Determination Of Transport Numbers Research Articles

Two Methods for Determination of Transport Numbers in Ion-Exchange Membranes

Two Methods for Determination of Transport Numbers in Ion-Exchange Membranes

ANALYTICAL 3D MIGRATION MODEL OF STEADY-STATE METAL ANODIZING: THE VELOCITY FIELDS AND TRAJECTORIES OF MIGRATING TRACERS

Mathematical 3D migration model of the motion of tracers migrating in the electric field is developed for the steady-state porous metal oxidation. Tracers can be introduced into the metal or solution for research purposes. In this work, the impurities in the anodized metal and the main electrolyte anions are also considered as tracers, if their content in the AOF is so small that a fraction of ionic current of their migration may be ignored, i.e. the entire ionic current is carried only by the main metal and oxygen ions. The tracers can migrate in the direction of oxygen ion motion or in the opposite direction. It is shown that the tracer migration can be taken into account by introducing the effective transport number. The effect of the direction and velocity of tracer migration on their trajectory is studied within the mathematic model developed. The phenomenon of oxide flow, which was discovered in the works of Garcia-Vergara, Skeldon, Thompson, Habazaki, is explained within a concept that the oxide flow is a result of oxide growth in the direction normal to the substrate and the migration of basic ions in the radial direction in the strong spherical electric field with no considerable effect of mechanical stresses. The calculated arrangement of tracers agrees well with the experimental data of many works, where the tracers were introduced from the metal and electrolyte. The model offers possibilities of experimental determination of transport numbers of metal and oxygen in the steady-state processes of anodic porous oxidation of metals.

Electromotive Force (emf) Determination of Transport Numbers for Native and Foreign Ions in Molten Alkali Metal Carbonates

Dense dual-phase membranes consisting of a molten carbonate embedded in the interconnected pores of a ceramic framework are considered for potential application in CO2 separation at elevated temperatures utilising ambipolar conduction of carbonate ions and other charge carriers in the molten or solid phase. We have developed an experimental setup for determining transport numbers of various species in the molten carbonate phase by means of electromotive force (emf) measurements. Transport numbers of native and foreign ions are characterized for the eutectic mixture of Li-Na-K carbonate, which is embedded in a porous alumina matrix with Pt or lithiated NiO electrodes. The voltage is measured under activity gradients of CO2, O2, or H2O at 550°C. Electrochemical impedance spectra are collected during emf measurements. The true transport numbers of both native and foreign ions are calculated by taking into account the electrode polarization. The corrected transport numbers of native (carbonate and alkali metal) ions are close to unity at 550°C based on the emf under a gradient. Minor transport of oxide ions and hydroxide ions in the molten carbonate is observed under a gradient and gradient, respectively. This offers an alternative understanding and operation of molten carbonate dual-phase membranes.

Applicability of emf measurements under external load resistance conditions for ion transport number determination

In order to evaluate the applicability of concentration cells for the ion transference number measurements with external load, the cell response was simulated with variable transport properties of the cell material, external load resistance, geometrical factors such as ion-conducting membrane thickness, and electrode kinetics. This technique is expected to be pertinent when ηF/RT<0.2, except possibly for conditions when the electrode kinetics is dependent on a relatively small limiting current density. In each particular case, the method validity can be verified by testing if the overpotential sum grows faster than current on decreasing the external load resistance. A pyrochlore-type material Gd1.9Ca0.1Ti2O7-δ with dominant oxygen ionic conductivity is used as a study case to demonstrate the criteria proposed to assess the applicability of emf measurements under short-circuit conditions.

