Relaxation times of an electrolytic cell subject to an external electric field: role of ambipolar and free diffusion phenomena

We evaluate the relaxation times for an electrolytic cell subject to a step-like external voltage, in the case in which the mobility of negative ions is different from that of positive ions. The electrodes of the cell, in the shape of a slab, are supposed to be perfectly blocking. The theoretical analysis is performed by assuming that the applied voltage is so small that the fundamental equations of the problem can be linearized. In this framework, the eigenvalues equations defining all relaxation times of the problem are deduced. In the numerical analysis, we solve the complete set of equations describing the time evolution of the system under the action of the external voltage. Two relaxation processes, connected with the ambipolar and free diffusion phenomena, are sufficient to describe the dynamics of the system, when the diffusion coefficients are of the same order of magnitude.     

Molecular dynamics simulation of the ionic liquid N-ethyl-N,N-dimethyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide

Thermodynamics, structure, and dynamics of an ionic liquid based on a quaternary ammonium salt with ether side chain, namely, N-ethyl-N,N-dimethyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide, MOENM2E TFSI, are investigated by molecular dynamics (MD) simulations. Average density and configurational energy of simulated MOENM2E TFSI are interpreted with models that take into account empirical ionic volumes. A throughout comparison of the equilibrium structure of MOENM2E TFSI with previous results for the more common ionic liquids based on imidazolium cations is provided. Several time correlation functions are used to reveal the microscopic dynamics of MOENM2E TFSI. Structural relaxation is discussed by the calculation of simultaneous space-time correlation functions. Temperature effects on transport coefficients (diffusion, conductivity, and viscosity) are investigated. The ratio between the actual conductivity and the estimate from ionic diffusion by the Nernst-Einstein equation indicates that correlated motion of neighboring ions in MOENM2E TFSI is similar to imidazolium ionic liquids. In line with experiment, Walden plot of conductivity and viscosity indicates that simulated MOENM2E TFSI should be classified as a poor ionic liquid.     

Testing ion-neutral interaction potentials using calculated ion transport coefficients

Several commonly measured ion transport coefficients were investigated in order to determine their sensitivity for testing and comparing proposed ion-neutral interaction potentials. A variety of positive ions, negative ions, neutrals, and temperatures were included in order to draw as general a conclusion as possible. All transport coefficients considered were found to be sufficiently sensitive to be used to clearly distinguish between less and more accurate interaction potentials. It was also found that the longitudinal diffusion coefficient is the most sensitive test, followed by both the transverse diffusion coefficient and the ratio of the longitudinal diffusion coefficient to mobility, followed by the ratio of the transverse diffusion coefficient to mobility and that the mobility is the least sensitive test. When presently achievable levels of experimental error were also taken into account, however, there was no significant difference in the sensitivities.     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.     

Dynamics in a room-temperature ionic liquid: a computer simulation study of 1,3-dimethylimidazolium chloride

The transport properties and solvation dynamics of model 1,3-dialkylimidazolium chloride melt at 425 K is studied using molecular-dynamics simulations. Long trajectories of a large system have been generated and quantities such as the self-diffusion coefficient of ions, shear viscosity, and ionic conductivity have been calculated. Interestingly, the diffusion of the heavier cation is found to be faster than the anion, in agreement with experiment. The interaction model is found to predict a higher viscosity and lower electrical conductivity compared to experimental estimates. Analysis of the latter calculations points to correlated ion motions in this melt. The solvation time correlation function for dipolar and ionic probes studied using equilibrium simulations exhibits three time components, which include an ultrafast (subpicosecond) part as well as one with a time constant of around 150 ps. The ultrafast solvent relaxation is ascribed to the rattling of anions in their cage, while the slow component could be related to the reorientation of the cations as well as to ion diffusion.     

