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.     

An Improved Approximation for the Primitive Model of the Electric Double Layer

Abstract

The primitive model for the one sided electrode interface consists of an electrode which is perfectly smooth and flat, and an electrolyte formed by charged hard spheres, all immersed in a dielectric continuum.

The early work of Gouy,¹ Chapman² and Stern³ is based on such a model, and in recent times it has received considerable attention by a number of researchers. Extensive computer simulations have been performed by Torrie, Valleau and coworkers.⁴ The approximate integral equations which have been used to compute the density and voltage profiles and differential capacitance can be divided into four groups. Mean Spherical Approximation (MSA) and its generalization (GMSA),^5,6 the Hypernetted Chain (HNC) and derived equations,^7,8 the Modified Poisson-Boltzmann's (MPB)⁹ and the Born-Green-Yvon (BGY)^10,11 type theories.     

Aqueous solutions of ionic liquids. Description of osmotic coefficients within the Binding Mean Spherical Approximation

The Binding Mean Spherical Approximation (BiMSA) is used to describe osmotic coefficients of aqueous solutions of salts containing imidazolium cations and bulky anions over the whole concentration range at temperature in the range (25 to 60) °C. A total of 13 salts have been considered altogether. The ion diameters, the permittivity of solution and the association constant were taken as adjustable parameters. Ionic liquids are described as being weakly associated in water, and association constants values obtained within the BiMSA model are in good agreement with those from the literature. Diameter values were assigned to 1-alkyl-3-methylimidazolium cations. The adjusted values obtained for the cation diameters increased with the number of carbons on the alkyl chain. For all systems studied, average relative deviations were found to be satisfactory.     

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ?₀ and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ?₀ and ξ potentials are increased.     

Study of the Electrical Double Layer of a Spherical Micelle: Functional Theoretical Approach

The electrical double layer theory is the base of the colloid stability theory (DLVO theory), and the PB eq. is a key to the study of the layer1,2. For a spherical particle, the PB eq. is (1) where and are the dielectric constant of the medium, the valence of ions, the elementary charge, the concentration of ions far away from the particle, the Boltzmann's constant and the temperature of the system, respectively. Since this eq. is a second order nonlinear differential one, only the anal…     

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

The electrophoretic mobility of a spherical colloidal particle with low zeta potential near a solid charged boundary is calculated numerically for arbitrary values of the double layer thickness by a generalization of Teubner's method to the case of bounded flow. Three examples are considered: a sphere near a nonconducting planar wall with electric field parallel to the wall, near a perfectly conducting planar wall with electric field perpendicular to the wall, and on the axis of a cylindrical pore with electric field parallel to the axis. The results are compared with recent analytical calculations using the method of reflections. For the case of a charged sphere near a neutral surface, the reflection results are quite good, provided there is no double layer overlap, in which case there can be extra effects for constant potential particles that are entirely missed by the analytical expressions. For a neutral sphere near a charged surface, the reflection results are less successful. The main reason is that the particle feels the profile of the electroosmotic flow, an effect ignored by construction in the method of reflections. The general case is a combination of these, so that the reflections are more reliable when the electrophoretic motion dominates the electroosmotic flow. The effect on particle mobility of particle-wall interactions follows the trend expected on geometric grounds in that sphere-plane interactions are stronger than sphere-sphere interactions and the effect on a sphere in a cylindrical pore is stronger still. In the latter case, particle mobility can fall by more than 50% for thick double layers and a sphere half the diameter of the pore. The agreement between numerical results and analytical results follows the same trend, being worst for the sphere in a pore. Nevertheless, the reflections can be reliable for some geometries if there is no double layer overlap. This is demonstrated for a specific example where reflection results have previously been compared with experiments on protein mobility through a membrane (J. Ennis et al., 1996, J. Membrane Sci. 119, 47). Copyright 1999 Academic Press.     

Infinite Basis Set Extrapolation for Double Hybrid Density Functional Theory 2: Effect of Adding Diffuse Basis Functions

We applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non‐covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP‐IB calculation with the combination of cc‐pVTZ and cc‐pVQZ reach the chemical accuracy limit (～2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP‐IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc‐pV(L+d)Z), (2) the addition of extra s, p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc‐L) basis sets. We found that the addition of extra s and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP‐IB to reach the chemical accuracy limit with the combination of the double ζ and triple ζ basis sets. Adding extra s, p diffuse functions to the pc‐L series permitted only a small improvement. This small improvement is due to the fact that the pc‐L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.     