Electron–hole conduction in Pr-doped Ce(Gd)O 2− δ by faradaic efficiency and emf measurements

Non-negligible electrode polarisation in faradaic efficiency and emf electrochemical cells used for transport number determination results in apparent ion transference numbers which are lower than the true values. However, appropriate modifications of these techniques combined with use of electrodes having a high polarisation resistance, enable a precise determination of even minor electronic contributions to the total conductivity of solid electrolytes. Experimental modification of the faradaic efficiency method, taking into account the electrode polarisation resistance, is proposed and verified using Ce 0.80Gd 0.18Pr 0.02O 2− δ ceramics. Substitution of 2% gadolinium cations in the lattice of Ce 0.80Gd 0.20O 2− δ solid electrolyte with praseodymium was found to increase the p-type electronic conductivity by 2.5–4 times, while the activation energy for the electron–hole transport decreases from 145 to 125 kJ mol −1. The oxygen ion transference numbers of Ce 0.80Gd 0.18Pr 0.02O 2− δ in air vary in the range 0.996–0.970 at 873–1223 K, decreasing with increasing temperature. No significant effect of co-doping with praseodymium on the ionic conductivity, crystal lattice and thermal expansion of ceria solid electrolyte was found.

Preparation and characterization of an electronically conductive and chemically modified ultrafiltration type membrane

We have prepared, for the first time, an electronically conductive polyethersulfone ultrafiltration membrane, noted as PS, by depositing an ultrathin gold coating. This conductive membrane has been chemically modified by electrodepositing a polymer-based nickel tetrasulfonated phthalocyanine film (NiTSPc) covered by Nafion ®. Atomic force microscopy (AFM) and membrane potential measurement experiments were carried out to characterize the morphology and the transport properties of the new PS membrane. AFM measurements showed that the topology of the surface pores of the PS membrane was modified by the deposition of Au, NiTSPc and Nafion ® layers and that the chemical modifications of the membrane do not obstruct the access to the inner pores. Li + transport number determination have corroborated AFM results and showed that the Li + transport was facilitated by electrostatic effect induced by the negative charge densities of NiTSPc and NiTSPc/Nafion ® coatings.

Equilibrium and transport properties of polydisperse polyelectrolytes in graft-modified porous charged membranes: forced permeation–diffusion of lignosulfonate

The convective diffusion of a polydisperse polyelectrolyte (lignosulfonate) through charged porous membranes is studied. The membranes are characterised by potentiometric transport number determination both in the presence and in the absence of lignosulfonate. The convective diffusion experiments are carried out with NaCl and HCl as supporting electrolytes. The effect of using different concentrations of supporting electrolyte in the two cell compartments is also studied. The Donnan equilibrium and steady-state transport of the polyelectrolyte in a convective diffusion cell are theoretically described, and the effects of changing the supporting electrolyte (and pH) are discussed. Good agreement between theoretical and experimental results is obtained. It is shown that the effective membrane fixed charge reverses its sign due to polyelectrolyte adsorption.

Potentiometric Determination of Transport Numbers of Ternary Electrolyte Systems in Charged Membranes

The potentiometric determination of transport numbers in charged membranes for the case of ternary systems is critically analyzed, and expressions are derived to evaluate these transport numbers close to equilibrium conditions. The apparent potentiometric transport number (i.e., that obtained by assuming that the ternary system behaves as a binary system) is also studied and the conditions that make it reliable for the estimation of the membrane fixed charge concentration are given. Particular attention is paid to the case of amphoteric membranes where the pH adjustment is necessary and the bathing solutions are often ternary systems. However, our theoretical study is general, and can also be applied to estimate the effect of any impurity ion present in the bathing solution. The main conclusion is that the interpretation of ion transport data in terms of the binary system equations can be an erroneous procedure even when the third ion present has a relatively low concentration.

A novel marker approach for the determination of transport numbers during the growth of anodic oxide films on tantalum

Abstract From knowledge of the immobility of incorporated silicon species in anodic films on tantalum, developed by high-field ionic conduction, a procedure has been developed for their use as a marker to determine the mobilities of species contributing to film growth on tantalum and other species incorporated from the electrolyte. In the example given, sequential anodizing, firstly in silicate electrolyte and subsequently in sulphuric acid, have been used to determine the transport number of tantalum cations, 0.24, which is an excellent agreement with the value determined by Rutherford back-scattering spectroscopy and chemical sectioning.

