Simulation of non-stationary electrodiffusion processes in charged membranes by the network approach

Single techniques of network approach have been used to obtain the numerical solution for a boundary value problem involving the Nernst-Planck and Poisson equations system. A network model has been proposed for a particular physical situation, namely, ionic transport in charged membranes including the Donnan equilibrium relations at the membrane/solution interfaces. With this network model and using the electrical circuit simulation program PSPICE, the ionic concentration profiles as well as electric potentials and ionic fluxes have been simulated as a function of time for the ternary systems HClKCl and NaClKCl.     

Modeling and simulation of chemo-electro-mechanical behavior of pH-electric-sensitive hydrogel

A chemo-electro-mechanical multi-field model, termed the multi-effect-coupling pH-electric-stimuli (MECpHe) model, has been developed to simulate the response behavior of smart hydrogels subject to pH and electric voltage coupled stimuli when the hydrogels are immersed in a pH buffer solution subject to an externally applied electric field. The MECpHe model developed considers multiphysics effects and formulates the fixed charge density with the coupled buffer solution pH and electric voltage effects, expressed by a set of nonlinear partial differential governing equations. The model can be used to predict the hydrogel displacement and the distributive profiles of the concentrations of diffusive ionic species and the electric potential and the fixed charge density in both the hydrogels and surrounding solution. After validation of the model by comparison of current numerical results with experiment data extracted from the literature, one-dimensional steady-state simulations were carried out for equilibrium of the smart hydrogels subject to pH and electric coupled stimuli. The effects of several important physical conditions, including the externally applied electric voltage, on the distributions of the concentrations of diffusive ionic species, the electric potential, the fixed charge density, and the displacement of the hydrogel strip were studied in detail. The effects of the ionic strength on the bending deformation of the hydrogels under the solution pH and electric voltage coupled stimuli are also discussed.     

Design and preparation of a novel temperature-responsive ionic gel. 2. Concentration modulation of specific ions in response to temperature changes

We have designed a novel temperature-responsive dialysis system consisting of mixed electrolyte solutions and an ionic gel whose charge density changes in response to temperature changes. The system can modulate the time-concentration profile of just bivalent ions in arbitrary forms by changing the transport modes of the ions in response to the temperature, as long as the system has a sufficient concentration difference of the driving electrolyte for the modulation. The simulation in a model system consisting of mixed KCl and CaCl(2) solutions and the ionic gel shows that the system modulates the time-concentration profile of Ca(2+) ions as a sawtooth waveform and also keeps the concentration a prearranged value for a certain time period by controlling the transport modes of just Ca(2+) ions in two ways: downhill (transport along their own concentration gradient in a system) and uphill (transport against their own concentration gradient), in response to temperature changes. The simulations agree quantitatively with the experiments using a temperature-responsive ionic gel prepared in the previous paper.     

Molecular dynamics simulations of ion transport through carbon nanotubes. III. Influence of the nanotube radius, solute concentration, and applied electric fields on the transport properties

The present investigations continue previous research on transport in aqueous ionic solutions through carbon nanotubes. Specifically, the effects of the nanotube radius, solute concentration, and applied external electric fields on the transport properties are investigated in terms of mobilities, currents, and pairing times of the solute ions. The simulated transport features are corroborated with general theoretical results of nanofluidics (such as the linear log-log regime of the nanochannel conductance as function of the solute concentration and the current-voltage curve of the channel). Discontinuities in the partial ionic currents are explained on the basis of a recent theoretical model of quantized ionic conductance in nanopores, developed by Zwolak et al. Correlations between the structural and dynamic properties are established, linking causally the highly structured spatial density profiles, the ion pairing phenomenon and the ionic currents.     

Steady-state and transient electrical properties of ion-exchange membrane systems in asymmetric arrangements

The steady-state and transient electrical properties of ion-exchange membranes placed between two solutions with different values of the electrolyte concentration, have been simulated using the network simulation method. The ionic transport processes are theoretically described on the basis of the Nernst-Planck and Poisson equations. The system under study is constituted by a cation-exchange membrane in which the fixed-charge is homogeneously distributed in space and two diffusion boundary layers on both sides of the membrane, the electric double layers at the interfaces being included. The steady-state voltage-current characteristic and the profiles of the ionic concentrations and the electric potential, are analysed. Also, the choronopotentiometric response of the system has been discussed and the time evolution of the electric energy consumption evaluated. In particular, the influence of the ratio of the bathing concentrations on the permselectivity and the chronopotentiometric response of the ion-exchange membrane systems, has been established.     

