Donnan Potential Research Articles

Effects of salt- and oxygen-coupled stimuli on the reactive behaviors of hemoglobin-loaded polymeric membranes

A high-performance polymeric membrane is usually associated with excellent electrochemical and mechanical behaviors. Thereby, this paper examines the effects of salt- and oxygen-coupled stimuli on reactive behaviors of hemoglobin-loaded polymeric membranes with varying initial fixed charge densities. For capturing the coupled chemo-electro-mechanical responses of the membrane, a multiphysics model is mathematically formulated and then experimentally validated. The numerical finding unveils that the Donnan potential strength of polyacidic membrane decreases with increase of ambient oxygen level, whereas the Donnan potential of present polyampholytic membrane, at neutral pH conditions, is almost invariant towards changes of environmental salt concentration. When the environmental salt concentration is smaller than the initial fixed charge concentration of the membrane, the surface conductivity of the system is enhanced bi-linearly with increase of the salt concentration due to weakened Donnan potential strength acting over the polymer-solution, while the ion transport in the system is dominantly diffusion-governed if environmental salt concentration is greater than the initial fixed charge concentration of the membrane. Ultimately, these findings can be employed to systematically design and optimize the dual salt-oxygen reactive hemoglobin-loaded polymeric membrane.

Ion Transport through Perforated Graphene

We investigated the dependence of ion transport through perforated graphene on the concentrations of the working ionic solutions. We performed our measurements using three salt solutions, namely, KCl, LiCl, and K2SO4. At low concentrations, we observed a high membrane potential for each solution while for higher concentrations we found three different potentials corresponding to the respective diffusion potentials. We demonstrate that our graphene membrane, which has only a single layer of atoms, showed a very similar trend in membrane potential as compared to dense ion-exchange membranes with finite width. The behavior is well explained by Teorell, Meyer, and Sievers (TMS) theory, which is based on the Nernst–Planck equation and electroneutrality in the membrane. The slight overprediction of the theoretical Donnan potential can arise due to possible nonidealities and surface charge regulation effects.

Carbonized peat moss electrodes for efficient salinity gradient energy recovery in a capacitive concentration flow cell

The globally extractable salinity gradient (SG) energy from the mixing of seawater and river water is estimated to be 3% of worldwide electricity consumption. Here we applied carbonized peat moss (CPM) electrodes to a capacitive concentration flow cell that is capable of harvesting SG energy based on the capacitive double layer expansion (CDLE) together with the Donnan potential. The electrodes were made from the visually inexhaustible peat moss by a facile and environmental benign pyrolysis process. With two identical CPM electrodes and a cation-exchange membrane, the cell produced a peak power density of 5.33 W m−2 and an average power density of 950 mW m−2, the highest ever reported for CDLE-based techniques, using synthetic seawater (30 g L−1 NaCl) and river water (1 g L−1 NaCl). The excellent performance was a result of the macroporous structure of the CPM electrodes, the assistance of Donnan potential, and the double-channel structure of the cell. This system was durable as it could extract energy from highly saline water (300 g L−1 NaCl) and it still worked well after 100 cycles. This study provides a new method to efficiently and continuously harvest SG energy based on the CDLE without an external charge.

Concentration Flow Cells Based on Chloride-Ion Extraction and Insertion with Metal Chloride Electrodes for Efficient Salinity Gradient Energy Harvest

Salinity gradient (SG) is a natural and renewable energy source existing in estuaries, and can also be produced during various desalination and industrial processes. Here, a new method is proposed to efficiently recover SG energy based on chloride-ion (Cl–) extraction and insertion with metal chloride electrodes and the Donnan potential over a cation-exchange membrane in a concentration flow cell. Three different metal chloride electrodes (BiCl3, CoCl2, and VCl3) were investigated in the cell, and their properties after discharging in 30 g L–1 (seawater) and 1 g L–1 (river water) NaCl solutions were studied by cyclic voltammetry, electrochemical impedance spectroscopy, and X-ray photoelectron spectroscopy. The cell with BiCl3 electrodes yielded the largest power density (max. = 3.17 W m–2) compared to that of CoCl2 and VCl3 electrodes, which was higher than those of most previous technologies for SG energy recovery. Fast Cl– extraction and insertion processes were observed on BiCl3 electrodes due to small charge transfer resistance and Cl– diffusion resistance. BiCl3 was reduced to metal Bi as Cl– released from the electrode to river water, while metal Bi was oxidized to BiCl3 as Cl– inserted into the electrode from seawater.

