Counterion Diffusion Coefficients Research Articles

Understanding the influence of sodium chloride concentration on ion diffusion in charged polymers

Previous observations made on sulfonated polysulfones equilibrated with solutions of increasing salinity, where salt diffusion coefficients increase concurrently with reductions in water content driven by osmotic de-swelling, are currently unexplained. To further explain the molecular underpinnings of these observations, we characterized the influence of external salt solution concentration on the average salt and ion diffusion properties of two sulfonated polymers: a model cross-linked material (XLAMPS) and a series of sulfonated polysulfones (HQ:BP – XX). Analysis of the average salt and co- and counter-ion diffusion coefficients in these polymers suggest that the increase in charge screening (of electrostatic interactions between anionic sulfonate groups and co-ions) that occurs with increasing salinity affects the salt diffusion coefficients of sulfonated polysulfone in a manner that is different from what would be expected based on changes in water content alone and from what was observed for XLAMPS. Free volume theory describes the influence of these electrostatic effects on salt diffusion using a parameter related to the characteristic free volume element size necessary for diffusion. The results and analysis suggest that charge screening reduces the characteristic free volume element size necessary for diffusion in sulfonated polysulfone, which provides an explanation for the observed increase in average salt diffusion coefficients with increased salinity.

Study of the Thermochemical Effect on the Transport and Structural Characteristics of Heterogeneous Ion-Exchange Membranes by Combining the Cell Model and the Fine-Porous Membrane Model.

For the first time, based on the joint application of the fine-porous and cell models, a theoretical analysis of the changing transport and structural characteristics of heterogeneous polymeric ion-exchange membranes (IEMs) MK-40, MA-40, and MA-41 after exposure to elevated temperatures in water and aggressive media (H2SO4 and NaOH solutions), as well as after long-term processing in electrodialyzers of various types, was carried out. The studied membranes are composites of ion-exchange polymers with polyethylene and nylon reinforcing mesh. The external influences provoke the aging of IEMs and the deterioration of their characteristics. The transport properties of IEMs are quantitatively described using five physicochemical parameters: counterion diffusion and equilibrium distribution coefficients in the membrane, characteristic exchange capacity, which depends on the microporosity of ion-exchanger particles, and macroscopic porosity at a known exchange capacity of IEMs. Calculations of the physicochemical parameters of the membranes were performed according to a specially developed fitting technique using the experimental concentration dependences of integral diffusion permeability and specific electrical conductivity, and their model analogs. This made it possible to identify and evaluate changes in the membrane micro- and macrostructure and examine the process of artificial aging of the IEM polymer material due to the abovementioned external impacts.

NMR investigation of counterion binding to undecyl LL-leucinevalanate micelles

NMR spectroscopy was used to investigate the binding of cationic counterions to anionic micelles formed by undecyl LL-leucinevalaninate (und-LV). Amino acid-based surfactants like und-LV are green alternatives to commercial surfactants. Monomeric and polymeric forms of und-LV micelles have also been used as chiral selectors in capillary electrophoresis (CE) separations. The counterions investigated were Na+, the tetraethylammonium ion, L-Lysine, 1,4-diaminobutane, 1,6-diaminohexane, and cis and trans isomers of 1,2-diaminocyclohexane and 1,4-diaminocyclohexane. NMR measurements of counterion and micelle diffusion coefficients were used to calculate micelle radii and the mole fraction of counterion molecules bound to the micelles. Two-dimensional NMR experiments were used to investigate the structures of the counterion: micelle complexes. The mole fraction of bound counterions did not change with pH in solutions containing Na+ or tetraethylammonium counterions. With all other counterions, however, the mole fraction of micelle-bound counterions was higher below pH 10 when counterions had a + 1 or +2 charge, and lower above pH 10–10.5 when the counterions were neutral or zwitterionic. Changes in micelle radii with pH and two-dimensional NMR experiments suggested that L-Lysine, 1,4-diaminobutane, and 1,6-diaminohexane bound parallel to the micelle surface with their amine functional groups interacting with different surfactant monomers. In contrast, the diaminocyclohexane isomers were found to bind perpendicular to the micelle surface. The mole fractions of micelle-bound cis-1,4-diaminocyclohexane and trans-1,4-diaminocyclohexane were very similar to one another. However, with 1,2-cyclohexanediamine, at low pH the mole fraction of micelle-bound counterions was larger for the cis isomer than for the trans isomer.

Structure and Diffusion of Ionic PDMS Melts.

Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.