Diffusion coefficients in ionic liquids: relationship to the viscosity

The relationship between the diffusion coefficient and the viscosity has been examined in computer simulations for a number of ions diffusing in a molten salt (alkali halide) solvent. The comparison gives a measure of a hydrodynamic radius for the diffusing ions which is then compared with the bare ionic radius and a characteristic radius of the coordination complex formed by halide ions around polyvalent cations. K(+) and Cl(-) ions appear to diffuse as isolated spherical particles, whereas the trivalent cations Sc(3+), Y(3+), and La(3+) diffuse as if with an intact coordination shell. These different behaviors can be related to the time scale for the relaxation of the coordination shell, compared to the structural relaxation time of the solvent.     

Diffusion in surfactant solutions

The diffusion coefficients in water of Triton X-100 and sodium dodecyl sulfate were measured as a function of concentration using the Taylor dispersion technique. For Triton X-100, a nonionic surfactant, the diffusion coefficient drops from 7.4 × 10^-7 cm²/sec at 0.45 g/liter to 6.45 x 10^-7 cm²/sec at 5 g/liter. The diffusion coefficient of methyl yellow solubilized in Triton X-100 is close to that of the surfactant. This behavior is quantitatively consistent with a chemical equilibrium between monomer and micelle. For sodium dodecyl sulfate, an anionic surfactant, the diffusion coefficient increases from 1.76 x 10^-6 cm²/sec at 0.01 M to 4.53 x 10^-6 cm²/sec at 0.125 M. The increase is less when 0.1 M NaCl is added. The diffusion coefficient of the methyl yellow solubilized by the SDS is significantly less than that of the surfactant, particularly at low ionic strength. This behavior can be quantitatively explained by including electrostatic coupling between monomer, micelle, and counterion.     

Solute size effects on the solvation structure and diffusion of ions in liquid methanol under normal and cold conditions

We have performed a series of molecular dynamics simulations of alkali metal (Li+, Na+, K+, Rb+, and Cs+) and halide (F-, Cl-, Br-, and I-) ions in liquid methanol at two different temperatures to investigate the effects of ion size on the hydration structure and diffusion of ions in methanol under normal and cold conditions. Simulations are also carried out for some of the larger cations such as I+, (CH3)4N+, and (C2H5)4N+ and also neutral alkali metal atoms in methanol at both temperatures. With the increase of ion size, the diffusion coefficients of both positive and negative ions are found to show anomalous behavior. For cations, it is found that the maximum of the diffusion coefficient versus ion size curve occurs at the rather large cation of (CH3)4N+ unlike in water where the maximum occurs at the relatively smaller ion of Rb+. For halide ions, the anomalous behavior, i.e., the increase of diffusion with ion size, continues up to iodide ion and no maximum is observed. These results are in good agreement with experimental observations. The diffusion coefficients of neutral atoms are found to be greater in methanol than that in water and they decrease monotonically with solute size, whereas the diffusion coefficients of the corresponding ions are found to be smaller in methanol. Accordingly, an ion experiences a smaller Stokes friction and a higher dielectric friction in methanol than in water. These contrasting effects are believed to be responsible for the shift of the maximum of ion diffusion toward a larger ion size when compared with similar anomalous size dependence in liquid water.     

A NEW MODEL FOR ESTIMATION OF DIFFUSION COEFFICIENT OF PHENOL DESORPTION WITHIN POLYMERIC RESIN UNDER ULTRASOUND

1. INTRODUCTION Ultrasound is a kind of mechanical wave whose frequency is more than 20 kilohertz. It can enhance the mass transfer, increase the rate and conversion of chemical reaction, change the reaction pathway [1,2] and accelerate the conversion of…     

Factors influencing the analytical performance of an atmospheric sampling glow discharge ionization source as revealed via ionization dynamics modeling

