L. Dammak

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.

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.

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.

From the multi-ionic to the bi-ionic potential

Abstract When an ion exchange membrane separates two electrolyte solutions, an electric potential is set up. In the particular case where the two solutions contain the same co-ion and different counter-ions at the same concentration, Co, this potential is named the bi-ionic potential (BIP). The ion interdiffusion fluxes transform every bi-ionic system to a multi-ionic one. We have set up an experimental device which permits us to obtain reliable measurements of BIPs. A cation exchange membrane (CM 2 ) has been used to study the BIP as a function of C 0 . The comparison of experimental results with the Helfferich equations shows that the former is only confirmed at high or low concentrations. The important role of diffusion layers, co-ion flux and/or influence of membrane structure are proved.

Theoretical study of the bi-ionic potential and confrontation with experimental results

A theoretical study of the bi-ionic potential (BIP) has been carried out using the extended Nernst‐Planck equation in the case of a mixed control of the interdiffusion process by the ion-exchange membrane (IEM) and the diffusion boundary layers (DBLs), a non-zero co-ion flux, a non-zero water flux, a variable selectivity coefficient and an affinity coefficient different from unity. The numerical integration of the two coupled differential transport equations allowed, for a given common concentration C0, the computation of the BIP from the values of 12 parameters required. Three of these 12 parameters are taken from the literature, the others are determined from independent experiments except the DBL thickness and the co-ion diffusion coefficient in the membrane. We have developed a procedure to deduce these two parameters from the experimental curves of the BIP vs. C0. For the NaCl/CM2/LiCl bi-ionic system, the DBL thickness changes from 59 mm at high stirring rate to 196 m mi n the absence of stirring. The chloride diffusion coefficient in the CM2 membrane has been estimated to be equal to 2.110 ˇ7 cm 2 s ˇ1 . Using these values, we have studied theoretically the influence of each of the three parameters: affinity coefficient, selectivity coefficient and water flow. We have shown that the affinity coefficient has the most important contribution but the selectivity coefficient and the water flow influence only the BIP at high common concentrations. # 1999 Elsevier Science B.V. All rights reserved.

Détermination du nombre de transport d’un contre-ion dans une membrane échangeuse d’ions en utilisant la méthode de la pile de concentration

Resume La permselectivite d’un polymere echangeur d’ions est une des principales caracteristiques physicochimiques permettant l’evaluation de ses performance. Elle constitue l’un de ses principaux criteres de choix pour une application chimique ou electrochimique. Le classement d’une serie de membranes selon leur permselectivite peut etre obtenu a partir des valeurs du nombre de transport des contre-ions ou des co-ions. Traditionnellement, la methode de Hittorf est la plus utilisee pour ce type de mesure malgre les defauts inherents a son principe. Nous avons montre que la methode de Hittorf peut etre avantageusement remplacee par la methode de la pile de concentration, initialement utilisee pour les parois inertes non chargees.

Determination of the diffusion coefficients of ions in cation-exchange membranes, supposed to be homogeneous, from the electrical membrane conductivity and the equilibrium quantity of absorbed electrolyte

Abstract Two ion-exchange membrane characteristics, the quantity of absorbed electrolyte and the electrical membrane conductivity have been measured and correlated for three cation-exchange membranes (CM2, CMx and MK-40), two electrolytes (KCl and LiCl), over a large concentration range of the solution (0.1 M≤ C 0 ≤3.0 M). The membrane conductivity has been measured according to a French standard. However, because of the lack of standards fixing all the operating conditions for good determination of the second parameter, we established an experimental protocol, validated by a statistical study and made a comparison with the theoretical Glueckaufs equation. This method will be proposed to be standardized for this category of measurements. Relationships have been established between the two parameters allowing us to determine both the counter-ion and the co-ion diffusion coefficients in a cation-exchange membrane, considered as homogeneous. The values of these coefficients for the counter-ions are in good agreement with those obtained from other methods. The variations of the computed diffusion coefficients of counter-ions and co-ions for the different studied systems are discussed in terms of internal interactions with the charged polymer matrix and the other diffusing species. The discussion also takes into account the free water content of the polymer.

