Electrostatic interaction between a cylinder and a planar surface

 An exact analytical expression for the potential energy of the electrostatic interaction between a plate-like particle 1 and a cylindrical particle 2 of radius a ₂ immersed in an electrolyte solution of Debye–Hückel parameter κ is derived on the basis of the linearized Poisson–Boltzmann equation without recourse to Derjaguin's approximation. Both particles may have either constant surface potential or constant surface charge density. In the limit of κa ₂→0, in particular, the interaction between a plate with zero surface charge density and a cylinder having constant surface charge density becomes identical to the usual image interaction between a line charge (a charged rod of infinitesimal thickness) and an uncharged plate. Received: 22 September 1998  Accepted in revised form: 27 January 1999     

High Energy Density Heteroatom (O,N and S) Enriched Activated Carbon for Rational Design of Symmetric Supercapacitors

Carbon-based symmetric supercapacitors (SCs) are known for their high power density and long cyclability, making them an ideal candidate for power sources in new-generation electronic devices. To boost their electrochemical performances, deriving activated carbon doped with heteroatoms such as N, O, and S are highly desirable for increasing the specific capacitance. In this regard, activated carbon (AC) self-doped with heteroatoms is directly derived from bio-waste (lima-bean shell) using different KOH activation processes. The heteroatom-enriched AC synthesized using a pretreated carbon-to-KOH ratio of 1:2 (ONS@AC-2) shows excellent surface morphology with a large surface area of 1508 m² g⁻¹. As an SC electrode material, the presence of heteroatoms (N and S) reduces the interfacial charge-transfer resistance and increases the ion-accessible surface area, which inherently provides additional pseudocapacitance. The ONS@AC-2 electrode attains a maximum specific capacitance (C_sp) of 342 F g⁻¹ at a specific current of 1 Ag⁻¹ in 1 m NaClO₄ electrolyte at the wide potential window of 1.8 V. Moreover, as symmetric SCs the ONS@AC-2 electrode delivers a maximum specific capacitance (C_sc) of 191 F g⁻¹ with a maximum specific energy of 21.48 Wh kg⁻¹ and high specific power of 14 000 W kg⁻¹ and excellent retention of its initial capacitance (98 %) even after 10000 charge/discharge cycles. In addition, a flexible supercapacitor fabricated utilizing ONS@AC-2 electrodes and a LiCl/polyvinyl alcohol (PVA)-based polymer electrolyte shows a maximum C_sc of 119 F g⁻¹ with considerable specific energy and power.     

Electrical Properties of Cylindrical Reverse Micelle

In this article, accurate analytic expressions of the surface charge density/surface potential and adsorption excesses for cylindrical reverse micelle in a solution of symmetric electrolyte are derived from the nonlinear cylindrical Poisson–Boltzmann equation. These expressions are in good agreement with numerical values and Van Aken's results for cylindrical reverse micelle with high surface potentials and large κa.     

Ternary [Al2O3–electrolyte–Cu] species: EPR spectroscopy and surface complexation modeling

Cu²⁺ binding on γ-Al₂O₃ is modulated by common electrolyte ions such as Mg²⁺, , and in a complex manner: (a) At high concentrations of electrolyte ions, Cu²⁺ uptake by γ-Al₂O₃ is inhibited. This is partially due to bulk ionic strength effects and, mostly, due to direct competition between Mg²⁺ and Cu²⁺ ions for the SO⁻ surface sites of γ-Al₂O₃. (b) At low concentrations of electrolyte ions, Cu²⁺ uptake by γ-Al₂O₃ can be enhanced. This is due to synergistic coadsorption of Cu²⁺ and electrolyte anions, and _. This results in the formation of ternary surface species (SOH₂SO₄Cu)⁺, (SOH₂PO₄Cu), and (SOH₂HPO₄Cu)⁺ which enhance Cu²⁺ uptake at pH < 6. The effect of phosphate ions may be particularly strong resulting in a 100% Cu uptake by the oxide surface. (c) EPR spectroscopy shows that at pH  pH_PZC, Cu²⁺ coordinates to one SO⁻ group. Phosphate anions form stronger, binary or ternary, surface species than sulfate anions. At pH  pH_PZC Cu²⁺ may coordinate to two SO⁻ groups. At pH  pH_PZC electrolyte ions and are bridging one O-atom from the γ-Al₂O₃ surface and one Cu²⁺ ion forming ternary [γ-Al₂O₃/elecrolyte/Cu²⁺] species.     

