Charged Counterions Research Articles

Role of Counterion in the Adsorption of Ionic Amphiphiles at Fluid Interfaces.

This communication represents the chemical alternative to the previous two papers dealing with the influence of positively charged alkali cations on the adsorption properties of the series of the standard surfactant system of alkali-perfluorocarbon octanoates. Now, this contribution describes the adsorption properties of the negatively charged cationic surfactant series of trimethyldodecyl-ammonium halides. In our latest contributions, we have put forward a new model of adsorption of ionic surfactants. It says that the surface excess of the adsorbed anionic surfactant is exclusively determined by the cross-sectional area of the positive counterion. This, however, has been demonstrated by applying relevant, positively charged (alkali) counterions only, i.e., by anionic surfactants. In this article, we extend the new model to negatively charged counterions (halides) applying the cationic standard surfactant series of the trimethyldodecylammonium-halides. A big difference between the hydration behavior of the positively charged alkali and the negatively charged counterions has become striking. Thus, for example, whereas the ratio between the naked ion radius of the cesium and of the lithium cation is almost 2-fold, it is practically equal for the chloride and the iodide anion. Surprisingly, however, the relevant adsorption data are practically identical. This means that the bigger, negatively charged halide counterions interact considerably more strongly with their residual ionic surfactant group than the positively charged alkali cations with theirs. Due to this, the size of the hydrated negative halide ions is considerably greater than that of the relevant positive alkali ions. These specialties can well be explained by the Stern model of charge distribution across a naked ion's surface. It shows that for the electrostatic interaction between counterion and ionic surfactant headgroup, the peculiarities of the polar solvent of water will play a crucial role, too. By these investigations our new model of adsorption of ionic amphiphiles is further extended and gives finally evidence that it is of general validity.

Effect of Nature and Charge of Counterions and Co-Ions on Electrotransport Properties of Heterogeneous Anion Exchange Membranes

A comprehensive characterization of heterogeneous anion exchange MA-40 and MA-41 membranes, differing in the nature of functional groups and the exchange capacity (3.32 and 1.41 mmol/gdry, respectively), was carried out. The MA-40 membrane contains low basic secondary and tertiary amino groups, while the MA-41 membrane contains predominantly quaternary ammonium bases. Concentration dependences of conductivity and diffusion permeability, current-voltage curves were obtained, and the transport and structural parameters of a microheterogeneous model of membrane in solutions of different natures (salts and acids) containing singly and doubly charged cations and anions (sodium and calcium chlorides, sodium sulfate and sulfuric acid). The influence of counter- and co-ions on the electrical transport properties of the studied membranes was revealed and it was shown that changes in their properties are determined not only by the nature of the electrolyte, but also by the value of the exchange capacity of the samples, as well as the nature of their functional groups.

Counterion Blockade in a Heterogeneously Charged Single-File Water Channel.

The Possion-Nernst-Planck theories fail to describe the ionic transport in Angstrom channels, where conduction deviates from Ohm's law, which is attributed to the dehydration/self-energy barrier and dissociation of Bjerrum ion pairs in previous work. Here, we find that the cations can be strongly bound to the surface charge, which blocks the ionic transport in a single-file water channel, causing nonlinear current-voltage curves. The presence of free ions significantly increases the probability of bound ions being released, resulting in an ionic current. We find that ionic conduction gradually becomes Ohmic as the surface charge density increases, but the conduction amplitude decreases due to the increased friction from the bound ions. We rationalize the ionic transport using 1D Kramers' escape theory framework, which describes nonlinear ionic current and the impact of surface charge density on the I-V curves. Our results show that the strong Coulomb interaction between the counterion and surface charge may cause ionic blockade in Angstrom channels.