The influence of the salt concentration and the diffusion boundary layers on the bi-ionic potential

Measurements of bi-ionic potential (BIP) across three cation-exchange membranes (CEMs) have been carried out for KCl/CEM/NaCl, KCl/CEM/LiCl, and NaCl/CEM/LiCl systems, where CEM is a polystyrene and divinylbenzene sulfonated membrane (CM2, from Tokuyama Soda), a perfluorosulfonic acid membrane (Nafion® 117, from Du Pont De Nemours) and an heterogenous membrane prepared by inclusion of cation-exchange resin in PVC (CRP, from Rhone Poulenc). The influence of the salt concentration and the diffusion boundary layers (DBLs) on the BIP values has been analysed both theoretically and experimentally. The theoretical model is based on the Nernst-Planck equations, and gives a good description for salt concentrations higher than 5×10−4 M. For the CM2 membrane, the DBL thickness changes from 20–23 μm in absence of stirring to 3–4 μm for high stirring rates. Also, the ion diffusion coefficients in this membrane have been estimated to be of the order of 10−6 cm2/s. It has been observed that the counter-ion diffusion coefficients ratio (DA/DB) in the membrane increases significantly when the membrane water content decreases, which suggests the possibility of achieving highly selective ion transport with low water content membranes.

Porous structure of ion exchange membranes investigated by various techniques

A comparative review of various techniques is provided: mercury intrusion porosimetry, nitrogen sorption porosimetry, differential scanning calorimetry (DSC)-based thermoporosimetry, and standard contact porosimetry (SCP), which allows determining pore volume distribution versus pore radius/water binding energy in ion-exchange membranes (IEMs). IEMs in the swollen state have a labile structure involving micro-, meso- and macropores, whose size is a function of the external water vapor pressure. For such materials, the most appropriate methods for quantifying their porosity are DSC and SCP. Especially significant information is given by the SCP method allowing measuring porosimetric curves in a very large pore size range from 1 to 105nm. Experimental results of water distribution in homogeneous and heterogeneous commercial and modified IEMs are presented. The effect of various factors on water distribution is reviewed, i.e. nature of polymeric matrix and functional groups, method for membrane preparation, membrane ageing. A special attention is given to the effect of membrane modification by embedding nanoparticles in their structure. The porosimetric curves are considered along with the results of electrochemical characterization involving the measurements of membrane conductivity, as well as diffusion and electroosmotic permeability. It is shown that addition of nanoparticles may lead to either increase or decrease of water content in IEMs, different ranges of pore size being affected. Hybrid membranes modified with hydrated zirconium dioxide exhibit much higher permselectivity in comparison with the pristine membranes. The diversity of the responses of membrane properties to their modification allows for formation of membranes suitable for fuel cells, electrodialysis or other applications.

Effect of counterion hydration numbers on the development of Electroconvection at the surface of heterogeneous cation-exchange membrane modified with an MF-4SK film

The transport of sodium, calcium, and magnesium ions through the heterogeneous cationexchange membrane MK-40, surface modified with a thin (about 15 μm) homogeneous film MF-4SK. By using chronopotentiometry and voltammetry techniques, it has been shown that the combination of relatively high hydrophobicity of the film surface with its electrical and geometrical (surface waviness) heterogeneity creates conditions for the development of electroconvection, which considerably enhances mass transfer in overlimiting current regimes. The electroconvection intensity substantially depends on the degree of counterion hydration. Highly hydrated calcium and magnesium ions involve in motion a much larger volume of water as compared with sodium ions. When constant overlimiting direct current is applied to the membrane, electroconvective vortices in 0.02 M CaCl2 and MgCl2 solutions are generated already within 5–8 s, a duration that is the transition time characterizing the change of the transfer mechanism in chronopotentiometry. The generation of vortices is manifested by potential oscillations in the initial portion of chronopotentiograms; no oscillation has been observed in the case of 0.02 M NaCl solution. More intense electroconvection in the case of doubly charged counterions also causes a reduction in the potential drop (Δφ) at both short times corresponding to the initial portion of chronopotentiograms and long times when the quasi-steady state is achieved. At a fixed ratio of current to its limiting value, Δφ decreases in the order Na+ > Ca2+ > Mg2+.