Donnan Potential Research Articles

Donnan equilibrium revisited: Coupling between ion concentrations, osmotic pressure, and donnan potential

This paper discusses the little-known fact that Donnan’s equilibrium criteria established over 100 years ago neglected the coupling between ion concentrations and the osmotic pressure. Such coupling can be treated based on general thermodynamic considerations including the solvent equilibrium, leading to a membrane potential that consists of not only the classical Donnan potential term but also an additional term due to the osmotic pressure, and the existence of a membrane potential even when the impermeable species are not charged. This coupled treatment conflicts with the well-established Poisson–Boltzmann equation and Nernst–Planck equation, but is consistent with the extension of these equations including the solvent effects by Freise and Schlogl, enables us to view the electrical double layer equilibrium as Donnan equilibrium.

Diffusiophoresis of a Soft Particle as a Model for Biological Cells

We derive the general expression for the diffusiophoretic mobility of a soft particle (i.e., polyelectrolyte-coated hard particle) in a concentration gradient of electrolytes for the case in which the particle’s core size is large enough compared with the Debye length. Therefore, the particle surface can be regarded as planar, and the electrolyte concentration gradient is parallel to the core surface. The obtained expression can be applied for arbitrary values of the fixed charge density of the polyelectrolyte layer and the surface charge density of the particle core. We derive approximate analytic mobility expressions for soft particles of three types, i.e., (i) weakly charged soft particles, (ii) soft particles with a thick polyelectrolyte layer, in which the equilibrium electric potential deep inside the polyelectrolyte layer is equal to the Donnan potential, and (iii) soft particles with an uncharged polymer layer of finite thickness.

Modeling the Gibbs–Donnan effect during ultrafiltration and diafiltration processes using the Poisson–Boltzmann theory in combination with a basic Stern model

The Gibbs–Donnan effect is a well-known phenomenon causing ions to be distributed unevenly across semi-permeable membranes that are permeable to ions but not to larger macromolecules such as proteins. In protein ultrafiltration and diafiltration (UF/DF) processes, this effect often leads to discrepancies between the pH and excipient concentrations in the final drug substance and in the DF buffer. In this work, a model describing the retentate and permeate composition throughout combined UF/DF processes is introduced. The model accounts for volume exclusion effects and electrostatic interactions between ions and the protein based on the Poisson–Boltzmann theory in combination with a basic Stern model. Advantages and limitations of the proposed model were analyzed using UF/DF experiments with multiple diafiltration buffers and proteins. A comparison between simulated and experimental permeate data showed good agreement for low to moderate Donnan potentials but model limitations for high Donnan potentials at protein concentration larger 100 gL -1 . In contrast, simulated retentate data showed good agreement for both low and high Donnan potentials and for protein concentrations up to 190 gL -1 . It was demonstrated that in this high protein concentration regime, the applied basic Stern model provides more accurate predictions compared to previous theories based on the Poisson–Boltzmann theory alone. This makes the model a valuable tool to describe discrepancies between pH and excipient concentrations in the final drug substance and DF buffer for highly concentrated protein formulations. As model predictions are based solely on structural information on the protein and the composition of the DF buffer, the model is particularly beneficial at an early stage in process development to streamline process development and improve process understanding. • Introduction of a model to describe the Gibbs–Donnan effect in UF/DF processes. • Advanced implementation of the cell model approximation. • Calibration solely based on structural information on the protein. • Validation using various proteins (up to 190 g/L) and buffer systems.

Differences in Bioenergetic Metabolism of Obligately Alkaliphilic Bacillaceae Under High pH Depend on the Aeration Conditions.