Evolution of 2D Nanostructures on Charged Surfaces through the Precipitation of Hydrolyzable Ions

The significance of surface charge at solid-liquid interfaces extends to crucial roles in diverse chemical processes, including crystallization, self-assembly, fuel cell reactions, and heterogeneous catalysis. Building upon the classical mean field description derived from the Gouy–Chapman model, the electrostatic attraction between a charged interface and counterions in solutions prompts oppositely charged ions from the solution to accumulate at the interface, forming an electric double layer (EDL), with distinct properties from those observed in bulk solutions. While the model accounts for the distribution of ions based on their spatial average perpendicular to the surface, the discussion regarding the lateral structure at the interface, particularly the local molecular-level details, is relatively limited.In this study, we explored the interfacial structure of mica, a mineral with an atomically flat surface and intrinsic negative charge, in electrolytes containing different multi-valent cations, utilizing in-situ liquid phase atomic force microscopy (LP-AFM). We find that, as the solution pH is gradually raised, cations precipitate and form a monolayer hydroxide film on mica surface. Divalent ions such as Mg2+, Ni2+, and Co2+, form large continuous monolayers in a manner that aligns with expectations based on classical nucleation theory. For trivalent ions like Al3+, Fe3+, and Cr3+, hydrolyzed species adsorb in increasing amounts as pH is increased. Instead of exhibiting a random distribution, these ions reveal intricate lateral ordering and eventually evolve into an ordered ion network. Upon further pH increase, the ion network undergoes a transition to a discontinuous film with a persistent network of gaps. The links between the surface nanostructure and local surface charge were investigated using three-dimensional fast force mapping (3D FFM) and complementary streaming potential apparatus (SPA) measurements. As films form, an inversion from negative to positive zeta potential on mica is observed through SPA and is accompanied by the appearance of a long-range tip-sample forces through 3D FFM. These findings suggest that electrostatic interactions between positively charged ions/films and a negatively charged substrate stabilize the surface nanostructure. Furthermore, films created by trivalent ions are more strongly charged compared to those formed by divalent ions.The lateral structure at mica-electrolyte interfaces was simulated using a charge-frustrated lattice gas model, where the ions experience competing interactions between short-range chemical bonding and long-range electrostatic forces. For weak charge effects, the film undergoes a first-order transition from sparse adsorbates to large continuous sheets, aligning with the behavior observed with divalent ions. When the charge effect is sufficiently strong, the surface forms various states, including ordered patterns of ions, ion clusters, and microphase-separated partial films, corresponding to the behavior observed with trivalent ions. This study provides molecular-level understanding of how electric fields control the spontaneous formation of interfacial nanostructures, and offers valuable insights into using electric fields to control crystallization processes for the development of functional materials.

Effect of Nature and Charge of Counterions and Co-Ions on Electrotransport Properties of Heterogeneous Anion Exchange Membranes

Effect of Nature and Charge of Counterions and Co-Ions on Electrotransport Properties of Heterogeneous Anion Exchange Membranes

Permeation of urea and water through sulfonated poly(styrene‐isobutylene‐styrene) membranes with counterion substitution

AbstractThis study describes the influence of counterion substitution on the transport of urea and water through sulfonated poly(styrene‐isobutylene‐styrene) (SIBS) membranes. SIBS was sulfonated to 66.4% to allow for enough ionic domains to transport urea and water through the membrane. Counterions, including alkyl‐substituted ammonium ions, influenced the ionic domains creating a selective barrier that hindered the transport of urea and water through SIBS. Permeability measurements demonstrated that counterion substitution significantly affected the transport of urea. Membranes with higher charge counterions exhibited a more pronounced reduction in permeability due to the formation of crosslinks and increased restriction on molecular diffusion. Membranes substituted with ammonium salts showed reduced permeability due to the alkyl chains' hydrophobic nature, which created a physical barrier against the passage of urea molecules. Pure water flux tests indicated that counterion substitution also reduced the water flux of the membranes. Membranes with +1 counterions showed a small reduction in the water flux, while membranes with higher charge counterions and alkyl chain substitutions exhibited larger reductions, highlighting the influence of crosslinking and hydrophobicity on water transport.

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders.

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.

