An improved Space-Charge model for flow through charged microporous membranes

The Space-Charge model is modified to better analyze the steady-state electrohydrodynamic behavior of aqueous monovalent electrolytes in charged microporous membranes. The effects of changes in solvent dielectric constant near the wall, ion hydration effects, finite ion sizes, and charge regulating surface effects, are incorporated into the governing electrohydrodynamic equations (i.e., Navier-Stokes (NSE), Nernst-Planck (NPE), and Poisson-Boltzmann (PBE) equations). Their effect on streaming potential, pore conductivity, excess conductivity, and maximum energy conversion efficiency for electro-osmosis is illustrated. It is shown that the dielectric saturation and ion hydration effects cause significant changes in the electric potential field and ion concentration inside the capillary tubes. Quantitative comparisons of model results with measured electrokinetic data reveal better agreement when compared with the existing model.     

Fibrinogen adsorption on mica studied by AFM and in situ streaming potential measurements

Adsorption of fibrinogen from aqueous solutions on mica was studied using AFM and in situ streaming potential measurements. In the first stage, bulk physicochemical properties of fibrinogen and the mica substrate were characterized for various ionic strength and pH. The zeta potential and number of uncompensated (electrokinetic) charges on the protein surfaces were determined from microelectrophoretic measurements. Analogously, using streaming potential measurements, the electrokinetic charge density of mica was determined for pH range 3-10 and the NaCl background electrolyte concentration of 10(-3) and 10(-2) M. Next, the kinetics of fibrinogen adsorption at pH 3.5 and 7.4 in the diffusion cell was studied using a direct AFM determination of the number of molecules per unit area of the mica substrate. Then, streaming potential measurements were performed to determine the apparent zeta potential of fibrinogen-covered mica for different pH and ionic strength in terms of its surface concentration. A quantitative interpretation of these streaming potential measurements was achieved in terms of the theoretical model postulating a side-on adsorption of fibrinogen molecules as discrete particles. On the basis of these results, the maximum coverage of fibrinogen Θ close to 0.29 was predicted, in accordance with previous theoretical predictions. It was also suggested that anomalous adsorption for pH 7.4, where fibrinogen and the mica substrate were both negatively charged, can be explained in terms of a heterogeneous charge distribution on fibrinogen molecules. It was estimated that the positive charge was 12 e (for NaCl concentration of 10(-2) M and pH 7.4) compared with the net charge of fibrinogen at this pH, equal to -21 e. Results obtained in this work proved that the coverage of fibrinogen can be quantitatively determined using the streaming potential method, especially for Θ < 0.2, where other experimental methods become less accurate.     

On the Role of Heterogeneous Nanopore Junction in Osmotic Power Generation

Osmotic power generated by mixing ionic solutions of different concentration is an underutilized clean energy resource that satisfy potentially the ever‐growing energy demand. For decades, substantial efforts are made to enhance the power density. Toward this goal, we once developed a heterogeneous nanoporous membrane comprising of heterojunctions between negatively charged mesoporous carbon and positively charged macroporous alumina to harvest electric power from salinity difference and achieved outstanding performance (J. Am. Chem. Soc. 2014 , 136, 12265). The heterogeneous nanopore junction effectively suppresses ion concentration polarization (ICP) at low concentration end, and consequently promotes the overall power density. However, to date, a systematic understanding of the role of the heterogeneous nanopore junction in osmotic energy conversion remains urgent and largely unexplored. Herein, we provide an in‐depth theoretical investigation on this issue with special emphasis on several influential factors, such as the ionic concentration, the surface charge density, and the geometry of heterogeneous part. To balance the suppression of ICP and maintenance of charge selectivity, we find that these influential factors in the heterogeneous part should be restricted to a specific range. These findings provide direct guidance for design and optimization of high‐performance nanofluidic power sources.     