Ion transport through single-walled carbon nanotubes: Effects of electric field and fixed surface charge

We investigate the ion permeation trends for an aqueous sodium chloride solution through negatively charged carbon nanotubes under the simultaneous effects of a concentration gradient and an electric field using Molecular Dynamics simulations. A two-stage ion transport process was observed that resulted in a tunable effective ion flux toward the low concentration reservoir wherein the first stage resembled an electric-field assisted counter-ion (sodium) migration to the downstream reservoir for a short period of time followed by a second stage consisting of diffusion-driven electrolyte transport governed by the strength of the Donnan potential formed by the fixed charge on the nanotube.

Zeta Potential, Effective Membrane Charge and Donnan Potential for TiO2 NF Ceramic Membrane

Nanofiltration (NF) ceramic membrane have found increasing applications particularly in wastewater and water treatment. In order to estimate and optimize the performance of NF membranes, the membrane should be characterized correctly in terms of their basic parameters such as effective pore radius (rp) and equivalent effective thickness as well as effective surface charge ( ), the effective charge density ( ) and Donnan potential ( ). The impact of electrokinetic (zeta) potential on the membrane surface charge density, effective membrane charge density and Donnan potential at two different concentrations of the reference solutions 0.001, 0.01 M sodium chloride at various pH values from 3 to 9, and effective pore radius (rp) for nominal 0.9 nm ceramic TiO2 NF membrane were evaluated. Experiments were conducted at cross flow (1.0 m/s) using Microelectrophoresis technique for measuring membrane zeta potential, effective pore radius, and Donnan steric pore model (DSPM). The TiO2 membrane isoelectric point (net membrane charge equals zero) was found at pH of 3.7, 3.5 for 0.001 and 0.01 M NaCl respectively. The results showed that the NF membrane zeta potential changes its sign from positive to negative after the isoelectric point. The evaluated effective pore radius was found to be equal to 0.56 nm by using (DSPM) and the membrane equivalent effective thickness equals to (2×10-6 m).

CFD Modelling of an Electrodialysis Cell

Electrodialysis (ED) cells are based on the selective transport of ions through membranes which ideally exclude the co-ions, so that when a potential difference is applied to the cell all ions are transported in solution but only the counter ions can cross the membrane. Thus, concentration polarization occurs in solutions adjacent to membrane surfaces due to the different transport number between the membrane and the solution. The concentration profiles formed in the solution near the membrane depends on the mass transport fluxes and hydrodynamic pattern in the channel; operating conditions and geometrical configuration of the cell affect greatly the concentration polarization [1]. Therefore, the performance of ED cells depends not only on the membrane properties but also on the electrolyte hydrodynamics being important to provide an adequate flow patter avoiding channeling, stagnant zones, jet formation, among others flow deviations. Keeping a homogeneous flow patter minimizes variations of mass transfer fluxes and current density over the membrane surface preventing high polarization zones that could give rise to water dissociation, low efficiency and premature membrane failure. The examination of relevant mass transport mechanisms by modelling can help to evaluate the effect of design characteristics and operating conditions on the performance of an electrodialysis cell through the analysis of concentration, potential and current density distributions. In this task, CFD has proven to be a valuable tool for the analysis of flow and mass transfer in membrane separation systems [2]. Therefore, this work presents the modelling of a laboratory ED cell coupling hydrodynamics and mass transport, taking into consideration changes of Donnan potential. The flow pattern inside channels of ED cell were obtained by 3D CFD modeling and the results were used to calculate the residence time distribution (RTD) to compare with experimental RTD. The hydrodynamic behavior was used then to solve the mass transport model to obtain a description of the concentration distribution of each of the ionic species in the cell, as well as of the amounts derived as fluxes of each of the components, current density and Donnan potentials at every point of the membrane.[1] Gurreri L., Tamburini A., Cipollina A., Micale G., Ciofalo M., CFD prediction of concentration polarization phenomena in spacer-filled channels for reverse electrodialysis J. Membr. Sci. 468, 133–148 (2014).[2] Fimbres-Weihs G.A., Wiley D.E., Review of 3D CFD modeling of flow and mass transfer in narrow spacer-filled channels in membrane modules, Chem. Eng. Process. 49 759–781 (2010).

