Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation

Thermodynamics of Mobile Ion in Ion Exchange Membranes: Water-Swollen-Membrane Reference State and Quasi-Regular Solution Model

Thermodynamics of mobile ions in swollen ion exchange membranes (IEM) are essential for understanding their permselectivity. The theoretical modeling of the ion activity coefficient and the ion partitioning of the IEM is challenging. Based on a water-swollen membrane reference state and a quasi-regular solution model, we successfully correlated the ion activity coefficient in various IEMs. For all the studied 59 systems, the correlation coefficient r and determination coefficient R2 are 0.973 and 0.947, respectively. As expected, the water activity in the IEM and the ion partitioning between the IEM and the external salt solution are represented. In the new theory framework, the standard chemical potential of the counterion is different from that of the aqueous solution. Moreover, the ion activity coefficient in the IEM reaches unity for the infinite dilution external salt concentration for all systems. Our quasi-regular solution model only considered the short-range interactions between the co-ions and the "effective free counterion", but it showed excellent correlation ability with the activity coefficient data of extensive systems. A power-law relation between the effective concentration of the free counterion and the apparent concentration of the free counterion was suggested. This indicates that the long-range electrostatic interactions in the swollen IEM are negligible due to abundant counterion condensation shielding the charge of the polymer chain.

Hydrodynamically Enhanced Brownian Motion in Flowing Polymer Solutions

Diffusion of a molecule in solution typically occurs via thermally driven Brownian motion, with solvent collisions leading to a random-walk trajectory for the solute. This physical principle guides our understanding of molecular transport in a wide variety of situations, ranging from protein diffusion in biological systems and mixing in solution processes to charge transport in polyelectrolyte solutions. Thermal diffusion represents a "speed limit" for molecular transport, which can typically only be surpassed by imposing a directional, external field. The other way particles expedite diffusion is via self-propulsion. This "active Brownian motion" is famously seen in some single-cell organisms and can also be shown in some colloidal systems, but because it requires self-propulsion, this is not seen at the molecular level. We show that it is possible to dramatically increase the diffusion of small molecules in a way that mimics active Brownian motion, instead driven by the disturbance flows of highly stretched polymers in strong flows to induce propulsion at a distance. We use molecular simulations that account for these hydrodynamic disturbances to demonstrate that it is possible to increase the effective diffusion constant by more than an order of magnitude, and we provide a mechanistic model for how the interplay of polymer concentration, flow-induced polymer stretching, and chain length gives rise to hydrodynamically enhanced Brownian motion. This effect has important implications for molecular transport, and we show that strong flows and a low concentration of stretched polymers can be used to promote rapid diffusion.

Approaching infinite selectivity in membrane-based aqueous lithium extraction via solid-state ion transport

As the gap between lithium supply and demand continues to widen, the need to develop ion-selective technologies, which can efficiently extract lithium from unconventional water sources, grows increasingly crucial. In this study, we investigated the fundamentals of applying a solid-state electrolyte (SSE), typically used in battery technologies, as a membrane material for aqueous lithium extraction. We find that the anhydrous hopping of lithium ions through the ordered and confined SSE lattice is highly distinct from ion migration through the hydrated free volumes of conventional nanoporous membranes, thus culminating in unique membrane transport properties. Notably, we reveal that the SSE provides unparalleled performance with respect to ion-ion selectivity, consistently demonstrating lithium ion selectivity values that are immeasurable by even the part-per-billion detection limit of mass spectrometry. Such exceptional selectivity is shown to be the result of the characteristic size and charge exclusion mechanisms of solid-state ion transport, which may be leveraged in the design of next-generation membranes for resource recovery.

