V.V. Nikonenko

Effect of structural membrane inhomogeneity on transport properties

There exist structural inhomogeneities of different scales in ion-exchange membranes. We suggest a microheterogeneous model for the description of inhomogeneities on the microphase scale, and show that they are the main factor determining the concentration dependence of membrane transport properties such as electrical conductivity, diffusion permeability and transport numbers. A set of tests is proposed for determination of model structural-kinetic parameters of membranes.

Intensive current transfer in membrane systems: Modelling, mechanisms and application in electrodialysis

Usually in electrochemical systems, the direct current densities not exceeding the limiting current density are applied. However, the recent practice of electrodialysis evidences the interest of other current modes where either the imposed direct current is over the limiting one or a non-constant asymmetrical (such as pulsed) current is used. The paper is devoted to make the mechanisms of mass transfer under these current regimes more clear. The theoretical background for mathematical modelling of mass transfer at overlimiting currents is described. Four effects providing overlimiting current conductance are examined. Two of them are related to water splitting: the appearance of additional charge 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. These effects result from formation of concentration gradients (known as concentration polarization) caused by the current flowing under conditions where ionic transport numbers are different in the membrane and solution. Similar effects take place not only in electrodialysis membrane systems, but in electrode ones, in electrophoresis and electrokinetic micro- and nanofluidic devices such as micropumps. The relation of these effects to the properties of the membrane surface (the chemical nature of the fixed groups, the degree of heterogeneity and hydrophobicity, and the geometrical shape of the surface) is analyzed. The interaction between the coupled effects is studied, and the conditions under which one or another effect becomes dominant are discussed. The application of intensive current modes in electrodialysis, the state-of-the-art and perspectives, are considered. It is shown that the intensive current modes are compatible with new trends in water treatment oriented towards Zero Liquid Discharge (ZLD) technologies. The main idea of these hybrid schemes including pressure- and electro-driven processes as well as conventional methods is to provide the precipitation of hardness salts before the membrane modules and that of well dissolved salts after.

Application of chronopotentiometry to determine the thickness of diffusion layer adjacent to an ion-exchange membrane under natural convection

A brief review of the evolution of the diffusion boundary layer (DBL) conception inspired by the works of Nernst, Levich and Amatore is presented. Experimental methods for studying the DBL in electrode and membrane systems are considered. The electrochemical behaviour of a CM2 cation-exchange membrane in NaCl and KCl solutions is studied by chronopotentiometry at constant under-limiting current. Chronopotentiometric curves are described theoretically by applying the Kedem-Katchalsky equations in differential form to a three-layer system including the membrane and two adjoining DBLs. The conductance coefficients entering the equations are found by treating the results of membrane characterisation: the electrical conductivity, transport numbers of ions and water, electrolyte uptake, as functions of the equilibrium electrolyte solution. The two-phase microheterogeneous model is used for this treatment resulting in presentation of the conductance coefficients as functions of (virtual) electrolyte solution concentration in the membrane. The steady-state DBL thickness (delta) is found by fitting experimental potential drop at sufficiently high times. It is found that delta is proportional to (Delta c)(-0.2), where Delta c is the difference between the electrolyte concentration in the solution bulk and at the interface. This result differs from the Levich equation, which gives the power equal to -0.25 for Delta c. This deviation is explained by the fact that the theory of Levich does not take into account microscopic chaotic convection motion recently described by Amatore et al. It is shown that the treatment of experimental chronopotentiometric curves with the model developed allows one to observe the role of streaming potential in the membrane. Different mechanisms of streaming potential and their effect on the shape of chronopotentiograms are discussed. A simple analytical solution of Navier-Stokes equations applied to natural convection near an infinite vertical ion-exchange membrane is found. It is shown that the formation of DBL induced by electric current is quasi-stationary. This fact allows the empirical expression found earlier and linking delta with Delta c under steady-state conditions to be used in transient regimes. The numerical solution of the non-stationary Kedem-Katchalsky equations together with this empirical expression results in quantitative description of the potential difference (pd) and delta as functions of time in chronopotentiometric experiments. The comparison of theoretical and experimental chronopotentiometric curves shows an excellent agreement, especially for the part after switching off the current. The reasons of a small deviation observed just before the curves attain steady state under a constant current applied are discussed.