Alkaliphilic Bacillaceae appear to produce ATP based on the H+-based chemiosmotic theory. However, the bulk-based chemiosmotic theory cannot explain the ATP production in alkaliphilic bacteria because the H+ concentration required for driving ATP synthesis through the ATPase does not occur under the alkaline conditions. Alkaliphilic bacteria produce ATP in an H+-diluted environment by retaining scarce H+ extruded by the respiratory chain on the outer surface of the membrane and increasing the potential of the H+ for ATP production on the outer surface of the membrane using specific mechanisms of ATP production. Under high-aeration conditions, the high ΔΨ (ca. -170 mV) of the obligate alkaliphilic Evansella clarkii retains H+ at the outer surface of the membrane and increases the intensity of the protonmotive force (Δp) per H+ across the membrane. One of the reasons for the production of high ΔΨ is the Donnan potential, which arises owing to the induction of impermeable negative charges in the cytoplasm. The intensity of the potential is further enhanced in the alkaliphiles compared with neutralophiles because of the higher intracellular pH (ca. pH 8.1). However, the high ΔΨ observed under high-aeration conditions decreased (∼ -140 mV) under low-aeration conditions. E. clarkii produced 2.5–6.3-fold higher membrane bound cytochrome c in the content of the cell extract under low-aeration conditions than under high-aeration conditions. The predominant membrane-bound cytochrome c in the outer surface of the membrane possesses an extra Asn-rich segment between the membrane anchor and the main body of protein. This structure may influence the formation of an H+-bond network that accumulates H+ on the outer surface of the membrane. Following accumulation of the H+-bond network producing cytochrome c, E. clarkii constructs an H+ capacitor to overcome the energy limitation of low aeration at high pH conditions. E. clarkii produces more ATP than other neutralophilic bacteria by enhancing the efficacy per H+ in ATP synthesis. In low H+ environments, E. clarkii utilizes H+ efficiently by taking advantage of its high ΔΨ under high-aeration conditions, whereas under low-aeration conditions E. clarkii uses cytochrome c bound on its outer surface of the membrane as an H+ capacitor.

Acetate Degradation at Low pH by the Moderately Acidophilic Sulfate Reducer Acididesulfobacillus acetoxydans gen. nov. sp. nov.

In acid drainage environments, biosulfidogenesis by sulfate-reducing bacteria (SRB) attenuates the extreme conditions by enabling the precipitation of metals as their sulfides, and the neutralization of acidity through proton consumption. So far, only a handful of moderately acidophilic SRB species have been described, most of which are merely acidotolerant. Here, a novel species within a novel genus of moderately acidophilic SRB is described, Acididesulfobacillus acetoxydans gen. nov. sp. nov. strain INE, able to grow at pH 3.8. Bioreactor studies with strain INE at optimum (5.0) and low (3.9) pH for growth showed that strain INE alkalinized its environment, and that this was more pronounced at lower pH. These studies also showed the capacity of strain INE to completely oxidize organic acids to CO2, which is uncommon among acidophilic SRB. Since organic acids are mainly in their protonated form at low pH, which increases their toxicity, their complete oxidation may be an acid stress resistance mechanism. Comparative proteogenomic and membrane lipid analysis further indicated that the presence of saturated ether-bound lipids in the membrane, and their relative increase at lower pH, was a protection mechanism against acid stress. Interestingly, other canonical acid stress resistance mechanisms, such as a Donnan potential and increased active charge transport, did not appear to be active.

Quantitative determination of cation-π interactions between metal ions and aromatic groups in aqueous media by a hydrogel Donnan potential method.

Cation-π interactions in aqueous media are known to play critical roles in various biological activities. However, quantitative experimental information, such as the binding ratio of metal ions to aromatic groups, is hardly available due to the lack of a suitable test system and method. Herein, we proposed a hydrogel Donnan potential method to determine the binding ratio of metal ions to aromatic groups on polymer networks in aqueous media. In this method, we adopted recently developed poly(cation-π) hydrogels with a rich adjacent sequence of the cationic group and the aromatic group on the polymer network. A microelectrode technique (MET) is used to measure the Donnan potential of the poly(cation-π) hydrogels. From the Donnan potential, the binding ratios of various metal ions to aromatic groups are quantitatively determined for the first time.

Increased Donnan exclusion in charged polymer networks at high salt concentrations.