Electrochemical Studies of the Benzoate Adsorption on Au (111) Electrode

Cyclic voltammetry (CV), differential capacity (DC), and charge densitymeasurements have been employed to study the benzoate (BZ) adsorption at the Au(111)electrode surface. Thermodynamic analysis of charge density (_M) data has beenperformed to describe the properties of the adsorbed benzoate ion. The Gibbsexcess , Gibbs energy of adsorption G, and the number of electrons flowingto the interface per adsorbed benzoate ion at a constant potential (electrosorptionvalency) and at a constant bulk concentration of the benzoate (reciprocal of theEsin—Markov coefficient) have been determined. The results demonstrate thatalthough benzoate adsorption starts at negative charge densities, it takes placepredominantly at a positively charged surface. At the most positive potentials,the surface concentration of benzoate attains a limiting value of about 7.3×10^–10mol-cm^–2, which is independent of the bulk benzoate concentration. This valueis consistent with packing density corresponding to a closed-packed monolayerof vertically adsorbed benzoate molecules. At negative charge densities, benzoateassumes a flat (-bonded) surface coordination. The surface coordination ofbenzoate changes, by moving from a negatively to positively charged surface.At the negatively charged surface, the electrosorption bond is quite polar. Thepolarity of the chemisorption bond is significantly reduced due either to a chargetransfer or a screening of the charge on the anion by the charge on the metal.     

The role of electrostatic interactions on the rejection of organic solutes in aqueous solutions with nanofiltration

The effects of electrostatic interactions on the rejection of organic solutes with nanofiltration membranes were investigated. For two different membranes, the rejection of selected organic acids, positively and negatively charged pharmaceuticals and neutral pharmaceuticals was investigated at different feed water chemistries (different ionic strengths and pH conditions, with and without the presence of NOM and divalent cations). It was concluded that for negatively charged membranes, electrostatic repulsion leads to an increase of the rejection of negatively charged solutes and electrostatic attraction leads to a decrease of the rejection of positively charged solutes, compared to neutral solutes. Neutral and positively charged solutes engage in hydrophobic interactions with negatively charged membranes, whereas negatively charged solutes do not engage in hydrophobic interactions since they cannot approach the membrane surface. This provides proof for the theory of an increased concentration of positively charged organic solutes and a decreased concentration of negatively charged organic solutes at the membrane surface compared to the bulk fluid. This concept may be denoted as “charge concentration polarisation”. The concept was further used as a modelling tool to predict the effects of electrostatic interactions on the rejection of trace organic solutes.     

Electrokinetic flow and electric conduction of salt-free solutions in a capillary

The electrokinetic flow and accompanied electric conduction of a salt-free solution in the axial direction of a charged circular capillary are analyzed. No assumptions are made about the surface charge density (or surface potential) and electrokinetic radius of the capillary, which are interrelated. The Poisson–Boltzmann equation and modified Navier–Stokes equation are solved for the electrostatic potential distribution and fluid velocity profile, respectively. Closed-form formulas for the electroosmotic mobility and electric conductivity in the capillary are derived in terms of the surface charge density. The relative surface potential, electroosmotic mobility, and electric conductivity are monotonic increasing functions of the surface charge density and electrokinetic radius. However, the rises of the relative surface potential and electroosmotic mobility with an increase in the surface charge density are suppressed substantially when it is high due to the effect of counterion condensation. The analytical prediction that the electroosmotic mobility grows with increases in the surface charge density and electrokinetic radius agrees with the experimental results for salt-free solutions in circular microchannels in the literature.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Characterization of capillary inner surface conditions with streaming potential

Streaming potential is created when an electrolyte solution is forced to flow pass a charged surface. For an uncoated fused silica capillary, the streaming potential is measured between the inlet and outlet vials while applying a pressure across the capillary. The changes in streaming potential can be used to characterize the properties of the capillary inner surface. In this work, HCl, NaCl, and NaOH solutions ranging from 0.4 to 6 mM were used as the background electrolyte (BGE) at temperatures of 15 to 35 °C for the mesurements. The streaming potential decreases with the increase in BGE concentration, and the trend is amplified at higher temperatures. When buffer solutions in the pH range of 1.5 to 12.7 were used as the BGE, streaming potential was shown to be sensitive to changes in pH but reaches a maximum at around 9.5. At pH < 3.3, no streaming potentials were observed. The pH of zero surface charge (streaming potential equals 0) changes with temperature, and is measured to be 3.3 to 3.1 when the temperature is changed from 15 to 35°C. Zeta potentials can be calculated from the measured streaming potential, conductivity, and the solution viscosity. Surface charge densities were calculated in this work using the zeta potentials obtained. We demonstrated that capillary surface conditions can significantly change the streaming potential, and with three different solutions, we showed that analyte-dependent adsorption can be monitored and mitigated to improve the peak symmetry and migration times reproducibility.     