Constructing new-generation ion exchange membranes under confinement regime

Ion exchange membranes (IEMs) enable fast and selective ion transport and the partition of electrode reactions, playing an important role in the fields of precise ion separation, renewable energy storage and conversion, and clean energy production. Traditional IEMs form ion channels at the nanometer-scale via the assembly of flexible polymeric chains, which are trapped in the permeability/conductivity and selectivity trade-off dilemma due to a high swelling propensity. New-generation IEMs have shown great potential to break this intrinsic limitation by using microporous framework channels for ion transport under a confinement regime. In this Review, we first describe the fundamental principles of ion transport in charged channels from nanometer to sub-nanometer scale. Then, we focus on the construction of new-generation IEMs and highlight the microporous confinement effects from sub-2-nm to sub-1-nm and further to ultra-micropores. The enhanced ion transport properties brought by the intense size sieving and channel interaction are elucidated, and the corresponding applications including lithium separation, flow battery, water electrolysis, and ammonia synthesis are introduced. Finally, we prospect the future development of new-generation IEMs with respect to the intricate microstructure observation, in-situ ion transport visualization, and large-scale membrane fabrication.

Relative contributions of mobility and partitioning to volatile fatty acid flux during electrodialysis

Economically valuable volatile fatty acids (VFAs) are sustainably produced via fermentation processes. To use VFAs downstream, they must be recovered using technologies like electrodialysis (ED). Solute transport properties (i.e., partition coefficient (K), diffusion coefficient (D), and permeability (P=KD)) govern flux in ED. Therefore, to advance understanding of VFA flux through anion exchange membranes (AEMs) in ED, we aimed to elucidate the relative contributions of VFA partitioning and mobility to their flux. Accordingly, for VFAs of different sizes (C1-C5) and inorganic anions (Cl-, Br-), we measured their fluxes during ED, permeabilities, and partition coefficients, and calculated the diffusion coefficients. We then evaluated the correlations between flux and transport properties and between transport properties and anion physicochemical properties. Results showed VFA flux had a strong correlation with permeability (R2=0.94, p<0.01), consistent with flux described by the Nernst-Planck equation. Further, while there was a negative correlation between VFA flux and partition coefficient (R2=0.46, p=0.21), there was a positive correlation between VFA flux and diffusion coefficient (R2=0.95, p<0.01) which showed VFA mobility governed VFA flux. We observed a negative correlation between VFA diffusion coefficient and carbon-chain length which was attributed to steric hindrance, and a positive correlation between partition coefficient and carbon chain-length which we attributed to hydrophobicity and polarizability. This work provides fundamental insight on interactions between VFAs and AEMs which affect anion flux during ED.

Bound Water Enhances the Ion Selectivity of Highly Charged Polymer Membranes

Electrochemical technologies for water treatment, resource recovery, energy generation, and energy storage rely on charged polymer membranes to selectively transport ions. With the rise of applications involving hypersaline brines, such as management of desalination brine or the recovery of ions from brines, there is an urgent need for membranes that can sustain high conductivity and selectivity under such challenging conditions. Current membranes are constrained by an inherent trade-off between conductivity and selectivity, alongside concerns regarding their high costs. Moreover, a gap in the fundamental understanding of ion transport within charged membranes at high salinities prevents the development of membranes that could meet these stringent requirements efficiently. Here, we present the synthesis of scalable, highly charged membranes that demonstrate high conductivity and selectivity while contacting 1 and 5 molal NaCl solutions. A detailed analysis of the membrane transport properties reveals that the high proportion of bound water in the membranes, enabled by the high charge content and hydrophilic structure of the polymers, enhances both the ion partitioning and diffusion selectivities of the membranes. These structure/property relationships derived from this study offer valuable guidance for designing next-generation membranes that simultaneously achieve exceptional conductivity and selectivity in high-salinity conditions.

Counterion Release from Macroion Assemblies of Planar Geometry

Macroions such as nanoparticles, polyelectrolytes, ionic gels, and amphiphiles can form condensed, often self-assembled, phases that are embedded in a solvent region. The condensed phase contains not only the partially or fully immobile charges of their macroions but also corresponding counterions that are mobile and thus free to migrate out of their confinement into the solvent region where they benefit from high translational entropy. Based on the nonlinear Poisson-Boltzmann model for monovalent ions, we quantify the corresponding fraction of released counterions for a planar slab geometry of the macroion phase. Slab thickness, extension of the solvent phase, fixed background charge density provided by the macroions, and dielectric constants inside slab and solvent combine into three dimensionless parameters that the fraction of released counterions depends on. We calculate that fraction and analyze the limits of a thin macroion phase, a large solvent phase, and linearized theory, where simple analytic results become available. Of particular interest is the presence of a single-planar interface that separates a bulk macroion phase from an extended solvent region. We calculate the apparent surface charge density that emerges due to the released counterions. Our model yields a comprehensive description of counterion partitioning between a planar macroion phase and a solvent region on the level of mean-field electrostatics in the absence of added salt ions.

