Molecular dynamics simulations of ion transport through carbon nanotubes. II. Structural effects of the nanotube radius, solute concentration, and applied electric fields

The reported work extends previously published 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 solution structuring are investigated in terms of spatial density distributions, pair distribution functions, and electrostatic potential profiles. Several simulated structural features are consistent with general theoretical results of nanofluidics and can be interpreted fairly well with respect to these (such as the Donnan-type voltages established at the channel apertures depending on the logarithm of the maximum ion concentration). The simulated properties are based on averages over the largest data collection times reported in the literature (0.8 μs), providing accurate estimates of the measured quantities.     

Modeling of electrokinetic transport in silica nanofluidic channels

We present a theoretical and numerical modeling study of the multiphysicochemical process in electrokinetic transport in silica nanochannels. The electrochemical boundary condition is solved by considering both the chemical equilibrium on solid-liquid interfaces and the salt concentration enrichment caused by the double layer interaction. The transport behavior is modeled numerically by solving the governing equations using the lattice Poisson-Boltzmann method. The framework is validated by good agreements with the experimental data for all range of ionic concentrations. The modeling results suggest that when the double layers interact, the bulk salt concentration enrichment results in the saturation of conductances for low ionic concentrations. Both the streaming conductance and the electrical conductance are enhanced by the double layer interaction, and such enhancements diminish when the channel size is larger than 10 times of the Debye length. The streaming conductance increases with pH almost linearly when pH < 8, while the electrical conductance increases with pH exponentially.     

Effect of ionic strength and protein concentration on the transport of proteins through chitosan/polystyrene sulfonate multilayer membrane

The influence of ionic strength and protein concentration on the transport of bovine serum albumin (BSA), ovalbumin and lysozyme through chitosan (CHI)/polystyrenesulfonate (PSS) multilayers on polyether sulfone supports are investigated under ultrafiltration conditions. The percentage transmission and flux of BSA, ovalbumin and lysozyme were found to increase with increase in salt concentration in the protein. The percentage transmission of BSA through 9 bilayer membrane was found to increase from 5.3 to 115.6 when the salt concentration was varied from 0 to 1 M. It was observed that 0.1 M NaCl in BSA solution is capable of permeating all the BSA. When the salt concentration in BSA was further increased, a negative solute rejection (solute enrichment in permeate) was found to take place. With 9 bilayer membrane, the percentage transmission of ovalbumin was found to increase from 23.3 to 125.8 when the salt concentration in protein was increased from 0 to 0.05 M. The effect of protein concentration on protein transport is studied taking BSA as a model protein. BSA was rejected by the multilayer membrane at all the studied concentrations (0.25, 0.5, 1 and 2 mg/ml). With increase in feed concentration, maximum rejection of protein occurred at higher number of CHI/PSS bilayers. BSA solution flux was found to decrease with an increase in BSA concentration. This study indicates that it is possible to fine tune the transport properties of proteins through multilayer membranes by varying the concentration and ionic strength of protein solutions.     

Conditions for purely diffusional transport of charged reactant and charged product in the absence of supporting electrolyte

Steady-state currents of charged reactants, at a hemispherical ultramicroelectrode, are independent of the concentration of supporting electrolyte if the relationship z_R/z_P=D_R/D_P (R=ionic reactant, P=ionic product) is satisfied. Under the above conditions no electric field gradient is present in the solution and no migrational transport takes place. Also, there should be no distortion of the results caused by ohmic drop. The paper presents the theoretical derivation of appropriate equations.     

Charge transport in confined concentrated solutions: A minireview

This Minireview summarizes several recent experiments clouding over prevailing theoretical understanding of charge transport behaviors in electrochemical systems; they are nonlinear concentration dependence of ionic conductivity, ultra-long Debye length in ionic liquids, nonmonotonic double layer charging behavior, and anomalous increase in area specific capacitance with decreasing nanopore size. Theoretical activities reveal that nanoconfinement and high concentration exert strong influence on charge distribution and transport via strong ion-ion correlations and ion-wall interactions. By exemplifying where and why classical theories of charge transport fail, we defy the popular point of view that theoretical electrochemistry is well-established and we are left with applications of these theories only.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.     

Ion transport and selectivity in nanopores with spatially inhomogeneous fixed charge distributions

Polymeric nanopores with fixed charges show ionic selectivity when immersed in aqueous electrolyte solutions. The understanding of the electrical interaction between these charges and the mobile ions confined in the inside nanopore solution is the key issue in the design of potential applications. The authors have theoretically described the effects that spatially inhomogeneous fixed charge distributions exert on the ionic transport and selectivity properties of the nanopore. A comprehensive set of one-dimensional distributions including the skin, core, cluster, and asymmetric cases are analyzed on the basis of the Nernst-Planck equations. Current-voltage curves, nanopore potentials, and transport numbers are calculated for the above distributions and compared with those obtained for a homogeneously charged nanopore with the same average fixed charge concentration. The authors have discussed if an appropriate design of the spatial fixed charge inhomogeneity can lead to an enhancement of the transport and selectivity with respect to the homogeneous nanopore case. Finally, they have compared the theoretical predictions with relevant experimental data.     

