Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

Heterocoagulation in Bidisperse Magnetorheological Fluids Containing Like-Charged Nanosized and Micron Particles Without a Magnetic Field

Based on extended Derjaguin–Landau–Verwey–Overbeek theory, a heterocoagulation model is proposed for magnetorheological (MR) fluids containing like-charged nanosized and micron particles without a magnetic field. This model considers three major interactions, namely van der Waals attraction, electrical double layer (EDL) interaction, and steric repulsion. The EDL interaction has been identified as the most important factor. The surface potential ratio β (ψ₂/ψ₁) between two dissimilar particles with like charge plays an important role in controlling the change of EDL interaction. At higher β ratios, the EDL interaction becomes attractive when the surface separation falls within a certain range. Two groups of MR fluid samples have been used in experimental studies based on electroacoustic measurements. In the first group, the ratio and the sum of the zeta potentials between carbonyl iron particles and ceria were 4 and ?734.57 mV, respectively. In the second group, these parameters were 1.38 and ?108.17 mV, respectively. The experimental results suggested that the second group did not undergo heterocoagulation, whereas the first group showed extensive heterocoagulation. The difference in surface potentials between particles of two different phases has been found to be critical for determining the state of dispersion or heterocoagulation in concentrated MR fluid systems.     

Behavior of mixtures of symmetric and asymmetric electrolytes near discretely charged planar surfaces: a Monte Carlo study

Canonical Monte Carlo (CMC) simulations are employed in this work in order to study the structure of the electrical double layer (EDL) near discretely charged planar surfaces in the presence of symmetric and asymmetric indifferent electrolytes within the framework of a primitive model. The effects of discreteness and strength of surface charge, charge asymmetry, and size asymmetry are specific focuses of this work. The CMC simulation protocol is initially tested against the classical theory, the modified Gouy-Chapman (GC) theory, in order to assess the reliability of the simulation results. The CMC simulation results and the predictions of the classical theory show good agreement for 1:1 electrolytes and low surface charge, at which conditions the GC theory is valid. Simulations with symmetric and asymmetric electrolytes and mixtures of the two demonstrate that size plays an important role in determining the species present in the EDL and how the surface charge is screened. A size-exclusion effect could be consistently detected. Although it is energetically favorable that higher-valence ions screen the surface charge, their larger size prevents them from getting close to the surface. Smaller ions with lower valences perform the screening of the charge, resulting in higher local concentrations of small ions close to the surface. The simulations also showed that the strength of the surface charge enhances the size-exclusion effect. This effect will definitely affect the magnitude of the forces between interacting charged surfaces.     

The importance of ion size and electrode curvature on electrical double layers in ionic liquids

Room-temperature ionic liquids (ILs) are an emerging class of electrolytes for supercapacitors. We investigate the effects of ion size and electrode curvature on the electrical double layers (EDLs) in two ILs 1-butyl-3-methylimidazolium chloride [BMIM][Cl] and 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM][PF(6)], using a combination of molecular dynamics (MD) and quantum density functional theory (DFT) simulations. The sizes of the counter-ion and co-ion affect the ion distribution and orientational structure of EDLs. The EDL capacitances near both planar and cylindrical electrodes were found to follow the order: [BMIM][Cl] (near the positive electrode) > [BMIM][PF(6)] (near the positive electrode) ≈ [BMIM][Cl] (near the negative electrode) ≈ [BMIM][PF(6)] (near the negative electrode). The EDL capacitance was also found to increase as the electrode curvature increases. These capacitance data can be fit to the Helmholtz model and the recently proposed exohedral electrical double-cylinder capacitor (xEDCC) model when the EDL thickness is properly parameterized, even though key features of the EDLs in ILs are not accounted for in these models. To remedy the shortcomings of existing models, we propose a "Multiple Ion Layers with Overscreening" (MILO) model for the EDLs in ILs that takes into account two critical features of such EDLs, i.e., alternating layering of counter-ions and co-ions and charge overscreening. The capacitance computed from the MILO model agrees well with the MD prediction. Although some input parameters of the MILO model must be obtained from MD simulations, the MILO model may provide a new framework for understanding many important aspects of EDLs in ILs (e.g., the variation of EDL capacitance with the electrode potential) that are difficult to interpret using classical EDL models and experiments.     