Electron transfer controlled by solvent and counter-anion dynamics in electrochemistry of viologen-type ionic liquid

Temperature-dependent diffusion coefficients (DO) and heterogeneous electron transfer rate constants (k0) were measured for the viologen dication (V2+) in 1-butyl-1′-heptyl-4,4′-bipyridinium bis[(trifluoromethane)sulfonyl]imide [C4VC7][Tf2N]2 redox-active ionic liquid (RAIL) and its solution. The measurements were made in three systems: (1) 10 mM of [C4VC7][Tf2N]2 dissolved in 0.1 M K[Tf2N]/acetonitrile (an organic electrolyte), (2) 10 mM [C4VC7][Tf2N]2 dissolved in a 1-n-hexyl-3-methylimidazolium tris(pentafluoroethyl)-trifluorophosphate, [HMIm][FEP] ionic liquid (IL) (an ionic liquid (IL) electrolyte), and (3) the undiluted RAIL of 1.68 M [C4VC7][Tf2N]2 with no additional solvents or supporting electrolytes. At 25 °C, the DO values in systems (1), (2), and (3) were 8.2 × 10−6, 6.7 × 10−8, and 1.3 × 10−9 cm2 s−1, and the k0 values were 1.1 × 10−2, 3.6 × 10−3, and 2.0 × 10−5 cm s−1, respectively. Temperature-dependent DO and k0 values were further interrelated to investigate heterogeneous interfacial electron transfer processes in systems (2) and (3). Solvent dynamics and counter-ion relaxation processes were used to describe the results. In system (3), k0 values were proportional to both DO and counter-ion diffusion coefficients (DCIon) but inversely proportional to the viscosity (η). Moreover, almost the same magnitude of thermal activation barrier (∼64 kJ mol−1) was found for k0, DO, DCIon, and η−1 in the system (3). In system (2), k0 values showed a non-linear relationship with DO, DCIon and η−1, and a thermal activation barrier was found to be 22.2 kJ mol−1. These results enabled us to conclude that the V+/V2+ heterogeneous electron transfer in system (3) is controlled concurrently by solvent dynamics (segmental motion of alkyl chains attached to viologen centers) and electro-inactive counter anion motion. This work reveals an inherent dependency of heterogeneous electron transfer kinetics on the solvent and counter-ion dynamics in viologen IL systems.

Morphological Response of a Spherical Polyelectrolyte Brush to Solvent Quality and Electrostatic Interaction Strength

We study surface morphologies of a spherical polyelectrolyte brush in the presence of trivalent counterions using molecular dynamics simulations. Solvent quality and electrostatic interaction strength are varied to generate a series of structures. Through a careful analysis on snapshots of morphologies, shape factor of tethered chains, and monomer–monomer pair correlation function we find a nonmonotonic dependence of surface morphology on electrostatic strength, which represents clearly the electrostatic correlation effect mediated by the multivalent counterions. Due to the very importance of counterions, we further study the correlation effect by classifying counterions into four states, calculating the monomer–counterion pair correlation function and diffusion coefficient of counterions. Our simulation results clearly demonstrate that ordered patterns can be induced by the electrostatic correlation effect in the presence of trivalent counterions, which is absent in the system with monovalent ions. Also,...

Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation

This study presents a new framework for extracting single ion diffusion coefficients in ion exchange membranes from experimental ion sorption, salt permeability, and ionic conductivity data. The framework was used to calculate cation and anion diffusion coefficients in a series of commercial ion exchange membranes contacted by aqueous NaCl solutions. Counterion diffusion coefficients were greater than co-ion diffusion coefficients for all membranes after accounting for inherent differences due to ion size. A model for ion diffusion coefficients in ion exchange membranes, incorporating ideas from counterion condensation theory, was proposed to interpret the experimental results. The model predicted co-ion diffusion coefficients reasonably well with no adjustable parameters, while a single adjustable parameter was required to accurately describe counterion diffusion coefficients. The results suggest that for cross-linked ion exchange membranes in which counterion condensation occurs condensed counterions mi...

The Effect of Simulation Cell Size on the Diffusion Coefficient of an Ionic Surfactant Aggregate

Results of all-atom molecular dynamics simulation have been presented for salt-free aqueous solutions of sodium dodecyl sulfate at its fixed total concentration in a simulation cell containing one to four preliminarily formed quasi-stable ionic aggregates with equal aggregation numbers n = 32. The obtained molecular dynamics trajectories have been used to study the structural and transport properties of the micellar solution. The value of the counterion diffusion coefficient obtained using the Green–Kubo relation has turned out to be somewhat higher than the corresponding value calculated by the Einstein equation. The diffusion coefficients of the aggregates in the systems containing from two to four aggregates have appeared to be higher than the diffusion coefficient of a single aggregate in a cell. The mean force potential obtained for the interaction between the aggregates having aggregation number n = 32 as a function the distance between the aggregate centers of mass has a local minimum in the system containing four such aggregates.