The potential of electrodialysis as a cost-effective alternative to reverse osmosis for brackish water desalination

While electrodialysis (ED) demonstrates lower energy consumption than reverse osmosis (RO) in the desalination of low salinity waters, RO continues to be the predominant technology for brackish water desalination. In this study, we probe this skewed market share and project the potential for future disruption by ED through systematic assessment of the levelized cost of water (LCOW). Using rigorous process- and economic-models, we minimize the LCOW of RO and ED systems, highlighting important tradeoffs between capital and operating expenditure for each technology. With optimized current state-of-the-art systems, we find that ED is more economical than RO for feed salinities ≤ 3 g L-1, albeit to a minor extent. Considering that RO is a highly mature technology, we focus on predicting the future potential of ED by evaluating plausible avenues for capital and operating cost reduction. Specifically, we find that reduction in the price of ion-exchange membranes (i.e., < 60 USD m-2) can ensure competitiveness with RO for feed salinities up to 5 g L-1. For higher feed salinities (≥ 5 g L-1) we reveal that the LCOW of ED may effectively be reduced by decreasing ion-exchange membrane resistance, while preserving high current efficiency. Through extensive assessment of structure-property-performance relationships, we precisely identify target membrane charge densities and diffusion coefficients which optimize the LCOW of ED, thus providing novel guidance for future membrane material development. Overall, we emphasize that with a unified approach - whereby ion-exchange membrane price is reduced and performance is enhanced - ED can become the economically preferable technology compared to RO across the entire brackish water salinity range.

Membrane Design Principles for Ion-Selective Electrodialysis: An Analysis for Li/Mg Separation

Selective electrodialysis (ED) is a promising membrane-based process to separate Li+ from Mg2+, which is the most critical step for Li extraction from brine lakes. This study theoretically compares the ED-based Li/Mg separation performance of different monovalent selective cation exchange membranes (CEMs) and nanofiltration (NF) membranes at the coupon scale using a unified mass transport model, i.e., a solution-friction model. We demonstrated that monovalent selective CEMs with a dense surface thin film like a polyamide film are more effective in enhancing the Li/Mg separation performance than those with a loose but highly charged thin film. Polyamide film-coated CEMs when used in ED have a performance similar to that of polyamide-based NF membranes when used in NF. NF membranes, when expected to replace monovalent selective CEMs in ED for Li/Mg separation, will require a thin support layer with low tortuosity and high porosity to reduce the internal concentration polarization. The coupon-scale performance analysis and comparison provide new insights into the design of composite membranes used for ED-based selective ion-ion separation.

Mobility of Condensed Counterions in Ion-Exchange Membranes: Application of Screening Length Scaling Relationship in Highly Charged Environments

Ion-exchange membranes (IEMs) are widely used in water, energy, and environmental applications, but transport models to accurately simulate ion permeation are currently lacking. This study presents a theoretical framework to predict ionic conductivity of IEMs by introducing an analytical model for condensed counterion mobility to the Donnan-Manning model. Modeling of condensed counterion mobility is enabled by the novel utilization of a scaling relationship to describe screening lengths in the densely charged IEM matrices, which overcame the obstacle of traditional electrolyte chemistry theories breaking down at very high ionic strength environments. Ionic conductivities of commercial IEMs were experimentally characterized in different electrolyte solutions containing a range of mono-, di-, and trivalent counterions. Because the current Donnan-Manning model neglects the mobility of condensed counterions, it is inadequate for modeling ion transport and significantly underestimated membrane conductivities (by up to ≈5× difference between observed and modeled values). Using the new model to account for condensed counterion mobilities substantially improved the accuracy of predicting IEM conductivities in monovalent counterions (to as small as within 7% of experimental values), without any adjustable parameters. Further adjusting the power law exponent of the screen length scaling relationship yielded reasonable precision for membrane conductivities in multivalent counterions. Analysis reveals that counterions are significantly more mobile in the condensed phase than in the uncondensed phase because electrostatic interactions accelerate condensed counterions but retard uncondensed counterions. Condensed counterions still have lower mobilities than ions in bulk solutions due to impedance from spatial effects. The transport framework presented here can model ion migration a priori with adequate accuracy. The findings provide insights into the underlying phenomena governing ion transport in IEMs to facilitate the rational development of more selective membranes.

