Diffusion and electrical conduction in molten salts of the type AZ + BZ. The phenomenological coefficients in the system LiNO3 + AgNO3 at 533 K

By superposing diffusion and electrical conduction the ionic phenomenological coefficients (l_ij) have been solved as functions of the measureable transport coefficients in the molten salt systems of the type AZ + BZ. A clear difference has been made between the entropy producing processes, diffusion and electrical conduction, and the reversible transport of matter with electric current. In the treatment the Onsager reciprocal relations of the ionic form appear as a result of the superposition and the ionic forces become functions of the gradient of the component chemical potential, the transport number, the electric current density, and the conductivity. The quantitative concentration dependences of the ionic l_{i + j +} s have been calculated for the system LiNO₃+ AgNO₃ at 533 K for the entire range of the composition. The relations between the l_{i + j +} s and the interfriction coefficients have also been given. Differing from aqueous electrolyte solutions the cross coefficient (l_{i + j +}/x_ix_j) (i ≠ j) does not vanish in approaching a pure molten salt component. Therefore the Nernst—Planck equations cannot be applied to these molten salts.     

Einführung in die Transportvorgänge in konzentrierten wäßrigen Elektrolytlösungen und Salzschmelzen

Introduction to transport phenomena in concentrated aqueous electrolyte solutions and molten salt mixtures . Up to this day there is no general theory of liquids. Since water-free molten salt mixtures are simpler in their structure than concentrated aqueous electrolyte solutions, it would be reasonable first to develop a theory for molten salts and then to apply this to aqueous electrolyte solutions by approximation. Such a theory does not yet exist. In this paper the system water + salt is therefore considered in the concentration range between pure water and pure salt in the liquid state. The phenomenological coefficients and friction coefficients of the different species of the system calculated from transport data are characteristic parameters for the entire concentration range which will probably offer possibilities for the analysis of transport phenomena, in close relation with the structure of the water + salt mixture. Common and essentially different properties, such as reference system and condition of electric neutrality, are discussed for concentrated aqueous electrolyte solutions and molten salt mixtures. The investigation of transport numbers from concentration cells with transference and the determination of the interdiffusion coefficients are illustrated for the system H₂O + CaCl₂ (highly concentrated electrolyte solution) and LiNO₃ + AgNO₃ (molten salt mixture). The phenomenological coefficients and the friction coefficients are calculated from the measured transport data.     

Moving ion fronts in mixed ionic‐electronic conducting polymer films

The aim of this paper is to analyze moving front dynamics of ions and holes in a planar, mixed ionic‐electronic conducting polymer film. As cations invade the film, holes evacuate; thus, an ionic current is converted to an electronic signal. Recent experiments show that the location of the advancing ion front increases as the square‐root of time, a scaling typically associated with diffusive transport, which is surprising given the large driving voltages utilized. Ionic and electronic transport is modeled via the drift‐diffusion equations. A similarity transformation reduces the governing partial differential equations to ordinary differential equations that are solved numerically. The similarity transformation elucidates the origin of the square‐root‐of‐time front scaling. The similarity solution is then compared to the numerical solution of the full drift‐diffusion equations, finding excellent agreement. When compared with experimental data, our model captures the front location; however, qualitative differences between the ion profiles are observed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1447–1454, 2015     

Mathematical modelling of CO2 facilitated transport through liquid membranes containing amines as carrier

An approximate analytical solution for the facilitated transport of carbon dioxide across a liquid membrane containing aqueous primary and secondary amine solutions has been developed in which the reversible reaction A(CO₂) + 2B(amine) AB(carbamate) + BH(protonated amine) occurs inside the liquid membranes. The current approximate analytical solution predicts the facilitated factor of CO₂ through the membrane and is based on the dimensionless, nonlinear diffusion‐reaction transport problem. The approximate analytical solution predicts the facilitation factors for the range from the moderate reaction rate to the equilibrium chemical reaction regime, allowing unequal diffusivities of complexes and carrier and cases of zero and nonzero permeate side solute concentrations. In the present mathematical model, a constant free carrier concentration is assumed throughout the membrane phase. In comparison with the numerically calculated results, the results obtained were found to be in well agreement.     