Improvement of MCDI operation and design through experiment and modelling: Regeneration with brine and optimum residence time

Membrane Capacitive Deionization (MCDI) is an energy efficient, electrochemical desalination technology, in which ions are removed from a salty stream upon applying a constant voltage or current. The ions are stored in carbon electrodes and then released back into the stream by reversing the polarity. In this work, we aimed to assess the feasibility of using a brine stream to regenerate the MCDI unit in order to improve water recovery. We further aimed to determine the optimum residence time in the MCDI unit. To achieve these objectives, we first enhanced the ion transport model previously developed for MCDI by independently measuring the counter-ion and co-ion diffusion coefficients in the ion-exchange membranes. These experiments allowed for an asymmetric model of the MCDI unit where the voltage drop across the cation exchange membrane was greater than that across the anion exchange membrane. Using this revised model, we found that in batch operation, a brine to feed water concentration ratio of around two was optimum. In continuous operation, over 40% enhancement in water recovery could be achieved when the regeneration brine was partially recycled, but water productivity dropped. We further showed that the maximum desalination capacity did not increase beyond a critical residence time in the MCDI cell, while the water recovery decreased.

Interpenetrated triple polymeric layer as electrochemomechanical actuator: Solvent influence and diffusion coefficient of counterions

Full polymeric trilayers formed by two lateral polypyrrole-dodecylbenzoesulfate (PPyDBS) films interpenetrating a polyvinylidene fluoride (PVdF) central membrane were electrochemically characterized. Square wave voltammetric and square wave amperometric responses in 0.5M LiClO4 solutions using different solvents was undertaken with parallel video-recording of the reversible angular displacements. According to the bending movements in aqueous and ethylene glycol (EG) solutions the PPyDBS films shrunk upon oxidation and swelled during reduction: the electrochemical reactions drive the exchange of cations in both solvents. In propylene carbonate (PC) and acetonitrile (AN) solutions the PPyDBS films swelled and shrunk by oxidation and reduction, respectively, driven by the exchange of anions. Propylene carbonate and acetonitrile hinder the dissociation of the LiDBS ionic couples inside the PPyDBS film forcing the exchange of anions to compensate polarons on polypyrrole. The diffusion coefficient of the exchanged ions and the angular rates follow the sequence: aqueous>PC>AN>EG solutions. Whatever the solvent, actuators are Faradaic devices: the described angle is a linear function of the consumed charge.

Dynamics of ions in model charged porous media: Influence of polyelectrolytes

We have studied by means of Brownian dynamics simulations the dynamics of small ions in model charged porous media. We have focused on the influence on this dynamics of short polyelectrolytes with the same charge sign as the solid phase. We have compared the self-diffusion coefficients of counterions of four families of systems with different compositions (presence or not of charged obstacles and of polyelectrolytes). Our main result is that the presence of polyelectrolytes only modulates a behavior we had already observed before: In the domain where the porosity is relatively high compared to the Debye length, diffusion coefficients of counterions increase when the porosity decreases. Moreover, we have shown that, in the systems investigated here without charges on obstacles, the self-diffusion of counterions is mostly affected by the presence of polyelectrolytes and not by concentration effects, contrarily to co-ions. Also, we have seen that even if the density of the probability of presence of counterions in the vicinity of polyelectrolytes is much higher than that on obstacles, the residence time of ions around polyelectrolytes is shorter than around charged obstacles.

Molecular dynamics study of salt influence on transport and structural properties of SDS micellar solutions

The results of all-atom molecular dynamics simulations of micellization in the salt-free sodium dodecyl sulphate (SDS) aqueous solution and in the solution with added 1:1 salt (sodium chloride) are reported. Micellar systems of different size are considered in order to study size effects. The influence of added salt on transport and structural properties of the SDS micellar solutions is investigated. The formation of a larger aggregate in the presence of the salt, compared to the salt-free surfactant solution, is observed. With the increase of the salt concentration the diffusion coefficients of coions, counterions, and water molecules decrease. The diffusivity of a premicellar aggregate demonstrates the non-linear dependence on the salt concentration, while the size of the aggregate remains constant. Along with transport properties, we also studied structural properties of the SDS micellar solution: aggregation numbers and sizes of surfactant aggregates, radial distributions of ions and various atoms.