Ion-Electron Coupling Enables Ionic Thermoelectric Material with New Operation Mode and High Energy Density

Ionic thermoelectrics (i-TE) possesses great potential in powering distributed electronics because it can generate thermopower up to tens of millivolts per Kelvin. However, as ions cannot enter external circuit, the utilization of i-TE is currently based on capacitive charge/discharge, which results in discontinuous working mode and low energy density. Here, we introduce an ion-electron thermoelectric synergistic (IETS) effect by utilizing an ion-electron conductor. Electrons/holes can drift under the electric field generated by thermodiffusion of ions, thus converting the ionic current into electrical current that can pass through the external circuit. Due to the IETS effect, i-TE is able to operate continuously for over 3000 min. Moreover, our i-TE exhibits a thermopower of 32.7 mV K-1 and an energy density of 553.9 J m-2, which is more than 6.9 times of the highest reported value. Consequently, direct powering of electronics is achieved with i-TE. This work provides a novel strategy for the design of high-performance i-TE materials.

Resistance of Ion Exchange Membranes in Aqueous Mixtures of Monovalent and Divalent Ions and the Effect on Reverse Electrodialysis

Salinity gradient energy has gained attention in recent years as a renewable energy source, especially employing reverse electrodialysis technology (RED), which is based on the role of ion exchange membranes. In this context, many efforts have been developed by researchers from all over the world to advance the knowledge of this green source of energy. However, the influence of divalent ions on the performance of the technology has not been deeply studied. Basically, divalent ions are responsible for an increased membrane resistance and, therefore, for a decrease in voltage. This work focuses on the estimation of the resistance of the RED membrane working with water flows containing divalent ions, both theoretically by combining the one-thread model with the Donnan exclusion theory for the gel phase, as well as the experimental evaluation with Fumatech membranes FAS-50, FKS-50, FAS-PET-75, and FKS-PET-75. Furthermore, simulated results have been compared to data recently reported with different membranes. Besides, the influence of membrane resistance on the overall performance of reverse electrodialysis technology is evaluated to understand the impact of divalent ions in energy generation. Results reflect a minor effect of sulfate on the gross power in comparison to the effect of calcium and magnesium ions. Thus, this work takes a step forward in the knowledge of reverse electrodialysis technology and the extraction of salinity gradient energy by advancing the influence of divalent ions on energy recovery.

Ion Transport and Process of Water Dissociation in Electromembrane System with Bipolar Membrane: Modelling of Symmetrical Case

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation-hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length, which shows the possibility of an ion that appeared because of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

Controlling Fractional Free Volume, Transport, and Co-Transport of Alcohols and Carboxylate Salts in PEGDA Membranes

Understanding multi-component transport through polymer membranes is critical for separation applications such as water purification, energy devices, etc. Specifically for CO₂ reduction cells, where the CO₂ reduction products (alcohols and carboxylate salts), crossover of these species is undesirable and improving the design of ion exchange membranes to prevent this behavior is needed. Previously, it was observed that acetate transport increased in copermeation with alcohols for cation exchange membranes consisting of poly(ethylene glycol) diacrylate (PEGDA) and 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) and that the inclusion of poly(ethylene glycol) methacrylate (PEGMA) (n = 5, n represents the number of ethylene oxide repeat units) could suppress this behavior. Here, we further investigate the role of PEGMA in modulating fractional free volume and transport behavior of alcohols and carboxylates. PEGDA-PEGMA membranes of varied membranes are fabricated with both varied pre -polymerization water content at constant PEGMA (n = 9) content and varied PEGMA content at two pre -polymerization water contents (20 and 60 wt.% water). Permeability to sodium acetate also decreases in these charge-neutral PEGDA-PEGMA membranes compared to PEGMA-free films. Therefore, incorporation of comonomers such as PEGMA with long side chains may provide a useful membrane chemistry structural motif for preventing undesirable carboxylate crossover in polymer membranes.

