Experimental Verification of the Electroosmotic Mechanism of Overlimiting Conductance Through a Cation Exchange Electrodialysis Membrane

The paper is concerned with convection at an ion-exchange electrodialysis membrane induced by nonequilibrium electroosmosis as a source of overlimiting conductance current through the membrane. Derivation of nonequilibrium electroosmotic slip condition is recapitulated along with the results of linear stability analysis of quiescent electrodiffusion through a flat ion-exchange membrane. Results of numerical calculation pertaining to nonlinear convection, developing from the respective instability, are reported along with those of recent experiments with modified membranes. These latter rule in favor of electroosmotic versus bulk electroconvective origin of overlimiting conductance through ion-exchange membranes.     

Coupled convection of solution near the surface of ion-exchange membranes in intensive current regimes

Mechanisms responsible for the overlimiting ion transfer in membranes systems are discussed. The overlimiting transfer is shown to be due largely to the action of four effects coupled with the concentration polarization of the system. Two of these are connected with the water dissociation near the membrane/solution interface: the emergence of additional charge carriers (ions H⁺ or OH^?) in the depleted solution layer and the exaltation of transfer of salt counterions. The latter effect is connected with the perturbation of electric field caused by the water dissociation products. The other two effects are two versions of coupled convection, which leads to partial destruction of the depleted diffusion layer. These include gravitational convection and electroconvection. The former is caused by the emergence of the solution’s density gradient. The latter develops via a mechanism of electroosmotic slip. In this work, methods of voltammetry and chronopotentiometry and pH measurements are used to study the transfer of ions through homogeneous membranes Nafion-117 and AMX as a function of the concentration of sodium chloride solutions in the underlimiting and overlimiting current regimes. In a 0.1 M NaCl solution, gravitational convection makes a considerable contribution to the transfer of salt ions near the membrane surface in intensive current regimes. The influence of this effect on the electrochemical behavior of membrane systems weakens with the solution dilution and with increasing relative transfer of the H⁺ and OH^? ions that are generated at the membrane/solution interface. In conditions where gravitational convection is suppressed and the water dissociation near the membrane/solution interface is not great, the major contribution to the overlimiting growth of current is made by electroconvection. Topics for discussion in the paper include the mutual influence of effects on one another, in particular, the effect the rate of generation of the H⁺ and OH^? ions exerts on the gravitational convection and electroconvection and the reasons for the different behavior of cation-and anion-exchange membranes in intensive current regimes.     

Effect of chemical modification of ion-exchange membrane MA-40 on its electrochemical characteristics

Transport characteristics of commercial heterogeneous anion-exchange membranes MA-40 and MA-41 are studied, together with those of membrane MA-40M fabricated by treating the MA-40 surfaces with a strong polyelectrolyte complex. It is demonstrated that, after modification, the electrical conductivity of MA-40M in an NaOH solution increases. At overlimiting currents, the water dissociation rate on this membrane decreases as compared with the initial membrane. At the same time, no noticeable change in the rate of transport of counter-ions (ions Cl^-) through the membrane at a fixed potential drop is discovered at under-and overlimiting currents. The MA-40M membrane behavior is explained by the conversion of secondary and tertiary functional ammonium groups in the near-surface membrane layers approximately 80 μm thick into quaternary groups during the treatment by the polyelectrolyte.     

Rate of Generation of Ions H<Superscript>+</Superscript> and OH<Superscript>−</Superscript> at the Ion-Exchange Membrane/Dilute Solution Interface as a Function of the Current Density

Partial currents of water dissociation products through cation- and anion-exchange membranes that form thin desalination channels in electrodialyzers are measured. The investigations are performed in a broad interval of flow rates during desalination of dilute sodium chloride solutions at overlimiting currents. A water dissociation theory, which was developed for bipolar membranes, and a mass transfer theory that allows for the space charge formation at overlimiting currents are used to derive an expression, according to which the rate of generation of the H⁺ and OH^? ions is defined by the ratio of the current density to its critical value at which water starts undergoing discernible dissociation.     

Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.     

Morphology and microtopology of cation-exchange polymers and the origin of the overlimiting current

In electrodialysis desalination processes, the operating current density is limited by concentration polarization. In contrast to other membrane processes such as ultrafiltration, in electrodialysis, current transport above the limiting current is possible. In this work, the origin of the overlimiting current at cation-exchange polymers is investigated. We show that, under certain experimental conditions, electroconvection is the origin of the overlimiting conductance. The theory concerning electroconvection predicts a shortening of the plateau length of membranes with increased conductive or geometrical heterogeneity. We investigate the influence of these two parameters and show that the creation of line undulations on the membrane surface normal to the flow direction, having distances in the range of approximately 50-200% of the boundary-layer thickness, lead to an earlier onset of the overlimiting current. The plateau length of the undulated membranes is reduced by up to 60% compared to that of a flat membrane. These results verify the existence of electroconvection as a mechanism destabilizing the laminar boundary layer at the liquid-membrane interface and causing ionic transport above the limiting current density.     

Transport of hydrogen and hydroxyl ions through ion-exchange membranes under overlimiting current densities

A direct method is suggested for measurement of fluxes of hydrogen and hydroxyl ions through ion-exchange membranes under overlimiting modes of electrodialysis. Fluxes of hydrogen and hydroxyl ions are measured for different immobilized membrane ions and counterions. The important role of counterions in generation of hydrogen and hydroxyl ions is shown. Exponential decrease in fluxes of hydroxyl or hydrogen ions is established at an increase in the Gibbs energy of counterion hydration.     

Electrochemical behavior of MF-4SK/polyaniline composites as investigated by membrane voltammetry

Membrane voltammetry was used to investigate composites consisting of perfluorinated MF-4SK membranes and polyaniline (PANI) and synthesized under various conditions. A theoretical analysis of the influence of transport-structure parameters of the ion-exchange membranes on their selectivity and limiting-current value is carried out. For MF-4SK/PANI composites, the increase in the exchange potential at the overlimiting state is found to be more than 2V compared to the original membrane. An analysis of how various factors influence the parameters of a current-voltage curve shows that the presence of anilinium and Fe³⁺ ions in the electromembrane system has no effect on the value of the potential at the onset of the overlimiting state. A phenomenological model is proposed to account for the increased plateau length at the limiting current through a change in the energetic state of water in the perfluorinated-membrane matrix resulting from the template synthesis of polyaniline.     

Effect of modification of ion-exchange membrane MF-4SK on its polarization characteristics

Modifications of perfluorinated membrane MF-4SK are studied by a membrane voltammetry method. Various techniques used for physicochemical modification of the membrane (variation of conditions of its chemical conditioning, insertion of tetrabutylammonium cations) exert predicted action on its structural and electrotransport properties. Correlation is established between variations in the slope of the ohmic segment of a voltammetric curve, the magnitude of the limiting electrodiffusion current, and the potential of the system’s conversion into an overlimiting state and the electrotransport properties of membranes and their structural characteristics that are obtained by independent methods of impedance conductimetry and standard porosimetry. The increase in the limiting current for membranes subjected to a thermal oxidizing treatment is explained by a change in the content and state of water in the membrane bulk. Effects of acceleration of the occurrence of an overlimiting state of the membrane saturated with tetrabutylammonium cations is discovered and possible reasons for this phenomenon are discussed. For membranes saturated with tetrabutylammonium cations, a correlation is established between the limiting current and electroosmotic phenomena.     

Ionic Transport in Electrodialysis of Ammonium Nitrate

During the electrodialysis of ammonium nitrate solution, the fluxes of salt ions pass through the maximum, which is observed near the limiting current, with increasing current density. A decrease in the flux of ammonium ions at the overlimiting current densities is caused by the effect of competitive transport of solution ions and by the formation of weak NH₃ ? H₂O electrolyte due to the alkalization of solution layer adjacent to the cation-exchange membrane in the desalination channel. A decrease in the flux of nitrate ions in the overlimiting current modes is caused by a change in the composition and catalytic activity of the functional groups of anion-exchange membrane towards the dissociation of water molecules due to the effect of ammonium ions.     

