Diffusiophoresis of concentrated suspensions of spherical particles with distinct ionic diffusion velocities

The diffusiophoresis of a concentrated spherical dispersion of colloidal particles subject to a small electrolyte gradient is analyzed theoretically for an arbitrary zeta potential and double layer thickness. In particular, the influence of the difference in the diffusivities of cations and anions is discussed. A unit cell model is used to simulate a spherical dispersion, and a pseudospectral method is adopted to solve the equations governing the phenomenon under consideration. We show that, as in the case of an infinitely dilute dispersion, when the diffusivities of cations and anions are different, the diffusiophoretic mobility is no longer an even function of the zeta potential or double layer thickness. In contrast to the case of identical diffusivity of cations and anions, a local electric field is induced in the present case due to an unbalanced charge distribution between higher and lower concentration regions. Depending upon the direction of this induced electric field, the diffusiophoretic mobility can be larger or smaller than that for the case of identical diffusivity. The diffusiophoretic mobility is influenced mainly by the induced electric field arising from the difference in the ionic diffusivities, the concentration gradient, and the effect of double layer polarization.     

Controlling the transport of cations through permselective mesoporous alumina layers by manipulation of electric field and ionic strength

The electric field-driven transport of ions through supported mesoporous gamma-alumina membranes was investigated. The influence of ion concentration, ion valency, pH, ionic strength, and electrolyte composition on transport behavior was determined. The permselectivity of the membrane was found to be highly dependent on the ionic strength. When the ionic strength was sufficiently low for electrical double-layer overlap to occur inside the pores, the membrane was found to be cation-permselective and the transport rate of cations could be tuned by variation of the potential difference over the membrane. The cation permselectivity is thought to be due to the adsorption of anions onto the pore walls, causing a net negative immobile surface charge density, and consequently, a positively charged mobile double layer. The transport mechanism of cations was interpreted in terms of a combination of Fick diffusion and ion migration. By variation of the potential difference over the membrane the transport of double-charged cations, Cu2+, could be controlled accurately, effectively resulting in on/off tunable transport. In the absence of double-layer overlap at high ionic strength, the membrane was found to be nonselective.     

Hindered diffusion of synthetic polyelectrolytes in charged microporous membranes

To examine electrostatic effects on the diffusion of macromolecules in membranes, diffusivities of narrow molecular-size fractions of the polyelectrolytes ficoll sulfate and dextran sulfate were measured in polycarbonate track-etch membranes. Radius, number density, and surface charge density of membrane pores were determined from a combination of hydraulic permeability, glucose diffusion, and streaming potential measurements. Molecular charge and Stokes—Einstein radius for each macromolecule fraction were determined from free-solution electrophoretic mobility and diffusivity in a large pore radius membrane, D∞, respectively. As ionic strength was increased from 0.005 to 0.1 M, D∞ for ficoll sulfate remained constant while D∞ for dextran sulfate increased slightly (15-18%). Macromolecule diffusivities in small pore membranes, D, were much more sensitive to ionic strength. For membranes where the ratio of Stokes—Einstein radius to pore radius ranged from 0.08 to 0.29, D/D∞ for ficoll sulfate and dextran sulfate increased by factors ranging from 2.5 to 14 for the same increase in ionic strength. Recent theoretical results for electrostatic double layer interactions in hindered diffusion are in good quantitative agreement with these findings.     

Molecular dynamics simulations of the structure and transport properties of tetra-butylphosphonium amino acid ionic liquids

Systematic molecular dynamics simulations are used to study the structure, dynamics and transport properties of the ionic liquids composed of the tetra-butylphosphonium ([TBP](+), or [P(C(4)H(9))(4)](+)) cation with six amino acid ([AA](-)) anions. The structural features of these ionic liquids were characterized by calculating the partial site-site radial distribution functions, g(r), and computing the dihedral angle distribution of n-butyl side chains in the [TBP](+) cations. The dynamics of the ionic liquids are described by studying the velocity autocorrelation function (VACF) and the mean-square displacement (MSD) for the centers of mass of the ions at different temperatures. The ionic diffusion coefficients and the electrical conductivities were evaluated from both the Einstein and Green-Kubo methods. The cross-correlation terms in the electric-current autocorrelation functions, which are an indication of the ion pair correlations, are investigated. The cationic transference numbers were also estimated to study the contributions of the anions and cations to the transport of charge in these ionic liquids. We determined the role of the amino acid anion structures on the dynamical behavior and the transport coefficients of this family of ionic liquids. In general, the MSD and self-diffusion coefficients of the relatively heavier non-planar [TBP](+) cations are smaller than those of the lighter amino acid anions. Introducing polar functional groups (acid or amide) in the side chain of [AA](-) decreases the diffusion coefficient and electrical conductivity of AAILs. The major factors for determining the magnitude of the transport coefficients are the chemical functionality and the length of the alkyl side chain of the [AA](-) anion of these [TBP][AA] ionic liquids.     