Multi-ionic Hydrogel with outstanding heat-to-electrical performance for low-grade heat harvesting

Ionic thermoelectric (i-TE) materials have attracted much attention due to their ability to generate ionic Seebeck coefficient of tens of millivolts per Kelvin. In this work, we demonstrate that the ionic thermopower can be enhanced by the introduction of multiple ions. The multi-ionic hydrogel possesses a record thermal-to-electrical energy conversion factor (TtoE factor) of 89.6 mV K-1 and an ionic conductivity of 6.8 mS cm-1, which are both better than single salt contact hydrogel. Subsequently we build a model to explain thermal diffusion of the ions in multi-ionic hydrogels. Finally, the possibility of large-scale integrated applications of multi-ionic hydrogels is demonstrated. By connecting 7 i-TEs hydrogels, we obtained an open-circuit voltage of 1.86 V at ΔT = 3 K. Our work provides a new pathway for the design of i-TEs and low-grade heat harvesting.

Kinetic model for moisture-controlled CO2 sorption

The understanding of the sorption/desorption kinetics is essential for practical applications of moisture-controlled CO₂ sorption. We introduce an analytic model of the kinetics of moisture-controlled CO₂ sorption and its interpretation in two limiting cases. In one case, chemical reaction kinetics on pore surfaces dominates, in the other case, diffusive transport through the sorbent defines the kinetics. We show that reaction kinetics, which is dominant in the first case, can be expressed as a linear combination of 1st and 2nd order kinetics in agreement with the static isotherm equation derived and validated in a previous paper. The interior transport kinetics can be described by non-linear diffusion equations. By combining all carbon species into a single equation, we can eliminate - in certain limits - the source terms associated with chemical reactions. In this case, the governing equation is . For a sorbent in a form of a flat sheet or a membrane, one can maintain the same functional form of a diffusion equation by introducing a generalized effective diffusivity D_M that combines contributions from both surface chemical reaction kinetics and interior diffusive transport kinetics. Experimental data of transient CO₂ flux in a preconditioned commercial anion exchange membrane fit well to the 1st order model as long as very dry states are avoided, validating the theory. The observed D_M for a preconditioned commercial anion exchange membrane ranges from 6.6 × 10^-14 to 7.1 × 10^-14 m² s^-1 at 35 °C. These small values compared to typical ionic diffusivities imply a very slow kinetics, which will be the largest issue that needs to be addressed for practical application. The collected transient CO₂ flux data are used to predict the magnitude of a continuous CO₂ pumping flux in an active membrane that transports CO₂ against a CO₂ concentration gradient. The pumped CO₂ flux is supported by water flux due to a water concentration gradient.

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

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.

Pseudo Polyampholytes with Sensitively Ion-Responsive Conformational Transition Based on Positively Charged Host-Guest Complexes

Biological polyampholytes are ubiquitous in living organisms with primary functions including that serving as transporters for moving chemical molecular species across the cell membranes. Synthetic amphoteric macromolecules that can change their phase states depending on the environment to simulate some properties of natural polyampholytes are of great interests. Here, we explore implementation of synthetic pseudo polymeric ampholytes with ion-recognition-triggered conformational change. The phase transition behaviors of the ion-recognition-creative polyampholytes that containing deprotonated carboxylic acid groups as negative charges and 18-crown-6 units for forming positively charged host-guest complexes are systematically investigated. The ion-recognition-triggered phase transition behaviors of pseudo polyampholytes are significantly dependent on cation species and concentrations. Only those specific ions like K⁺ , Ba²⁺ , Sr²⁺ and Pb²⁺ ions that can form 1:1 host-guest complexes with 18-crown-6 units in polymers enable to control over the conformational change like that of the traditional pH-dependent polyampholytes. By regulating the content of the carboxylic acid groups to match the content of the ion-recognized positive charges provided by the host-guest complexes, the pseudo polyampholytes are more sensitive to the recognizable cations. Such ion-recognition-triggered amphoteric characteristics make the pseudo polyampholytes acting like biological proteins, nucleic acids and enzymes as molecular transporters, genetic code storage and biocatalysts in artificial systems. This article is protected by copyright. All rights reserved.