Improvement in design of electrodialysis desalination plants by considering the Donnan potential

Electrodialysis desalination (ED) is an efficient process to desalinate brackish water and to minimize brine salinities to the level of seawater salinity. From the many models reported in the literature, some are simple but have a limited accuracy while others are complicated with a good accuracy. In this context, we explore the improvement of a fundamentally ‘lumped’ model by considering the voltage drop at the interfaces between membranes and solutions (which is the so-called Donnan potential) while conserving the model simplicity. The present model is developed by accounting for an electrical resistance of the Donnan potential in the total cell pair resistance. The results are presented in terms of total membrane area, flow path length, number of stacks and specific energy consumption. The results show that the improvement resulting from involving the Donnan potential was substantial for a high difference between the feed and product salinities as well as for low salinities (<500 ppm) of the product water and low flow velocities (<0.05 m/s). In general, the inclusion of Donnan potential improved the results from 4.4% up to 39.2% based on the studied cases.

Modelling the transport of ions and electrochemical regeneration of the resin in a hybrid ion exchange/electrodialysis process for As(V) removal

This paper presents the 2D modeling of a laboratory scale ion exchange/electrodialysis (IXED) flow cell for removal of As(V) ions from water. The cell consists of a central compartment (DS) delimited by two anion membranes and packed with anion exchange resin, one compartment on each side of the central compartment (CC and AC compartment) lined with a cation exchange membrane and a rinse compartment at each end of the cell. The developed model comprises: the anion exchange in the resin bed in a process controlled by the mass transport rate; the ion transport in the solutions of resin-free compartments, in the membranes and resin, based on Nernst–Planck equation; and enhanced water dissociation at the anion membrane/solution interface. The obtained results show the potential profiles, Donnan potential, concentration polarization and the contribution of each mechanism (diffusion and migration) to ion transport rate as well as the effect of the potential difference on water dissociation rate along the membrane surface. The results show that, at typically low arsenic concentrations in arsenic removal processes, water dissociation plays a key role in ion exchange resin regeneration, process whose intensity grows as the cell potential rises. Moreover, the non-homogeneous distribution of current produces uneven resin regeneration that depends on design and operating parameters. The ion exchange/electrodialysis model is applied to the IXED cell operating in recirculation mode by using individual tanks connected to each cell compartment to describe the experimental batch behavior where arsenic concentration varied from (initial) 13.3 ppm to (final concentration) less than 0.01, 8.9 and 21.3 ppm in DS, CC and AC compartments, respectively, at an operating current density of 8.4 A m−2 removing 99.9% of arsenic in DS compartment with 18.9% of total current efficiency. The model results of As(V) concentration decline in the solution flowing over the ion exchange bed agree very closely with experimental data; however, the As(V) concentration results in the resin-free compartments show deviations from experimental data during the process with 6 and 16% deviations at the end of the batch. These deviations are attributed to model assumptions, in particular to the effect of diverse, non-considered, As(V) ion species.

Потенциометрическое определение метионина в щелочных растворах с помощью мембран Nafion и МФ-4СК, подвергшихся обработке и модификации

Разработаны массивы перекрестно чувствительных ПД-сенсоров (аналитический сигнал – потенциал Доннана) на основе мембран Nafion и МФ‑4СК, подвергшихся модификации и обработке, для определения анионов и цвиттерионов метионина совместно с катионами калия в щелочных растворах. Выявлено влияние кислотно-основных свойств и объемной доли наночастиц гидратированных оксидов ЭO2 (Э=Ce, Zr, Si), вводимых в мембраны разными методами, на перекрестную чувствительность ПД-сенсоров в исследуемых растворах. Выявлена зависимость чувствительности ПД-сенсоров к анионам и цвиттерионам метионина от диффузионной проницаемости мембран, подвергшихся обработке при различных температуре и относительной влажности. Выбраны образцы, обеспечивающие достаточно низкие значения относительной погрешности и относительного стандартного отклонения определения анионов и цвиттерионов метионина совместно с катионами калия в диапазоне концентраций от 1.0·10‑4 до 5.0·10‑2 М, не смотря на переменные значения рН растворов, изменяющиеся в широком диапазоне (от 8 до 11).