Effects of the desalination chamber design on the mass-transfer characteristics of electrodialysis apparatuses at overlimiting current densities

The overlimiting current modes are being increasingly used in electrodialysis (ED) of dilute aqueous solutions. Of great importance is establishing a relationship between the design of ED apparatuses and the character of phenomena observed at overlimiting current densities, primarily, electroconvection and H⁺ and OH^? ion generation during water dissociation at the membrane-solution interface. In this work, we analyze the factors governing the efficiency of dilute solutions using modern theoretical concepts and experimental data obtained in laboratory cells and large-scale electrodialysis apparatuses. We also analyze the relationship between the mechanisms of the overlimiting transfer and the design of the desalinating channel. ED apparatuses of different types are considered, namely, apparatuses with profiled membranes, inert spacers, monolayer of ionite granules, and dipolar fillers of unwoven ionite fibers. The optimum concentration ranges of the desalinated solutions were found, and the operating conditions of membrane stacks, providing maximum overlimiting ion transfer, were determined.     

Electric Double Layer at the Membrane/Solution Interface in a Three-Layered Membrane System

Transport of ions through a three-layered membrane system at overlimiting currents is simulated mathematically. To allow for the space charge, the Poisson equation is used in both the first diffusion layer and the membrane. Two modes are shown to exist at overlimiting currents: a quasi-equilibrium state of the interface and a Schottky mode.     

Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer

Four effects providing overlimiting current transfer in ion-exchange membrane systems are examined. Two of them are related to water splitting: the appearance of additional current carriers (H+ and OH- ions) and exaltation effect. Two others are due to coupled convection partially destroying the diffusion boundary layer: gravitational convection and electroconvection. Three anion-exchange membranes, which differ in surface morphology and the nature of ion-exchange sites within a surface layer, are examined. The ion transfer across these membranes in NaCl solutions is studied by voltammetry, chronopotentiometry, and pH-metry. By excluding the effects of water splitting and gravitational convection, it is shown that the main mechanism of overlimiting mass transfer in narrow membrane cells at low salt concentrations is electroconvection. The reasons explaining why water splitting suppresses electroconvection are discussed. The scenario of development of potential oscillations with growing current and time is compared with that described theoretically by Rubinstein and Zaltzman.     

Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents

This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current-voltage curves.     

Structural change of ion-exchange membrane surfaces under high electric fields and its effects on membrane properties

Structural change of an ion-exchange membrane under a high electric field was investigated by comparing water dissociation and the FTIR spectra between the virgin membrane and that used at an overlimiting current density. From a series of water dissociation experiments at overlimiting current densities, it was observed that water dissociation in an anion-exchange membrane used at an overlimiting current density was higher than that in a virgin membrane at the same current density. The FTIR study revealed that the tertiary amine groups are formed from the quaternary ammonium groups on the anion-exchange membrane surface where ion depletion occurs under the influence of the applied strong electric field. The occurrence of increased water dissociation is considered to be caused by the protonation and deprotonation of the tertiary amine groups in the anion-exchange membrane. On the other hand, there was no structural change for the cation-exchange membrane under the electric field investigated in this study, which is coincident with the results of water dissociation experiments for the CMX membrane. In addition, we found that membrane resistance, permselectivity, and plateau length of the current-voltage curve were affected by the converted tertiary amine groups depending on the solution pH.     