Study of the Electrical Conductivity of Ion-Exchange Resins and Membranes in Equilibrium Solutions of Inorganic Electrolytes

The study of the electrical conductivity of ion-exchange membranes in equilibrium electrolyte solutions is of great importance for the theory of membrane processes, in particular for practical electrodialysis. The purpose of the work is to determine the electrical conductivity of industrial ion-exchange membranes MK-40 and MA-40, as well as their basis—granules of a bulk layer of industrial ion exchangers KU-2-8 and EDE-10p, by differential and modified contact methods in electrolyte solutions and the development of a new methodology that will give the values that are closest to the true ones; determination of the dependence of electrical membrane conductivity depending on the type of counterion and concentration equilibrium solution and granules of a bulk layer of ion exchangers on the volume fraction of a dry ion exchanger with different degrees of compaction. It is shown that the dependence of the electrical conductivity of diaphragms on the electrolyte concentration, according to theoretical ideas, disappears under compression. It has been experimentally established that the difference method gives lower values of electrical conductivity in the region of low concentrations. The data obtained by the contact method are in good agreement with the results obtained for compressed diaphragms. The membrane conductivity decreases with increasing ion size.

Where in the world are condensed counterions?

A scaling model of the concentration profiles of both condensed and free counterions is presented for solutions of spherical and cylindrical charged nanoparticles of different charge valences, nanoparticle sizes, and salt concentrations. The distribution of counterions for both spherical and cylindrical charged particles in salt-free solutions is determined by the condensation parameter γ₀ defined as the ratio of nanoparticle valence Z₀ to the number of Bjerrum lengths l_B = e²/(εkT) per nanoparticle size (γ₀ = Z₀l_B/(2r₀) for spherical nanoparticles with radii r₀ or γ₀ = Z₀l_B/L for cylindrical particles with length L), where ε is solution dielectric permittivity, e is elementary charge and kT is thermal energy. Depending on the magnitudes of the condensation parameter γ₀ and nanoparticle volume fraction ϕ, we find three qualitatively different regimes for the counterion distribution near charged particles: (i) weakly charged particles with no condensed counterions, (ii) regime of weak counterion condensation with less than half of the counterions condensed, and (iii) regime of strong counterion condensation with the majority of counterions condensed. The magnitude of electrostatic energy of a condensed counterion with respect to solution locations with zero electric field is larger than thermal energy kT, and the fraction of condensed counterions increases from less than half in the weak condensation regime to the majority of all counterions in the strong condensation regime. The condensed counterions are not bound to the nanoparticle surface but instead are localized within the condensed counterion zone near the charged particle. The thickness of the condensed counterion zone varies with the condensation parameter γ₀, the nanoparticle shape and volume fraction ϕ, and the salt concentration and can be as narrow as Bjerrum length (∼nm) or as large as the particle size (∼L the length of charged cylinder).

Selectively tuning ionic thermopower in all-solid-state flexible polymer composites for thermal sensing

There has been increasing interest in the emerging ionic thermoelectric materials with huge ionic thermopower. However, it's challenging to selectively tune the thermopower of all-solid-state polymer materials because the transportation of ions in all-solid-state polymers is much more complex than those of liquid-dominated gels. Herein, this work provides all-solid-state polymer materials with a wide tunable thermopower range (+20~-6 mV K-1), which is different from previously reported gels. Moreover, the mechanism of p-n conversion in all-solid-state ionic thermoelectric polymer material at the atomic scale was presented based on the analysis of Eastman entropy changes by molecular dynamics simulation, which provides a general strategy for tuning ionic thermopower and is beneficial to understand the fundamental mechanism of the p-n conversion. Furthermore, a self-powered ionic thermoelectric thermal sensor fabricated by the developed p- and n-type polymers demonstrated high sensitivity and durability, extending the application of ionic thermoelectric materials.