Numerical investigation of the solute dispersion in finite-length microchannels with the interphase transport

This paper utilizes a combined approach of the convection-diffusion theory and the moment analysis to conduct a comprehensive investigation of the solute dispersion under the influence of the interphase transport in finitely long inner coated microchannels. The present work has threefold novel contributions: (1) The 2D solute concentration contours in the stationary phase are calculated for the first time to facilitate the understanding the role of the interphase transport in the solute dispersion in the mobile phase. (2) The skewness of the elution curves is investigated to guide the control of solute band shape at the channel outlet. (3) The 2D diffusion-convection theory and zero-dimensional (0D) moment analysis complement each other to present a characterization of the solute dispersion behaviors more comprehensive than that by either of the two methods alone. Parametric studies are performed to clarify the effects of four major parameters related to the interphase transport (i.e., stationary phase Péclet number, interphase transport rate, partition coefficient, and stationary phase thickness) on the solute dispersion characteristics. The results from this study provide a straightforward understanding of the effects of interphase transport on the solute dispersion in finitely long microchannels and are of potential relevance to the design and operation of the microfluidics-based analytical devices.     

Improved analytical prediction of facilitation factors in facilitated transport

An improved analytical solution for the facilitation factor in facilitated transport that covers a wide range from diffusion-limited to reaction-limited mass transport has been developed. This solution is attained after assuming a small non-zero solute concentration at the membrane exit. Based on previous analysis a graph that provides a reasonable downstream solute concentration was extracted. The exit solute concentration was found to be dependent on both the mobility ratio, , and the inverse Damkohler number, ε. The quick and reasonable results in this work can be used for design and scale-up purposes.     

Computer simulation study on the concentration distribution of spherical colloids within confined spaces of well‐defined pores

Aside from the virial expansion and density functional methods, theoretical results on the concentration partitioning behavior for charged colloids within cylindrical pores have not been presented so far. With the increase of relative solute size as well as solute concentration, however, the approximate analytic methods have proven to be unreliable. A suitable Monte Carlo simulation, which is proved as a rigorous technique for concentrated colloids, has been applied in the present study. The concentration profiles within the pore representing the effects of solute concentration as well as solution ionic strength are obtained via a stochastic process, from which the partition coefficient is estimated. Previously developed analyses on the linearized Poisson‐Boltzmann (P‐B) equation are employed for the estimation of long‐range electrostatic interaction. Both the singularity method and the analytical solution with series representation properly determine respective interaction energies between pairs of solute particles and between the solute particle and the pore wall. The effect of solute‐solute and solute‐wall interactions associated with repulsive energy is presented on the partitioning of colloids. Simulation results show that the partition coefficient is evidently enhanced when no particle‐wall interaction exists. Hindered diffusion can be predicted by the simplifying assumption of the centerline approximation analogy, where a dependence on the solute concentration becomes greater as the solution ionic strength decreases.     

Preferential glycerol transport by electroosmosis through ionic membranes

This paper describes a process in which glycerol is preferentially sorbed relative to water by an ionic membrane and transported into the product solution by electroosmosis at a significantly higher concentration than that in the feed solution. Direct measurement of the membrane distribution coefficient demonstrated preferential glycerol sorbtion for Neosepta CL-25T and AV-4T membranes. Both DC and AC electric currents significantly increase glycerol transport over that of a concentration difference alone.     

Determining the radius and the apparent charge of a micelle from electrical conductivity measurements by using a transport theory: explicit equations for practical use

We propose here a procedure which combines experiments and simple analytical formulas that allows us to determine good estimations of the size and charge of ionic micelles above the critical micellar concentration (cmc). First, the conductivity of n-tetradecyltrimethylammonium bromide and chloride (TTABr and TTACl, respectively) aqueous solutions was measured at 25 degrees C, before and above their cmc. Then, an analytical expression for the concentration dependence of the conductance of an ionic mixture with three species (monomers, micelles, and counterions) was developed and applied to the analysis of the experiments. The theoretical calculations use the mean spherical approximation (MSA) to describe equilibrium properties. Here, we propose new expressions for the electrical conductivity, adapted to the case of electrolytes that are dissymmetric in size, and applicable up to a total surfactant concentration of 0.1 mol L(-1). Moreover, we show that they are good approximations of the corresponding numerical results obtained from Brownian dynamics simulations. Since the analytical formulas given in the present paper involve a small number of unknown parameters, they allow one to derive the size and charge of macroions in solution from conductivity measurements.     