Simulations predict water uptake and transport in nanostructured ion exchange membranes

Ion exchange membranes are made up of polymers with charged groups randomly tethered to the backbone. In humid conditions, these membranes absorb water to form nanostructures: the polymers reside in a hydrophobic domain, while the charged groups and counterions reside in interconnected water-filled paths that facilitate ion and water transport. Consequently, these membranes find their application in energy storage and water filtration. Molecular dynamics simulations can be used to investigate the effect of polymer structure and hydration level on the nanostructured pore space and transport within it. Here, we investigate polystyrene-polymethylbutylene (PS-PMB) block copolymer membranes, with the PS block randomly sulfonated to an experimentally relevant level of 25 mole percent. The counterion distribution in the pore space is not uniform; counterions are mainly found near the polymer-water interface, which is decorated with negative sulfonate groups. We vary the water content in the membrane, and predict an equilibrium water uptake consistent with experiments. Surprisingly, even at a water content 8 times smaller than equilibrium, the aqueous paths remain connected; however, the pores shrink down to narrow ribbons. We measure both short-time and long-time diffusivity of counterions and water, and find that diffusivity increases with water content and is impacted by pore tortuosity.

Galactose isomerization to tagatose over MgBr2 follows a temperature-dependent reaction rate kinetics as predicted by first principles-based theories

Tagatose, a classified low-calorie sugar, possesses anti-hyperglycaemic and prebiotic characteristics. Therefore, it is considered a potential food additive supplement (sweetener) for lifestyle health problems in humans. While many reports on its production via biological and chemical methods have been published, the thermodynamic behavior of its synthesis using galactose is rarely focused on. Herein, we report the MgBr2-mediated galactose interconversion to tagatose (single-step) and its kinetic mechanism. The oppositely charged counterions (Mg2+ and Br‒) can induce the reaction via different pathways in a parallel fashion, i.e., the Mg2+ behaving as a Lewis acid can enable via a 1,2-hydride shift pathway, whereas the Br‒ offering the Brønsted basic sites via a proton transfer pathway. This resulted in a tagatose production as high as 22% and 73% selectivity within 60 min at 120 °C in water. Furthermore, the reaction has yielded a single co-product formation (talose up to 7%). From the inverse-gated quantitative NMR analysis, the contribution of the counterions in the reaction is roughly 52%:48% by Mg2+:Br‒. The determination of the temperature-dependent reaction kinetics (elementary steps) was made by employing the first-principles-based theories (i.e., transition state-Eyring theory for the proton transfer pathway that involves no hydride shift and Marcus theory for the hydride shift pathway). The energy calculations of the pathways made via DFT modeling suggested the higher feasibility of a hydride shift mechanism of galactose to tagatose.

Colloidal Stability Window for Carboxylated Cellulose Nanocrystals: Considerations for Handling, Characterization, and Formulation.

The scale of production of cellulose nanocrystals (CNCs) has increased dramatically to meet the growing demand for sustainably sourced materials. This work defines the colloidal stability window for commercially produced carboxylated CNCs (DextraCel) compared to the more traditional sulfated CNCs. Phase diagrams showing the stable, reversibly agglomerated, irreversibly aggregated/sedimented, and colloidal glass "zones" as a function of suspension pH, ionic strength, CNC surface charge content, counterion, and concentration are presented. The pKa of carboxylated CNCs was measured to be 5.1, and suspensions of carboxylated CNCs (0.5-1.5 wt %) were visually stable from pH 3 to 11 (without salt). Carboxylated CNCs were highly sensitive to ionic strength, demonstrating some agglomeration with as little as 5 mM NaCl, supporting that weak acid surface groups and lower charge contents make CNCs more sensitive to solution conditions. Surface charge content had the greatest influence on colloidal stability followed by the counterion; carboxylated CNCs were more stable in the "as-received" sodium form, whereas sulfated CNCs had improved stability in acid form after ion exchange. The stability of carboxylated CNCs with industrially relevant additives (ionic and nonionic surfactants and initiators) was also investigated. Less concentrated suspensions were more colloidally stable, emphasizing that characterization and processing of CNCs favor dilute conditions. If carboxylated CNCs are subjected to conditions outside of their colloidal stability window, simple dilution or pH adjustment does not return them to colloidally stable discrete nanoparticles; however, ultrasonication can redisperse agglomerates. This study offers guidelines for handling carboxylated CNCs to broaden the range of products that can be improved by their incorporation.