Study on protein adsorption kinetics to a dye-ligand adsorbent by the pore diffusion model

Adsorption kinetics of bovine serum albumin (BSA) and bovine hemoglobin (bHb) to Cibacron Blue 3GA (CB) modified Sepharose CL-6B has been studied. The effects of liquid-phase ionic strength and CB coupling density on the uptake rates of these two proteins in Tris-HCl buffer (pH 7.5) were evaluated by effective pore diffusivity derived from a pore diffusion model. The results showed that despite their similar molecular masses and sizes, the effects of aqueous-phase ionic strength and CB density on the effective pore diffusivities of BSA and bHb were distinctly different. The effective pore diffusivity of BSA to CB-Sepharose increased significantly with decreasing CB density and increasing liquid-phase ionic strength. This was considered due to the decrease in electrostatic repulsion between the BSA and CB molecules of like charge. That is, the increase in ionic strength and the decrease in CB coupling density reduced the electrostatic hindrance effect on BSA diffusion to CB-Sepharose, facilitating the hindered pore diffusion. In contrast, because of the higher isoelectric point of bHb (7.0) compared to BSA (4.7), bHb suffered little electrostatic hindrance effect during its diffusion to CB-Sepharose. Therefore, the effective pore diffusivity of bHb was unchanged with the change in liquid-phase ionic strength and CB coupling density.     

Pore network modelling of the behaviour of a solute in chromatography media: transient and steady-state diffusion properties

A pore network model is presented, that is a geometrical simplification of a porous medium. The network consists of pore chambers interconnected by pore throats. A recursive algorithm for the simulation of mercury intrusion porosimetry in the network is presented. Calculations indicate that it is possible to fit simulated mercury intrusion data to experimental data, and thereby obtain parameters of the pore size distribution and pore topology (pore connectivity). A time-dependent material balance equation for diffusion on the pore level is set up and solved for the pore network. By calculating the concentration evolution in the network, the transient diffusivity and the steady-state diffusivity are found. When the network is well connected, those two diffusivities are equal, but for poorly-connected networks they differ. For migrating solutes that are non-negligibly small compared to the pore throats, considerable differences between the transient and steady-state diffusivities were found.     

Diffusion of ionic species in bentonite

We present a macroscopic model of ionic diffusion in bentonites including the effect of the hydraulic-electrical-chemical couplings expected in such charged porous medium. The anomalous concentrations of the ions in the pore water of the bentonite are modeled with a modified Donnan model in which we account for the partition of the counterions between the Stern and Gouy-Chapman layers. This is accomplished using an electric triple layer (TLM) model combined with an explicit complexation model at the mineral/water interface. The porosity entering into the determination of the formation factor of the medium is an effective porosity obtained by removing the fraction of hydration water covering the surface of the clay minerals. We investigate two different cases of diffusion. In the first case, we consider a salinity gradient between two reservoirs in contact with a cylindrical sample of bentonite. The model predicts an increase of the diffusivity of the salt with the salinity of the solution in contact with the bentonite in agreement with experimental data. In the second case, we analyze a self-diffusion experiment of an ionic tracer. The model predicts an increase of the diffusivity of anions with the effective porosity and with the ionic strength. This is also in good agreement with experimental data.     