Transport number determination by the concentration-cell/open-circuit voltage method for oxides with mixed electronic, ionic and protonic conductivity

Wagner's theory of mixed conduction has been applied to foreign and native species simultaneously in determining the open-circuit potential (OCV) of a concentration cell. We present general derivations for the OCV for mixed conductors containing protonic species, native ions and electrons and propose experiments for discriminating transport by the various species.

A novel marker for the determination of transport numbers during anodic barrier oxide growth on aluminium

Abstract Anodic oxidation of thermally oxidized aluminium leads to the local development of thin disc-shaped γ′-Al2O3 crystals in the amorphous barrier oxide layers. The possibility of utilizing these γ′-Al2O3 crystals as ‘markers’ for the determination of the transport numbers during anodic barrier oxide growth on aluminium has been assessed. An excellent agreement was observed between the cationic transport numbers obtained using the present marker and by the usual implanted xenon marker method. Thus, the inertness and immobility of the usual xenon markers has now been confirmed. Additionally, the development of γ′-Al2O3 in the growing barrier oxide gives important insight into the effects of structure of the various oxides of alumina on the ionic transport processes during anodic oxidation. For example, a significantly higher field strength is required for ionic migration through γ′-alumina than the usual amorphous anodic alumina.

Characterization of electrodialysis membranes by chronopotentiometry

In the present work, chronopotentiometry is used to measure transport numbers of ion-exchange membranes in contact with solutions having a concentration up to 1 M, similar to that found in applications of electromembrane separation processes. Usually, only dilute solutions, with a concentration lower than 0.01 M, can be used for the determination of transport numbers of membranes. For the case of concentrated solutions up to 1 M, we finally used a flat bilayer membrane where one layer consists of the ion-exchange membrane under study, the other being a neutral membrane of agar-agar. But, for the calculation of transport numbers, it was necessary to measure the diffusion coefficient in the neutral agar-agar layer for the electrolyte used; this was done by means of varying the concentration. Then, the determination of the passage of chloride ions through a heterogeneous Rhone-Poulenc ion-exchange membrane, shows a decrease in transport numbers when the concentration of counter-ions rises, in agreement with the reduction of the Donnan exclusion.

The Effect of an Intermediate Layer on the Determination of Transport Numbers in Ion Exchange Membrane.

Lorsque les nombres de transport sont mesures simultanement dans des membranes echangeuses d'ions on utilise une membrane composite (une pile de membranes a empilage compact). On considere l'influence de la couche limite entre des membranes identiques

A Method for Determination of Transport Numbers in Ion Exchange Membranes.

On propose une methode de determination simultanee de nombres de transport de divers ions dans des membranes echangeuses d'ions. Utilisation dans ce travail d'une pile de membranes echangeuses de cations a empilement compact. Les nombres de transport sont calcules a partir des variations de taux des ions dans chaque membrane sous l'effet de courant electrique, comme dans la methode de Hittorf. Application au cas des nombres de transport des ions Na + et K + dans des membranes echangeuses de cations (Ionics 61 AZL 389)

A new modified Hittorf method for the determination of transport numbers in polyelectrolyte solutions

A new method for determining transport numbers in polyelectrolyte solutions is described. The method is a modification of the Hittorf method, the main difference being that the current-induced concentration change is measured in a compartment to which current is supplied through an ion-exchange membrane. As the current in the membrane is carried by counterions only, the solution in the measuring compartment remains free from foreign ions, and thus the concentration change can be monitored accurately by conductivity measurements. Experiments have been carried out with sodium and potassium salts of polyacrylic acid and carboxymethylated hydroxyethyl cellulose of low degree of substitution. The measurements clearly indicate that for polyacrylic acid a difference exists in the ion binding of Na+ and K+ ions and that the polyion equivalent conductivity is dependent on the counterion species.