An approximate method of self-consistent electronic structure calculations of a crystal surface. The Ir(111) surface

The Slater approximation for atomic electron energies is employed to calculate the electronic structure of the Ir(111) surface. The results are used to estimate the shift of the 4f_7/2 level on the surface relative to its position in the volume. The electron state densities in the neighborhood of the center of the surface Brillouin zone (SBZ) are compared with photoelectronic spectra for emission normal to the Ir(111) surface. On this basis, the accuracy of this approximation is estimated. Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 1, pp. 17–24, January–February, 1994. Translated by O. Kharlamova     

Reactivity of molecular oxygen on the surface of ionic crystals

A possibility of multiplicity change for ground‐state molecular oxygen adsorbed on the surface of regular and doped broad‐gap ionic crystals was considered in the framework of cluster approximation by using SCF MO LCAO quantum chemical methods [semiempirical INDO approximation and ab initio calculation with the 6‐311G** basis set taking into account the correlation effects on the level of second‐order Meller–Plesset perturbation theory (MP2)]. The formation energetics of cyclic products of addition reactions of dioxygen in different multiplet states to furan and cis‐butadiene in the gas phase and on the surface of ionic crystals was considered. (These reactions are typical for the O₂ singlet state in the gas phase.) It is shown that the presence of sites with high effective charge on the crystal surface can result in a situation not requiring, as in the gas phase, multiplicity change in the transition of a system from an initial to the final state, which can significantly affect the kinetic parameters of the reactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Interaction between two similar plane parallel double layers for Mg<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> type asymmetric electrolytes at positive surface potential

The interaction between two similar plane double-layers for Mg₃(PO₄)₂ type asymmetric electrolytes was investigated with the aid of λ parameter method. The interaction energies for the system at positive surface potential were expanded in power series at low and high potential, respectively. The accurate numeral results and V′-ξ _d curves were given for y ₀ ≤ 20 and they can be used to check up 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 is small, the interaction energies for Mg₃(PO₄)₂ type electrolytes increase more drastically than for other type electrolytes. The present results are also fit for Al₂(SO₄)₃ type asymmetric electrolytes at negative surface potential. The article is published in the original.     

First‐principles study of the (001) surface of cubic PbTiO3

We present first‐principles calculations on the (001) surfaces of cubic PbTiO₃ with PbO and TiO₂ terminations. The cleavage energy, surface energy, surface grand potential, surface relaxation and surface electronic structure have been investigated by using the projector‐augmented wave method under generalized gradient approximation (GGA). The results show that surface energy of a TiO₂‐terminated surface is a little lower than that of a PbO‐terminated one, thus allowing both terminations to coexist. The PbO‐termination is stable in O‐ and Pb‐rich environments, while on the contrary, the TiO₂‐termination is stable in O‐ and Pb‐poor conditions. In addition, the surface rumpling S of a PbO‐terminated surface is slightly larger than that of a TiO₂‐terminated one. The relaxations dominantly take place on the outermost three layers, and an oscillatory (? + ?) damping (|Δd₁₂ | > | Δd₂₃ | > | Δd₃₄|) relaxation phenomenon appears for both terminations. The band gaps of both PbO‐ and TiO₂‐terminations are slightly lower than that of the bulk. Moreover, the DOS curves of each layer show that for the TiO₂‐termination, the top of the valence band of the first and third TiO₂ layers moves toward Fermi level. Copyright © 2008 John Wiley & Sons, Ltd.     

A novel polymer gel electrolyte: Direct polymerization of ionic liquid from surface of silica nanoparticles

A novel polymer electrolyte is synthesized by directly grafting poly ionic liquids onto silica nanoparticles. The kinetic study of this surface‐initiated polymerization has also been included. A gel‐state electrolyte is formed by mixing this type of polymer/silica nanocomposite with ionic liquids under 60 °C, which exhibits an excellent conductivity of 0.8 mS/cm at room temperature and 14.7 mS/cm at 90 °C. In addition, the mechanism of gel formation has also been discussed in this article. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 121–127     

Momentum transfer effects in near surface electron energy loss

We examine two formulations for the differential surface excitation parameter (DSEP): one provided by Tung et al. and the other given by the Chen–Kwei position‐dependent differential inverse inelastic mean free path integrated over the electron trajectory. We demonstrate that the latter converges to the former provided that the dielectric function of the solid does not depend on the momentum transfer or it depends on just the momentum transfer component parallel to the surface. Tung's DSEP represents therefore an approximation to the Chen–Kwei DSEP calculated for a dielectric function with no restrictions on the momentum dependence. The approximation is shown to work in the limit of small momentum transfer and to imply an error of 4%–5% for electrons traveling through the solid with energy E = 1 keV. Copyright © 2015 John Wiley & Sons, Ltd.     