Understanding correlation effects for ion conduction in polymer electrolytes

Polymer electrolytes typically exhibit diminished ionic conductivity due to the presence of correlation effects between the cations and anions. Microscopically, transient ionic aggregates, e.g., ion-pairs, ion-triplets, or higher order ionic clusters, engender ionic correlations. Employing all-atom simulation of a model polymer electrolyte comprising of poly(ethylene oxide) and lithium iodide, the ionic correlations are explored through construction of elementary functions between pairs of the ionic species that qualitatively explains the spatio-temporal nature of these correlations. Furthermore, commencing from the exact Einstein-like equation describing the collective diffusivity of the ions in terms of the average diffusivity of the ions (i.e., the self-terms) and the correlations from distinct pairs of ions, several phenomenological parameters are introduced to keep track of the simplification procedure that finally boils down to the recently proposed phenomenological model by Stolwijk and Obeidi (SO) [Stolwijk, N. A.; Obeidi, S. Phys. Rev. Lett. 2004, 93, 125901]. The approximation parameters, which can be retrieved from simulations, point to the necessity of additional information in order to fully describe the correlation effects apart from the mere fraction of ion-pairs that apparently accounts for the correlations originating from only the nearest neighbor structural correlations. These parameters are close to, but are not exactly unity, as assumed in the SO model. Finally, as an application of the extended SO model, one is able to estimate the dynamics of the free and non-free ions as well as their fractions from the knowledge of the single particle diffusivities and the collective diffusivity of the ions.     

Parallel pore and surface diffusion of levulinic acid in basic polymeric adsorbents

The equilibrium and kinetics of levulinic acid (LA) adsorption on two basic polymeric adsorbents, 335 (highly porous gel) and D315 (macroreticular), were investigated. Experimental adsorption rates in batch stirred vessels under a variety of operating conditions were described successfully by the parallel pore and surface diffusion model taking into account external mass transfer and nonlinear Toth isotherm. The film-pore diffusion model was matched with the rate data and the resulting apparent pore diffusivities were strongly concentration-dependent and approached to a constant value for 335 adsorbent. Thus, the constant value was taken as the accurate pore diffusivity, while the pore diffusivity in D315 was estimated from the particle porosity. The surface diffusivities decreased with increasing initial bulk concentration for both adsorbents. The inverse concentration dependence was correlated reasonably well to the change of isosteric heat of adsorption as amount adsorbed.     

Diffusion Mechanisms of Zeolite Catalysts

The diffusion mechanisms within zeolite catalysts, such as resistance to diffusion at pore mouths, configurational diffusion, adsorption-controlled diffusion, influence of co-existing molecules and pore blocking, were overviewed. Two kinds of diffusivities, the intracrystalline diffusivity and the effective diffusivity, were discussed separately to clarify the diffusion mechanism.     

Determining the Zeta Potential of Porous Membranes Using Electrolyte Conductivity inside Pores

The zeta potential is an important and reliable indicator of the surface charge of membranes, and knowledge of it is essential for the design and operation of membrane processes. The zeta potential cannot be measured directly, but must be deduced from experiments by means of a model. The possibility of determining the zeta potential of porous membranes from measurements of the electrolyte conductivity inside pores (lambda(pore)) is investigated in the case of a ceramic microfiltration membrane. To this end, experimental measurements of the electrical resistance in pores are performed with the membrane filled with KCl solutions of various pHs and concentrations. lambda(pore) is deduced from these experiments. The farther the pH is from the isoelectric point and/or the lower the salt concentration is, the higher the ratio of the electrolyte conductivity inside pores to the bulk conductivity is, due to a more important contribution of the surface conduction. Zeta potentials are calculated from lambda(pore) values by means of a space charge model and compared to those calculated from streaming potential measurements. It is found that the isoelectric points are very close and that zeta potential values for both methods are in quite good agreement. The differences observed in zeta potentials could be due to the fact that the space charge model does not consider the surface conductivity in the inner part of the double layer. Measurements of the electrolyte conductivity within the membrane pores are proved to be a well-adapted procedure for the determination of the zeta potential in situations where the contribution of the surface conduction is significant, i.e., for small and charged pores. Copyright 2001 Academic Press.     

Density, viscosity and electrical conductivity of protic alkanolammonium ionic liquids

Ionic liquids are molten salts with melting temperatures below the boiling point of water, and their qualification for applications in potential industrial processes does depend on their fundamental physical properties such as density, viscosity and electrical conductivity. This study aims to investigate the structure-property relationship of 15 ILs that are primarily composed of alkanolammonium cations and organic acid anions. The influence of both the nature and number of alkanol substituents on the cation and the nature of the anion on the densities, viscosities and electrical conductivities at ambient and elevated temperatures are discussed. Walden rule plots are used to estimate the ionic nature of these ionic liquids, and comparison with other studies reveals that most of the investigated ionic liquids show Walden rule values similar to many non-protic ionic liquids containing imidazolium, pyrrolidinium, tetraalkylammonium, or tetraalkylphosphonium cations. Comparison of literature data reveals major disagreements in the reported properties for the investigated ionic liquids. A detailed analysis of the reported experimental procedures suggests that inappropriate drying methods can account for some of the discrepancies. Furthermore, an example for the improved presentation of experimental data in scientific literature is presented.     