The swelling of univalent and multivalent charged polymeric networks in electrolytic solutions is studied using a classical thermodynamic model. Such systems were first modeled by Donnan, who derived an expression for the chemical potential of the ions by introducing an electric potential that is commonly referred to as the Donnan potential. This well-established theory leads to a simple quadratic relationship for the partitioning of ions between the network and the external solution. When the concentration of fixed charges in the swollen gel is large enough, the electrolyte in the external solution is "excluded" from the gel (commonly referred to as Donnan exclusion). In the standard Donnan theory, and in virtually all subsequent theories, the magnitude of Donnan exclusion decreases with increasing electrolyte concentration in the external solution. Our model predicts this is not necessarily true; we show that the magnitude of Donnan exclusion increases with increasing electrolyte concentration over a broad range of parameter space (average chain length between crosslinks, fraction of charged monomers in the network, the nature of the interactions between the ions, solvent molecules and polymer chains, and ion concentration in the external solution). We also present explicit bounds for the validity of Donnan's original theory. Model predictions are compared to simulations and experimental data obtained for a cationic gel immersed in electrolytic solutions of salts containing univalent and bivalent cations.

In Situ Evaluation of the Polymer Concentration Distribution of Microphase-Separated Polyelectrolyte Hydrogels by the Microelectrode Technique

The heterogeneous structure that exists in virtually all hydrogels has a significant influence on the resulting strength and toughness. While the internal structure has been observed with electron microscopy, it is difficult to measure the in situ local polymer concentration in the native swollen state. In this study, a modified microelectrode technique (MET) was employed to measure the Donnan potential of a heterogeneous hydrogel with a phase-separated structure. With this method, we succeeded in observing quantitative in situ polymer concentrations ranging from 10.2 μmol/L to several hundred mmol/L. From the obtained concentration profiles, we could successfully evaluate the internal phase-separated structure with a resolution of less than 0.8 μm. Using MET, we could estimate the average activity coefficient of the hydrogel, and we found a difference in concentration between the dense and sparse phases. We demonstrate that MET is a powerful method that can locally and quantitatively measure the polyelectrolyte concentration distribution within hydrogels. Furthermore, this method can be applied to cells and organs in vivo due to their similarities with polyelectrolytes. Enabling the in situ determination of the internal structures of biomaterials could have important implications toward the characterization of damaged and diseased tissues on the local scale.

Electrostatic Potential Analysis in Polyelectrolyte Brush-Grafted Microchannels Filled with Polyelectrolyte Dispersion

In this study, the model framework that includes almost all relevant parameters of interest has been developed to quantify the electrostatic potential and charge density occurring in microchannels grafted with polyelectrolyte brushes and simultaneously filled with polyelectrolyte dispersion. The brush layer is described by the Alexander-de Gennes model incorporated with the monomer distribution function accompanying the quadratic decay. Each ion concentration due to mobile charges in the bulk and fixed charges in the brush layer can be determined by multi-species ion balance. We solved 2-dimensional Poisson–Nernst–Planck equations adopted for simulating electric field with ion transport in the soft channel, by considering anionic polyelectrolyte of polyacrylic acid (PAA). Remarkable results were obtained regarding the brush height, ionization, electrostatic potential, and charge density profiles with conditions of brush, dispersion, and solution pH. The Donnan potential in the brush channel shows several times higher than the surface potential in the bare channel, whereas it becomes lower with increasing PAA concentration. Our framework is fruitful to provide comparative information regarding electrostatic interaction properties, serving as an important bridge between modeling and experiments, and is possible to couple with governing equations for flow field.

Principles of slowed hydrogen diffusion through a mucus layer.