On the origin of membrane potential in membranes with polarizable nanopores

We report a new mechanism for the generation of membrane potential in polarizable nanoporous membranes separating electrolytes with different concentrations. The electric field generated by diffusion of ions with different mobilities induces a non–uniform surface charge, which results in charge separation inside the nanopore. The corresponding Donnan potentials appear at the pore entrance and exit leading to a dramatic enhancement of membrane potential in comparison with an uncharged non–polarizable membrane. At high concentration contrast, the interaction between electric field and uncompensated charge at a low concentration side results in the development of electrokinetic vortices. The theoretical predictions are based on the Space–Charge model, which is extended to nanopores with polarizable conductive surface for the first time. This model is validated against full Navier–Stokes, Nernst–Planck, and Poisson equations, which are solved in a high aspect ratio nanopore connecting two reservoirs. The experimental measurements of membrane potential of dielectric and conductive membranes in KCl and NaCl aqueous solutions confirm the theoretical results. The membranes are prepared from Nafen nanofibers with ∼10nm in diameter and modified by depositing a conductive carbon layer. It is shown theoretically that the membrane potential enhancement becomes greater with decreasing the electrolyte concentration and pore radius. A high sensitivity of membrane potential to the ratio of ion diffusion coefficients is demonstrated. The described phenomenon may find applications in precise determination of ion mobilities, electrochemical and bio–sensing, as well as design of nanofluidic and bioelectronic devices.

Donnan-Potential Sensors Based on Zirconia-Modified Nafion Membranes Treated under Different Conditions for the Determination of Amino Acids with Several Nitrogen-Containing Groups

The effect of heat treatment at varying relative humidity and mechanical deformation on the properties of Nafion perfluorosulfonic cation-exchange membranes and Nafion-based hybrid materials containing hydrated zirconia nanoparticles has been studied. It has been shown that the treatment of the materials makes it possible to change their water uptake, ionic conductivity, and diffusion permeability over wide ranges. Variations in the water uptake and intrapore space volume of the membranes provided by their treatment and modification have led to a decrease in the sensitivity of DP-sensors (the analytical signal is the Donnan potential) to interfering hydroxonium cations in arginine and histidine solutions in 1.5−5 times. The material samples providing a high accuracy of determination of amino acid ions in a concentration range from 1.0 × 10–4 to 1.0 × 10–1 mol/L at pH < 7 have been selected.

Determination of sulfur-containing anions in alkaline solutions using arrays of DP-sensors based on hybrid perfluorinated membranes with proton-donor dopants

The influence of proton-donor properties and concentration of dopant nanoparticles introduced into Nafion and MF-4SС perfluorosulfonic cation-exchange membranes on the characteristics of cross-sensitive DP-sensors (sensors whose analytical signal is the Donnan potential) in alkaline solutions of sulfur-containing organic compounds were studied. The dopants were acid salts of heteropoly acids (HPAs) and hydrated silica SiO2 and zirconia ZrO2 surface-modified with sulfur-containing groups and an acid HPA salt. A correlation was revealed between the DP-sensor sensitivity to anions (and zwitter-ions) in alkaline solutions, size and proton-donor ability of the added particles, and diffusion permeability of hybrid membranes. Optimum compositions of membranes for arrays of cross-sensitive DP-sensors ensuring the simultaneous determination of cations and anions (and zwitter-ions) in the test solutions with an error of less than 18% were selected.

Potentiometric Cross-Sensitive Sensors Based on Perfluorinated Membranes Treated at Different Relative Humidity for Codetermination of Cations and Anions in Alkaline Solutions of Amino Acids

The results of studying characteristics of potentiometric DP-sensors (sensors with the Donnan potential as their analytical signal) are presented for alkaline solutions of a sulfur-containing amino acid with perfluorosulfonic cation exchange membranes subjected to thermal treatment and mechanical deformation at different relative humidity. Correlation between the distribution of sensitivity of DP-sensors towards cations and anions and diffusion permeability of membranes was found. A multisensor system including two DP-sensors based on membranes with optimized properties and a glass electrode for codetermination of potassium cations and amino acid anions and zwitterions in solutions at pH >7 are developed.

High Electrical Power Densities from Salinity Gradients By Combining Electrode and Donnan Potentials in a Single Electrochemical Cell

Salinity gradients exist when two waters have different salt concentrations (e.g., when freshwater reaches seawater at coasts or when desalination brine is mixed with less saline water). Salinity gradients contain an immense amount of potential energy, which can theoretically provide 40% of the global electrical demand. One means to harvest salinity gradient energy is to use electrochemical techniques. In an electrochemical cell, a voltage can be created by using salinity gradients to alter electrode potentials in Capacitive Mixing or creating Donnan potentials across ion-exchange membranes in Reverse Electrodialysis. The main challenge with these techniques is that they yield power densities that are too low for commercialization (Capacitive Mixing: ~0.4 W/m2, Reverse Electrodialysis: ~3 W/m2). Here, we combined these two types of potentials in a single electrochemical cell, greatly increasing power densities to values that exceed 12 W/m2 when mixing synthetic freshwater and seawater. We examined how cell design and operating parameters as well as electrode and membrane materials influenced power production and energy efficiency. The results suggest that this type of cell may be used to effectively harvest salinity gradient energy at coasts and produce electricity from saline desalination brines.