Modification of the Quartz Surface by the Adsorption of a Cationic Polyelectrolyte

A capillary electrokinetics method is applied to measure the electrokinetic potential of the surface of quartz capillaries during the continuous flow of the aqueous solutions of a cationic polyelectrolyte (PE). At a low polymer concentration (10^–5 g/l), the adsorption is determined mainly by the electrostatic forces and its kinetics, by the conformational rearrangement of adsorbed macromolecules. As the concentration of PE increases, the charge of quartz surface reverses; and further adsorption is due to the forces of hydrophobic and molecular attraction between macromolecules. The adsorption energy is estimated for this case. The charge reversal of the surface is associated with the presence of adsorption sites of two different types. At a low concentration of PE, the adsorption takes place on negatively charged sites of quartz surface. At higher concentrations of PE, after the neutralization of the surface, the adsorbed PE molecules become new adsorption sites, and the adsorption acquires two-layer character. After adsorption, the quartz surface is hydrophobized: the contact angle measured by the bubble method is close to 33°–34°.     

Effects of fluid slippage on pressure-driven electrokinetic energy conversion in conical nanochannels

The effects of fluid slippage on the pressure-driven electrokinetic energy conversion in conical nanochannels are systematically investigated in this paper. We present a multiphysical model that couples the Planck–Nernst–Poisson equations and the Navier–Stokes equation with a Navier slip condition to fulfill this purpose. We systematically look into the variation of various performance indicators of electrokinetic energy conversion, for example, streaming current, streaming potential, generation power, energy conversion efficiency, regulation parameter, and enchantment ratio, with the conicity of nanochannels and the slip length for two pressure differences of the same magnitude but opposite directions. Particularly, enhancement ratios related to streaming current, streaming potential, generation power, and energy conversion efficiency are defined to comprehensively measure the enhancement of the performance of electrokinetic energy conversion due to the slip length. The results demonstrate that a combination of large slip length and small conicity enhances the electrokinetic energy conversion performance significantly. Furthermore, the fluid slippage-induced enhancement of the electrokinetic energy conversion in the backward pressure difference mode is stronger than that in the forward pressure difference mode. Our results provide design and operation guidelines for pressure-driven electrokinetic energy conversion devices.     

Correlation of the Surface Charge Characteristics of Polymers with Their Antithrombogenic Characteristics

A knowledge of the structure of the double layer is essential in the investigation of reactions at an inierface between two dissimilar media. This aspect is briefly presented in respect to charge separation and potential distribution in the interfacial region. The types of reactions that can occur at solid-solution interfaces (electron transfer, electrosorption, and electro-phoretic deposition) are discussed. The electrokinetic methods for determination of surface charge characteristics of insulator materials in electrodes are reviewed. Thrombosis on the blood vessel wall and on prosthetic materials is an interfacial chemical reaction. The evidence for an electrochemical mechanism of thrombosis on conducting materials is outlined. Under normal conditions, the blood vessel wall is negatively charged. Injury or atherosclerosis makes it less negatively or even positively charged. With decrease of pH, there is an increase in the surface charge density of the blood vessel wall with an isoelectric point at a pH of about 4.5. Materials treated chemically so as to introduce negatively charged groups (sulfonate, carboxylate, heparinized, anionic ioplex) tend to be antithrombogenic while positively charged surfaces (cationic Ioplex, quarternary ammonium group) are thrombogenic. A useful criterion for antithrombogenic polymer materials is that their surfaces must have a uniform negative charge.     

Adsorption of poly(vinyl formamide-co-vinyl amine) onto silica particle surfaces and stability of the formed hybrid materials

In order to produce silica/polyelectrolyte hybrid materials the adsorption of the polyelectrolyte poly(vinyl formamide-co-vinyl amine), P(VFA-co-VAm) was investigated. The adsorption of the P(VFA-co-VAm) from an aqueous solution onto silica surface is strongly influenced by the pH value and ionic strength of the aqueous solution, as well as the concentration of polyelectrolyte. The adsorption of the positively charged P(VFA-co-VAm) molecules on the negatively charged silica particles offers a way to control the surface charge properties of the formed hybrid material. Changes in surface charges during the polyelectrolyte adsorption were studied by potentiometric titration and electrokinetic measurements. X-ray photoelectron spectroscopy (XPS) was employed to obtain information about the amount of the adsorbed polyelectrolyte and its chemical structure. The stability of the adsorbed P(VFA-co-VAm) was investigated by extraction experiments and streaming potential measurements. It was shown, that polyelectrolyte layer is instable in an acidic environment. At a low pH value a high number of amino groups are protonated that increases the solubility of the polyelectrolyte chains. The solvatation process is able to overcompensate the attractive electrostatic forces fixing the polyelectrolyte molecules on the substrate material surface. Hence, the polyelectrolyte layer partially undergoes dissolving process.     