Nomenclature for transport phenomena in electrolytic systems

The document deals with the transport phenomena of importance to electrochemists and electrochemical engineers. In the absence of a report on mass transport at large, the first section presents general definitions of mass flux, of flux density and of phenomonological coefficients, as appearing in the relationships of irreversible thermodynamics, which express the proportionality between the driving forces and the fluxes. the main part is concerned with electrolytic systems, in particular with ideal dilute solutions. Mass transport by diffusion, by convection and by migration of ions under the influence of an electric field is considered. The diffusion coefficient of a species is distinguished from that of an electrolyte. A section is devoted to the transport of charges, including transport numbers, the flow of current through the solution and through the electrode, current efficiency, and current distribution. The report also discusses the precise meaning of concepts related to mass transport, such as the Nernst diffusion layer, mass transport control, interfacial concentrations, concentration overpotential, mass transport coefficients and diffusion potentials. However, the diffusion in solid electrolytes and surface diffusion are not treated.Recommendations for symbols and definitions are given. In many cases, it is endeavoured to clarify by a brief discussion the concept itself.     

Influence of dc electric current on the electrochemical impedance of ion-exchange membrane systems

The influence of dc electric current on the electrochemical impedance and the linearity of the current–voltage relationship in ion-exchange membrane systems, has been investigated. The system under study is constituted by a membrane with negative fixed-charge and two diffusion boundary layers on both sides of the membrane, ionic transport being described by the Nernst–Planck and Poisson equations. The electrochemical impedance and a decomposition into Fourier components of the potential–time response of the system to a sine electric current superimposed on a dc electric current, have been obtained by using the network simulation method. Some of the results obtained for the electrochemical impedance are compared with the corresponding analytical expressions for ideal membranes. The great influence that the dc component of the electric current exerts on the linearity of the current–voltage relationship of an ion-exchange membrane system, is also shown.     

Numerical simulation of salt water electrolysis in parallel-plate electrode channel under forced convection

A steady-state numerical model for multi-ion parallel-plate electrode (PPE) system is developed to investigate the concentration and electric distribution in the process of salt water electrolysis under forced convection. The finite-element method is used to solve this multi-ion transport model coupled with ionic diffusion, convection and ionic migration. The flow field and the electrode current's effect on the concentration distribution are investigated. The comparison between the diffusion-transported current and the migration-transported current demonstrates that the current is almost fully transported by the ionic migration, with the result that the diffusion-transported current can be neglected and the control equation of potential is simplified. For comparison, a hypothetical model with uncoupled situation of concentration and electric field is taken into consideration. The variation of electric field strength near the cathode can reach 25% of the value of the uncoupled model in the condition of u₀ = 0.01 m/s. Compared with this, the variation of ionic electro-conductivity shows a reverse tendency.     

Solution of the Diffusion Equations in a Gas Centrifuge for Separation of Multi component Mixtures

Abstract

The demand for stable isotopes in physical and chemical research and in medical diagnostics is growing, and the gas centrifuge process is able to provide large quantities of stable isotopes. A set of diffusion equations describing separation in a gas centrifuge for a multi component mixture is established. These equations involve general diffusion coefficients. Using the radial averaging method and the simplified diffusion transport vector for a multi component isotopic mixture, nonlinear partial differential equations are transformed to a set of nonlinear ordinary differential equations. An iteration method for the solution is presented. The relationship between the separation factor and the mass difference, γ _ij = γ ^Mj _o ^?Mi , is shown to be in agreement with both the computational and the experimental results with very high precision.     

Transport properties of proton conductive Y-doped BaHfO3 and Ca or Sr-substituted Y-doped BaZrO3