The control of transport through mucus layers is a ubiquitous phenomenon in physiological systems. Mucus is often tasked with the mediation of passive, diffusive transport of small ionic species. However, questions remain regarding how mucin gel characteristics (charge density of the polymeric network, binding affinity of ions with mucus) govern the rate at which ions diffuse through mucus layers. Experimental studies measuring hydrogen diffusion through gastric mucus have provided conflicting results, and it is not clear if the rate of ionic diffusion through mucus layers is appreciably different than in aqueous environments (depending on experimental preparation). Here, we present a mathematical analysis of electrodiffussion of two ionic species (hydrogen and chloride) through a mucus layer. In addition to accounting for the chemical binding of hydrogen to the mucus network, we enforce a zero net current condition (as mucus layers in physiological systems are not generally electrogenic) and calculate the Donnan potential that occurs at the edge of the mucus layer. The model predicts the steady-state fluxes of ionic species and the induced potential across the layer. We characterize the dependence of these quantities on the chemical properties of the mucus gel, the composition of the bath solution, and the molecular mobility of the dissolved anion, and we show that the model predictions are consistent with a large portion of the experimental literature. Our analysis predicts that mucus layers generically slow the diffusive transport of hydrogen, but that chemical binding with the network attenuates this effect.

Electrophoresis of Liquid-Layer Coated Particles: Impact of Ion Partitioning and Ion Steric Effects.

The biomimetic core-shell nanoparticles coated with membranes of various biological cells have attracted significant research interest, because of their extensive applications in targeted drug delivery systems. The cell membrane consists of a lipid bilayer, which can be regarded as a two-dimensional oriented viscous liquid with low dielectric permittivity, compared to a bulk aqueous medium. Such a liquid layer comprised of cell membrane may bear additional mobile charges, because of the presence of free lipid molecules or charged surfactant molecules, which further results in nonzero charge along the surface of the peripheral layer. In this article, we present an analytical theory for electrophoresis of such cell membrane coated functionalized nanoparticles in the extent of electrolyte solution, considering the combined effects of finite ion size and of ion partitioning. Going beyond the Debye-Huckel approximations, we propose an analytical theory for Donnan potential and electrophoretic mobility. The derived expressions are applicable for moderate to highly charged undertaken core-shell particles when the thickness of the peripheral liquid layer greatly exceeds the electric double layer thickness. The impact of pertinent parameters on the electrophoretic response of such a particle is further discussed.

Graphene oxide proton permselective membrane for electrodialysis-based waste acid reclamation: Simulation and validation

Nowadays, the development of novel technology for economical and efficient reclamation of waste acid containing metal ions is still the top priority. The graphene oxide (GO)-based membrane has gained attention in the relevant membrane processes driven by pressure gradient, concentration difference and even Donnan potential because of its special two-dimension (2D) structure and abundant hydrophilic sites. However, its work performances for electrodialysis (ED)-based acid recovery process are still unknown. In this work, GO-based proton permselective membranes (PPM) are designed and applied in the ED-based acid recovery. Above all, the possibility of selective separating protons from metal cations by GO membrane under a direct electric field and the related influencing factors are comprehensively explored by molecular dynamic simulation. Furthermore, a series of GO-based PPMs with designed thickness, interlayer spacing and charged state are prepared by adjusting GO loading, employing different crosslinking agents and attaching the relevant polyelectrolytes. Therein, the work performances of GO-based PPMs in a typical ion substitution ED process, including the metal cation leakage, water transport phenomenon and nonideal migration of anions are investigated and compared with those of commercial membrane. Results show that GO membranes prepared and used according to the optimized conditions embrace sharp separating property between protons and metal ions which is hardly deteriorated along with the change of their relative content. On the other hand, it is noticed that the leakage of organic anions and water transport seem to be unavoidable due to the exploitation of the porous support. Obviously, this work can contribute to not only developing a novel PPM for ED but extending the applications of the 2D nanomaterial as well.

Donnan Potential across the Outer Membrane of Gram-Negative Bacteria and Its Effect on the Permeability of Antibiotics.