Engineering Li/Na selectivity in 12-Crown-4-functionalized polymer membranes

Lithium is widely used in contemporary energy applications, but its isolation from natural reserves is plagued by time-consuming and costly processes. While polymer membranes could, in principle, circumvent these challenges by efficiently extracting lithium from aqueous solutions, they usually exhibit poor ion-specific selectivity. Toward this end, we have incorporated host-guest interactions into a tunable polynorbornene network by copolymerizing 1) 12-crown-4 ligands to impart ion selectivity, 2) poly(ethylene oxide) side chains to control water content, and 3) a crosslinker to form robust solids at room temperature. Single salt transport measurements indicate these materials exhibit unprecedented reverse permeability selectivity (∼2.3) for LiCl over NaCl-the highest documented to date for a dense, water-swollen polymer. As demonstrated by molecular dynamics simulations, this behavior originates from the ability of 12-crown-4 to bind Na+ ions more strongly than Li+ in an aqueous environment, which reduces Na+ mobility (relative to Li+) and offsets the increase in Na+ solubility due to binding with crown ethers. Under mixed salt conditions, 12-crown-4 functionalized membranes showed identical solubility selectivity relative to single salt conditions; however, the permeability and diffusivity selectivity of LiCl over NaCl decreased, presumably due to flux coupling. These results reveal insights for designing advanced membranes with solute-specific selectivity by utilizing host-guest interactions.

Transport and Co-Transport of Carboxylate Ions and Ethanol in Anion Exchange Membranes

Understanding multi-component transport behavior through hydrated dense membranes is of interest for numerous applications. For the particular case of photoelectrochemical CO2 reduction cells, it is important to understand the multi-component transport behavior of CO2 electrochemical reduction products including mobile formate, acetate and ethanol in the ion exchange membranes as one role of the membrane in these devices is to minimize the permeation of these products. Anion exchange membranes (AEM) have been employed in these and other electrochemical devices as they act to facilitate the transport of common electrolytes (i.e., bicarbonates). However, as they act to facilitate the transport of carboxylates as well, thereby reducing the overall performance, the design of new AEMs is necessary to improve device performance through the selective transport of the desired ion(s) or electrolyte(s). Here, we investigate the transport behavior of formate and acetate and their co-transport with ethanol in two types of AEMs: (1) a crosslinked AEM prepared by free-radical copolymerization of a monomer with a quaternary ammonium (QA) group and a crosslinker, and (2) Selemion® AMVN. We observe a decrease in diffusivities to carboxylates in co-diffusion. We attribute this behavior to charge screening by the co-diffusing alcohol, which reduces the electrostatic attraction between QAs and carboxylates.

Application and Analysis of Bipolar Membrane Electrodialysis for LiOH Production at High Electrolyte Concentrations: Current Scope and Challenges

The objective of this work was to evaluate obtaining LiOH directly from brines with high LiCl concentrations using bipolar membrane electrodialysis by the analysis of Li⁺ ion transport phenomena. For this purpose, Neosepta BP and Fumasep FBM bipolar membranes were characterized by linear sweep voltammetry, and the Li⁺ transport number in cation-exchange membranes was determined. In addition, a laboratory-scale reactor was designed, constructed, and tested to develop experimental LiOH production tests. The selected LiCl concentration range, based on productive process concentrations for Salar de Atacama (Chile), was between 14 and 34 wt%. Concentration and current density effects on LiOH production, current efficiency, and specific electricity consumption were evaluated. The highest current efficiency obtained was 0.77 at initial concentrations of LiOH 0.5 wt% and LiCl 14 wt%. On the other hand, a concentrated LiOH solution (between 3.34 wt% and 4.35 wt%, with a solution purity between 96.0% and 95.4%, respectively) was obtained. The results of this work show the feasibility of LiOH production from concentrated brines by means of bipolar membrane electrodialysis, bringing the implementation of this technology closer to LiOH production on a larger scale. Moreover, being an electrochemical process, this could be driven by Solar PV, taking advantage of the high solar radiation conditions in the Atacama Desert in Chile.