Indirect photometric detection in capillary zone electrophoresis

An indirect photometric detection method is described which is based on the use of an absorbing co-ion as the principal component of the background electrolyte. The zones of non-absorbing ionic species are revealed by changes in light absorption due to charge displacement of the absorbing co-ion. Theoretical considerations are given for selecting a suitable absorbing co-ion to achieve a high sensitivity of detection.The role of electromigration dispersion is illustrated by experiments and the effects of the differences in the effective mobilities of sample ions and that of the absorbing co-ion are discussed. The highest sensitivity can be achieved for sample ions having an effective mobility close to the mobility of the absorbing co-ion. In such a case, the concentration of the sample component in its migrating zone can be high while electromigration dispersion is still negligible. The useful dynamic range of the detection is then limited by the linearity and noise of the detector, the former parameter being given mostly by the shape of the on-column detection cell. The best sensitivities can be obtained in low-concentration background electrolytes containing a co-ion with high absorption at a given detection wavelength.It is shown that indirect photometric detection can be useful for detecting substances that have no optical absorption in the UV and/or visible region, provided that the composition of the background electrolyte is selected correctly.     

静电位阻模型在纳滤膜跨膜电位解析中的应用

采用静电位阻模型对纳滤膜的跨膜电位进行了理论解析, 考察了溶液体积通量密度、原料液浓度、阴阳离子扩散系数比、膜孔半径和膜体积电荷密度对KCl(1-1型电解质)和MgCl2(2-1型电解质)中的纳滤膜跨膜电位的影响. 研究结果表明, 随着通量密度的增大, KCl和MgCl₂的跨膜电位线性程度增强; 两种电解质的跨膜电位均随着原料液浓度和膜孔半径的增大而下降; 在不同的考察范围内, 阴阳离子扩散系数比对1-1型和2-1型电解质的跨膜电位的影响差别较大; KCl的跨膜电位随着膜体积电荷密度的变化关于零点呈现出对称性, 而MgCl₂的跨膜电位零点则出现在膜体积电荷密度为负的条件下.     

A general Poisson-Boltzmann model with position-dependent dielectric permittivity for electric double layer analysis

In this paper, we propose a general Poisson-Boltzmann model for electric double layer (EDL) analysis with the position dependence of dielectric permittivity considered. This model provides physically reasonable property profiles in the EDL region, and it is then utilized to investigate the depletion layer effect on EDL structure and interaction near hydrophobic surfaces. Our results show that both the electric potential and the interaction pressure between surfaces decrease due to the lower permittivity in the depletion layer. The reduction becomes more profound at larger variation magnitude and range. This trend is in general agreement with that observed from the previous stepwise model; however, that model has overestimated the influence of permittivity variation effect. For the thin depletion layer and the relative thick EDL, our calculation indicates that the permittivity variation effect on EDL usually can be neglected. Furthermore, our model can be readily extended to study the permittivity variation in EDL due to ion accumulation and hydration in the EDL region.     

