Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.     

Internal mobilities and diffusion in an ionic liquid mixture

The internal mobility gives the rate at which one ionic species moves relative to the other species present in an ionic mixture, it mirrors the differential strength of the interactions between different ionic species. In this work we examine the dependence of the internal mobilities of the Li(+) and K(+) ions on the composition in molten mixtures of LiF and KF. We compare them to the behaviour of the individual diffusion coefficients and the self-exchange velocities, which measure the rate at which an ion separates from its nearest-neighbour coordination shell. The examination is made using molecular dynamics simulations with polarizable, first-principles parameterised interaction potentials which are shown to reproduce the limited available experimental data on the transport properties of these mixtures extremely well. The results confirm that the composition-dependence of the internal mobilities in LiF/KF follows the unusual type-II behaviour, which is not reflected in that of the diffusion coefficients or the self-exchange velocities.     

NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.     

Ion mobilities and microscopic dynamics in liquid (Li,K)Cl

The dynamical properties of ionic melts formed from mixtures of LiCl and KCl have been studied across the full composition range in computer simulations of sufficient length to enable reliable values for such collective transport coefficients as the viscosity, conductivity, and internal mobilities to be determined reliably. Interest centers on the nontrivial concentration dependence exhibited by these transport coefficients, which agrees well with that observed experimentally, and in relating this to the strength of the association between an ion and its first coordination shell. The relationships between the various transport coefficients, such as those between the diffusion coefficient and the viscosity (Stokes-Einstein) and the conductivity (Nernst-Einstein) also exhibit composition dependences that reflect this association. The connection between the internal mobility and two measures of the coordination shell dynamics (the cage relaxation time and the self-exchange velocity) is explored; it is shown that the self-exchange velocity follows the composition and temperature dependence of the internal mobility very well. Finally, it is shown that allowing for anion polarization in the interaction model increases the mobility of all species without changing the structure of the melt discernibly, with the largest effect being found for the Li(+) ion.     

Communication: Turnover behavior of effective mobility in a tube with periodic entropy potential

Using Brownian dynamics simulations, we study the effective mobility and diffusion coefficient of a point particle in a tube formed from identical compartments of varying diameter, as functions of the driving force applied along the tube axis. Our primary focus is on how the driving force dependences of these transport coefficients are modified by the changes in the compartment shape. In addition to monotonically increasing or decreasing behavior of the effective mobility in periodic entropy potentials reported earlier, we now show that the effective mobility can even be nonmonotonic in the driving force.     

Generalized Einstein relations from a three-temperature theory of gaseous ion transport

Generalized Einstein relations between mobility and diffusion coefficients are derived within the framework of a recently developed three-temperature kinetic theory of gaseous ion transport. A previously assumed connection between diffusion and differential mobility is firmly established within low-order approximations of the kinetic theory. Equations are obtained for the approximate calculation of the unobservable parallel and perpendicular ion temperatures, and for two higher moments of the ion velocity distribution function that appear as correction terms in the generalized Einstein relations. The present theory is tested on inverse-power potentials and on several alkali ion-noble gas systems, and is compared to two previous semi-empirical generalized Einstein relations. Simple procedures are recommended for the estimation of the parameters and correction terms that occur, to permit approximate calculation of gaseous ion diffusion coefficients from mobility data without the need of a computer or specific knowledge of the ion-neutral interaction potential.     

Atomistic simulations of hydrated nafion and temperature effects on hydronium ion mobility

The effects of hydration level and temperature on the nanostructure of an atomistic model of a Nafion (DuPont) membrane and the vehicular transport of hydronium ions and water molecules were examined using classical molecular dynamics simulations. Through the determination and analysis of structural and dynamical parameters such as density, radial distribution functions, coordination numbers, mean square deviations, and diffusion coefficients, we identify that hydronium ions play an important role in modifying the hydration structure near the sulfonate groups. In the regime of low level of hydration, short hydrogen bonded linkages made of water molecules and sometimes hydronium ions alone give a more constrained structure among the sulfonate side chains. The diffusion coefficient for water was found to be in good accord with experimental data. The diffusion coefficient for the hydronium ions was determined to be much smaller (6-10 times) than that for water. Temperature was found to have a significant effect on the absolute value of the diffusion coefficients for both water and hydronium ions.     