A Selective Parameter for lonic Membrane Transport. Determination of Transport Numbers from Passive Membrane Potentials

Considerations du cas ou une membrane passive homogene separe 2 solutions aqueuses isothermes d'un electrolyte binaire de concentrations differentes c 2 >c 1 , sans gradients de tension electrique appliquee et de pression. Considerations, dans ces conditions de la relation entre les nombres de transport apparent dans la membrane, t + et t − , en fonction de c 2 /c 1 et d'un parametre experimental K. Cas des membranes Nuclepore et des solutions de NaCl

Permselectivity of ion exchange membranes from sorption data and its relation to nonuniformity of membranes

AbstractTransport numbers of the hydrogen ion within the cation permselective membranes equilibrated with sulfuric acid solutions have been calculated employing sorption data. Calculations were performed according to the equation of Arnold and Swift. The validity of this equation and resulting t+(app) has been verified by independent determination of transport numbers by the EMF method. The equation has been derived which relates the permselectivity of membranes to the parameters describing their nonuniformity, i. e. to the nonuniformity factor Z and volume fraction of nonselective domains (Δϕ).

The Behavior of Implanted Xenon When Used as a Marker during the Anodic Oxidation of Aluminum: Evidence for an Explanation of a Dose‐Dependant Splitting Effect

Using 2 MeV lithium ions backscattering and transmission electron microscopy techniques, some of the xenon atoms introduced by implantation in aluminum metal under the initial oxide layer are shown to be transported by the moving metal‐oxide interface during anodic oxidation. For specific anodization conditions (, ) this splitting of the initial xenon distribution is interpreted in terms of bubble formation and growth above a given local concentration threshold. A schematic model for this behavior evolution is proposed. This dose dependance is of practical interest in the determination of transport numbers. Although unambiguously measured they may be subject to significant systematic uncertainties which are discussed.

A new cell design for the determination of transport numbers in molten silver nitrate-rubidium nitrate system

A new design of a concentration cell with transference for the determination of transport numbers is described. Very small asymmetry potentials and steady emf's without fluctuation could be observed using the new cell in molten silver nitrate-rubidium nitrate system. The internal transport numbers of silver and rubidium ions relative to nitrate ion were determinedat 250, 300 and 350°C. A comparison is made among the internal mobilities of the cations in several molten silver nitrate-alkali metal nitrate systems.

Charge transfer and thermal decomposition of NH 4ClO 4 crystals

On the basis of previous work on the determination of transport numbers the following mechanism has been proposed for the formation and migration of the conduction proton in the NH 4ClO 4 (AP) lattice. 1. Transfer of the proton from cation to anion NH 4 + +ClO 4 − →NH 3 +HClO 4. 2. Reorientation of the protonated anion HClO 4 →ClO 4H. 3. Proton jump to a neighboring anion ClO 4H+ClO 4 − →ClO 4 − +HClO 4 The conductivity of AP crystals is increased proportionally to the concentration of added proton donor impurity HSO 4 − ion. analysis of the impurity conductivity allows one to write for the mobility of protons in the AP lattice the expression μ = 20exp (−0.81 eV/ kT) cm 2/V sec. The dielectric relaxation of AP crystals has been investigated. Agreement has been shown of the time of dielectric relaxation with the correlation time of the diffusion process as determined by the Nernst-Einstein relation from the magnitude of the mobility. Values of the activation energy for the mobility and for the time of dielectric relaxation are also close to each other. These data are considered in the nature of experimental evidence for use of the proposed mechanism of conductivity in AP. The influence of the indicated impurity on formation rate V n and growth rate V g of nuclei on thermal decomposition of AP has been investigated and corresponding activation energies E n and E g calculated. For pure AP, E n = 70 ± 4kcal/mole; whereas for doped AP, 50 ± 4 kcal/mole. Significant differences between pure and doped AP with respect to corresponding values of V g and E g were not detected. Attention is directed to the closeness of the values of the activation energy for the overall rate of low temperature decomposition E 1 t = 33.9 ± 1.6kcal/mole and E g = 35 ± 5kcal/mole. Consequently, just the processes of nuclear growth determine the total rate of thermal decomposition of AP. Arguments are presented in favor of a proton-donating character for the effect of adding HSO 4 − on the thermal decomposition of AP. It is predicted that addition of proton acceptors, among them (NH 4) 2HPO 4, will significantly decrease the value of V n in AP.