Comparative Electrokinetic Study of Alginate-Coated Colloidal Particles.

Alginates are a family of natural polysaccharides with promising potential in biomedical applications and tissue regeneration. The design of versatile alginate-based structures or hydrogels and their stability and functionality depend on the polymer's physicochemical characteristics. The main features of alginate chains that determine their bioactive properties are the molar ratio of mannuronic and glucuronic residues (M/G ratio) and their distribution along the polymer chain (MM-, GG-, and MG blocks). The present study is focused on investigating the influence of the physicochemical characteristics of alginate (sodium salt) on the electrical properties and stability of the dispersion of polymer-coated colloidal particles. Ultrapure and well-characterized biomedical-grade alginate samples were used in the investigation. The dynamics of counterion charge near the vicinity of adsorbed polyion is studied via electrokinetic spectroscopy. The results show that the experimental values of the frequency of relaxation of the electro-optical effect are higher compared to the theoretical ones. Therefore, it was supposed that polarization of the condensed Na+ counterions occurs at specific distances according to the molecular structure (G-, M-, or MG-blocks). In the presence of Ca2+, the electro-optical behavior of the particles with adsorbed alginate molecules almost does not depend on the polymer characteristics but was affected by the presence of divalent ions in the polymer layer.

Elucidating the role of interlayer structure in the permeance-selectivity trade-off of ceramic nanofiltration membrane

Reasonable design of a rational interlayer in an asymmetric ceramic nanofiltration (NF) membrane facilitates water transport as well as solute retention. Nevertheless, the inherent relationship between the microstructure of the interlayer and the permselectivity in ceramic NF membrane remains to be unclear. In this study, a quantitative model is developed to predict the influence of the factors (i.e., particle diameter and layer thickness) controlling the structure of interlayer on the permselectivity by integrating the cake filtrated theory and Donnan-Steric Pore model with the Dielectric Exclusion model. The simulations demonstrate that interlayer thickness dominates the solute rejection rather than particle diameter that constitutes the interlayer when an appropriate top-layer structure is applied. However, the enhancement of water permeance requires simultaneous regulation of the microstructures of both interlayer and top layer. For negatively charged ceramic NF membranes, the comprehensive effect of diffusion, convection, and electro-migration is the transport mechanism of positively charged counter-ion (i.e., Na+), whereas the transport of negatively charged co-ion (i.e., SO42-) is merely dominated by diffusion. This study thereby elucidates the role of the interlayer in terms of improving the permeance-selectivity trade-off relationship, which is of great significance to the future development of a high-performance ceramic NF membrane.

Characterization of Micelle Formation by the Single Amino Acid-Based Surfactants Undecanoic L-Isoleucine and Undecanoic L-Norleucine in the Presence of Diamine Counterions with Varying Chain Lengths

The binding of linear diamine counterions with different methylene chain lengths to the amino-acid-based surfactants undecanoic L-isoleucine (und-IL) and undecanoic L-norleucine (und-NL) was investigated with NMR spectroscopy. The counterions studied were 1,2-ethylenediamine, 1,3-diaminopropane, 1,4-diaminobutane, 1,5-diaminopentane, and 1,6-diaminohexane. These counterions were all linear diamines with varying spacer chain lengths between the two amine functional groups. The sodium counterion was studied as well. Results showed that when the length of the counterion methylene chain was increased, the surfactants’ critical micelle concentrations (CMC) decreased. This decrease was attributed to diamines with longer methylene chains binding to multiple surfactant monomers below the CMC and thus acting as templating agents for the formation of micelles. The entropic hydrophobic effect and differences in diamine counterion charge also contributed to the size of the micelles and the surfactants’ CMCs in the solution. NMR diffusion measurements showed that the micelles formed by both surfactants were largest when 1,4-diaminobutane counterions were present in the solution. This amine also had the largest mole fraction of micelle-bound counterions. Finally, the und-NL micelles were larger than the und-IL micelles when 1,4-diaminobutane counterions were bound to the micelle surface. A model was proposed in which this surfactant formed non-spherical aggregates with both the surfactant molecules’ hydrocarbon chains and n-butyl amino acid side chains pointing toward the micelle core. The und-IL micelles, in contrast, were smaller and likely spherically shaped.