Diffusion of ions in unsaturated porous materials

In a salinity gradient, the diffusion of ions through the connected porosity of a porous and charged material is influenced by the charged nature of the interface between the pore water and the solid. This influence is exerted through the generation of a macroscopic electrical field termed the diffusion or membrane potential. This electrical field depends on the excess of counterions located in the pore space counterbalancing the charge density of the surface of the solid. In unsaturated porous materials, we have to consider (1) the effect of the charged nature of the air/water interface, (2) the increase of the counterion density as the counterions are packed in a smaller volume when the saturation of the nonwetting phase (air) increases, and (3) the influence of the water saturation upon the tortuosity of the water phase. The volume average of the Nernst-Planck equation is used to determine the constitutive equations for the coupled diffusion flux and current density of a multicomponent electrolyte in unsaturated conditions. We assume that water is the wetting phase for the solid phase. We neglect the electro-osmotic flow in the coupled constitutive equations and the deformation of the medium (the medium is assumed to be both isotropic and rigid). This model explains well the observed tendency of strong decreases of the apparent diffusion coefficient of ions with the decrease of the saturation of the water phase under steady-state conditions. This decrease is mainly due to the influence of the saturation upon the tortuosity of the water phase.     

Determinants of thermal conductivity and diffusivity in nanostructural semiconductors

The origin of size effects in the thermal conductivity and diffusivity of nanostructural semiconductors was investigated through the establishment of a unified nanothermodynamic model. The contributions of size-dependent heat capacity and cohesive energy as well as the interface scattering effects were considered during the modeling. The results indicate the following: (1) both the thermal conductivity and diffusivity decrease with decreasing nanocrystal sizes (x) of Si and Si/SiGe nanowires, Si thin films and Si/Ge(SiGe) superlattices, and GaAs/AlAs superlattices when x > 20 nm; (2) the heat transport in semiconductor nanocrystals is determined largely by the increase of the surface (interface)/volume ratio; (3) the interface scattering effect predominates in the reduction of thermal conductivity and diffusivity while the intrinsic size effects on average phonon velocity and phonon mean free path are also critical; (4) the quantum size effect plays a crucial role in the enhancement of the thermal conductivity with a decreasing x (<20 nm). These findings provide new insights into the fundamental understanding of high-performance nanostructural semiconductors toward application in optoelectronic and thermoelectric devices.     

Electrochemistry of room temperature protic ionic liquids

Eighteen protic ionic liquids containing different combinations of cations and anions, hydrophobicity, viscosity, and conductivity have been synthesized and their physicochemical properties determined. In one series, the diethanolammonium cations were combined with acetate, formate, hydrogen sulfate, chloride, sulfamate, and mesylate anions. In the second series, acetate and formate anions were combined with amine bases, triethylamine, diethylamine, triethanolamine, di-n-propylamine, and di-n-butylamine. The electrochemical characteristics of the eight protic ionic liquids that are liquid at room temperature (RTPILs) have been determined using cyclic, microelectrode, and rotating disk electrode voltammetries. Potential windows of the RTPILs have been compared at glassy carbon, platinum, gold, and boron-doped diamond electrodes and generally found to be the largest in the case of glassy carbon. The voltammetry of IUPAC recommended potential scale reference systems, ferrocene/ferrocenium and cobaltocenium/cobaltocene, have been evaluated and found to be ideal in the case of the less viscous RTPILs but involve adsorption in the highly viscous ones. Other properties such as diffusion coefficients, ionic conductivity, and double layer capacitance also have been measured. The influence of water on the potential windows, viscosity, and diffusion has been studied systematically by deliberate addition of water to the dried ionic liquids. The survey highlights the problems with voltammetric studies in highly viscous room temperature protic ionic liquids and also suggests the way forward with respect to their possible industrial use.     

