On the effects of ion-wall chemical association on the electric double layer: a density functional approach for the restricted primitive model at a charged wall

We describe a density functional theory for the restricted primitive model of ionic fluid at a charged wall with active sites to which ions can bond. The theory is an extension of our recent approach [Pizio et al., J. Chem. Phys. 121, 11957 (2004)] and is focused in the effects of specific adsorption of ions on the wall, besides the electrostatic phenomena. In order to solve the problem, we use the first-order thermodynamic perturbation theory of chemical association developed by Wertheim [J. Chem. Phys. 87, 7323 (1987)]. The microscopic structure of the electric double layer and the amount of adsorbed charge are investigated. Also, the temperature dependence of capacitance is analyzed. The capacitance depends on the kind of ions that form associative bonds with the surface sites and is determined by a net charge acting on the diffuse layer. The shape of the temperature dependence of capacitance essentially depends on the association energy and the density of bonding sites.     

Simple density functional approach to adsorption of biomolecules on solid surfaces

A simple density functional approach for modeling the adsorption of biomolecules is considered. The model comprises a three-component mixture consisting of spherical and differently charged ions and chain molecules. Spherical ions can form associative bonds with selected segments of a chain. To enable the formation of bonds between chain segments and spherical ions, the statistical associating fluid theory is applied. The present theory is used to study the structure of adsorbed layers, the excess adsorption isotherms, and the capacitance of the double layer.     

A local density functional approximation for the ion distribution near a charged electrode in the restricted primitive model electrolyte

A local HNC/MSA approximation is developed and applied to the 1:1 restricted primitive model electrolyte. Improvement of ion density profiles in front of a charged electrode is achieved by employing ion—ion direct correlation functions from homogeneous systems of non-neutral composition as found locally in the inhomogeneous double layer. This approximation is related to the density functional approach for inhomogeneous fluids. The local HNC/MSA method predicts, at higher surface charges, layering of counterions and charge inversion as seen in Monte Carlo data, a strong increase of the surface potential with charging and a maximum in the double layer capacitance.     

The electric double layer capacitance for a hard sphere ion-dipole electrolyte in the mean field approximation

The electric double layer capacitance for a hard sphere ion-dipole system in the neighbourhood of a plane charged wall is calculated in the mean field approximation. To order ka the capacitance predicts the same structural features as the MSA capacitance.     

A continuum model for yttria-stabilized zirconia incorporating triple phase boundary,lattice structure and immobile oxide ions

A continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

     

Ion penetration into an ‘unfriendly medium’ and the double layer capacitance of the interface between two immiscible electrolytes

We develop a theory of the double layer at electrolyte | electrolyte interfaces with account for the finite thickness of the interfacial region. This includes the distribution of ions between the two phases and smooth variation of dielectric properties across the interface. The theory offers simple laws for the dependence of the double layer capacitance on the nature of ions, ionic concentrations and potential, which are in line with experimental observations. The theory shows which parameters reflect the nature of ions and the structure of the interface, and how these parameters can be extracted from the capacitance data.     

The modelling of solvent structure in the electrical double layer

A Civilized Model electrolyte is one in which the ions and solvent molecules are regarded as distinct molecular species and treated on an equal basis. Recent efforts to use a Civilized Model to study the effects of solvent structure in the properties of the electrical double layer are discussed. By modelling the electrolyte as a simple ion-dipole mixture, it is possible to gain valuable insight in areas such as: 1) the successes and limitations of the Gouy-Chapman-Stern picture; 2) the derivation as opposed to a postulation of the Stern layer; 3) the influence of the charged surface on the magnitudes of the apparent Stern capacities (e.g. the “low” capacitances of the mercury/solution interface vs. the “high” capacitance of inorganic oxides); 4) the effect of solvent structure on the potential profile in the diffuse layer; 5) the interpretation of the electrokinetic potential; and 6) the role of solvent orientation on the x potential.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

Density-functional theory for fluid mixtures of charged chain particles and spherical counterions in contact with charged hard wall: Adsorption, double layer capacitance, and the point of zero charge

We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.     