泛函数迭代法求解反胶束内双电层电势

用泛函数分析理论中的迭代法求解了反胶束内关于双电层势的Poisson- Boltzmann（PB）方程，导出了泛电位下的第一、二次迭代的解析表达式。与 Debye-Huckel（DH）线性近似及计算机的数值解进行对比表明，迭代解不仅在低电 位条件下能与两者相符合，而且在高电位下与数值解在相吻合。     

Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi-quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near-surface region, for example if a substrate is solid like aforementioned cellulose.     

非导电球型粒子悬浮液宽频介电谱——薄双电层理论的计算机模拟

以Shilov等提出的带有紧密层表面电导率的非导电球型粒子悬浮液宽频介电弛豫的薄双电层理论为基础, 从电动力学角度解释了粒子分散系两种典型介电弛豫(高频和低频弛豫)的机制. 在此基础上, 利用Mathcad程序将该理论定量程序化并建立了粒子/水相分散系介电谱参数与体系内部相参数的关系. 进而利用该程序模拟了溶液浓度、Zeta电位以及分散粒子半径等内相参数对两种弛豫的影响, 结合该理论阐述了不同环境下这两种弛豫的变化规律, 从而为今后更好地利用这两种弛豫表征纳米至毫米级球形粒子分散系的各相电及界面性质提供了有价值的参考.     

An Application of Functional Analysis Method to the Potential of Electrical Double Layer for Spherical Micelles

With the help of the iterative method in functional analysis theory based on the Gouy–Chapman model in the colloid and interface chemistry an analytic solution of the potential of electrical double layer of spherical micelles has been obtained. This method has eliminated the restriction that the Poisson–Boltzmann equation, which represents the distribution of the potential in the double layer, can be solved only under the condition of zekT so far. The connections between the present results and those from Verwey and Overbeek's previous work have also been discussed. Our approach provides a simple but effective method for the calculation of the potential of electrical double layer under general potential condition.     

Charge and Potential of the Diffuse Part of the Double Layer for Sodium Dodecyl Sulfate Micelles in NaCl Solutions

A method is proposed for calculating the ψ_d potential of the diffuse part of the electrical double layer in micelles on the basis of data concerning the binding of counterions by these micelles, the composition of the intermicellar medium, and the association of surface-active ions. The charges of sodium dodecyl sulfate micelles in aqueous solutions at various concentrations of the surfactant and background electrolyte are determined by the potentiometric method. The calculated ψ_d values turned out to be much lower than the values of the electrokinetic potentials, thus allowing the conclusion that the slipping plane corresponding to the electrophoretic motion of micelles with respect to the intermicellar medium is localized in the dense part of the double layer.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 3, 2005, pp. 410–415.Original Russian Text Copyright © 2005 by Us’yarov.     

An Analytical Solution to the Electrical Double Layer Potential for Spherical Particles: A Functional Theoretical Approach

Based on the Gouy-Chapman electrical double layer model, an analytical solution to the Poisson-Boltzmann equation describing the distribution of the electrical potential around spherical particles has been obtained. The advantage of this method is that it is not restricted to the Debye-Hückel approximation condition, where ze ψ ? kT. The present results compare favorably to results obtained under the ze ψ ? kT condition for spherical particles and to results obtained for the general solution for flat plate geometry. This approach provides an effective method for the iterative calculation of the electrical double layer potential for spherical particles.     

Numerical Simulation of Electrochemical Systems by Coupling Analytical Calculation of the Diffuse Double Layer and Finite Element Description of Solution Bulk

Numerical modelling of electrochemical systems covers length scales from the nanometers up to the macroscopic scale. With finite element methods, the mesh must be extremely fine to describe the diffuse double layer, thus increasing the needed computational resources. We propose a method to describe the diffuse double layer by analytical equations, expressed as boundary conditions for the partial differential equations describing the solution bulk. We apply the method to a one-dimensional system, i. e. to a cell with plane parallel electrodes, in the presence of a redox couple and a supporting electrolyte. We provide evidence of the precision of the method.     