Understanding anomalous current-voltage characteristics in microchannel-nanochannel interconnect devices

The integration of a microchannel with a nanochannel is known to exhibit anomalous nonlinear current-voltage characteristics. In this paper, we perform detailed numerical simulations considering a 2-D nonlinear ion transport model, to capture and explain the underlying physics behind the limiting resistance and the overlimiting current regions, observed predominantly in a highly ion-selective nanochannel. We attribute the overlimiting current characteristics to the redistribution of the space charges resulting in an anomalous enhancement in the ionic concentration of the electrolyte in the induced space charge region, beyond a critical voltage. The overlimiting current with constant conductivity is predicted even without considering the effects of fluidic nonlinearities. We extend our study and report anomalous rectification effects, resulting in an enhancement of current in the non-ohmic region, under the application of combined AC and DC electric fields. The necessary criteria to observe these enhancements and some useful scaling relations are discussed.     

Overlimiting Electrodiffusion Transport in the Diffusion Layer as a Function of Rate Constants of Dissociation and Recombination of Water: A Numerical Calculation

A boundary-value problem, which permits discovering the effect the rate constants of dissociation and recombination of water have on the electrical and mass transfer in a diffusion layer at the ion-exchange membrane/solution interface in an overlimiting mode, is solved numerically. According to the calculation, the only value of the rate constant for reactions of dissociation and recombination of pure water determined experimentally and reported in the literature is underrated by several orders of magnitude.     

A mathematical model describing voltammograms and transport numbers under intensive electrodialysis modes

A three-layer mathematical model of overlimiting state is developed. A reactive layer with a thickness depending on the current density is introduced into the model. A decrease in the thickness of diffusion layer, which donates the counterions, with increasing current density as a result of electroconvection is also taken into account. A boundary-value problem is formulated within the Nernst-Planck and Poisson’s model in the three-layer region with the boundary conditions of constant concentrations in the bulk solution. It is shown that an increase in the reactive layer thickness with increasing current density determines the behavior of effective transport numbers in the overlimiting state of ion-exchange electromembrane system. In the current range under consideration (from 1 to 20 limiting currents), the reactive layer thickness is several tens nanometers and reaches 70 nm at a 100-fold excess over the limiting current. To calculate the voltammograms, the dependence of effective thickness δ_N of diffusion layer on the current density is required. This dependence can be obtained by solving an inverse problem, from the laser interferometry experiments, or calculated by the Navier-Stokes hydrodynamic model. The model enables one to calculate the distribution of electric field strength, potential, concentrations in the diffusion layers and membrane.     

Effect of the ion-exchange-membrane/solution interfacial characteristics on the mass transfer at severe current regimes

In the electrodialysis of dilute solutions, performed at intense current regimes, the membrane electrical conductance and diffusion permeability are no more crucial. Of more importance become the membrane properties that control increase in the overlimiting mass transfer of salt ions, as well as H⁺ and OH^? ions in membrane systems. In this work different methods of the improving of mass-exchange characteristics of commercial ion-exchange membranes intended for operation at intense current regimes are discussed. They are based on modern concepts of mechanisms of the electroconvection (which proceeds as electroosmosis of 2nd kind), as well as mechanisms of H⁺ and OH^? ions generation at the membrane/solution interface. Influence on the membrane electrochemical and mass-exchange characteristics is possible via (a) control of chemical nature of fixed groups at membrane surfaces, in order to weaken their catalytic activity with respect to water dissociation reaction, (b) increase in the surface hydrophobicity, and (c) design of electrical inhomogeneity of the membrane/solution interface; the purpose is the facilitating of intense development of electrical convection.     

Extended space charge in concentration polarization

This paper is concerned with ionic currents from an electrolyte solution into a charge-selective solid, such as, an electrode, an ion-exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization — formation of solute concentration gradients under the passage of a DC current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed non-equilibrium electroosmotic instability, result from the formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface. In this paper we review the peculiar features of the non-equilibrium electric double layer and extended space charge and the possibility of their direct probing by harmonic voltage/current perturbations through a linear and non-linear system's response, by the methods of electrical impedance spectroscopy and via the anomalous rectification effect. On the relevant microscopic scales the ionic transport in the direction normal to the interface is dominated by drift-diffusion; hence, the extended space charge related viscous flows remain beyond the scope of this paper.