The cell envelope structure of Gram-negative bacteria is unique, composed of two lipid bilayer membranes and an aqueous periplasmic space sandwiched in between. The outer membrane constitutes an extra barrier to limit the exchange of molecules between the cells and the exterior environment. Donnan potential is a membrane potential across the outer membrane, resulted from the selective permeability of the membrane, which plays a pivotal role in the permeability of many antibiotics. In this review, we discussed factors that affect the intensity of the Donnan potential, including the osmotic strength and pH of the external media, the osmoregulated periplasmic glucans trapped in the periplasmic space, and the displacement of cell surface charges. The focus of our discussion is the impact of Donnan potential on the cellular permeability of selected antibiotics including fluoroquinolones, tetracyclines, β-lactams, and trimethoprim.

Constructing a selective blocked-nanolayer on nanofiltration membrane via surface-charge inversion for promoting Li+ permselectivity over Mg2+

The separation of Li+ and Mg2+ is a decisive step for achieving high-grade lithium extraction from salt-lake brines to circumvent the lithium supply shortage and sustainability. However, polymer nanofiltration membranes suffer from low lithium selectivity and are hindered by complicated preparation and miniaturized scales. Here, we report a facile surface charge-inversion strategy via a unique secondary non-aqueous medium interfacial reaction of polyethyleneimine to construct a selective positive-nanolayer on nanofiltration membranes surface for selective separation of lithium ions from concentrated magnesium/lithium mixtures. The introduction of amine moieties not only increases the Donnan potential but also improves the compactness of the membrane, which simultaneously enhances the Donnan exclusion and size sieving for the Mg2+ ion with higher valence and larger hydration ion size. The surface interaction theory (DLVO) verified that the high positive-charge density provided an excellent selectivity to allow passage of Li + but reject Mg2+, and the separation factor (SLi/Mg) achieved 12.37 at a high Mg2+/Li+ mass ratio of 150. Such highly positive transmembrane potential barrier simultaneously endowed the membrane surface with the anti-fouling performance against Ca2+. We anticipate that our facile and scalable surface charge-inversion will greatly advance lithium ions permselectivity membranes design and application in lithium extraction.

Techno-economic assessment of electrodialysis and reverse osmosis desalination plants

• Economics of electrodialysis and reverse osmosis desalination plants are compared. • The specific water cost consists of all the elements of capital and operation aspects. • Sensitivity analysis identified the most influential parameters impacting the cost model. • ED is found economically feasible when salinity is less than 9 ppt compared to RO. • Highly saline water can be desalinated with ED at about 5 $/m 3 for a salinity <100 ppt. Assessment of desalination plants is essential to evaluate potable water production, energy consumption, and economic feasibility. A design model with a boundary layer effect, water transport effect, spacer effect, and Donnan potential was used for ED desalination. Similarly, a design model is also investigated for RO desalination with and without a pressure energy recovery device. Specific product water cost is evaluated based on annual expenses consisting of energy cost, fixed cost, labor cost, membrane replacement cost, maintenance cost, chemical cost, and insurance cost. Normalized sensitivity analysis is also conducted to identify the most influential parameters impacting the cost model. It is found that ED is economically feasible when salinity is less than 7 and 9 ppt compared to RO with and without PX, respectively. The product water cost is 0.384, 0.46, and 0.494 $/m 3 for ED, RO with PX, and RO without PX, respectively, at a salinity of 5 ppt (e.g., groundwater salinity). The product water cost increases to be 1.532, 0.559, and 0.857 $/m 3 for ED, RO with PX, and RO without PX, respectively, at a feed salinity of 35 ppt (e.g., seawater salinity). Also, highly saline water can be desalinated with ED at the cost of <5 $/m 3 for a salinity <100 ppt.