An electrolyte in fuel cells requires not only high ionic conductivity, but also high transport numbers of ionic conduction. Although Y-doped BaZrO₃ is regarded to be the most promising candidate as the electrolyte in protonic ceramic fuel cells (PCFCs), significant hole conduction generates in wet oxygen at high temperatures. With the aim to increase the transport number of ionic conduction, in this work, Sr and Ca were introduced to partially substitute Ba in BaZr_0.8Y_0.2O_3-δ. The results revealed that a single cubic perovskite phase was obtained for Ba_0.95Ca_0.05Zr_0.8Y_0.2O_3-δ and Ba_1-xSr_xZr_0.8Y_0.2O_3-δ (x = 0.05, 0.10, 0.15, 0.20 or 0.40). However, replacing Ba with Sr resulted in almost no increase in the transport number of ionic conduction in wet oxygen atmosphere, but drastic decrease in proton conductivity at all replacement levels. In addition, Ba_0.95Ca_0.05Zr_0.8Y_0.2O_3-δ shows no meaningful change in the transport number of ionic conduction, compared with BaZr_0.8Y_0.2O_3-δ. Incorporating Ca or Sr into the Ba-site of BaZr_0.8Y_0.2O_3-δ appears to impart no positive influence on electrochemical properties. These interesting results also indicate that the hole conductivity decreases with the decrease in proton conductivity, and will aid to consider the hole conduction mechanism. BaHfO₃ doped with 10 and 20 mol% Y was also prepared. A bimodal microstructure was observed for BaHf_0.9Y_0.1O_3-δ, whereas BaHf_0.8Y_0.2O_3-δ shows uniform grain size after sintering at 1600°C for 24 hours. The transport numbers of ionic conduction and bulk conductivity in such Y-doped BaHfO₃ samples are close to those of BaZrO₃ doped with the same amount of Y.     

Crystallinity,thermal properties,morphology and conductivity of quaternary plasticized PEO‐based polymer electrolytes

Quaternary plasticized solid polymer electrolyte (SPE) films composed of poly(ethylene oxide), LiClO₄, Li_1.3Al_0.3Ti_1.7(PO₄)₃, and either ethylene carbonate or propylene carbonate as plasticizer (over a range of 10–40 wt%) were prepared by a solution‐cast technique. X‐ray diffraction (XRD), differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and electrochemical impedance spectroscopy (EIS) indicated that components such as LiClO₄ and Li_1.3Al_0.3Ti_1.7(PO₄)₃ and the plasticizers exerted important effects on the plasticized quaternary SPE systems. XRD analysis revealed the influence from each component on the crystalline phase. DSC results demonstrated the greater flexibility of the polymer chains, which favored ionic conduction. SEM examination revealed the smooth and homogeneous surface morphology of the plasticized polymer electrolyte films. EIS suggested that the temperature dependence of the films' ionic conductivity obeyed the Vogel–Tamman–Fulcher (VTF) relation, and that the segmental movement of the polymer chains was closely related to ionic conduction with increasing temperature. The pre‐exponential factor and pseudo activation energy both increased with increasing plasticizer content and were maximized at 40 wt% plasticizer content. The charge transport in all polymer electrolyte films was predominantly reliant on lithium ions. All transference numbers were less than 0.5. Copyright © 2006 Society of Chemical Industry     

Transport numbers and ionic mobilities in nitrate melts by EMF-measurements on concentration cells with transference

The transport numbers of the cation constituents, referred to the common anion constituent, have been measured for the molten systems KNO₃ + AgNO₃, RbNO₃ + AgNO₃, and CsNO₃ + AgNO₃ over the entire range of compositions at temperatures varying from 230° to 350°C by the use of concentration cells with transference. The ionic mobilities have been calculated from the existing data of the densities and electric conductivities for these systems. For all three systems, the mobility of Ag⁺ is higher than that of the other cation in the region rich in silver nitrate while the opposite is true for the region rich in alkali nitrate. This is equivalent to the statement that the curve representing the transport numbers as a function of composition crosses the diagonal (“inversion point”). This inversion varies systematically with the temperature and the ion diameter of the alkali ion.     

Multicomponent diffusion and chemical reaction of gases in porous catalysts—I: Ternary gasdiffusion and chemical reaction without volume change (ν = 0)

The overall conversion rate for catalytic reactions of gases in porous catalysts is often controlled by transport processes in the porous pellet. Since in general more than two gases take part in the reaction, one has to calculate the conversion rate by using the transport equations for multicomponent mixtures. These equations, however, are rather complicated; thus calculations of conversion rates are commonly done by using Fick's transport law.First of all it is shown that the equations for multicomponent diffusion can be reduced to simple linear laws by using the stoichiometric coupling of the fluxes. With these equations, the calculation of the conversion rate for a reaction of the general type: ν₁R₁ + ν₂R₂ ? ν₃R₃ is as simple as for the case of binary diffusion. Using the example of hydrogenolysis of ethane it is then demonstrated that in general Fick's law leads to higher conversion rates than the Maxwell-Stefan, diffusion equations. With this example some basic questions arising in the discussion of heterogeneous catalytic reactions in porous systems (e.g. the choice of the “key component”) are discussed in detail.     