The effect of obstacle conductivity and electric field on effective mobility and dispersion in electrophoretic transport: a volume averaging approach

The method of volume averaging has been used to determine the effective electrophoretic mobility and dispersion coefficients for molecular transport of point-like solutes in a two-phase porous medium where the electrical conductivity and the diffusion and mobility coefficients may vary in both phases. The formal theory, derived in previous work, is numerically evaluated for cases where the obstacle phase has a large or small conductivity relative to the fluid phase and where the diffusion coefficient of the solute in the obstacle phase can be large or small relative to that in the fluid phase. In agreement with previous Monte Carlo methods, the effective electrophoretic mobility is not a function of media conductivity or electric field when the obstacles are impermeable to solute transport or have small diffusion solute diffusion coefficients. However, the dispersion coefficient is a strong function of electric field and varies with obstacle conductivity when diffusive transport is small in the obstacles relative to the fluid. In contrast, the effective electrophoretic mobility is a function of electric field when conductivity of the obstacles is much larger than the fluid and when the obstacles are very permeable to solute but have low electrical conductivity.     

Relating chromatographic retention and electrophoretic mobility to the ion distribution within electrosprayed droplets

Ions that are observed in a mass spectrum obtained with electrospray mass spectrometry can be assumed to originate preferentially from ions that have a high distribution to the surface of the charged droplets. In this study, a relation between chromatographic retention and electrophoretic mobility to the ion distribution (derived from measured signal intensities in mass spectra and electrospray current) within electrosprayed droplets for a series of tetraalkylammonium ions, ranging from tetramethyl to tetrapentyl, is presented. Chromatographic retention in a reversed-phase system was taken as a measure of the analyte’s surface activity, which was found to have a large influence on the ion distribution within electrosprayed droplets. In addition, different transport mechanisms such as electrophoretic migration and diffusion can influence the surface partitioning coefficient. The viscosity of the solvent system is affected by the methanol content and will influence both diffusion and ion mobility. However, as diffusion and ion mobility are proportional to each other, we have, in this study, chosen to focus on the ion mobility parameter. It was found that the influence of ion mobility relative to surface activity on the droplet surface partitioning of analyte ions decreases with increasing methanol content. This effect is most probably coupled to the decrease in droplet size caused by the decreased surface tension at increasing methanol content. The same observation was made upon increasing the ionic strength of the solvent system, which is also known to give rise to a decreased initial droplet size. The observed effect of ionic strength on the droplet surface partitioning of analyte ions could also be explained by the fact that at higher ionic strength, a larger number of ions are initially closer to the droplet surface and, thus, the contribution of ionic transport from the bulk liquid to the liquid/air surface interface (jet and droplet surface), attributable to migration or diffusion will decrease.     

The effect of salt stoichiometry on protein-salt interactions determined by ternary diffusion in aqueous solutions

We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 degrees C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross-diffusion coefficients are very sensitive to salt stoichiometry. One of the cross-diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical-potential cross-derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.     

Interaction potentials and transport properties of coinage metal cations in rare gases

High-level ab initio calculations are performed on the coinage metal cations (Cu+, Ag+, and Au+) interacting with each of the rare gases [Rg (Rg=He to Rn)]. The RCCSD(T) procedure is employed, with basis sets being of approximately quintuple-zeta quality, but with the heavier species using relativistic effective core potentials. The interaction potentials are compared to experimental and theoretical data where they exist. In addition, transport coefficients for the mobility and diffusion of the cations in the rare gases are calculated. The latter have involved a rewriting of some of the programs used, and the required modifications are discussed. The mobility results indicate that, rather than being a rare occurrence, mobility minima may be common phenomena. Finally, a new estimate is put forward for the validity of zero-field mobilities in ion mobility spectrometry.     