Highly Altered State of Proton Transport in Acid Pools in Charged Reverse Micelles.

Transport mechanisms of solvated protons of 1 M HCl acid pools, confined within reverse micelles (RMs) containing the negatively charged surfactant sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT) or the positively charged cetyltrimethylammonium bromide (CTABr), are analyzed with reactive force field simulations to interpret dynamical signatures from TeraHertz absorption and dielectric relaxation spectroscopy. We find that the forward proton hopping events for NaAOT are further suppressed compared to a nonionic RM, while the Grotthuss mechanism ceases altogether for CTABr. We attribute the sluggish proton dynamics for both charged RMs as due to headgroup and counterion charges that expel hydronium and chloride ions from the interface and into the bulk interior, thereby increasing the pH of the acid pools relative to the nonionic RM. For charged NaAOT and CTABr RMs, the localization of hydronium near a counterion or conjugate base reduces the Eigen and Zundel configurations that enable forward hopping. Thus, localized oscillatory hopping dominates, an effect that is most extreme for CTABr in which the proton residence time increases dramatically such that even oscillatory hopping is slow.

Spin-Crossover and Slow Magnetic Relaxation Behavior in Hexachlororhenate(IV) Salts of Mn(III) Complexes [Mn(5-Hal-sal2323)]2[ReCl6] (Hal = Cl, Br)

The cationic complexes of Mn(III) with the 5-Hal-sal2323 (Hal = Cl, Br) ligands and a paramagnetic doubly charged counterion [ReCl6]2− have been synthesized: [Mn(5-Cl-sal2323)]2[ReCl6] (1) and [Mn(5-Br-sal2323)]2[ReCl6] (2). Their crystal structures and magnetic properties have been studied. These isostructural two-component ionic compounds show a thermally induced spin transition at high temperature associated with the cationic subsystem and a field-induced slow magnetic relaxation of magnetization at cryogenic temperature, associated with the anionic subsystem. The compounds are the first examples of the coexistence of spin crossover and field-induced slow magnetic relaxation in the family of known [MnIII(sal2323)] cationic complexes with various counterions.

Convergent evolutionary counterion displacement of bilaterian opsins in ciliary cells.

Opsins are universal photoreceptive proteins in animals. Vertebrate rhodopsin in ciliary photoreceptor cells photo-converts to a metastable active state to regulate cyclic nucleotide signaling. This active state cannot photo-convert back to the dark state, and thus vertebrate rhodopsin is categorized as a mono-stable opsin. By contrast, mollusk and arthropod rhodopsins in rhabdomeric photoreceptor cells photo-convert to a stable active state to stimulate IP3/calcium signaling. This active state can photo-convert back to the dark state, and thus these rhodopsins are categorized as bistable opsins. Moreover, the negatively charged counterion position crucial for the visible light sensitivity is different between vertebrate rhodopsin (Glu113) and mollusk and arthropod rhodopsins (Glu181). This can be explained by an evolutionary scenario where vertebrate rhodopsin newly acquired Glu113 as a counterion, which is thought to have led to higher signaling efficiency of vertebrate rhodopsin. However, the detailed evolutionary steps which led to the higher efficiency in vertebrate rhodopsin still remain unknown. Here, we analyzed the xenopsin group, which is phylogenetically distinct from vertebrate rhodopsin and functions in protostome ciliary cells. Xenopsins are blue-sensitive bistable opsins that regulate cAMP signaling. We found that a bistable xenopsin of Leptochiton asellus had Glu113 as a counterion but did not exhibit elevated signaling efficiency. Therefore, our results show that vertebrate rhodopsin and L. asellus xenopsin regulate cyclic nucleotide signaling in ciliary cells and displaced the counterion position from Glu181 to Glu113 via convergent evolution, whereas subsequently only vertebrate rhodopsin elevated its signaling efficiency by acquiring the mono-stable property.