Extended space charge in concentration polarization

This paper is concerned with ionic currents from an electrolyte solution into a charge-selective solid, such as, an electrode, an ion-exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization — formation of solute concentration gradients under the passage of a DC current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed non-equilibrium electroosmotic instability, result from the formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface. In this paper we review the peculiar features of the non-equilibrium electric double layer and extended space charge and the possibility of their direct probing by harmonic voltage/current perturbations through a linear and non-linear system's response, by the methods of electrical impedance spectroscopy and via the anomalous rectification effect. On the relevant microscopic scales the ionic transport in the direction normal to the interface is dominated by drift-diffusion; hence, the extended space charge related viscous flows remain beyond the scope of this paper.     

Current density analysis of electron transport through molecular wires in open quantum systems

The current density in molecular wires connected to contacts is investigated within the nonequilibrium Green's function formalism combined with the Landauer approach. Energy-dependent and total current density through a series of molecular junctions are calculated in real space representation. A rich variety of current patterns including pronounced ring currents (“vortices”) are found even in the defect-free minimal building blocks of molecular devices. The influences of contact positions, functional groups as well as atomic defects on the transport properties are examined systematically for prototypical ortho-, meta-, and para-substituted benzenes as well as heteroaromatic systems. It is found that substitutional functional groups mainly shift the molecular levels and retain characteristic transport channels, while a significant change of electronic pathways and conductance is induced by hetero-aromaticity. The current distribution is used to calculate the static magnetic field distribution in the carbon-based conductors. © 2017 Wiley Periodicals, Inc.     

Simulations of photomodulated solute transport in doubly illuminated liquid membranes containing photoactive carriers

A steady-state model describing photofacilitated transport in liquid membranes under double illumination is presented. The model allows for the exploration of the effects of a wide range of thermodynamic and kinetic carrier properties on the control of photoinduced transport rates of solutes, called photomodulation. Most previous experimental and theoretical studies have explored the illumination of only the feed or sweep side of the membrane, while this study examines the effects of illuminating both sides simultaneously. Under double illumination, solute transport rates can be as much as five times greater than those measured in the dark and 2.5 times greater than rates obtained under single illumination. Carriers that are predominantly in the weakly binding form in the dark generally provide slightly better performance at lower light intensities than do carriers that are predominantly in the strongly binding form in the dark. The greatest enhancement in solute transport under double illumination is seen for carriers with very slow interconversion rate constants between the strongly and weakly binding forms. These results provide guidelines to help those studying photofacilitated membranes select or design photoactive molecules that will act as optimal carriers in liquid membranes under double illumination.     

Structure and dynamics of N,N-diethyl-N-methylammonium triflate ionic liquid, neat and with water, from molecular dynamics simulations

We investigated by means of molecular dynamics simulations the properties (structure, thermodynamics, ion transport, and dynamics) of the protic ionic liquid N,N-diethyl-N-methylammonium triflate (dema:Tfl) and of selected aqueous mixtures of dema:Tfl. This ionic liquid, a good candidate for a water-free proton exchange membrane, is shown to exhibit high ion mobility and conductivity. The radial distribution functions reveal a significant long-range structural correlation. The ammonium cations [dema](+) are found to diffuse slightly faster than the triflate anions [Tfl](-), and both types of ions exhibit enhanced mobility at higher temperatures, leading to higher ionic conductivity. Analysis of the dynamics of ion pairing clearly points to the existence of long-lived contact ion pairs. We also examined the effects of water through characterization of properties of dema:Tfl-water mixtures. Water molecules replace counterions in the coordination shell of both ions, thus weakening their association. As water concentration increases, water molecules start to connect with each other and then form a large network that percolates through the system. Water influences ion dynamics in the mixtures. As the concentration of water increases, both translational and rotational motions of [dema](+) and [Tfl](-) are significantly enhanced. As a result, higher vehicular ionic conductivity is observed with increased hydration level.     