A kinetic model is developed for the dynamic events occurring within an atmospheric sampling glow discharge that affect its performance as an ion source for analytical mass spectrometry. The differential equations incorporate secondary electron generation and thermalization, reagent and analyte ion formation via electron capture and ion-molecule reactions, ion loss via recombination processes, diffusion, and ion-molecule reactions with matrix components, and the sampling and pumping parameters of the source. Because the ion source has a flow-through configuration, the number densities of selected species can be estimated by applying the steady-state assumption. However, understanding of its operation is aided by knowledge of the dynamic behavior, so numerical methods are applied to examine the time dependence of those species as well. As in other plasma ionization sources, the ionization efficiency is essentially determined by the ratio of the relevant ion formation and recombination rates. Although thermal electron and positive reagent ion number densities are comparable, the electron capture/ion-molecule reaction rate coefficient ratio is normally quite large and the ion-electron recombination rate coefficient is about an order of magnitude greater than that for ion-ion recombination. Consequently, the efficiency for negative analyte ion formation via electron capture is generally superior to that for positive analyte ion generation via ion-molecule reaction. However, the efficiency for positive analyte ion formation should be equal to or better than that for negative analyte ions when both ionization processes occur via ion-molecule reaction processes (with comparable rate coefficients), since the negative reagent ion density is considerably less than that for positive reagent ions. Furthermore, the particularly high number densities of thermal electrons and reagent ions leads to a large dynamic range of linear response for the source. Simulation results also suggest that analyte ion number densities might be enhanced by modification of the standard physical and operating parameters of the source.     

Molecular simulation of a concentrated aqueous KCl solution

A 1.0 M aqueous KCl solution was studied by molecular dynamics simulations at 293 K in order to study the influence of the ionic concentration on the hydration structure of the ions as well as the formation of ion clusters. The hydration structures of the ions are almost independent of the ionic concentration unless in respect to the perturbation that appears due to ionic clustering. Fractions equal to 31.9% of the anions and 37.8% of the cations are associated. Clusters constituted by two, three and four ions were detected. Their mean lifetimes are always affected by thermal effects, reorientational relaxation while the longest lifetimes are a consequence of ionic cloud relaxations. The pairs constituted by two anions or two cations are stabilized by water molecules belonging to the solvation shells of both ions. The neutral K⁺Cl⁻ pairs are formed under the influence of the electrostatic attraction that, however, is small due to the ionic radii of these ions. Consequently, this kind of pairs contains only 8.8% of the ions while the fraction of ions in the negative and positive pairs are equal to 29.2 and 39.3%, respectively, when the same ion can pertain to more than one pair.     

The significance of the surface condition in solutions to the diffusion equation: explaining “anomalous” sigmoidal, Case II, and Super Case II absorption behavior

Absorption into polymers is frequently described by the terms Fickian, sigmoidal (S-shaped), Case II, or Super Case II. This terminology is used to describe absorption that is respectively, linear with the square root of time, has a slight delay or S-shape with the square root of time, is linear with linear time, or increases more rapidly than with linear time. Solutions to the diffusion equation, Fick’s second law, that include a potentially significant surface condition are shown to reproduce all of these. Sigmoidal absorption results when the surface condition is moderately significant for either a constant diffusion coefficient or exponential diffusion coefficients. Exponential diffusion coefficients and a lower surface mass transfer coefficient result in Case II type behavior, with Super Case II behavior resulting when the surface condition becomes still more significant. The results reported here are supported by extensive experimental data with reasonable and verifiable values for the diffusion coefficients and surface mass transfer coefficients.     

Effects of conformational flexibility of alkyl chains of cations on diffusion of ions in ionic liquids