Pt纳米催化剂在质子交换膜燃料电池催化层中的尺寸效应研究

以XC-72碳黑为载体, H2[PtCl6]为前驱体, 采用浸渍还原法并结合后续高温处理, 制备出不同尺寸Pt颗粒(3～8 nm)的Pt/C催化剂. 在基于质子交换膜燃料电池(PEMFC)单电池的电化学电解池中, 对实际PEMFC催化层中燃料电池反应的Pt催化剂尺寸效应进行了研究. 结果表明, 在PEMFC催化层环境中, Pt/C纳米催化剂对氢氧化和氧还原反应均有显著的粒度尺寸效应. 随着Pt粒度减小, 氢氧化和氧还原反应的表面积活性均降低.     

Effect of Anion-Induced Cation Adsorption on the Electrical Double Layer Structure

Effect of supporting cations on the EDL structure is analyzed in the region of specific adsorption of anions. The analysis assumes that cations are pulled into the EDL dense part due to their interaction with specifically-adsorbed anions. The model describing this phenomenon is based on the introduction of a second, cationic IHP situated between the plane where centers of charges of specifically-adsorbed anions are localized and OHP. The adsorption of ions, electrode charge, PZC, and EDL capacitance are calculated using two adsorption isotherms for anions and cations.     

Double Layer Impedance in Mixtures of Acetonitrile and Water

Double layer (DL) impedances were evaluated in mixed solutions of water and acetonitrile at various ratios in the polarized potential domain in order to find competitive orientation of the two solvent molecules on the platinum electrode. The DL capacitance at any ratio of the mixture shows the common power law of the ac‐frequency. The capacitance at molar fractions of water less than 0.2 increases linearly with the fraction, and reaches the value for aqueous solution. This variation indicates accumulation of water molecules on the electrode excluding acetonitrile molecules. It is modelled on the concept of the Langmuir‐type isotherm in which water and acetonitrile molecules have competitive interaction with the electrode. The experimental variations by the use of the isotherm yield the difference in the interaction energy, 6 kJ mol⁻¹. The accumulation of water in the DL is supported by the formation of the adsorbed layer by insoluble ferrocene.     

An Experimental Test of the Ion Condensation Theory for Spherical Colloidal Particles

This paper deals with the notion of ion condensation for spherical colloids and, more specifically, with a recent model developed to predict effective charges (Y. Levin, M. C. Barbosa, and M. N. Tamashiro, Europhys. Lett. 41, 123, 1998). Electrophoretic mobility measurements (carried out for a set of well-characterized latexes) were used to find out to what extent this theory is able to accounts for: (i) the insensitivity of mobility to surface charge, and (ii) the small values of electrokinetic charge found at low ionic strength. As the Levin theory was developed assuming no added salt, a previous discussion about the effect of additional electrolyte was needed. Contrary to what other authors have reported, our results do not support the above-mentioned theory. Copyright 2001 Academic Press.     

Double Electric Layer on Liquid Sn-Ga Alloy in Acetonitrile Solutions of Electrolytes

The structure of the double electric layer (DEL) on a liquid dropping Sn-Ga electrode containing 8 at. % of Sn is studied in acetonitrile (AN) solutions of electrolytes. It is shown that the transition from aqueous to AN solutions of electrolytes makes it possible to expand the region of investigation of parameters of DEL on an Sn-Ga electrode from negative charges to a zero charge and to small positive charges. As follows from the obtained data, throughout the entire interval of charges studied, an excess, as compared with an Hg electrode, chemisorption interaction (Sn-Ga)-AN is absent. It is established that the distance of the closest approach of AN dipoles to an ionic core increases upon going from Hg to Sn-Ga to Ga. The Ga, Bi-Ga, and Sn-Ga electrodes, which possess close values of the “electrochemical work function,” are used as an example to show that the metal-solvent chemisorption interaction increases with decreasing distance of the closest approach of its dipoles to the ionic core of the metal. The effect of this factor becomes stronger as the donor number of the solvent increases.     

Mathematical Modeling of Corrosive Alloy Cracking on the Basis of Generalized Dimensionless Electrochemical Factor

A new generalized dimensionless electrochemical factor of corrosive alloy cracking was developed and a quantitative theory of corrosive-mechanical destruction was constructed on its base. The existence of a threshold value of the proposed factor, above which there is no corrosion cracking, was revealed.