Pseudolattice theory of charge transport in ionic solutions: Corresponding states law for the electric conductivity

A statistical mechanical framework for charge transport in ionic liquid–solvent mixtures based on the existence of a statistical lattice structure (pseudolattice) throughout the whole range of concentration is reported. The ion distribution is treated in a mean-field Bragg–Williams-like fashion, and the ionic motion is assumed to take place through hops between cells of two different types separated by non-random-energy barriers of different heights depending on the cell type. Assuming non-correlated ion transport, the electrical conductivity is shown to have a maximum, arising from the competition between the concentration of charge carriers in the bulk medium and their mobilities in the pseudolattice. An explicit expression for the concentration at which this maximum occurs is given in terms of microscopic parameters, and the electrical conductivity normalized by its maximum value (κ/κ_max) is shown to follow rather closely a universal corresponding states law in concentration space when represented against the ionic concentration scaled by its value at the conductivity maximum (?_α/?_max). Ion–ion and ion–solvent interactions are explicitly considered combining the path probability method for charge transport in solid electrolytes and the Bragg–Williams approximation for interparticle interactions, and their impact on the deviations of experimental data from the universal behavior of non-correlated transport analyzed. The theoretical predictions are shown to satisfactorily predict experimental values of electrical conductivity of aqueous solutions of conventional electrolytes and of mixtures of room temperature molten salts with typical solvents.     

Determination of concentration-dependent transport coefficients in nanofiltration: Experimental evaluation of coefficients

To characterize solute transport in nanofiltration (NF) the Spiegler–Kedem equation requires that two coefficients be determined for two-component solutions (a solute in water), solute permeability ω and reflection coefficient σ. For salts both coefficients strongly and in a complex way depend on concentration, which greatly complicates their evaluation from experiments. For this reason, the parameters are usually assumed constant for a given feed and the concentration dependence is assessed from flux–rejection curves for several feeds. This procedure however ignores the fact that the solute concentration and hence the coefficients significantly vary across the membrane. One way to overcome this inconsistency and address concentration dependence is to use physical models explicitly introducing exclusion mechanism(s) and fitting relevant membrane-specific parameters, such as fixed charge or dielectric properties. This procedure often fails to produce unique values of parameters for a given membrane and different salts. In the present study a new phenomenological approach is proposed and critically analyzed, based on the assumption of a similar concentration dependence of ω and 1 − σ, previously shown to be valid under fairly general conditions, thereby the Peclét coefficient A = (1 − σ)/ω may be assumed to be independent of concentration. The coefficients and their concentration dependence for a given solute may be directly and consistently evaluated by fitting flux–rejection data for several feeds and fluxes to numeric solution of the modified transport equations without the need to invoke specific physical models. The values of transport parameters deduced in this way for representative membranes and salts allow important conclusions regarding the transport mechanism. In particular, the roles of different mechanisms in overall salt exclusion could be addressed directly from the variation of ω or 1 − σ with concentration. On the other hand, the value of the Peclét coefficient, free of the effect of salt partitioning, may be analyzed in terms of hindered transport. Using the proposed method, this value was found to be very small for studied thin-film composite membranes, which may significantly simplify the transport equations.     

Flexibility is the key to tuning the transport properties of fluorinated imide-based ionic liquids

Ionic liquids are becoming increasingly popular for practical applications such as biomass processing and lithium-ion batteries. However, identifying ionic liquids with optimal properties for specific applications by trial and error is extremely inefficient since there are a vast number of potential candidate ions. Here we combine experimental and computational techniques to determine how the interplay of fluorination, flexibility and mass affects the transport properties of ionic liquids with the popular imide anion. We observe that fluorination and flexibility have a large impact on properties such as viscosity, whereas the influence of mass is negligible. Using targeted modifications, we show that conformational flexibility provides a significant contribution to the success of fluorination as a design element. Contrary to conventional wisdom, fluorination by itself is thus not a guarantor for beneficial properties such as low viscosity.

The interplay of fluorination, flexibility, and mass affects the transport properties of imide ionic liquids. Here we show how the combination of experimental and theoretical techniques can disentangle such confounding variables.     

Studies on the selective transport of organic compounds by using ionic liquids as novel supported liquid membranes

The possibility of using room-temperature ionic liquids (RTILs) in bulk (nonsupported) and supported liquid membranes for the selective transport of organic molecules is demonstrated. A systematic selective transport study, in which 1,4-dioxane, propan-1-ol, butan-1-ol, cyclohexanol, cyclohexanone, morpholine, and methylmorpholine serve as a model seven-component mixture of representative organic compounds, and in which four RTILs based on the 1-n-alkyl-3-methylimidazolium cation (n-butyl, n-octyl, and n-decyl) are used together with the anions PF(6)(-) or BF(4)(-), immobilized in five different supporting membranes, confirms that the combination of the selected RTILs with the supporting membranes is crucial to achieve good selectivity for a specific solute. The use of the RTIL 1-n-butyl-3-methylimidazolium hexafluorophosphate, immobilized in a polyvinylidene fluoride membrane, allows an extremely highly selective transport of secondary amines over tertiary amines (up to a 55:1 ratio). The selective transport of a given solute through the RTIL/membrane system results from the high partitioning of the solute to the liquid membrane phase which, in the case of amines, is rationalized mainly by the formation of a preferential substrate/H[bond]C(2) hydrogen bonding to the imidazolium cation.