A triple-layer model of the mica/water electrical double layer (EDL) unifies prediction of zeta potential, ion-exchange, and surface-force isotherms. The theory treats cations as partially dehydrated and complexed specifically to the anionic exchange sites of mica. A diffuse layer commencing at the outer Helmholtz plane (OHP) balances the surface charge not neutralized by adsorbed cations in the inner Helmholtz plane (IHP). Ion-binding equilibrium constants are assessed from zeta-potential measurements and used thereafter to predict ion-exchange isotherms and surface forces. Basal-plane mica surface charge is almost completely neutralized by specific binding of cations, including hydronium ions. The charge in the diffuse layer is only a few percent of the mica crystallographic charge density but leads to long-range electrostatic interactions between charged surfaces. The Grahame triple-layer model of the aqueous EDL provides a robust, quantitative, and unified description of the mica/water interface.

A mean-field local-density theory is outlined for ion transport in perfluorinated-sulfonic-acid (PFSA) membranes. A theory of molecular-level interactions predict nanodomain and macroscale conductivity. The effects of solvation, dielectric saturation, dispersion forces, image charge, finite size, and confinement are included in a physically consistent 3D-model domain geometry. Probability-distribution profiles of aqueous cation concentration at the domain-scale are in agreement with atomistic simulations using no explicit fitting parameters. Measured conductivities of lithium-, sodium-, and proton-form membranes with equivalent weights of 1100, 1000, and 825 g/mol(SO3) validate the macroscale predictions using a single-value mesoscopic fitting parameter. Cation electrostatic interactions with pendant sulfonate groups are the largest source of migration resistance at the domain-scale. Tortuosity of ionically conductive domains is the largest source of migration resistance at the macroscale. Our proposed transport model is consistent across multiple length scales. We provide a compelling methodology to guide material design and optimize performance in energy-conversion applications of PFSA membranes.

On the basis of work by Bernard and Blum [Bernard, O.; Blum, L. Binding Mean Spherical Approximation for Pairing Ions: An Exponential Approximation and Thermodynamics. J. Chem. Phys. 1996, 104, 4746-4754], Barthel et al. [Barthel, J.; Krienke, H.; Holovko, M.; Kapko, V.; Protsykevich, I. The Application of the Associative Mean Spherical Approximation in the Theory of Nonaqueous Electrolyte Solutions. Condens. Matter Phys. 2000, 3, 23], and Simonin et al. [Simonin, J.-P.; Bernard, O.; Blum, L. Real Ionic Solutions in the Mean Spherical Approximation. 3. Osmotic and Activity Coefficients for Associating Electrolytes in the Primitive Model. J. Phys. Chem. B 1998, 102, 4411-4417], this work presents and validates a molecular-thermodynamic model for lithium salt activity coefficients in aqueous and nonaqueous single- and mixed-solvent systems. The Binding Mean Spherical Approximation gives electrolyte activity due to long-range electrostatic forces, short-range hard-sphere repulsion, and ion-pair formation. The theory shows good agreement with measured salt activities up to 3 molar in aqueous and nonaqueous solvents using a solvent-dependent, concentration-independent, center-to-center distance of closest approach between ions as the single fitting parameter for each electrolyte system. For mixed-solvent electrolytes, the local solvation environment around the ions dictates short-range interactions. To account for preferential ion solvation in a mixed solvent, the center-to-center distance is obtained from Wang and co-workers' Dipolar Self-Consistent-Field Theory [Nakamura, I.; Shi, A.-C.; Wang, Z.-G. Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization. Phys. Rev. Lett. 2012, 109, 257802]. For a particular salt in a binary solvent mixture at fixed temperature, the model predicts salt activity coefficients using only the fitted single-solvent distances-of-closest approach.

Multicomponent mass-transport in cation-exchange membranes involves the movement of multiple species whose motion is coupled one to another. This phenomenon mediates the performance of numerous electrochemical and water purification technologies. This work presents and validates against experiment a mathematical model for multicomponent mass transport in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). Stefan-Maxwell-Onsager theory describes concentrated-solution transport. Hydrodynamic theory provides constitutive relations for the solute/solvent, solute/membrane, and solvent/membrane friction coefficients. Classical porous-medium theories scale membrane tortuosity. Electrostatic relaxation creates friction between ions. The model uses calculated ion and solvent partitioning between the external solution and the membrane from Part I of this series and incorporates the corresponding ion speciation into the transport coefficients. The proposed transport model compares favorably to properties (e.g., membrane conductivity, transference numbers, electroosmosis, and permeability) measured in dilute and concentrated aqueous binary and ternary electrolytes. The results reveal that the concentration and type of ions in the external solution alter the solvent volume fraction and viscosity in the hydrophilic pathways of the membrane, changing macroscale ionomer conductivity, permeability, and transference numbers. This work provides a physicochemical framework to predict ion-exchange-membrane performance in multicomponent systems exhibiting coupled transport.

We present and validate a mathematical model for multicomponent thermodynamic activity in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). The model consists of an expression for the free energy of the membrane and of the surrounding electrolyte solution. A modified Stokes-Robinson ionic solvation framework treats the solution-like non-idealities resulting from hydration, electrostatics, ion association, and physical interactions in bulk solution and in ionomer hydrophilic domains. Inside the membrane, a mechanics-based composite approach accounts for the swelling of the hydrophobic matrix. Treating the membrane microstructure as a disordered system of domains calculates steric exclusion of ions. Electroneutrality guarantees that the charge of mobile ions in the membrane is equal to the charge on polymer groups. Osmotic coefficients for electrolytes from literature parameterize solution-like interactions while mechanical and X-ray scattering characterization gives most membrane-specific parameters. Model predictions compare favorably to measured membrane thermodynamics (i.e., water and ion uptake) in dilute and concentrated binary and ternary salt electrolytes and in water vapor. Interactions between ions in the membrane are similar to those present in bulk electrolytes. Our results reveal that water and ion uptake is dictated by a balance between solution-like energetics and membrane swelling.