Double layer interactions between charge-regulated colloidal surfaces: pair potentials for spherical particles bearing ionogenic surface groups

The variational approach of Reiner and Radke (1990) is employed to investigate the effect of surface charge regulation upon the double layer interaction free energy V_e of pairs of colloidal particles immersed in an electrolyte. A model for dissociating surface groups that permits the consideration of an arbitrary number ofion-complexation reactions is introduced. The variational method is then used to derive (in the Poisson-Boltzmann approximation) the configurational free energy functional Ω of an ensemble of particles bearing such groups. The Debye-Hückel (DH) linearization process is applied to this functional, and ensuing consistency issues are examined.The DH free energy is extremized for a configuration of two interacting flat plates, and Derjaguin's (1934 and 1939) method is used to obtain an approximate analytical form for V_e for two different-sized spherical particles bearing different surface groups. This second problem is next considered from the perspective ofLevine's (1934, 1939b) exact multipole expansion of the electrostatic potential surrounding two axisymmetric particles. It is shown that the linear superposition approximation (LSA) for V_e developed by Levine (1939c) and Verwey and Overbeek (1948) emerges rigorously from this formulation in the limit of large interparticle separations. The interaction free energy from Levine's expansion is calculated te a six digit accuracy for identical spheres over the range of regulated behavior from fixed surface charge density q_s to fixed surface potential ψ_s for surface-surface separation h to Debye length λ ratios from 0 to 2 and ratios of the particle radius a to λ of 0.1, 1, and 10. These results are compared to those obtained from Derjaguin's method and the linear superposition approximation. Derjaguin's method is only quantitatively accurate (in error by less than 10%) for the largest value of a/λ and becomes progressively less so as the boundary is changed from perfectly regulating (constant ψ_s) to unregulated (constant q_s). Agreement of the LSA with the exact V_e is good over a wide range of parameters, but worsens for large a/λ and small h/λ. Appendices present extensions of our approach to surfaces bearing more than one type of complexing group and to the consideration of Stern layer formation at the particle-electrolyte boundary in the context of a standard model for metal oxide-aqueous interfaces.     

Diffuse double layer interaction between two parallel plates with constant surface charge density in an electrolyte solution

Summary The double layer interaction between two parallel metallic plates with adsorbed surface charge of constant density in a symmetrical electrolyte solution is considered. Numerical calculations using the nonlinearPoisson-Boltzmann equation are made. Analytic expressions for the interaction are also obtained by using theDebye-Hückel approximation. The double layer interaction is found to be influenced by true charges induced on the plate surface due to electrostatic induction. This influence becomes important at small plate separations. It is also shown that the force and potential energy of interaction between metallic plates are small compared with those between insulating plates.

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Zusammenfassung Die Wechselwirkung der Doppelschichten zwischen zwei parallelen metallischen Platten mit der konstanten Dichte der adsorbierten Oberflächenladung in einer symmetrischen Elektrolytlösung wird betrachtet. Numerische Berechnungen werden mittels der nichtlinearenPoisson-Boltzmannschen Gleichung ausgeführt. Durch Benutzung der Debye-Hückel-Näherung werden auch analytische Ausdrücke für die Wechselwirkung gewonnen. Es zeigt sich, daß die Wechselwirkung der Doppelschichten von reellen Ladungen, die an der metallischen Oberfläche durch elektrostatische Induktion induziert werden, beeinflußt wird. Dieser Einfluß wird besonders wichtig für kleine Plattenabstände. Die Kraft und die potentielle Energie der Wechselwirkung zwischen metallischen Platten sind kleiner als die zwischen Isolierplatten.