Electrokinetics in nanochannels: part I. Electric double layer overlap and channel-to-well equilibrium

In this paper a new model is described for calculating the electric potential field in a long, thin nanochannel with overlapped electric double layers. Electrolyte concentration in the nanochannel is predicted self-consistently via equilibrium between ionic solution in the wells and within the nanochannel. Differently than published models that require detailed iterative numerical solutions of coupled differential equations, the framework presented here is self-consistent and predictions are obtained solving a simple one-dimensional integral. The derivation clearly shows that the electric potential field depends on three new parameters: the ratio of ion density in the channel to ion density in the wells; the ratio of free-charge density to bulk ion density within the channel; and a modified Debye-Hückel thickness, which is the relevant scale for shielding of surface net charge. For completeness, three wall-surface boundary conditions are analyzed: specified zeta-potential; specified surface net charge density; and charge regulation. Predictions of experimentally observable quantities based on the model proposed here, such as depth-averaged electroosmotic flow and net ionic current, are significantly different than results from previous overlapped electric double layer models. In this first paper of a series of two, predictions are presented where channel depth is varied at constant well concentration. Results show that under conditions of electric double layer overlap, electroosmosis contributes only a small fraction of the net ionic current, and that most of the measurable current is due to ionic conduction in conditions of increased counterion density in the nanochannel. In the second of this two-paper series, predictions are presented where well-concentration is varied and the channel depth is held constant, and the model described here is employed to study the dependence of ion mobility on ionic strength, and compare predictions to measurements of ionic current as a function of channel depth and ion density.     

Parametrical studies of electroosmotic transport characteristics in submicrometer channels

Spatially two-dimensional nonequilibrium mathematical model describing electroosmotic flow through a submicrometer channel with an electric charge fixed on the channel walls is presented. This system is governed by the hydrodynamic, electrostatic, and mass transport phenomena. The model is based on the coupled mass balances, Poisson, Navier-Stokes, and Nernst-Planck equations. Nonslip boundary conditions are employed. The effect of an imposed electric field on the system behavior is studied by means of a numerical analysis of the model equations. We have obtained the following findings. If the channel width is comparable to the thickness of the electric double layer, the system behaves as an ion-exchange membrane and the dependence of the electric current passing through the channel on the applied voltage is strongly nonlinear. In the case of negatively (positively) charged walls, a narrow region of very low conductivity (so-called ionic gate) is formed in the free electrolyte near the channel entry facing the anode (cathode) side. For a wide channel, the electric current is proportional to the applied voltage and the velocity of electrokinetic flow is linearly proportional to the electric field strength. Complex hydrodynamics (eddy formation and existence of ionic gates) is the most interesting characteristics of the studied system. Hence, current-voltage and velocity-voltage curves and the corresponding spatial distributions of the model variables at selected points are studied and described in detail.     

The Influence of Charge Transport and Recombination on the Performance of Dye‐Sensitized Solar Cells

Electrochemical impedance spectroscopy (EIS) and transient voltage decay measurements are applied to compare the performance of dye sensitized solar cells (DSCs) using organic electrolytes, ionic liquids and organic‐hole conductors as hole transport materials (HTM). Nano‐crystalline titania films sensitized by the same heteroleptic ruthenium complex NaRu(4‐carboxylic acid‐4′‐carboxylate) (4,4′‐dinonyl‐2,2′‐bipyridyl)(NCS)₂ , coded Z‐907Na are employed as working electrodes. The influence of the nature of the HTM on the photovoltaic figures of merit, that is, the open circuit voltage, short circuit photocurrent and fill factor is evaluated. In order to derive the electron lifetime, as well as the electron diffusion coefficient and charge collection efficiency, EIS measurements are performed in the dark and under illumination corresponding to realistic photovoltaic operating conditions of these mesoscopic solar cells. A theoretical model is established to interpret the frequency response off the impedance under open circuit conditions, which is conceptually similar to photovoltage transient decay measurements. Important information on factors that govern the dynamics of electron transport within the nanocrystalline TiO₂ film and charge recombination across the dye sensitized heterojunction is obtained.     

Electrochemical impedance spectroscopic analysis of dye-sensitized solar cells

Electrochemical impedance spectroscopy (EIS) has been performed to investigate electronic and ionic processes in dye-sensitized solar cells (DSC). A theoretical model has been elaborated, to interpret the frequency response of the device. The high-frequency feature is attributed to the charge transfer at the counter electrode while the response in the intermediate-frequency region is associated with the electron transport in the mesoscopic TiO2 film and the back reaction at the TiO2/electrolyte interface. The low-frequency region reflects the diffusion in the electrolyte. Using an appropriate equivalent circuit, the electron transport rate and electron lifetime in the mesoscopic film have been derived, which agree with the values derived from transient photocurrent and photovoltage measurements. The EIS measurements show that DSC performance variations under prolonged thermal aging result mainly from the decrease in the lifetime of the conduction band electron in the TiO2 film.     