Effect of Ferroelectric Polarization on Ionic Transport and Resistance Degradation in BaTiO3 by Phase‐Field Approach

We proposed a model to study the resistance degradation behavior of ferroelectric oxides in the presence of ferroelectric spontaneous polarization by combining the phase‐field model of ferroelectric domains and nonlinear diffusion equations for ionic/electronic transport. We took into account the nonperiodic boundary conditions for solving the electrochemical transport equations and Ginzburg–Landau equations using the Chebyshev collocation algorithm. We considered a single domain structure relative to a thin film BaTiO₃ single crystal orientated to the normal of the electrode plates (Ni) in a single parallel plate capacitor configuration. The capacitor was subjected to a dc bias of 0.5 V either along the polarization direction or opposite to the polarization direction at 25°C. It is shown that the polarization bound charges at the metal/ferroelectric interface play an important role in charge carrier transport and leakage current evolution in BaTiO₃ capacitor.     

Calculation of limiting current density of metal electrodeposition on vertical plane electrode under conditions of natural convection

An approximate analytical solution of problem of ion transfer near a vertical plane electrode surface is obtained for the metal electrodeposition proceeding at the limiting current from electrolyte containing ions of three types under the conditions of natural convection. In contrast to previous studies, no transport numbers are used here, and the migration transfer of electroactive electrolyte component is taken into account. The equations obtained take into consideration the effect of supporting electrolyte concentration and its migration on the limiting current. The limiting current densities (mass-transfer coefficients), which are calculated by equations proposed here and by the finite-difference method, are compared.     

Effect of nanofiller concentration on conductivity and dielectric properties of poly(ethylene oxide)–poly(methyl methacrylate) polymer electrolytes

This paper reports the effect of nanofiller concentration on the conductivity and dielectric properties of the poly(ethylene oxide)–poly(methyl methacrylate)–poly(ethylene glycol)–AgNO₃–Al₂O₃ polymer electrolyte system. The preparation of polymer films was done using the solution‐casting technique and characterization of the films was carried out using scanning electron microscopy, differential scanning calorimetry and ionic transport techniques. The ionic conductivity, investigated using impedance spectroscopy, was expected to show interesting behaviour at below and above the melting temperature of poly(ethylene oxide) in the polymer blend films. Complex impedance data were analysed in an alternating current conductivity and dielectric permittivity formalism in order to throw light on the transport mechanism. The effect of nanofiller concentration on conduction and relaxation processes at various temperatures was studied. © 2013 Society of Chemical Industry     

Oxygen Ion Conduction in Bulk and Grain Boundaries of Nominally Donor‐Doped Lead Zirconate Titanate (PZT): A Combined Impedance and Tracer Diffusion Study

Oxygen ion conduction in Nd³⁺‐doped Pb(Zr_xTi_1?x)O₃ (PZT) was investigated by impedance spectroscopy and ¹⁸O‐tracer diffusion with subsequent secondary ion mass spectrometry (SIMS) analysis. Ion blocking electrodes lead to a second relaxation feature in impedance spectra at temperatures above 600°C. This allowed analysis of ionic and electronic partial conductivities. Between 600°C and 700°C those are in the same order of magnitude (10^?5–10^?4 S/cm) though very differently activated (2.4 eV vs. 1.2 eV for ions and electron holes, respectively). Oxygen tracer experiments showed that ion transport mainly takes place along grain boundaries with partly very high local ionic conductivities. Numerical analysis of the tracer profiles, including a near‐surface space charge zone, revealed bulk and grain‐boundary diffusion coefficients. Calculation of an effective ionic conductivity from these diffusion coefficients showed good agreement with conductivity values determined from impedance measurements. Based on these data oxygen vacancy concentrations in grain boundary and bulk could be estimated. Annealing at high temperatures caused a decrease in the grain‐boundary ionic conductivity and onset of additional defect chemical processes near the surface, most probably due to cation diffusion.     