Lead removal from aqueous solutions by 732 cation‐exchange resin

AbstractKinetics and thermodynamics of the removal of Pb2+ from an aqueous solution by 732 cation‐exchange resin in hydrogen type (732‐CR) were studied in the temperature range of 298–328 K and Pb2+ concentration range of 5–50 mol/m3. The effects of ion exchange temperature and initial lead ion concentration on the time evolution of the experimental concentration for the metal ion were investigated. Ion exchange kinetics of Pb2+ onto 732‐CR follow the Nernst‐Planck equation and unreacted‐core model (UCM). The diffusion coefficients of counter ions and the efficient diffusion coefficient of lead ions within the resin were calculated. The results show that the ion exchange process is favoured under the particle diffusion control mechanism. The ion exchange isotherm data agreed closely with the Langmuir isotherm. The maximum monolayer exchange capacity for Pb2+ was found to be 484.0 mg/g at 308 K. Thermodynamic studies show that Pb2+ onto 732‐CR is spontaneous and exothermic in nature. The ion exchange processes were verified by Energy Disperse Spectroscopy (EDS).

Estimation of Ion Diffusion Coefficients at the Stagnant Layer Using TiO2 Aqueous Suspension Zeta Potential Data

The solid-liquid interface of anatase-water nanofluids has been characterized. Combined data of electrophoretic mobility and conductivity of the colloidal suspensions have been used to evaluate zeta-potentials. Plots of the suspension conductivity as a function of the bulk conductivity are essentially linear, allowing for the establishment of the entire surface conductivity. The main contribution to the surface conductivity stemmed from the counter charge behind the slip plane. Whereas the diffuse layer surface conductivity is generic, the stagnant layer conductivity is system-specific; therefore, evaluation of the later requires insight into such properties as the distribution of charges and lateral mobilities. Based on a simple analytical theory we can also estimate the diffusion coefficient of counterions in the stagnant layer. The results lead to a good agreement between theory and experiment.

Theory of the formation of the electric double layer at the ion exchange membrane-solution interface.

This work aims to extend the study of the formation of the electric double layer at the interface defined by a solution and an ion-exchange membrane on the basis of the Nernst-Planck and Poisson equations, including different values of the counter-ion diffusion coefficient and the dielectric constant in the solution and membrane phases. The network simulation method is used to obtain the time evolution of the electric potential, the displacement electric vector, the electric charge density and the ionic concentrations at the interface between a binary electrolyte solution and a cation-exchange membrane with total co-ion exclusion. The numerical results for the temporal evolution of the interfacial electric potential and the surface electric charge are compared with analytical solutions derived in the limit of the shortest times by considering the Poisson equation for a simple cationic diffusion process. The steady-state results are justified from the Gouy-Chapman theory for the diffuse double layer in the limits of similar and high bathing ionic concentrations with respect to the fixed-charge concentration inside the membrane. Interesting new physical insights arise from the interpretation of the process of the formation of the electric double layer at the ion exchange membrane-solution interface on the basis of a membrane model with total co-ion exclusion.

Influence of counter ions in electrochemical properties and kinetic parameters of poly tyramine electroactive film

This work present that the electrodeposited poly tyramine (PTy) film by using potentiostatic method on the surface of the graphite electrode is fractal object with semiconductor properties. Electrosynthesized polymers in the presence of the different anions have been characterized by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The effect of different anions and electrosynthesis parameters on the morphology, kinetic parameters and fractal dimension of the polymer was evaluated. Diffusion coefficient of counter ions calculated from the slope of the Warburg line in the Nyquist plot. A value of γ that is the characteristic of anomalous diffusion is obtained by EIS method and then the relation between fractal dimension and anomalous diffusion has been investigated.