Monte Carlo simulation of ion transport in non-linear ion mobility spectrometry

A program for Monte Carlo simulation of ion transport in non-linear ion mobility spectrometry, also known as field asymmetric ion mobility spectrometry (FAIMS) or differential mobility spectrometry (DMS), has been developed. Simulations are based on elastic collisions between the ions and the gas particles, and take into account the effects of flow dynamics and asymmetric electric fields. Using this program, the separation and diffusion of the ions moving in a planar DMS filtration gap are demonstrated. Ion focusing in a cylindrical filtration gap is also confirmed. A characteristic compensation voltage is found to provide insight for understanding separation in non-linear ion mobility spectrometry. The simulation program is used to study the characteristics of non-linear ion mobility spectrometry, the effect of the carrier gas flow, and the dependence of the compensation voltage and nonlinear mobility coefficient (α) on the applied asymmetric electric field.     

Potentiometric selectivity coefficients of liquid ion-exchange membranes for univalent and divalent ions

Digital simulation has been used to calculate potential—activity responses and concentration-dependent selectivity coefficients for membranes bathed in mixtures of univalent and divalent ions. For an ideal, dissociated, univalent-site liquid ion-exchange membrane, more accurate computations, based on Nernst—Planck equations, were possible than have been reported previously. Simulation results were used with four suggested equations for the membrane potential (including the IUPAC recommendation) to determine which equation gives best fit and most nearly constant selectivity coefficients. When concentration profiles found by digital simulation are employed, improved response equations are given which closely describe the dependence of surface concentrations on the mobility ratio for the bi-ionic case. From these equations a closed form solution to the diffusion equation yields an explicit expression relating the bi-ionic selectivity coefficient to membrane loading, single ion partition coefficients, and ion mobilities.     

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

The carrier transport properties in nanocrystalline semiconductors and organic materials play a key role for modern organic/inorganic devices such as dye-sensitized (DSC) and organic solar cells, organic and hybrid light-emitting diodes (OLEDs), organic field-effect transistors, and electrochemical sensors and displays. Carrier transport in these materials usually occurs by transitions in a broad distribution of localized states. As a result the transport is dominated by thermal activation to a band of extended states (multiple trapping), or if these do not exist, by hopping via localized states. We provide a general view of the physical interpretation of the variations of carrier transport coefficients (diffusion coefficient and mobility) with respect to the carrier concentration, or Fermi level, examining in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states. We treat both the multiple trapping models and the hopping model in the transport energy approximation. The analysis is simplified by thermodynamic properties: the chemical capacitance, C(mu), and the thermodynamic factor, chi(n), that allow us to derive many properties of the chemical diffusion coefficient, D(n), used in Fick's law. The formulation of the generalized Einstein relation for the mobility to diffusion ratio shows that the carrier mobility is proportional to the jump diffusion coefficient, D(J), that is derived from single particle random walk. Characteristic experimental data for nanocrystalline TiO(2) in DSC and electrochemically doped conducting polymers are discussed in the light of these models.     

Kinetic Monte Carlo model of charge transport in hematite (alpha-Fe(2)O(3))

The mobility of electrons injected into iron oxide minerals via abiotic and biotic electron transfer processes is one of the key factors that control the reductive dissolution of such minerals. Building upon our previous work on the computational modeling of elementary electron transfer reactions in iron oxide minerals using ab initio electronic structure calculations and parametrized molecular dynamics simulations, we have developed and implemented a kinetic Monte Carlo model of charge transport in hematite that integrates previous findings. The model aims to simulate the interplay between electron transfer processes for extended periods of time in lattices of increasing complexity. The electron transfer reactions considered here involve the IIIII valence interchange between nearest-neighbor iron atoms via a small polaron hopping mechanism. The temperature dependence and anisotropic behavior of the electrical conductivity as predicted by our model are in good agreement with experimental data on hematite single crystals. In addition, we characterize the effect of electron polaron concentration and that of a range of defects on the electron mobility. Interaction potentials between electron polarons and fixed defects (iron substitution by divalent, tetravalent, and isovalent ions and iron and oxygen vacancies) are determined from atomistic simulations, based on the same model used to derive the electron transfer parameters, and show little deviation from the Coulombic interaction energy. Integration of the interaction potentials in the kinetic Monte Carlo simulations allows the electron polaron diffusion coefficient and density and residence time around defect sites to be determined as a function of polaron concentration in the presence of repulsive and attractive defects. The decrease in diffusion coefficient with polaron concentration follows a logarithmic function up to the highest concentration considered, i.e., approximately 2% of iron(III) sites, whereas the presence of repulsive defects has a linear effect on the electron polaron diffusion. Attractive defects are found to significantly affect electron polaron diffusion at low polaron to defect ratios due to trapping on nanosecond to microsecond time scales. This work indicates that electrons can diffuse away from the initial site of interfacial electron transfer at a rate that is consistent with measured electrical conductivities, but that the presence of certain kinds of defects will severely limit the mobility of donated electrons.     