On the role of gravitational convection in the transfer enhancement of salt ions in the course of dilute solution electrodialysis

Abstract The gravitational convection contribution to the increment of salt ion transfer through ion-exchange membranes at overlimiting currents is estimated by measuring total and partial current voltage characteristics of membrane desalination channels. The experiments were carried out by means of the technique enabling one to maintain the solution composition constant. The gravitational convection contribution is shown to increase with the growth of the distance between the membranes, with the decrease of the solution flow rate, as well as with the increase of the solution concentration. However, during the diluted solution electrodialysis in the channels with a small intermembrane distance (0.5 to 0.8 mm) the gravitational convection contribution is insignificant. High current densities of salt ions with a 2-4-fold excess of their “limiting” values are accounted for by the influence of the “exaltation effect” and electroconvection.

Correlation between transport parameters of ion-exchange membranes

Abstract A deduction of a relation between transport coefficients of ion-exchange membranes is considered by comparison the Kedem–Katchalsky and Onsager forms of transport equations in the framework of irreversible thermodynamics. This relation is analysed by using the experimental data of Narebska et al., Berezina et al., and the results of other authors. Transport equations generalising the Nernst–Planck equation with the coefficients determined directly from the practical transport characteristics are obtained either taking into account or disregarding the above mentioned relation. The Nernst–Einstein relation and its generalizations are discussed.

Self diffusion and conductivity in NafionR membranes in contact with NaCl+CaCl2 solutions

Abstract The ion-exchange isotherm of sodium and calcium ions is drawn for the Nafion R 117 membrane in contact with [NaCl] + 2[CaCl 2 ] = 0.1 M. The self-diffusion coefficients of sodium and calcium ions, obtained from steady-state self-diffusion ionic fluxes by a radiotracer method are independent of the ionic composition of the membrane phase. They are compared to those obtained from high frequency electrical resistance by means of the ac impedance technique. The values of electric conductivity of the membrane can be derived from a simple additivity law.

Modelling the transport of carbonic acid anions through anion-exchange membranes

Electrodiffusion of carbonate and bicarbonate anions through anion-exchange membranes (AEM) is described on the basis of the Nernst � /Planck equations taking into account coupled hydrolysis reactions in the external diffusion boundary layers (DBLs) and internal pore solution. The model supposes local electroneutrality as well as chemical and thermodynamic equilibrium. The transport is considered in three layers being an anion exchange membrane and two adjoining diffusion layers. A mechanism of

Dependence of composition of anion-exchange membranes and their electrical conductivity on concentration of sodium salts of carbonic and phosphoric acids

Abstract Concentration dependencies of electrical conductivity of AFN, AMX, ACS and ACM anion-exchange membranes (from Tokuyama Soda), equilibrated with solutions of sodium salts of carbonic and phosphoric acids as well as with sodium sulfate solutions, are studied. Analysis of the data on electrolyte desorption from the membranes equilibrated initially with solutions of the weak-acid salts as well as the application of the microheterogeneous model allowed to explain the change of the conductivity with a concentration growth by the effect of two factors: (i) a change (an increase, in the most cases) of the conductivity of the electroneutral solution forming the membrane ‘inter-gel’ phase, (ii) a variation of the conductivity of the membrane ‘gel’ phase caused by hydrolysis reactions of the weak-acid anions in the pore solution.

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.

A simplified procedure for ion-exchange membrane characterisation

A new procedure for the characterisation of the transport properties of ion-exchange membranes (IEM) is proposed. Only three characteristics have to be measured: the electrical conductivity, the diffusion permeability coefficient and the apparent transport number. To complete the set of parameters, two complementary characteristics, the true counter-ion transport number and the water transport number, are calculated from the Scatchard equation and from a novel equation deduced earlier. The possibilities to reduce the number of initial measurements are discussed in three cases.