Dielectric relaxations of poly(acrylic acid)-graft-poly(ethylene oxide) aqueous solution: Analysis coupled with scaling approach and hydrogen-bonding complex

Dielectric properties of poly(acrylic acid)-graft-poly(ethylene oxide) (PAA-g-PEO) aqueous solution were measured as a function of concentration and temperature over a frequency range of 40 Hz to 110 MHz. After subtracting the contribution of electrode polarization, three relaxation processes were observed at about 20 kHz, 220 kHz, and 4 MHz, and they are named low-, mid- and high-frequency relaxation, respectively. The relaxation parameters of these three relaxations (dielectric increment Δε and relaxation time τ) showed scaling relations with the polyelectrolyte concentration. The mechanisms of the three relaxations were concluded in light of the scaling theory: The relaxations of low- and mid frequency were attributed to the fluctuation of condensed counterions, while the high-frequency relaxation was ascribed to the fluctuation of free counterions. Based on the dielectric measurements of varying temperatures, the thermodynamic parameters (enthalpy change ΔH and entropy change ΔS) of the three relaxations were calculated and these relaxation processes were also discussed from the microscopic thermodynamical view. In addition, the impacts of PEO side chains on the conformation of PAA-g-PEO chains were discussed. PEO side chains greatly strengthen the hydrogen-bonding interactions between PAA-g-PEO chains, resulting in the chains overlapping at a very low concentration and the formation of a hydrogen-bonding complex. Some physicochemical parameters of PAA-g-PEO molecules were calculated, including the overlap concentration, the effective charge of the chain, the friction coefficient, and the diffusion coefficient of hydrogen counterions.

Electrochemical study of anomalous diffusion and fractal dimension in poly ortho aminophenol electroactive film: Comparative study

The poly ortho aminophenol (POAP) films were electropolymerised on graphite electrode using potentiostatic method. POAP films were also characterized by electrochemical impedance spectroscopy (EIS) in wide frequency range. The fractal dimension of poly ortho aminophenol (POAP) films in the presence of different counter ions was investigated. The effect of different anions on the electron conduction of POAP was explained in terms of their abilities to reduce repulsive interactions between redox sites and fractal dimension of the polymer. Diffusion coefficient of counter ions calculated from the slope of the Warburg line of impedance response of the film. A value of γ that is the characteristic of anomalous diffusion is obtained by EIS method and then the relation between fractal dimension and anomalous diffusion has been investigated. The resulting Mott–Schottky plot of the polymer capacitance describes the reduced polymer as a p-type semiconductor.

Self-diffusion of ions in charged nanoporous media

Self-diffusion coefficients of ions of a charge and size symmetric +1 : −1 electrolyte were studied in the presence of ionic obstacles carrying ten negative elementary charges within a “soft” version of the primitive model of electrolytes. The Brownian dynamics method was used to calculate the diffusion coefficients of mobile species. Simulations were complemented with the replica Ornstein–Zernike theory for partly-quenched systems to calculate the activity coefficients of individual ions and the Donnan exclusion coefficient. We study the influence of (i) the size of the pores, which varies with the concentration of quenched charged nanoparticles, and (ii) the presence of added salt on the mobility and thermodynamics of small ions. We show that for dilute matrices (low concentration of charged obstacles) the diffusion coefficient of counterions is smaller or equal to that of co-ions. The opposite is true for concentrated matrices: here counterions are considerably faster than co-ions. In dilute matrices, where obstacles are distributed at larger distances, the counterions are strongly attracted by fixed obstacles. As a consequence, they are slowed down in comparison with the co-ions. In concentrated matrices, where the average size of the pores is small, the counterions can take advantage of hopping from one obstacle to another, whereas the co-ions, repelled by the obstacles, need to diffuse in the space between the layers of counterions surrounding the obstacles. Thermodynamic calculations are consistent with the Brownian dynamics results.

How water and counterions diffuse into the hydrated montmorillonite

Molecular dynamics simulations have been performed to study the diffusive transport properties of water and counterions in 1-, 2- and 3-layer hydrated Wyoming-type montmorillonite (MMT). The considered counterions included in the clay are monovalent cations, such as Li +, Na +, K +, Rb +, Cs +, and divalent cations, such as Ca 2+, Ni 2+, Zn 2+ and Pb 2+. The diffusion simulation results of Li-, Na-, K-, Cs-MMT, based on NVE ensemble and SPC/E water model, compared well to available experimental quantities and previous simulations, which permit us to study the diffusion behaviour of heavy metal counterion including in the different hydrated montmorillonite. Our simulation results show that the diffusion coefficients of both water molecule and counterions increase versus the quantity of water content. At the same hydrated state, the diffusion of cations strongly depends on their size, weight and capacity of attracting water. Monovalent cations diffuse always much faster than divalent ones. Although the increasing of hydrate degree can raise the diffusion coefficient of divalent heavy cations, the activity of these heavy counterions is still very weak. The diffusion of cations in the interlayer space of clay is much weaker than that in bulk water. That means the presence of charged clay has great influence on the diffusion of cations, which change totally the diffusion behaviour of cations.