Thermodynamic aspects of energy conversion systems with focus on osmotic membrane and selectively permeable membrane (Donnan) systems including two applications of the Donnan potential

Thermodynamic aspects of energy conversion systems with focus on osmotic membrane and selectively permeable membrane (Donnan) systems including two applications of the Donnan potential

A two dimensional numerical model of the membrane-divided soluble lead flow battery

Dividing the soluble lead flow battery (SLFB) is known to improve the cycle life of the SLFB by preventing failure mechanisms such as short-circuiting and by allowing electrode specific electrolyte additives. Modelling (SLFB) is a complex multiphysics problem due to the electrolyte flow, composition changes and reaction environment geometry variations associated with the deposition and dissolution of the active material as a function of state of charge. Here we studied the membrane divided SLFB using a two-dimensional, transient, numerical model, built in COMSOL Multiphysics. Divided cells using cationic and anionic ion-exchange membranes and simple, porous separators are compared with the undivided SLFB. The model successfully predicts the complex, non-linear relationship between Pb2＋ ion concentration and conductivity of the electrolyte as a function of free acid concentration. There is a deviation of less than 22 mS cm−1 between the simulated electrolyte conductivity and the experimental data. We show the conductivity of the Nafion-115 membrane in the SLFB dominated the potential drop across the membrane. However, at higher current densities, the Donnan potential becomes more dominant.

Repulsive and attractive depletion forces mediated by nonadsorbing polyelectrolytes in the Donnan limit.

In mixtures of colloids and nonadsorbing polyelectrolytes, a Donnan potential arises across the region between surfaces that are depleted of the polyelectrolyte and the rest of the system. This Donnan potential tends to shift the polyelectrolyte density profile toward the colloidal surface and leads to the local accumulation of polyelectrolytes. We derive a zero-field theory for the disjoining pressure between two parallel flat plates. The polyelectrolyte is allowed to enter the confined interplate region at the cost of a conformational free energy penalty. The resulting disjoining pressure shows a crossover to a repulsive regime when the interplate separation gets smaller than the size of the polyelectrolyte chain, followed by an attractive part. We find a quantitative match between the model and self-consistent field computations that take into account the full Poisson-Boltzmann electrostatics.

The PLB measurement for the connector in Phi29 bacteriophage reveals the function of its channel loop

The connector protein, also known as the portal protein, located at the portal vertex in the Phi29 bacteriophage has been found to play a key role in the genome DNA packaging motor. There is a disordered region, composed of 12 sets of 18-residue loops N229–N246, that has been assumed to serve as a “clamp” to retain the DNA within the pressurized capsid when DNA is fully packaged. However, the process remains undefined about how the clamping of DNA occurs and what signal is used to engage the channel loops to clamp the DNA near the end of DNA packaging. In this study, we use the planar lipid bilayer (PLB) membrane technique to study the connector with its loops cleaved. The channel properties are compared with those of the connector with corresponding wild-type loops at different membrane potentials. On the basis of the hypothesis of the Donnan effects in the flashing Brownian ratchet model, we associate the PLB experimental results with the outcomes from the relevant biochemical experiments on the proheads containing the connectors without the loops, which enables us to provide a clear picture about how the DNA clamping occurs. A mathematical relationship between the Donnan potential and the DNA packaging density is established, demonstrating that they are both in essence the same signal that is received and transmitted by the connector to dictate DNA clamping and the termination of DNA packaging. At the end of the study, the PLB technique is proposed as a viral research tool, and its potential use to study the functions of specific domains in a portal protein of the tailed bacteriophages is highlighted.

Thermoelectric Response of Ion‐Selective Membranes: Modelling and Experimental Studies

AbstractThermoelectricity of ion‐selective membrane refers to the phenomenon that the membrane potential is generated in the presence of a temperature gradient, which plays a crucial role in low‐grade heat energy harvesting. Here, a new thermoelectric model is proposed, in which the entire membrane is divided into the intra‐membrane region and two diffusion boundaries. Simulated results suggest the thermally inducted membrane potential is composed of the diffusion potential inside membrane and two Donnan potentials at the membrane boundaries. The effects of the membrane charge density, electrolyte concentration, and solution temperature are theoretically explored in detail. This model is confirmed experimentally with cation‐selective hybrid nanochannels and a commercial cation‐selective polymer membrane. We believe the new thermoelectric model is beneficial to understanding the mechanism of thermoelectric response and promoting practical applications of thermal energy conversion.