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With 4 figures and 3 tables     

Electrostatic Interaction between Two Dissimilar Spheres with Constant Surface Charge Density

Explicit exact analytic expressions are obtained in the form of infinite series for the potential energy of the electrostatic interaction for the system of two dissimilar hard spheres with constant surface charge density in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. The effects of the particle polarization, that is, the internal fields induced within tim interacting spheres, which are found to be of the order of instead of 1/κa (where κ is the Debye-Hückel parameter and a is the sphere radius), are taken into account. As in the case of the interaction at constant surface potential, the zeroth-order approximation to the interaction energy corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres ("soft" spheres) and to that obtained by the linear superposition approximation. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft sphere, with the other being a hard sphere with constant surface charge density. The first-order correction term can be interpreted as the image interaction between the soft sphere and its image with respect to the hard sphere.     

1.2 Volt manganese oxide symmetric supercapacitor

Capacitance fading of MnO₂ supercapacitor electrode under negative polarization below 0.0 V (versus Ag/AgCl/sat. KCl_(aq)) arises from extensive reduction of Mn(IV) to form inactive Mn(II) species, and this has typically limited the operating voltage window of an aqueous symmetric MnO₂ supercapacitor to be no greater than 0.8 V. As this lower potential limit is close to the onset potential of MnO₂-catalyzed oxygen reduction reaction (ORR), the fading problem can be alleviated by effectively passing the accumulated electrons in the oxide electrode to the dissolved oxygen molecules in electrolyte in order to avoid the formation of the surface Mn(II) species. This has been demonstrated by either increasing the dissolved oxygen content or using the Ti(IV)/Ti(III) redox couple in the electrolyte as a charge-transfer mediator to enhance the electrocatalytic activity of MnO₂ for ORR. Therefore, a MnO₂ symmetric supercapacitor showing remarkable cycling stability over an operating voltage window of 1.2 V has been achieved by using Ti(IV)-containing neutral electrolyte (1 M KCl_(aq)).     

Hierarchically Porous Carbons Derived from Metal–Organic Framework/Chitosan Composites for High‐Performance Supercapacitors

Hierarchically porous carbon materials with high surface areas are promising candidates for energy storage and conversion. Herein, the facile synthesis of hierarchically porous carbons through the calcination of metal–organic framework (MOF)/chitosan composites is reported. The effects of the chitosan (CS) additive on the pore structure of the resultant carbons are discussed. The corresponding MOF/chitosan precursors could be readily converted into hierarchically porous carbons (NPC‐V, V=1, 2, 4, and 6) with much higher ratios of meso‐/macropore volume to micropore volume (V_meso‐macro/V_micro). The derived carbon NPC‐2 with the high ratio of V_meso‐macro/V_micro=1.47 demonstrates a high specific surface area of 2375 m² g^?1, and a high pore volume of 2.49 cm³ g^?1, as well as a high graphitization degree, in comparison to its counterpart (NPC) without chitosan addition. These excellent features are favorable for rapid ion diffusion/transport, endowing NPC‐2 with enhanced electrochemical behavior as supercapacitor electrodes in a symmetric electrode system, corresponding to a high specific capacitance of 199.9 F g^?1 in the aqueous electrolyte and good rate capability. Good cycling stability is also observed after 10 000 cycles.     

Nonlocal density functional calculations of the jellium metal surface

The Becke exchange functional is used for calculation of properties of the jellium model using the slab geometry inside a box with the infinite potential barriers at the boundaries. We simplify semianalytical representation of matrix elements. We calculate the surface energies and work functions with self-consistent electron densities. For all densities (here, we give results in erg/cm² for r_s = 2.07 bohr, in comparison with the LSD approximation (?602)) and the uncorrected Pw GGA -II (?730), the Becke-II exchange only (?1212), and the Becke-II exchange with Perdew86 correlation (?830) [always close to Pw GGA -I (?814)] give smaller surface energies. The most important factor determining values of surface energies from different GGAS seems to be a form of a correlation potential. We also calculate the effect of finite slab thickness and the vacuum region thickness on the surface energy at the LSD level and indicate its importance in various jellium model calculations. © 1995 John Wiley & Sons, Inc.     