Transport through vanadium redox-flow-battery membranes strongly influences cell performance. In this work, we use a multicomponent concentrated-solution model of transport and thermodynamics in phase-separated cation-exchange membranes, the most common separator type, to develop structure-performance relationships. The model incorporates species partitioning into the membrane, thermodynamic nonidealities, and Stefan-Maxwell-Onsager frictions between species. Molecular-thermodynamics and -transport theories parameterize the model. We validate the calculations against measured Coulombic and voltage efficiencies of a vanadium flow battery as a function of current density. Our model shows that species transport is the result of collective interactions between all species present in the system. The magnitude of coupling suggests that predictions made using dilute-solution theory for transport in these systems will be misleading in many situations. As a demonstration of the capabilities of the model, we predict cell performance, incorporating these interactions, as a function of electrolyte concentration and composition and membrane equivalent weight and backbone modulus. We find that electrolytes with high sulfuric acid concentrations provide the greatest cell performance (quantified by maximizing power density at a target energy efficiency). In the case of membrane properties, low equivalent-weight polymers perform better; at high equivalent weights, a low membrane modulus is preferred.

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.

One of the primary limiting factors for proton-exchange-membrane (PEM) fuel-cell lifetime is membrane degradation driven by operational stressors such as generation of highly reactive radical species, which result in cell failure and voltage decay. To extend the lifetime of the membrane, cerium ions are added to the membrane to mitigate the effects of chemical degradation by scavenging radicals produced by crossover of reactant gases across the PEM. Although cerium has shown to be very effective at reducing chemical degradation during PEM fuel cell operation, the cerium ions also lead to a decrease in performance due to changes in the membrane transport properties and possible site blockage in the catalyst layers. In this paper, a full-cell, transient performance and durability model is presented in which a micro-kinetic framework accounts for gas crossover induced degradation and concentrated-solution theory describes transport in the PEM. The transport model takes into account the coupled nature of the electrochemical driving forces that cause transport of cerium ions, protons, and water. The cell model predicts the migration of cerium out of the membrane and into the catalyst layers and its impact on performance. A comparison between dilute-solution-theory and concentrated-solution-theory models shows how water management in the cell also effects cerium distribution, where higher relative humidity leads to better retention of cerium in the membrane. A voltage loss breakdown shows that cerium leads to performance losses in the cell both by decreasing proton activity and by modifying transport properties of water and protons through the membrane. Transient simulations show that the optimal tradeoff between performance and durability metrics is reached at low cerium concentrations in the membrane (less than 1% of membrane sulfonic acid sites occupied by cerium for our analysis). Finally, analysis of membrane thickness and catalyst layer thickness as design parameters shows that thicker membranes and thinner catalyst layers best optimize both performance and durability.

The electrolysis of HCl to form Cl2 is an integral part of the production of polycarbonates and polyurethanes. In recent years, the direct gas-phase electrolysis was shown to be significantly more efficient than the current state-of-the-art process based on the oxidation of hydrochloric acid. Still, three phenomena significantly limit the performance and industrial applicability of this process and have so far only been investigated theoretically. Firstly, a limiting behavior in the HCl oxidation reaction was observed, which seems to be of purely kinetic origin. Secondly, also in the full-cell employing an oxygen depolarized cathode, a limiting behavior was detected, which however appears to have a different origin. Lastly, the performance of the oxygen reduction is significantly reduced in comparison to classical H2 PEM fuel cells. The present work utilizes a combined experimental and theoretical approach to confirm that the HCl oxidation is purely reaction limited while the limiting behavior in the full-cell system employing an oxygen depolarized cathode is caused by flooding at low reactor temperatures and, lastly, that the reduced performance of the oxygen reduction reaction is a consequence of significant HCl crossover that can be mitigated by means of increased cathode humidification. These insights are furthermore used to operate the HCl gas phase electrolyzer employing an oxygen depolarized cathode at current densities of more than 5000 A/m2 for the first time, while also substituting the previously employed platinum based cathode catalyst with RhxSy, decreasing the impact of HCl crossover and allowing for the lowest so far measured cell potentials over a wide interval of current densities.

Perfluorosulfonic acids (PFSAs) are commonly used as solid polymer electrolyte membranes (PEMs) in electrochemical energy devices, where they are vulnerable to attack by radical species during operation. A popular strategy to combat this problem is to introduce radical scavengers like cerium (Ce) ions that neutralize these species before they attack the PFSA. Such cation doping creates a multi-ion system, in which understanding the mechanisms of cation solvation and transport becomes important for the effective design and utilization of PFSA-cation systems. Ce ions also provide a representative model system for multication-exchanged ionomers in electrochemical systems. In this study, hydration and conductivity measurements, along with X-ray fluorescence and scattering, are employed to elucidate how Ce ion exchange alters PFSA's ionic solvation, as well as nano- and mesoscale morphologies, which ultimately control its ion transport properties. A molecular transport model is used to deconvolute the impact of Ce ions on the local solvation structure of water in the membrane from mesoscale changes of the transport pathways. The combined experimental and theoretical analysis reveals a nonlinear decrease in conductivity driven by cation solvation at the molecular level and morphological changes at longer length scales. Migration-diffusion coupling, its nonlinear dependence on ion exchange and hydration, and its overall implications for ionomer performance are also discussed. These findings have the potential to be translated into other mixed cation-ionomer systems for a wide range of energy and environmental devices.