Density functional study of the charge on Aun clusters (n=1-7) supported on a partially reduced rutile TiO2(110): are all clusters negatively charged?

It is widely believed that small gold clusters supported on an oxide surface and adsorbed at the site of an oxygen vacancy are negatively charged. It has been suggested that this negative charge helps a gold cluster adsorb oxygen and weakens the O-O bond to make oxidation reactions more efficient. Given the fact that an oxygen vacancy is electron rich and that Au is a very electronegative element, the assumption that the Au cluster will take electron density from the vacancy is plausible. However, the density functional calculations presented here show that the situation is more complicated. The authors have used the Bader method to examine the charge redistribution when a Aun cluster (n=1-7) binds next to or at an oxygen vacancy on rutile TiO2(110). For the lowest energy isomers they find that Au1 and Au3 are negatively charged, Au5 and Au7 are positively charged, and Au2, Au4, and Au6 exchange practically no charge. The behavior of the Aun isomers having the second-lowest energy is also unexpected. Au2, Au3, Au5, and Au7 are negatively charged upon adsorption and very little charge is transferred when Au4 and Au6 are adsorbed. These observations can be explained in terms of the overlap between the frontier molecular orbitals of the gold cluster and the eigenstates of the support. Aun with even n becomes negatively charged when the lowest unoccupied molecular orbital has a lobe pointing in the direction of the oxygen vacancy or towards a fivefold coordinated Ti (5c-Ti) located in the surface layer; otherwise it stays neutral. Aun with odd n becomes negatively charged when the singly occupied molecular orbital has a lobe pointing in the direction of a 5c-Ti located at the vacancy site or in the surface layer, otherwise it donates electron density into the conduction band of rutile TiO2(110) becoming positively charged.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.     

Permanent gold nanoparticle coatings on polyelectrolyte multilayer modified capillaries for open-tubular capillary electrochromatography

This paper reports on a new strategy to coat fused silica capillaries through ionic adsorption of gold nanoparticles (AuNPs) on a polyelectrolyte multilayer (PEM) modified capillary wall. The coating was constructed in situ by alternating rinses with positively charged poly(diallydimethylammonium chloride), negatively charged poly(sodium-4-styrenesulfonate), and positively charged AuNPs. After self-assembly of n-octadecanethiol onto the surface of AuNPs, the modified capillary was investigated as a new medium for the separation of neutral analytes and proteins in open-tubular capillary electrochromatography (OT-CEC). The surface coverage of the capillary wall was increased using the high density of AuNPs which were dynamically capped with 4-dimethylaminopyridine (DMAP). The chromatographic performance of the column coated with positively charged AuNPs was remarkably improved compared with a column modified with negatively charged AuNPs. The coating was robust over more than 810 runs in this study and also showed high stability against 0.01 M NaOH, 0.01 M HCl, and electrolyte concentrations up to 70 mM. The run-to-run, day-to-day, and capillary-to-capillary reproducibilities of electroosmotic flow were satisfying with relative standard deviation values of less than 1% in all cases. The AuNP-coated PEM modified capillary column not only showed good performance for neutral analytes but also was suitable for the analysis of both basic and acidic proteins.     

A numerical study on ion concentration polarization and electric circuit performance of an electrokinetic battery

Ion concentration polarization (ICP) imposes remarkable adverse effects on the energy conversion performance of the pressure-driven electrokinetic (EK) flows through a capillary system that can be equivalently treated as a battery. An optimized dimensionless numerical method is proposed in this study to investigate the causes and the effects of the ICP. Results show that remarkable ICP phenomena are induced under certain conditions such as high applied pressure, high surface charge density, and small inversed Debye length at dimensionless values of 6000, ‒10, and 0.5. Meanwhile, different factors influence the ICP and the corresponding electric properties in different ways. Particularly for the overall electric resistance, the applied pressure and the surface charge density mainly affect the variation amplitude and the level of the overall electric resistance when varying the output electric potential, respectively. Differently, the Debye length affects the overall electric resistance in both aspects. Ultimately, the induced ICP leads to significant nonlinear current–potential curves.     