Molecular dynamics simulations of the electrical double layer on smectite surfaces contacting concentrated mixed electrolyte (NaCl-CaCl2) solutions

We report new molecular dynamics results elucidating the structure of the electrical double layer (EDL) on smectite surfaces contacting mixed NaCl-CaCl(2) electrolyte solutions in the range of concentrations relevant to pore waters in geologic repositories for CO(2) or high-level radioactive waste (0.34-1.83 mol(c) dm(-3)). Our results confirm the existence of three distinct ion adsorption planes (0-, β-, and d-planes), often assumed in EDL models, but with two important qualifications: (1) the location of the β- and d-planes are independent of ionic strength or ion type and (2) "indifferent electrolyte" ions can occupy all three planes. Charge inversion occurred in the diffuse ion swarm because of the affinity of the clay surface for CaCl(+) ion pairs. Therefore, at concentrations ≥0.34 mol(c) dm(-3), properties arising from long-range electrostatics at interfaces (electrophoresis, electro-osmosis, co-ion exclusion, colloidal aggregation) will not be correctly predicted by most EDL models. Co-ion exclusion, typically neglected by surface speciation models, balanced a large part of the clay mineral structural charge in the more concentrated solutions. Water molecules and ions diffused relatively rapidly even in the first statistical water monolayer, contradicting reports of rigid "ice-like" structures for water on clay mineral surfaces.     

Role of electrostatic interactions in particle adsorption

The role of the electrostatic double-layer interactions in adsorption of colloid particles at solid/liquid interface was reviewed. The phenomenological formulation of the governing PB equation was presented with the expressions for the pressure tensor enabling one to calculate forces, torques and interaction energies between particles in electrolyte solutions. Then, the limiting analytical results for an isolated double-layer (both spherical and planar) were discussed in relation to the effective surface potential concept. The range of validity of the approximate expression connecting the surface potential and the effective surface potential with surface charge for various electrolytes was estimated. The results for double-layer systems were next presented including the case of two planar double-layers and two dissimilar spherical particles. Limiting solutions for short and long distances as well as for low potentials (linear HHF model) were discussed. The approximate models for calculating interactions of spheres, i.e., the extended Derjaguin summation method and the linear superposition approach (LSA) were also introduced. The results stemming from these models were compared with the exact numerical solution obtained in bispherical coordinate system. Possibilities of describing interactions of nonspherical particles (e.g., spheroids) in terms of the Derjaguin and the equivalent sphere methods were pointed out. In further part of the review the role of these electrostatic interactions in adsorption of colloid particles was discussed. Theoretical predictions were presented enabling a quantitative determination of both the initial adsorption flux for low surface coverages and the surface blocking effects for larger surface coverages. Possibility of bilayer adsorption for dilute electrolytes was mentioned. The theoretical results concerning both the adsorption kinetics and structure formation were then confronted with experimental evidences obtained in the well-defined systems, e.g., the impinging-jet cells and the packed-bed columns of monodisperse spherical particles. The experiments proved that the initial adsorption flux was considerably increased in dilute electrolytes whereas the monolayer coverages were considerably decreased due to lateral interactions among particles. It was then concluded that the good agreement between experimental and theoretical data confirmed the thesis of an essential role of the electrostatic interactions in adsorption phenomena of colloid particles.     

Second-order Impedance in Electrode Kinetics

The kinetics of electrode reactions with a rather severe influence of the EDL structure is studied by nonlinear second-order impedance spectroscopy. Polarization impedance spectra and potential dependences of a nonlinear impedance are obtained for the reaction of electroreduction of the ferricyanide anion on the cadmium and bismuth electrodes in surface-inactive supporting NaF and Na₂SO₄ electrolytes. The results of measurements for the reaction Eu³⁺ + e Eu²⁺ on the bismuth and mercury electrodes are presented. It is shown that such important parameters of EDL as the potential of zero charge and the second derivative of potential with respect to the charge of the electrode surface can be determined directly from experimental curves even under conditions of occurrence of a faradaic process.     

Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.     