Molecular dynamics simulations of ionic liquids [1-alkyl-3-methylimidazolium (alkyl = ethyl, butyl and hexyl), N-butylpyridinium, N-butyl-N,N,N-trimethylammonium and N-butyl-N-methylpyrrolidinium cations combined with the (CF(3)SO(2))(2)N(-) (TFSA) anion] show that the conformational flexibility of the alkyl chains in the cations is one of the important factors determining the diffusion of ions. Artificial constraint imposed on the internal rotation of alkyl chains significantly decreases the self-diffusion coefficients of cations and anions. The internal rotation of the C-N bond connecting the alkyl chain and the aromatic ring has large effects on the diffusion of ions in imidazolium and pyridinium based ionic liquids. The calculated self-diffusion coefficients of cations and anions decrease 20-40% by imposing the torsional constraint of the C-N bond. On the other hand the torsional constraint of the C-N bond does not largely change the diffusion of ions in the quaternary alkyl ammonium based ionic liquids. The conformational flexibility of the terminal C-C-C-C bond of the alkyl chains has large effects on the diffusion of ions in the quaternary alkyl ammonium based ionic liquids. The influence of the electrostatic interactions and the high density of ionic liquids on the diffusion of ions were studied. The electrostatic interactions have the paramount importance on the slow diffusion of ions in ionic liquids, while the high density of ionic liquids is also responsible for the slow diffusion. The electrostatic interactions and the high density of ionic liquids enhance the effects of the torsional constraint on the diffusion of ions, which suggests that the charge-ordering structure and small free volume originated in the strong electrostatic interactions are the causes of the significant effects of the conformational flexibility on the diffusion of ions in ionic liquids.     

Blended silicone-ionic liquid membranes: Transport properties of butan-1-ol vapor

This paper is focused on modeling of sorption and desorption kinetics as well as on equilibrium butan-1-ol vapor sorption in blended poly(dimethylsiloxane)-benzyl-3-butylimidazolium tetrafluoroborate membranes. Based on the generalized Fick’s second law, on time-dependent boundary conditions and on two models of equilibrium sorption, the diffusion coefficients of butan-1-ol were calculated from the experimental data using the finite difference modeling. Although anomalous sorption occurred at higher concentrations of butan-1-ol, the diffusion coefficients calculated from the data on sorption and desorption kinetics were in a good agreement. The increase of the ionic liquid content in poly(dimethylsiloxane) elevated the butan-1-ol equilibrium concentration in the membrane, and, at the same time, decreased the values of butan-1-ol diffusion coefficient.     

Study of the translational diffusion of the benzophenone ketyl radical in comparison with stable molecules in room temperature ionic liquids by transient grating spectroscopy

Transient grating (TG) spectroscopy has been applied to the photoinduced hydrogen-abstraction reaction of benzophenone (BP) in various kinds of room temperature ionic liquids (RTILs). After the photoexcitation of BP in RTILs, the formation of a benzophenone ketyl radical (BPK) was confirmed by the transient absorption method, and the TG signal was analyzed to determine the diffusion coefficients of BPK and BP. For comparison, diffusion coefficients of carbon monoxide (CO), diphenylacetylene (DPA), and diphenylcyclopropenone (DPCP) in various RTILs were determined by the TG method using the photodissociation reaction of DPCP. While the diffusion coefficients of the stable molecules BP, DPA, and DPCP were always larger than those predicted by the Stokes-Einstein (SE) relation in RTILs, that of BPK was much smaller than those of the stable molecules and relatively close to that predicted by the SE relation in all solvents. For the smallest molecule CO, the deviation from the SE relation was evident. The diffusion coefficients of stable molecules are better represented by a power law of the inverse of the viscosity when the exponent was less than unity. The ratios of the diffusion coefficient of BP to that of BPK were larger in RTILs (2.7-4.0) than those (1.4-2.3) in conventional organic solvents. The slow diffusion of BPK in RTILs was discussed in terms of the fluctuation of the local electric field produced by the surrounding solvent ions.     

Influence of ionic strength and shear rate on the desorption of polystyrene particles from a glass collector as studied in a parallel-plate flow chamber