Molecular Dynamics Simulation of the Ionic Liquid 1-n-Butyl-3-Methylimidazolium Methylsulfate [Bmim][MeSO4]: Interfacial Properties at the Silica and Vacuum Interfaces

Molecular dynamics simulations are done to investigate the structure and dynamics of a thin [Bmim][MeO₄] film in contact with a hydroxylated silica surface on one side and with vacuum on the other. An examination of the microscopic structure of ionic liquid (IL) film shows that strong layered anionic/cationic structures are formed at both interfaces. At the silica interface, the imidazolium rings are closer to the silica surface (compared to anions) and are coplanar with it. At the vacuum interface, the charged imidazolium ring more concentrates in the interior of the film, but the butyl side chain stretches out toward the vacuum interface. While there exists an excess concentration of the cations at the silica interface, at the vacuum interface an excess concentration of anions (dissolved in the butyl chain) is found. The influence of the interface on the dynamical properties is shown to depend on their time scales. A short-time dynamical property, such as hydrogen bond formation is not noticeably perturbed at the interface. In contrary, long-time properties such as ion-pair formation/rupture and translation of ions across the film are largely decelerated at the silica interface but are accelerate at the vacuum interface. Our findings indicate that the structural relaxation time of ion-pairs, is comparable to diffusion time scale in the IL film. Therefore, ion-pairs are not stable species; the IL is composed of short-lived ion-pairs and freely diffusing ions. However, the structural relaxation times of ion-pairs is still long enough (comparable to the time scale of diffusion) to conclude that correlated motions of counterions influence the macroscopic properties of IL, such as diffusion and ionic conductivity. In this respect, we have shown that correcting the Nernst-Einstein equation for the joint translation of ion-pairs considerably improves the accuracy of calculated ionic conductivities.     

Membrane potential in charged porous membranes

For charged porous membranes, the separation efficiency to charged particles and ions is affected by the electrical properties of the membrane surface. Such properties are most commonly quantified in terms of zeta-potential. In this paper, it is shown that the zeta-potential can be calculated numerically from the membrane potential. The membrane potential expression for charged capillary membranes in contact with electrolyte solutions at different concentrations is established by applying the theory of non-equilibrium thermodynamic to the membrane process and considering the space-charge model. This model uses the Nernst–Planck and Navier–Stokes equations for transport through pores, and the non-linear Poisson–Boltzmann equation, which is numerically solved, for the electrostatic condition of the fluid inside pores. The integral expressions of the phenomenological coefficients coupling the differential flow (solute relative to solvent) and the electrical current with the osmotic pressure and the electrical potential gradients are established and calculated numerically. The mobilities of anions and cations are individually specified. The variations of the membrane potential (or the apparent transport number of ions in the membrane pores) are studied as a function of different parameters: zeta-potential, pore radius, mean concentration in the membrane, ratio of external concentrations and type of ions.     

多孔离子交换树脂内Eu3+离子的分步扩散

用同位素交换法研究了Eu³⁺离子在D72和D751树脂内的扩散过程.应用分步孔道扩散方程将粒内有效扩散系数D_e分解为孔道扩散系数D_p和固相扩散系数D_g,表明该方程可用于描述多孔树脂内的动力学过程.实验表明,D_e、D_p、D_g均随反应温度的升高而增大.计算了实验条件下的Eu³⁺的自扩散活化能;D72树脂的D_p和D_g对温度的响应比D751树脂大,其D_e、D_p、D_g值亦均大于D751树脂;Eu³⁺在溶液中的自扩散系数D_s＞D_p,说明离子在树脂孔道内的自扩散不能完全等同于其在溶液中的自扩散.     

Nitrate and chloride transport through a smart membrane

To develop membranes having ionic selective properties under control of external stimuli is a challenge of the membrane and material scientific community. Conducting polymers swell and shrink under electrochemical control, so they are good candidates to prepare such smart membranes. The ionic transport through a new free-standing polypyrrole film working as a membrane in a diffusion cell was studied. The driving forces were transversal electric fields or concentration gradients across the film. The obtained ionic conductivity was dependent on both the electrolyte nature and concentration, as well as on the oxidation degree of the film, which was controlled by the applied external electric potential. Reverse and continuous changes of up to one order of magnitude on the transversal ionic conductivity are obtained when the membrane is in stationary oxidation states attained by polarisations at a constant potential in the range between −0.6 V and +0.4 V, respectively. A prevalent conductivity of anions (t₋ = 0.94) was obtained from Donnan potential measurements. The experimental results indicate that the oxidised film behaves as a nanoporous membrane highly permeable to nitrate ions, while the rejection of these ions is very high in the reduced film. The free-standing polypyrrole film works then as a smart membrane selective to nitrate ions under concentration gradient.     

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.