Structure and Diffusion of Ionic PDMS Melts.

Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.

Microsolvation Effects in the Spectral Tuning of Heliorhodopsin

Heliorhodopsins (HeR) are a new category of heptahelical transmembrane photoactive proteins with a covalently linked all-trans retinal. The protonated Schiff base (PSB) nitrogen in the retinal is stabilized by a negatively charged counterion. It is well-known that stronger or weaker electrostatic interactions with the counterion cause a significant spectral blue- or red-shift, respectively, in both microbial and animal rhodopsins. In HeR, however, while Glu107 acts as the counterion, mutations of this residue are not directly correlated with a spectral shift. A molecular dynamics analysis revealed that a water cluster pocket produces a microsolvation effect on the Schiff base, compensating to various extents the replacement of the native counterion. Using a combination of molecular dynamics and quantum mechanical/molecular mechanics (QM/MM), we study this microsolvation effect on the electronic absorption of the retinylidene Schiff base chromophore of HeR.

Formulation, development & evaluation of antihypertensive microsphere ionotropic gelatin method

Captopril is an ACE inhibitor that is used for the treatment of high blood pressure. The reason of this examine became to encapsulate the drug in unique polymer having mucoadhesive belongings and hence combining the benefits of microparticulates with mucoadhesive drug transport device. The microcapsules with a coat which include alginate and a mucoadhesive polymer including sodium carboxymethylcellulose (SCMC), methylcellulose, Carbopol 934P and hydroxyl propylmethylceullulose (HPMC) E15V have been organized through ionotropic gelation method, in which gelation became finished with oppositely charged counter ions to shape microparticles. The organized microcapsules have been subjected for diverse evaluations. The ensuing microparticles had been discrete, large, round and loose–flowing. Captopril release from those microcapsules became gradual and prolonged over longer duration of time. Drug launch for a few formula became diffusion controlled and others exhibited anomalous behavior. The organized microcapsules exhibited correct mucoadhesive belongings in the in vitro wash–off test. Among all formulations, batch containing sodium alginate and carbopol 934 confirmed better encapsulation efficiencies, correct float belongings and most prolongation of drug launch and correct mucoadhesion residences drug release and excellent mucoadhesion residences.

Mathematical Modeling of Monovalent Permselectivity of a Bilayer Ion-Exchange Membrane as a Function of Current Density.

Modification of an ion-exchange membrane with a thin layer, the charge of which is opposite to the charge of the substrate membrane, has proven to be an effective approach to obtaining a composite membrane with permselectivity towards monovalent ions. However, the mechanism of permselectivity is not clear enough. We report a 1D model based on the Nernst–Planck–Poisson equation system. Unlike other similar models, we introduce activity coefficients, which change when passing from one layer of the membrane to another. This makes it possible to accurately take into account the fact that the substrate membranes usually selectively sorb multiply charged counterions. We show that the main cause for the change in the permselectivity coefficient, P1/2, with increasing current density, j, is the change in the membrane/solution layer, which controls the fluxes of the competing mono- and divalent ions. At low current densities, counterion fluxes are controlled by transfer through the substrate membrane, which causes selective divalent ion transfer. When the current increases, the kinetic control goes first to the modification layer (which leads to the predominant transfer of monovalent ions) and then, at currents close to the limiting current, to the depleted diffusion layer (which results in a complete loss of the permselectivity). Thus, the dependence P1/2 − j passes through a maximum. An analytical solution is obtained for approximate assessment of the maximum value of P1/2 and the corresponding fluxes of the competing ions. The maximum P1/2 values, plotted as a function of the Na+ ion current density at which this maximum is reached, gives the theoretical trade-off curve between the membrane permselectivity and permeability of the bilayer monovalent selective ion-exchange membrane under consideration.