Description of the Hg/[H<Subscript>2</Subscript>O + <Emphasis Type="Italic">mc</Emphasis> KCl + (1 − <Emphasis Type="Italic">m</Emphasis>)<Emphasis Type="Italic">c</Emphasis> KF] system in terms of the modified model of electrical double layer

Specific adsorption of anion Cl⁻ at the Hg/H₂O interface from mixed solutions mc KCl + (1 − m)c KF is analyzed in terms of a recently put forward modified model of electrical double layer. The calculations showed that the modified model of electrical double layer not only adequately gives the form of experiment curves of differential capacitance but also allows explaining the deviation from linearity of the dependence of the adsorption energy on the electrode charge. Of importance is a decrease in the dense layer capacitance when passing from KF to KCl under the condition of constant surface coverage with the Cl⁻ ions. The results of calculations in terms of the modified model of electrical double layer are compared with those obtained in terms of the Sanz-Gonzalez model.     

Ionic liquid ion sources: suppression of electrochemical reactions using voltage alternation

The problem of electrochemical decomposition due to extraction of single polarity ions from a novel ionic liquid ion source (ILIS) is solved by periodically alternating the voltage source so that the potential difference that appears across the double layer formed between the emitter conductive material and the liquid is maintained below the electrochemical window limit, thus eliminating electronic reactions. The ionic liquid EMI-BF(4) is used to externally wet a solid tungsten emitter, establishing a physical boundary with a certain liquid-metal contact area. Theoretical and experimental evidence suggests that this area is close to the effective surface involved in the double layer charging dynamics. The extent of this surface is relatively large, thus increasing the net capacitance and consequently the double layer charging time, demonstrating that low frequency voltage alternation of the order of 1 Hz is enough to obtain clean and reliable ion emission.     

The double layer at the interface between two immiscible electrolyte solutions: Part II. Structure of the water/nitrobenzene interface in the presence of 1:1 and 2:2 electrolytes

From fast galvanostatic pulse measurements at 25°C the capacitance of the water/nitrobenzene interface was evaluated as a function of the interfacial potential difference Δ_o^w? for systems consisting of NaBr, LiCl or MgSO₄ in water and tetrabutylammonium tetraphenylborate, tetraphenylarsonium tetraphenylborate or tetraphenylarsonium dicarbollylcobaltate in nitrobenzene. The modified Verwey—Niessen model, in which an inner layer of solvent molecules separates two space-charge regions (the diffuse double layer), describes the structure of the water/nitrobenzene interface well at electrolyte concentrations above ca. 0.02 mol dm^?3, provided that the ions are allowed to penetrate into the inner layer over some distance. For all the systems studied the zero-charge potential difference was found at Δ^w_o?_pzc ≈ 0 on the basis of the standard potential difference Δ^w_o?⁰_TMA + = 0.035 V for tetramethylammonium cation which was used as a reference ion. At zero surface charge a comparison was made with the theoretical capacitance calculated using the mean spherical approximation for a model consisting of two ion and dipole mixtures facing each other. The effect of ion penetration on the interfacial capacitance was estimated from the solution of the linearized Poisson-Boltzmann equation for a triple dielectric model with a continuous distribution of the point ions. The concentration-independent inner layer potential difference and capacitance can only be inferred from the capacitance data if the ion size effect is taken into account. A non-iterative procedure based on the hypernetted-chain equation was used for the evaluation of the potential drop across the diffuse double layer. The extend of the penetration into the inner layer appears to be a function of ion solvation, e.g. the more hydrated ion the less extensive ion penetration is likely.     

电解液离子与炭电极双电层电容的关系

以酚醛树脂基纳米孔玻态炭(NPGC)为电极, 通过微分电容伏安曲线的测试, 研究了水相体系电解液离子与多孔炭电极双电层电容的关系. 结果表明, 稀溶液中, 多孔炭电极的微分电容曲线在零电荷点(PZC)处呈现凹点, 电容降低, 双电层电容受扩散层的影响显著；若孔径小, 离子内扩散阻力大, 电容下降更为迅速, 扩散层对双电层电容的影响增大. 而增大炭材料的孔径或电解液浓度, 可明显减弱甚至消除扩散层对电容的影响. 炭电极的单位面积微分电容高, 仅表明孔表面利用率高, 如欲获得高的电容量, 还要有大的比表面积. 离子水化对炭电极的电容产生不利影响, 选用大离子和增大炭材料的孔径, 可有效降低离子水化对炭电极电容性能的影响.     

双电层电容法在电化学生物传感器中的研究与应用

对双电层电容法在电化学生物传感器中的研究和应用进行了较全面的综述,并展望了其发展前景。     

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.     