Ab initio study of molecular oxygen adsorption on Pu (111) surface

Using the generalized gradient approximation to density functional theory (DFT), molecular and dissociative oxygen adsorptions on a Pu (111) surface has been studied in detail. Dissociative adsorption with a layer‐by‐layer alternate spin arrangement of the plutonium layer is found to be energetically more favorable, and adsorption of oxygen does not change this feature. Hor1 (O₂ is parallel to the surface and lattice vectors) approach on the center2 (center of the unit cell, where there is a Pu atom directly below on the third layer) site, both without and with spin polarization, was found to be the preferred chemisorbed site among all cases studied with chemisorption energies of 8.365 and 7.897 eV, respectively. The second‐highest chemisorption energy occurs at the Ver (O₂ is vertical to the surface) approach of the bridge site with chemisorption energies of 8.294 eV (non‐spin‐polarized) and 7.859 eV (spin‐polarized), respectively. We find that 5f electrons are more localized in the spin‐polarized case than the non‐spin‐polarized counterparts. Localization of the 5f electrons is higher in the oxygen‐adsorbed plutonium layers compared with the bare layers. The ionic part of O? Pu bonding plays a significant role in the chemisorption process, along with Pu 5f? O 2p hybridization. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Voltammetric studies of microcrystalline C60 adhered to a carbon electrode surface and placed in contact with aqueous electrolyte containing potassium ions

The reduction of microcrystalline C₆₀ fullerene, adhered at a carbon electrode and immersed in aqueous electrolyte, has been studied under various voltammetric conditions. This work reports mainly the voltammetric studies carried out principally in electrolyte containing potassium ions. Comparison of adherence techniques, such as solvent casting and mechanical transfer methods, are made to assess if the type of adhered techniques has any significant influence on the observed electrochemistry. The solvent casting method is found to produce three peaks in the potential for C₆₀^0/n- redox couple as compared to a single and large peak produced when a mechanical transfer technique is employed. When the reduction potential of microcrystalline C₆₀ in the presence of K⁺ is compared with other cations, such as Li, Na, Rb and Cs, it is observed that the shift of reduction potential follows the change in the hydration energy in the order Cs>Rb>K>Na>Li. In a mixed electrolyte study of CsCl/KCl, the reduction potential and peak shape of C₆₀^0/n- redox couple during cyclic voltammetry is observed to change with concentration of the cations and the observed electrochemistry can be attributed to a cation-exchange mechanism. The reduction of C₆₀ is irreversible in aqueous electrolyte containing alkaline cations as the re-oxidation process does not produce any observed electro-activity. Evidence of the formation of a passive coating of K _n C₆₀ fulleride, which does not appear to undergo dissolution is obtained under cyclic voltametric conditions. This coating remains electrochemically active in the presence of tetrabutylammonium ions in acetonitrile. Scan rate, chronocoulometric, and scanning electron microscopic studies provide evidence of the presence of a surface process involving solid–solid transformation.     

Electrochemical and surface science investigations of PtCr alloy electrodes

Electrodes of supported Pt, modified with Cr, have shown an increase in electrochemical activity for oxygen reduction in phosphoric acid fuel cells over supported Pt only electrodes. To clarify the role of chromium and its chemical nature at the electrode surface, we have characterized a series of Pt_xCr(_1-x) bulk alloys (x = 0.9, 0.65, 0.5, 0.2) by electrochemical and ex-situ surface science methods. In this paper we report the surface characterization of native and post-electrochemical electrodes by XPS, cyclic voltammetry in 0.05 M H₂SO₄ and 85% H₃PO₄, and analysis of 0.05 M H₂SO₄ electrolyte following electrochemical treatment. The surface Cr(1 to 2 nm) was oxidized to Cr³⁺ oxide for surfaces at open circuit and those exposed to potentials < + 1.3 V vs DHE in 0.05 M H₂SO₄ and < + 1.55 V vs. DHE in 85% H₂PO₄. In 0.05 M H₂SO₄ the Cr component was electrooxidized to solube Cr⁶⁺ species at potentials > +1.3 V with the extent of Cr dissolution dependent on initial alloy stoichiometry. Alloys with Cr content 0.5 are capable of producing (dependent on time spent at potentials above +1.3 V in 0.05 M H₂SO₄) very porous Pt-rich surfaces. Loss of Cr was also observed in 85% H₃PO₄ for the alloys with Cr content 0.5, although at the more positive potential limit of +1.55 V. For the Pt_0.2Cr_0.8, treatment in 85% H₃PO₄ at +1.4 V and above led to the appearance of Pt⁴⁺ and Cr⁶⁺ species, apparently stabilized in a porous phosphate overlayer up to 5 nm thick (dependent on time spent at potentials above this limit). The enhancement reported for supported Pt+Cr oxygen cathodes is discussed in the light of these results.