A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density

A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the ternary system NaClHClH₂O.     

Single ion diffusive transport within a Poly(styrene sulfonate) polymer brush matrix probed by fluorescence correlation spectroscopy

Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials.     

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.     

Kinetic considerations of ion selectivity coefficients of ion-selective electrodes based on neutral carriers

Ion selectivity coefficients of ion-selective electrodes based on neutral carriers are described by means of a mixed potential model of ion transport reactions at the aqueous solution/ion-sensitive membrane interface. The decrease in ion selectivity can be explained by the deviations from the equilibrium conditions, which arise from the ionic partial current across the interface, but the proposed correspondence of the exchange current density of ion transfer reactions with the ion selectivity coefficients is rationalized only for certain conditions of the kinetic parameters. The ion selectivity for liquid membrane transport is discussed starting from three different rate-determining steps. It is shown that the potentiometric selectivities of ion-selective electrodes and the transport selectivities are correlated when the ionic transfer across the aqueous solution/ membrane interface is fast compared with the complex ion transport through the membrane. The significance of a kinetic approach for the design of neutral carriers for ion-selective electrodes is stressed.     

pH-Regulated nanopore conductance with overlapped electric double layers

There has been a significant growth of interest in single nanopore ionic devices that could control the transport of ions and rectify ionic current. To improve the advance of relevant nanofluidic devices, a model is derived for the first time to investigate the zeta potential and ionic conductance of a cylindrical nanopore with overlapped electric double layer as functions of pH, salt concentration as well as the Stern layer capacitance. The developed model is validated by the experimental data of the nanopore conductance. Results show that in addition to the magnitudes, the relevant behaviors of zeta potential and conductance of the nanopore might be significantly influenced by the Stern layer.     

Electric field-controlled water permeation coupled to ion transport through a nanopore

We report molecular dynamics simulations of a generic hydrophobic nanopore connecting two reservoirs which are initially at different Na(+) concentrations, as in a biological cell. The nanopore is impermeable to water under equilibrium conditions, but the strong electric field caused by the ionic concentration gradient drives water molecules in. The density and structure of water in the pore are highly field dependent. In a typical simulation run, we observe a succession of cation passages through the pore, characterized by approximately bulk mobility. These ion passages reduce the electric field, until the pore empties of water and closes to further ion transport, thus providing a possible mechanism for biological ion channel gating.     

Electrodialysis of uranium(VI) through cation exchange membranes and modeling of electrodialysis processes

The transport of ionic species through ion exchange membranes found several applications for water effluents purification and metal ion separation. To enhance the transport performance, the effect of electric fields was suggested in this work. The transport of U(VI) species in nitric acid solutions across cation exchange membranes was investigated. Different parameters affecting the transport of U(VI) were studied. These parameters include: nitric acid concentration in the feed solution, stripping solution concentration and applied electric field. From the results obtained, the cationic flux of U(VI) was 6.5^.10^–8 geq^.cm^–2.s^–1 at the optimal conditions of 10^–3M HNO₃ in the feed solution, 0.5M Na₂CO₃ in the stripping solution and 30 V. The modeling of the electrodialysis process was also made. The model correlates the mass transfer as a function of current density and voltage as variables and takes into account the electro-osmotic effect. The model is applied to the experimental data.     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Effect of charge density gradient on characteristics of electric double layer for salt melts

The equilibrium conditions are analyzed for a spatially inhomogeneous ionic liquid using the density functional theory with allowance made for the second order gradient corrections. Solutions for the distribution of potential and charge density in the electric double layer at the ionic liquid/vapor interface are obtained using a parameterized total density profile normal to the surface. It is shown that taking into account the effects of the charge density gradient in the theory results in the appearance of damped oscillations of the charge density near the surface, while the double layer localized on the surface is reduced.     

离子液体内耦合液膜迁移苯酚的研究

本文以N-甲基咪唑为原料,采用微波合成法,制备了疏水性离子液体1-丁基-3-甲基咪唑六氟磷酸盐([BMIM]PF6),并将其作为液膜,对苯酚的内耦合液膜迁移进行了研究,考察了温度、搅拌速度、料液相酸度、初始浓度及解析相NaOH浓度等因素对苯酚迁移的影响,得出了最佳迁移条件:温度300 K,搅拌速度350 r/min,料液相pH为3.65,解析相NaOH浓度为0.8 mol/L.在最佳液膜条件下,对于10 mg/L苯酚溶液,迁移110 min,迁移率可以达到97.3%,膜相中有少量苯酚滞留.离子液体可循环使用.