Membrane potential measurements on cellulose acetate membranes

Membrane potentials and apparent transport numbers of the cation are reported for cured cellulose acetate membranes bounded by HCl, NaCl, KCl and MgCl₂ solutions, using Ag/AgCl electrodes and a flow-cell method. Membranes cured at 70°, 80° and 90° are used. Bounding solution concentrations vary from 0.005 to 0.05 M at the high concentration side (bounding the dense side of the membrane), and are kept constant at 0.002 M for the low concentration solution. In the KCl 90° membrane case the low concentration solution is varied as well, from 0.0001 to 0.002 M. Results show that cured cellulose acetate membranes are permselective towards univalent cations. This is interpreted as resulting from a low cation-exchange capacity of the dense layer of the cured membrane. The permselectivity increases with increased curing temperature. Addition of a non-electrolyte to the low concentration side reverses the osmotic flow and leads to higher apparent transport numbers of the cation. It is concluded that diffusion in small pores contributes significantly to the transport of ionic solutes through uncompacted membranes.     

Cyclic wet drying of an epoxy coating using an ionic liquid

The barrier protection of an organic coating for a metallic substrate is compromised by the transport of water, oxygen and ions from the environment to the metal/coating interface. Metallic outdoor structures are exposed to the weather and undergo cyclic wetting and drying conditions. In the absence of holidays, the transport of water is diffusion limited. The diffusion coefficients associated with water ingress D_in and egress D_out are indicators of the wetting and drying rates, respectively, of the coating. Gravimetric and capacitance methods are used for the measurement of D_in whereas D_out measurement has been limited to the gravimetric method. The objective of this paper is to demonstrate the application of a recently reported method that employed a hydrophilic room temperature ionic liquid to monitor the capacitance changes associated with the egress of water from which D_out was calculated. Experimental results associated with cyclic dilute NaCl wetting and ionic liquid drying are presented for an epoxy coating on an AA 2024-T3 substrate that was subjected to 50 cycles. The D_in and D_out values were calculated using a short-time approximate solution and a series solution to Fick's second law. Presented electrochemical impedance spectra associated with the ends of wet and dry stages of the cycles were analyzed using an equivalent circuit model that separated the bulk coating and metal/coating characteristics.     

Simulation studies on a rotating ring disk electrode: Effects of ionic migration with kinetic complication-disk results

In continuation to my previous work (Guha S. AIChE J. 2013;59(4):1390-1399), in this work, effects of ionic migration are evaluated for disk region of a rotating ring disk electrode system by numerically solving complex differential equations, developed for mass transfer along with kinetic complication in presence of ionic migration under limiting current condition. The system for simulation is 0.01 M Fe₂(SO₄)₃ solution with H₂SO₄ as supporting electrolyte. Simulation cases are presence and absence of ionic migration with kinetic complication (oxidation of Fe²⁺ to Fe³⁺ under O₂ pressure). Results show that concentration boundary layer thickness of reactant Fe³⁺ reduces appreciably and steady-state disk current reduces substantially in presence of migration. Simulated steady-state disk current in absence of migration case agrees well with published data. Results indicate higher Fe²⁺ concentration in presence of migration and thereby higher rate of oxidation of Fe²⁺ to Fe³⁺ at all rate constant values.     

THE TRANSPORT OF CARBON DIOXIDE IN HIGH MOLECULAR WEIGHT BUFFER SOLUTIONS

The diffusion of carbon dioxide in biological media such as tissues and blood is an important physiological phenomenum. Transport of carbon dioxide in aqueous biological media causes, through chemical reactions, the simultaneous flux of several ionic species. The reversible reactions of CO₂ are coupled to amino acid dissociations of the protein species which have a large buffer capability. Due to the great difference in mobility of bicarbonate and protein, a diffusion potential evolves, which has a considerable influence upon the total CO₂ transport in the medium. The electrical potentials impede the carrier-facilitated CO₂transfer associated with the bicarbonate flux. New data on carbon dioxide transport in hemoglobin solutions are presented which clearly show the large reduction of CO₂ transport due to the electrical potentials. The experimental results correlate with diffusion potential data obtained previously. A theoretical model correctly predicts both the CO₂ transport and diffusion potential data as a function of The ionic composition of the solution. It is concluded that applied or electrical fields can have a significant effect on CO₂ transport in reactive biological media.