The residence-time-dependent desorption during the deposition of polystyrene particles 736 nm in diameter on glass was studied in situ using a parallel-plate flow chamber and automated image analysis. Comparison of successively grabbed images yielded the initial desorption rate coefficient, and final desorption rate coefficient and a relaxation time for the transition from the initial to the final desorption state, i.e. ageing of the bonds. Desorption experiments were performed from suspensions with different potassium nitrate concentrations (1, 10 and 50 mM) and at varying shear rates (15–200 s⁻¹. The initial desorption rate coefficient β₀ ranging from 1 × 10⁻³ to 20 × 10⁻³s⁻¹, and the final desorption rate coefficient β_∞, ranging from 0.01 × 10⁻³ to 0.65 × 10⁻³s⁻¹ were both larger than the desorption rate coefficients calculated neglecting a possible residence time dependence. These desorption rate coefficients, β, ranged from 0.005 × 10⁻³ to 0.40 × 10⁻³s⁻¹. The relaxation times, at which the adhesion of the polystyrene particles entered a more irreversible state of adhesion compared with their initial state of adhesion, varied from 100 to 1000 s. The desorption rate coefficients as well as the relaxation time showed major variations with the shear rate and the ionic strength of the suspension. At high ionic strength, the initial and final desorption rate coefficients increase and the relaxation time decreases with increasing shear rate, whereas at low ionic strength the desorption rates decrease and the relaxation time increases with increasing ionic strength. This study provides direct evidence that the interaction forces between adhering particles and a collector surface change over time.     

Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

Two-cation competition in ionic-liquid-modified electrolytes for lithium ion batteries

It is a common observation that when ionic liquids are added to electrolytes the performances of lithium ion cells become poor, while the thermal safeties of the electrolytes might be improved. In this study, this behavior is investigated based on the kinetics of ionic diffusion. As a model ionic liquid, we chose butyldimethylimidazolium hexafluorophosphate (BDMIPF(6)). The common solvent was propylene carbonate (PC), and lithium hexafluorophosphate (LiPF(6)) was selected as the lithium conducting salt. Ionic diffusion coefficients are estimated by using a pulsed field gradient NMR technique. From a basic study on the model electrolytes (BDMIPF(6) in PC, LiPF(6) in PC, and BDMIPF(6) + LiPF(6) in PC), it was found that the BDMI(+) from BDMIPF(6) shows larger diffusion coefficients than the Li(+) from LiPF(6). However, the anionic (PF(6)(-)) diffusion coefficients present little difference between the model electrolytes. The higher diffusion coefficient of BDMI(+) than that of Li(+) suggests that the poor C-rate performance of lithium ion cells containing ionic liquids as an electrolyte component can be attributed to the two-cation competition between Li(+) and BDMI(+).     

离子半径的质量和电量综合因子的标度

根据作者曾建立的万有引力势与电势的关系式和系统的对比质电比(单位电量的质量)Sr的物理意义, 研究了离子半径r与Sr的关系: 对于相同电子构型的阳离子, 离子半径与lgSr呈线性关系; 对于相同电子构型的阴离子, 离子半径与Sr的关系满足Michealis-Menten 数学模型. 采用回归分析方法, 拟合出周期表中94种元素108种阳离子的半径和16种阴离子的半径. 从相关系数R和回归方程的显著性检验(F)都说明r与Sr密切相关, 其中102种阳离子半径数据与具有代表性的离子半径参考值相比平均绝对误差仅0.9 pm, 相对误差1.1%. 同时给出一条获取离子半径(包括复杂离子)数据的新途径.     

离子质电比和相差异因子对离子半径的综合标度

根据万有引力势与电势的关系式和系统的质电比(单位电量的质量)Sr的物理意义, 研究了离子半径r与离子的Sr和相差异因子的关系. 对于阳离子, r与lgSr和相差异因子呈线性关系; 对于稳定构型阴离子, r与Sr和相差异因子也存在定量关系. 采用回归分析方法, 给出稳定构型和非稳定构型阳离子半径计算公式, 以及稳定构型阴离子半径计算公式. 从相关系数R和回归方程的显著性检验(F)都可说明r与Sr和相差异因子密切相关, 其中拟合的96种元素的138种阳离子半径数据与具有代表性参考值相比, 平均绝对误差为2.0 pm, 相对误差为2.5%. 并预测出较为合理的稀有气体等30种离子半径数据. 同时给出一条获取离子半径(包括复杂离子)数据的新途径.