Inner- and outer-sphere complexation of ions at the goethite-solution interface

Formation of inner- and outer-sphere complexes of environmentally important divalent ions on the goethite surface was examined by applying the charge distribution CD model for inner- and outer-sphere complexation. The model assumes spatial charge distribution between the surface (0-plane) and the next electrostatic plane (1-plane) for innersphere complexation and between the 1-plane and the head end of the diffuse double layer (2-plane) for the outersphere complexation. The latter approach has been used because the distance of closest approach to a charged surface may differ for different ions. The surface structural approach implies the use of a Three-Plane model for the compact part (Stern layer) of solid-solution interface, which is divided into two layers. The thickness of each layer depends on the capacitance and the local dielectric constant. The new approach has been applied to describe the adsorption of magnesium, calcium, strontium, and sulfate ions. It is shown that the concept can successfully describe the development of surface charge in the presence of Ca(+2), Mg(+2), Sr(+2), and SO4(-2) as a function of loading, pH, and salt level, and also the shift in the isoelectric point (IEP) of goethite. The CD modeling revealed that, for the conditions studied, magnesium is mainly adsorbed as a bidentate innersphere complex, calcium can be a combination of bidentate innersphere and a monodentate inner- or outer-sphere complexes, and strontium is probably adsorbed as an outersphere complex. Sulfate is present as a mixture of inner- and outer-sphere monodentate complexes. Outersphere complexation is less pH dependent than innersphere complexation. The CD model predicts that the outersphere complexation of divalent cations and anions is relatively favorable at respectively low and high pH. Increase of ion loading favors the formation of innersphere complexes.     

酚醛基活性炭纤维孔结构及其电化学性能研究

利用水蒸汽活化法制备了酚醛基活性炭纤维(ACF-H2O), 对其比表面积、孔结构与在LiClO4/PC(聚碳酸丙烯酯)有机电解液中的电容性能之间的关系进行了探讨. 用N2(77 K)吸附法测定活性炭纤维的孔结构和比表面积, 用恒流充放电法和交流阻抗技术测量双电层电容器(EDLC)的电容量及内部阻抗. 研究表明, 在LiClO4/PC有机电解液中, ACF-H2O电极的可用孔径(d)应在0.7 nm以上. 随着活化时间的延长, ACF-H2O的孔容和比表面不断增大, 但微孔(0.7 nm ＜ d ＜ 2.0 nm)和中孔(d ＞ 2.0 nm)率变化很小, 活化过程中孔的延伸和拓宽同步进行, 但过度活化则造成孔壁塌陷, 孔容和比表面迅速下降. 因此, 除活化过度的样品外, 电容量随比表面积呈线性增长, 最高达到109. 6 F•g-1. 但中孔和微孔的孔表面对电容的贡献不同, 其单位面积电容分别为8.44 μF•cm-2和4.29 μF•cm-2, 中孔具有更高的表面利用率. ACF-H2O电极的电容量、阻抗特性和孔结构密切相关. 随着孔径的增大, 时间常数减小, 电解液离子更易于向孔内快速迁移, 阻抗降低, 电极具有更好的充放电倍率特性. 因此, 提高孔径和比表面积, 减少超微孔(d ＜ 0.7 nm), 是提高 EDLC能量密度和功率密度的重要途径. 然而仅采用水蒸汽活化, 只能在小中孔以下的孔径范围内进行调孔, ACF-H2O电极电容性能的提高受限.     

Adsorption behavior of bis (2-ethylhexyl) sodium sulfosuccinate (AOT) at the mercury-electrolyte solution interface as a function of electrode potential and time

The dependence of the differential capacitance (C) of the electrode double layer of a hanging mercury drop electrode in bis (2-ethylhexyl) sodium sulfosuccinate (AOT) solutions on electrode potential (E) and time is measured using three-dimensional phase sensitive ac voltammetry. This methodology, possessing a very wide time window that permits a detailed study of the adsorption phenomena, is based on the reconstruction of C vs E curves, sampled after many phase-sensitive ac chronoamperometric experiments. The shape of these curves allows an estimation of the structure of the layer of AOT molecules absorbed at the electrode surface. AOT molecules form micelles in bulk solutions and they also associate in the charged interface under the strong influence of the electric field into surface aggregates which depend on their concentration and applied potential. The presence of AOT micelles in the bulk solution can be linked with the appearance of a surface film at potentials more negative than those corresponding to a condensed film linked with a capacitance value slightly higher than that normally attributed to a compact layer. The whole phenomenon is proved to be very dependant upon time.