopping, all of which depend strongly on polymer concentration, arm length, and the association/dissociation rate constants. The molecular model establishes that superdiffusive scaling results primarily from molecular hopping, which only occurs when the kinetics of attachment are slower than the relaxation time of dangling strands. Scaling relationships can be used to identify the range of rate constants over which this behavior is expected. The formation of loops in the networks promotes this superdiffusive scaling by reducing the total number of arms that must detach in order for a hopping step to occur.

Nucleation and growth of ice in the fibrous gas-diffusion layer (GDL) of a proton-exchange membrane fuel cell (PEMFC) are investigated using isothermal differential scanning calorimetry (DSC). Isothermal crystallization rates and pseudo-steady-state nucleation rates are obtained as a function of subcooling from heat-flow and induction-time measurements. Kinetics of ice nucleation and growth are studied at two polytetrafluoroethylene (PTFE) loadings (0 and 10 wt %) in a commercial GDL for temperatures between 240 and 273 K. A nonlinear icecrystallization rate expression is developed using Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory, in which the heat-transfer-limited growth rate is determined from the moving-boundary Stefan problem. Induction times follow a Poisson distribution and increase upon addition of PTFE, indicating that nucleation occurs more slowly on a hydrophobic fiber than on a hydrophilic fiber. The determined nucleation rates and induction times follow expected trends from classical nucleation theory. A validated rate expression is now available for predicting icecrystallization kinetics in GDLs.

Perfluorosulfonic‐acid (PFSA) membranes are widely used as the solid electrolyte in electrochemical devices where their main functionalities are ion (proton) conduction and gas separation in a thermomechanically stable matrix. Due to prolonged operational requirements in these devices, PFSA membranes’ properties change with time due to hygrothermal aging. This paper studies the evolution of PFSA structure/property relationship changes during hygrothermal aging, including chemical changes leading to changes in ion‐exchange capacity (IEC), nanostructure, water‐uptake behavior, conductivity, and mechanical properties. Our findings demonstrate that with hygrothermal aging, the storage modulus increases, while IEC and water content decrease, consistent with the changes in nanostructure, that is, water‐ and crystalline‐domain spacings inferred from small‐ and wide‐angle X‐ray scattering (SAXS/WAXS) experiments. In addition, the impact of aging is found to depend on the membrane's thermal prehistory and post‐treatments, although universal correlations exist between nanostructural changes and water uptake. The findings have impact on understanding lifetime, durability, and use of these and related polymers in various technologies. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 570–581

Biological systems routinely regulate biomolecular transport with remarkable specificity, low energy input, and simple mechanisms. Here, the biophysical mechanisms of nuclear transport inspire the development of gels for recognition and selective permeation (GRASP). GRASP presents a new paradigm for specific transport and selective permeability, in which binding interactions between a biomolecule and a hydrogel lead to faster penetration of the gel. A molecular transport theory identifies key principles for selective transport: entropic repulsion of noninteracting molecules and affinity-mediated diffusion of multireceptor biomolecules through a walking mechanism. The ability of interacting molecules to walk through hydrogels enables enhanced permeability in polymer networks. To realize this theoretical prediction in a novel material, GRASP is engineered from a poly(ethylene glycol) network (entropic barrier) containing antibody-binding oligopeptides (affinity domains). GRASP is synthesized using simultaneous bioconjugation and polycondensation reactions. The elastic modulus, characteristic pore size, biomolecular diffusivity, and selective permeability are measured in the resulting materials, which are applied to regulate the transport of equally sized molecules by preferentially transporting a monoclonal antibody from a polyclonal mixture. Overall, this work presents rationally designed, nucleopore-inspired hydrogels that are capable of controlling biomolecular transport.

Nucleation and growth of ice in the catalyst layer of a proton-exchange-membrane fuel cell (PEMFC) are investigated using isothermal differential scanning calorimetry and isothermal galvanostatic cold-starts. Isothermal ice-crystallization rates and icenucleation rates are obtained from heat-flow and induction-time measurements at temperatures between 240 and 273 K for four commercial carbon-support materials with varying ionomer fraction and platinum loading. Measured induction times follow expected trends from classical nucleation theory and reveal that the carbon-support material and ionomer fraction strongly impact the onset of ice crystallization. Conversely, dispersed platinum particles play little role in ice crystallization. Following our previous approach, a nonlinear ice-crystallization rate expression is obtained from Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. A validated rate expression is now available for predicting ice crystallization within water-saturated catalyst layers. Using a simplified PEMFC isothermal cold-start continuum model, we compare cell-failure time predicted using the newly obtained rate expression to that predicted using a traditional thermodynamic-based approach. From this comparison, we identify conditions under which including ice-crystallization kinetics is critical and elucidate the impact of freezing kinetics on low-temperature PEMFC operation. The numerical model illustrates that cell-failure time increases with increasing temperature due to a longer required time for ice nucleation. Hence, ice-crystallization kinetics is critical when induction times are long (i.e., in the "nucleation-limited" regime for T > 263 K). Cell-failure times predicted using ice-freezing kinetics are in good agreement with the isothermal cold-starts, which also exhibit long and distributed cell-failure times for T > 263 K. These findings demonstrate a significant departure from cell-failure times predicted using the thermodynamic-based approach.Proton-exchange-membrane fuel cells (PEMFCs) show promise in automotive applications because of their high efficiency, high power density, and potentially low emissions. To be successful in automotive applications, PEMFCs must permit rapid startup with minimal energy from sub-freezing temperatures, known as cold-start. In a PEMFC, reduction of oxygen to water occurs in the cathode catalyst layer (cCL). Under subfreezing conditions, water solidifies and hinders access of gaseous oxygen to the catalytic sites in the cCL, severely inhibiting cell performance and potentially causing cell failure. 1-3 Elucidation of the mechanisms and kinetics of ice formation within the cCL is, therefore, critical to successful cell startup and high performance at low temperatures.Because of degradation and cell failure under subfreezing conditions, much attention has been given to understanding cold-start fundamentals. To date, experiments predominately focus on characterizing overall low-temperature cell performance.