Applying a modified Donnan model to describe the surface complexation of chromate to iron oxyhydroxide agglomerates with heteromorphous pores

In this study, a modified Donnan model (mDM) is incorporated into surface complexation model (SCM) to better understand the physicochemical processes for adsorption of hexavalent chromium, Cr(VI), on porous iron oxyhydroxide agglomerates (IOAs). The mDM includes a chemical potential term μatt to account for ionic transport and electrostatic interaction in micropores (dmi<2nm) which is usually neglected in typical Donnan model (tDM). To estimate the parameters of mDM in a simple and accurate way, a rigorous protocol was presented. First, the prepared IOAs was characterized with a heteromorphous pore structure (i.e., co-existing micropores and macropores, dma>2nm) demonstrating high Cr(VI) adsorption in a broad range of ionic strengths. The batch data was then fitted with Donnan model in PHREEQC to obtain Stern (ψS) and Donnan (ψD) potentials used for μatt calculation. The decreasing μatt values with ionic strength indicated obstructing effect of electrolyte ions on Cr(VI) uptake in micropores. Finally, the ionic activity coefficients and reaction constants were corrected using Pitzer model due to the high level electrolytes accumulated in the Donnan layer through osmotic and electrostatic attraction. Results of this study have captured the effects of inner structure of IOAs on Cr(VI) uptake and quantitatively discerned the contribution of micropores and macropores for adsorption reactions at different ionic strengths.

Effect of solvent polarization on electric double layer of a charged soft surface in an electrolyte solution

We study the electric double layer near a charged soft surface by using a mean-field approach including non-uniform size effect and solvent polarization. Based on a free energy model, electrostatic potential and number densities of water and ions are obtained numerically by solving coupled differential equations including the Poisson's equation. We find that the solvent polarization significantly affects electrostatic potential, ion number densities and permittivity in an electrolyte solution near a charged soft surface. We prove that the consideration of the solvent polarization increases the magnitude of Donnan potential. We also demonstrate that within the fixed charge layer the number densities of counterions and coions are slightly smaller than when the solvent polarization is not considered. An increase in the ionic size enhances the influence of solvent polarization on the electrostatic properties within the fixed charged layer of charged soft surface. In the region of high surface-charge-density, the permittivity and the number density of water dipoles considerably decrease due to water polarization.

Monovalent and divalent ion sorption in a cation exchange membrane based on cross-linked poly (p-styrene sulfonate-co-divinylbenzene)

Many fundamentals of ion sorption in ion exchange membranes (IEMs) are not fully understood, and few modern studies focus on multivalent ion sorption, despite the importance of divalent ion transport properties in water purification applications. Here, MgCl2 and CaCl2 sorption in a commercial cross-linked, styrene-divinylbenzene cation exchange membrane (CEM) with fixed sulfonate groups was measured and compared with NaCl, LiCl and KCl sorption in the same material. The data were correlated with counter-ion size and valence, as well as membrane water content. Divalent salts had higher sorption coefficients than monovalent salts, even though membrane water content significantly decreased in the presence of divalent counter-ions. The Donnan potential is weaker in the presence of multivalent counter-ions, which increases co-ion sorption, contributing to the observed increase in salt sorption coefficients for divalent salts. Ion activity coefficients in the membrane were calculated and compared to predictions of the recently proposed Manning-Donnan model. This model showed much better agreement with the experimental data than the ideal Donnan model, suggesting that ion non-ideality in the membrane is important when analyzing ion sorption and transport in IEMs.

Pure water and energy production through an integrated electrochemical process

In this study, an electrochemical integrated process was developed that integrates a three-pass capacitive deionization (CDI) with capacitive donnan potential (CDP) for water and energy production. Energy required to operate the desalination process CDI was partially fulfilled through the use of CDP process, which in turn reduced the use of fossil fuel energy sources and the CDI brine disposal. Electrochemical process integration with a novel three-pass desorption method increased the water recovery and energy production. Results indicated that almost 95.7% water desalinated and salinity power gradient were produced through the provided design methodology. Performance evaluation graphs revealed that the concentration gain ratio and water recovery were increased up to 20 and 96%, respectively, with the increase in desorption current to 15 A. In addition, 1.4 kJ L−1 energy consumption for water production without process integration was reduced to 0.35 kJ L−1 through the implementation of the proposed system.

High power densities created from salinity differences by combining electrode and Donnan potentials in a concentration flow cell

A concentration flow cell combines electrode and Donnan potentials, enabling high power densities from salinity differences.