Tomé L, Olmedo‐Martínez JL, Udabe E, Jenkins EPW, Mecerreyes D, Malliaras GG, McLeod RR, Proctor CM. Reducing Passive Drug Diffusion from Electrophoretic Drug Delivery Devices through Co-Ion Engineering

Implantable electrophoretic drug delivery devices have shown promise for applications ranging from treating pathologies such as epilepsy and cancer to regulating plant physiology. Upon applying a voltage, the devices electrophoretically transport charged drug molecules across an ion-conducting membrane out to the local implanted area. This solvent-flow-free "dry" delivery enables controlled drug release with minimal pressure increase at the outlet. However, a major challenge these devices face is limiting drug leakage in their idle state. Here, a method of reducing passive drug leakage through the choice of the drug co-ion is presented. By switching acetylcholine's associated co-ion from chloride to carboxylate co-ions as well as sulfopropyl acrylate-based polyanions, steady-state drug leakage rate is reduced up to sevenfold with minimal effect on the active drug delivery rate. Numerical simulations further illustrate the potential of this method and offer guidance for new material systems to suppress passive drug leakage in electrophoretic drug delivery devices.

Use of the Microheterogeneous Model to Assess the Applicability of Ion-Exchange Membranes in the Process of Generating Electricity from a Concentration Gradient

The paper shows the possibility of using a microheterogeneous model to estimate the transport numbers of counterions through ion-exchange membranes. It is possible to calculate the open-circuit potential and power density of the reverse electrodialyzer using the data obtained. Eight samples of heterogeneous ion-exchange membranes were studied, two samples for each of the following types of membranes: Ralex CM, Ralex AMH, MK-40, and MA-41. Samples in each pair differed in the year of production and storage conditions. In the work, these samples were named “batch 1” and “batch 2”. According to the microheterogeneous model, to calculate the transport numbers of counterions, it is necessary to use the concentration dependence of the electrical conductivity and diffusion permeability. The electrolyte used was a sodium chloride solution with a concentration range corresponding to the conditional composition of river water and the salinity of the Black Sea. During the research, it was found that samples of Ralex membranes of different batches have similar characteristics over the entire range of investigated concentrations. The calculated values of the transfer numbers for membranes of different batches differ insignificantly: ±0.01 for Ralex AMH in 1 M NaCl. For MK-40 and MA-41 membranes, a significant scatter of characteristics was found, especially in concentrated solutions. As a result, in 1 M NaCl, the transport numbers differ by ±0.05 for MK-40 and ±0.1 for MA-41. The value of the open circuit potential for the Ralex membrane pair showed that the experimental values of the potential are slightly lower than the theoretical ones. At the same time, the maximum calculated power density is higher than the experimental values. The maximum power density achieved in the experiment on reverse electrodialysis was 0.22 W/m², which is in good agreement with the known literature data for heterogeneous membranes. The discrepancy between the experimental and theoretical data may be the difference in the characteristics of the membranes used in the reverse electrodialysis process from the tested samples and does not consider the shadow effect of the spacer in the channels of the electrodialyzer.

Understanding the ionic activity and conductivity value differences between random copolymer electrolytes and block copolymer electrolytes of the same chemistry

Herein, a systematic study where the macromolecular architectures of poly(styrene-block-2-vinyl pyridine) block copolymer electrolytes (BCE) are varied and their activity coefficients and ionic conductivities are compared and rationalized versus a random copolymer electrolyte (RCE) of the same repeat unit chemistry. By performing quartz crystal microbalance, ion-sorption, and ionic conductivity measurements of the thin film copolymer electrolytes, it is found that the RCE has higher ionic activity coefficients. This observation is ascribed to the fact that the ionic groups in the RCE are more spaced out, reducing the overall chain charge density. However, the ionic conductivity of the BCE is 50% higher and 17% higher after the conductivity is normalized by their ion exchange capacity values on a volumetric basis. This is attributed to the presence of percolated pathways in the BCE. To complement the experimental findings, molecular dynamics (MD) simulations showed that the BCE has larger water cluster sizes, rotational dynamics, and diffusion coefficients, which are contributing factors to the higher ionic conductivity of the BCE variant. The findings herein motivate the design of new polymer electrolyte chemistries that exploit the advantages of both RCEs and BCEs.