Breakdown of the Gouy-Chapman model for highly charged Langmuir monolayers: counterion size effect

Deviations from the classic Gouy-Chapman (GC) model due to the finite size of hydrated counterions were tested for negatively charged Langmuir monolayers with different surface charge densities. Monolayers with the largest charge density (>0.6 C.m(-2)) show an increase of the surface potential for a series of alkali metal cations from Li(+) to Cs(+) by 200-250 mV. The increase is similar for different monolayers and suggests that this effect is independent of the particular type of headgroup. The magnitude of variation is comparable with model estimations of the electrical double layer (EDL) potential implying that the deviation from the GC model is drastic. Deviations from the GC model rapidly vanish with decreasing monolayer charge density and become hardly observable below 0.3 C.m(-2). For monolayers with a high charge density on subphases containing different sized counterions, preferential participation of the smallest ions in the EDL should be favorable in terms of electrostatic free energy because of packing density limitations. This effect was demonstrated for behenyl sulfate (BS) monolayers (0.64 C.m(-2)) with the X-ray reflectivity technique. For the Cs(+)-Li(+) system, the fraction of Cs(+) in the EDL is 50-60% compared with only 10% of Cs(+) in the subphase. Providing high surface charge density, a small univalent Cs(+) is capable to compete even with a bulky divalent Mg(2+). For equal concentrations of Cs(+) and Mg(2+) in the subphase, the Cs(+)/Mg(2+) ratio in EDL of BS monolayer is 1.3 to 2.0 (in contrast to 0.04, predicted by the GC model). All experimental results of this study are described in terms of packing density limitations for hydrated counterions in the EDL.     

Interactions between two similar plane parallel double layers for Na<Subscript>3</Subscript>PO<Subscript>4</Subscript> type asymmetric electrolytes at positive surface potential

The interactions between two similar plane double-layers for Na₃PO₄ type asymmetric electrolytes are described using hyperelliptic integrals. The mathematical treatments of hyperelliptic integrals are much more difficult than those of elliptic integrals. The system was successfully treated with the aid of the λ parameter method. The interaction energies for the system at positive surface potential are expanded in power series at low, moderate, and high potentials, respectively. The accurate numeral results and V′-ξ _d curves are given for y ₀ ≤ 20 and can be used to check the validity of approximate expressions obtained. When y ₀ ≥ 5, V′ hardly changes with y ₀. The interaction energies between two similar plane parallel double layers for symmetric and asymmetric electrolytes at y ₀ = 1 were compared; when ξ _d → 0, the interaction energies for Na₃PO₄ type electrolytes are much larger than for electrolytes of other types. The present results are also fit for FeCl₃-type asymmetric electrolytes at negative surface potential. The text was submitted by the author in English.     

A rapidly convergent series for calculation of the interaction between two similar plane double-layers for z+/z- = -2 asymmetric electrolytes at positive surface potential

A rapidly convergent series for calculation of the interaction energies between two similar plane double-layers for z+/z- = -2 asymmetric electrolytes at positive surface potential are obtained by introducing a parameter lambda in elliptical integral. When dimensionless surface potential is less or equal to 20, the number of the series terms required to obtain the interaction energies with six significant digits are not more than 4. The accurate numeral results are given and they can be used to check up the validity of approximate expressions people obtain. The present results are also fit for z+/z- = -1/2 asymmetric electrolytes at negative surface potential.     

Temperature and concentration effects on electrolyte transport across porous thin-film composite nanofiltration membranes: Pore transport mechanisms and energetics of permeation

The influence of temperature and concentration on nanofilter charge density and electrolyte pore transport mechanisms is reported. Crossflow filtration experiments were performed to measure transport of several electrolytes (NaCl, NaNO3, NaClO4, CaCl2, MgCl2, and MgSO4) across two commercially available thin-film composite nanofiltration membranes in the range 5-41 degrees C. Experiments were also performed with selected salts in the range 1-50 meq/L to quantify concentration effects. Three different approaches, irreversible thermodynamics, extended Nernst-Planck formulation, and theory of rate processes, were employed to interpret retentions of these symmetric and asymmetric electrolytes at varying temperature and concentration. Increasing feed water temperature slightly increased electrolyte reflection coefficients and only weakly increased permeability compared with neutral solutes. Electromigration and convection tended to counteract each other at high fluxes explaining the weak temperature dependence of the reflection coefficient. Changes in membrane surface charge density with temperature were attributed to increased adsorption of electrolytes on the polymer constituting the active layer. Activation energy of permeation for charged solutes was primarily determined by the Donnan potential at the membrane-feed water interface. Electrolyte permeation was shown to be an enthalpy-driven process that resulted in small entropy changes. Increasing sorption capacity with temperature and low sorption energies indicated that co-ion sorption on polymeric membranes was an endothermic physicosorption process, which appears to determine temperature dependence of electrolyte permeation at increased feed concentrations.     