Facilitated transport mechanism in fixed site carrier membranes

Facilitated transport of gases, such as O₂, has been observed for fixed site carrier membranes. Carrier-impregnated ion-exchange membranes have also been used to produce facilitated transport of CO₂, H₂S and olefins when the carriers are not completely mobile. The actual mechanism for this facilitated transport has not been determined previously. The facilitated transport is provided by the exchange of solute between the free solute region and the bound complexing agent combined with gradients in the free solute and complexed carrier. The ratio of mobility for exchange between the regions is the dimensionless equilibrium constant of the reversible reaction. An expression is also derived for the relationship between the effective diffusion coefficient of the complex in facilitated transport, D_AB, and the diffusion coefficients for exchange between free and complexed solute, D_DH and D_HD. Since D_AB can be determined from experimental results, D_DH and D_HD can be calculated. The results also show the morphology dependence of D_AB. The diffusion coefficient of the free solute D_A also changes with the loading of the complexing agent in the film. This morphology dependence can explain why the gas permeability can decrease when the concentration of the complexing agent increases in the membrane.     

Kinetic studies for sorption of some metal ions from aqueous acid solutions onto TDA impregnated resin

Summary Kinetic studies for sorption of uranium, thorium and cobalt ions from hydrochloric acid solutions using tri-dodecyl amine (TDA) loaded on Amberlite XAD4 (polystyrene resin supplied by Rohm and Haas) using the batch technique, have been evaluated and assessed. Analysis of the respective data in accordance with three kinetic models revealed that the particle diffusion mechanism is the rate determining step, and the sorption for each metal ion on the impregnated sorbent follows the first order reversible kinetics. Values of the first order rate constants, rate constants of intraparticle transport, and the particle diffusion coefficients for the studied ions were determined. Sorption isotherms, which have been evaluated from the distribution coefficients for these ions, were found in good fit with the Langmuir and Freundlich isotherms.     

铁离子(II/III)/Nafion膜体系的阻抗分析

对Fe(Ⅱ/Ⅲ)离子在Nafion膜中的电荷传输以及在溶液扩散层中的传质过程进行了理论上的分析, 利用小幅度阶跃电位作为激励信号的阻抗测量法测定了该体系的阻抗并求出了Fe(Ⅱ/Ⅲ)离子在膜中的扩散系数和标准速度常数。同时讨论了电极电位和支持电解质浓度对体系阻抗的影响。实验的结果与理论推导的结果相一致。     

Interaction between anionic polyelectrolytes and anion exchange membranes and change in membrane properties

Electrodialytic transport properties of anion exchange membranes were measured after formation of anionic polyelectrolyte layers on the membrane surfaces: relative transport number of various anions to chloride ions, current efficiency and apparent diffusion coefficients of neutral molecules. The anionic polyelectrolyte layers were formed by immersing the membrane into an aqueous solution of polycondensation product of sodium naphthalene sulfonate and formaldehyde or polystyrene sulfonic acid.

The change in the relative transport number between anions was remarkable in the anion exchange membrane with high ion exchange capacity by forming the layer. Results were: the relative transport number of sulfate ions to chloride ions decreased and those of nitrate ions to chloride ions, fluoride ions to chloride ions and bromide ions to chloride ions increased compared with the corresponding membrane. Although the apparent diffusion coefficient of neutral molecules suggested clogging of the membrane pores by the polyelectrolyte, anions with higher hydrated ionic diameter were able to permeate through the membrane easily. This means that difference of electrostatic repulsion force against two anions is effective on the change in the relative transport number of anions.