Evaluating the charge of nanofiltration membranes

In this study, several methods were used to determine the charge of commercially available nanofiltration membranes, and were compared. First the ion-exchange capacity was determined by titration, this method is able to distinguish between positively and negatively charged functional groups on the membrane. Secondly, measurements of the streaming potential gave a value for the charge density at the exterior membrane surface; the effect of the pH of the solution on the membrane charge was studied. Finally, measurements of the membrane potential allowed to evaluate the total membrane charge density.The results of the three methods were used to compare the membrane charge of nanofiltration membranes mainly in a qualitative way. It is shown that measurements of the membrane potential are preferred for the evaluation of the membrane charge.     

Electrophoretic mobility, zeta potential, and fixed charge density of bovine knee chondrocytes, methyl methacrylate-sulfopropyl methacrylate, polybutylcyanoacrylate, and solid lipid nanoparticles

The electrophoretic mobility and zeta potential of bovine knee chondrocytes (BKCs), methyl methacrylate-sulfopropyl methacrylate (MMA-SPM) nanoparticles (NPs), polybutylcyanoacrylate (PBCA) NPs, and solid lipid nanoparticles (SLNs) were investigated under the influences of Na+, K+, and Ca2+ with various ionic strengths. The fixed charge density in the surface layers of the four biocolloidal particles was estimated from the experimental mobility of capillary electrophoresis with a theory of soft charged colloids. The results revealed that, for a specific cationic species, the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density decreased with an increase in ionic strength. For a constant ionic strength, the effect of ionic species on the reduction in the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density followed the order Na+>K+>Ca2+ for the negatively charged BKCs, MMA-SPM NPs, and SLNs. The reverse order is true for the positively charged PBCA NPs.     

Core-level shifts and their relation to surface effects and dimensionality of a system

In the spirit of Jean-Louis Calais's endeavor to effectively combine the tools of quantum chemistry and solid-state physics to study the electronic structure of materials, Hartree-Fock calculations of core-level binding energy shifts in Li chains and Li slabs and their relation to surface effects, charge oscillations, and dimensionality of a system are presented. For the one-dimensional system the 1s binding energy oscillates regularly from the edge Li atom to the center, the 1s level of the edge atom being shifted to a larger binding energy. For two-dimensional Li slabs which model the (001) surface of Li, the 1s level of the top layer atom is found to have the largest binding energy, being ∼ 0.5 eV below the 1s levels of the other layers, and the binding energy is constantly decreasing from the surface to the bulk, independent of the charge population and without oscillations. Both Mulliken population analysis and charge difference plots indicate that the edge atom in the chain is positively charged, whereas the surface atoms in the slab are negatively charged. This shows that a positive or negative net valence population alone does not determine the direction of the shifts. The predicted core-level binding energy shifts should be observable with high-resolution synchroton measurements. The distinct differences predicted for core-level shifts for one- and two-dimensional systems can be used to characterize and probe the geometry of nanostructures. © 1997 John Wiley & Sons, Inc.     

Oppositely Charged Ti3C2Tx MXene Membranes with 2D Nanofluidic Channels for Osmotic Energy Harvesting

Membrane‐based reverse electrodialysis (RED) is considered as the most promising technique to harvest osmotic energy. However, the traditional membranes are limited by high internal resistance and low efficiency, resulting in undesirable power densities. Herein, we report the combination of oppositely charged Ti₃C₂T_x MXene membranes (MXMs) with confined 2D nanofluidic channels as high‐performance osmotic power generators. The negatively or positively charged 2D MXene nanochannels exhibit typical surface‐charge‐governed ion transport and show excellent cation or anion selectivity. By mixing the artificial sea water (0.5 m NaCl) and river water (0.01 m NaCl), we obtain a maximum power density of ca. 4.6 Wm^?2, higher than most of the state‐of‐the‐art membrane‐based osmotic power generators, and very close to the commercialization benchmark (5 Wm^?2). Through connecting ten tandem MXM‐RED stacks, the output voltage can reach up 1.66 V, which can directly power the electronic devices.