Study on Interaction Between Two Parallel Plates with Iteration Method in Functional Theory

By introducing the functional theory into the calculation of electric double layer (EDL) interaction, the interaction energies of two parallel plates were calculated respectively at low, moderate, and high potentials. Compared with the results of two existing methods, Debye-H?uckel and Langmuir methods, which are applicable just to the critical potentials and perform poorly in the intermediate potential, the functional approach not only has much simpler expression of the EDL interaction energy, but also performs well in the entire range of potentials.     

A rapidly convergent series for calculation of the interaction between two similar plane double layers for Na(2)SO(4) type asymmetric electrolytes at positive surface potential

A rapidly convergent series for calculation of the interaction energies between two similar plane double layers for Na(2)SO(4) type asymmetric electrolytes at positive surface potential was obtained by introducing a parameter lambda into an elliptical integral. When the dimensionless surface potential is less or equal to 20, the number of the series terms required to obtain the interaction energies with six significant digits is not more than 2. The accurate numeral results were given and they can be used to check up the validity of approximate expressions obtained. The present results are also fit for CaCl(2) type asymmetric electrolytes at negative surface potential.     

Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores

The formation of the electrical double layer (EDL) in the presence of trivalent and monovalent ions inside a slit-type nanopore was simulated via the canonical Monte Carlo method using a primitive model. In large pores, the distribution of ionic species is similar to that observed in an isolated planar double layer. Screening of surface charge is determined by the competitive effects between ion size and charge asymmetry of the counterions. On the other hand, as the pore size approaches the dimension of the ionic species, phenomena such as EDL overlapping become enhanced by ion-size effects. Simulation results demonstrate that EDL overlapping is not only a function of such parameters as ionic strength and surface charge density, but also a function of the properties of the ionic species involved in the EDL. Furthermore, charge inversion can be observed under certain conditions when dealing with mixtures of asymmetric electrolytes. This phenomenon results from strong ion-ion correlation effects and the asymmetries in size and charge of ionic species, and is most significant in the case of trivalent counterions with larger diameters. The simulation results provide insights into the fundamental mechanisms behind the formation of EDL within nanopores as determined by pore size and by the properties of ionic species present in solution. The findings of this work are relevant to ion sorption and transport within nanostructured materials.     

Carbon/carbon supercapacitors

Supercapacitors, or electrochemical capacitors, are a power storage system applied for harvesting energy and delivering pulses during short periods of time. The commercially available technology is based on charging an electrical double-layer (EDL), and using high surface area carbon electrodes in an organic electrolyte. This review first presents the state-of-the-art on EDL capacitors, with the objective to better understand their operating principles and to improve their performance. In particular, it is shown that capacitance might be enhanced for carbons having subnanometric pores where ions of the electrolyte are distorted and partly desolvated. Then, strategies for using environment friendly aqueous electrolytes are presented. In this case, the capacitance can be enhanced through pseudo-faradaic contributions involving i) surface functional groups on carbons, ii) hydrogen electrosorption, and iii) redox reactions at the electrode/electrolyte interface. The most promising system is based on the use of aqueous alkali sulfate as electrolyte allowing voltages as high as 2 V to be reached, due to the high overpotential for di-hydrogen evolution at the negative electrode.