A quantitative theory of the Stern electric double layer

A quantitative theory of the Stern electric double layer is suggested. It is based on the view that every ion possesses a geometrical and an electrokinetic radius, that the ionic atmosphere begins from the geometrical one, and that the difference between these radii is the Stern quantity delta. The equations of the mentioned radii and the quantity delta are established and the values of the different potentials characterizing an ion and its ionic atmosphere are determined.     

A modified Poisson-Boltzmann analysis of the capacitance behavior of the electric double layer at low temperatures

The modified Poisson-Boltzmann theory is used to analyze the anomalous behavior of the electric double layer capacitance for small surface charge at low temperatures and densities. Good agreement is found with simulation and recent density-functional theory results. Negative adsorption is also found in line with theory and simulation. An unsatisfactory feature is the relatively poor structure in this region due to the inherent approximations in the theory. This feature is unimportant in relation to the capacitance results but has implications when calculating adsorption properties.     

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.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Statistical mechanical theories of the electric double layer

A comparison is made of present-day statistical mechanical theories of the diffuse part of the electric double layer in aqueous 1-1 electrolyte at a charged plane interface. These theories fall into three categories: (1) the modified Poisson-Boltzmann equation (MPB) based on the Kirkwood-Loeb charging of an ion; (2) the adaption to the electric double layer of the Bogoliubov-Born-Green-Yvon (BBGY) hierarchy of integral equations; (3) the use of the Ornstein-Zernike equation (OZ) for the direct correlation functions of the pair interfacial plane wall-molecular particle, as derived by Henderson, Abraham and Barker (HAB). The HAB-OZ equation is used in conjunction with the mean spherical approximation (MSA) or hypernetted chain approximation (HNC). All the theories make use of the primitive model of the bulk electrolyte, so that inhomogeneity of the dielectric permittivity next to the plane wall is neglected. Except perhaps for a variation of the BBGY theory, which uses a closure based on electrical neutrality, all the theories predict oscillatory behaviour in potential distribution as a function of distance at the higher electrolyte concentrations. The HAB-OZ model has the defect that electrostatic imaging is not consistent with the assumptions of central forces and pair-wise additivity of ionic interactions. It is found that the MPB provides the best overall agreement with Monte Carlo calculations.     

Study on the electric double layer of a cylindrical reverse micelle with functional theoretical approach

Some surfactants, such as AOT (bis-(2-ethylhexyl sodium sulfosuccinate), have such a special structure with a smaller hydrophilic head group but a bigger hydrophobic tail. Some mixtures of surfactants (or surfactant/co-surfactant) also take the same special structure[1―3]. If their concentrations are much higher than their critical micelle concentrations (cmc) in oil/water system, these surfactants or mixtures usually assemble as W/O cylindrical (or wormlike) micelles with their lengths bei…     

双电层电容器用新型无灰煤(HyperCoal)基活性炭的制备

以无灰煤(HyperCoal)为原料,KOH和CaCO3为活化剂制备了煤基活性炭,采用低温N2吸附法表征了活性炭的比表面积和孔结构,测定了活性炭用作双电层电容器(EDLC)电极材料的电化学性能。考察了炭化温度、活化温度、活化时间和活化剂对活性炭电容特性的影响。研究结果表明,比表面积和比电容随着炭化温度的升高而降低,活化温度过高或活化时间太长对比电容有不利影响。此外,CaCO3影响活化过程中孔的开发,显著降低所制备活性炭的比表面积和比电容。在炭化温度为500℃、活化温度为800℃、KOH与焦的质量比为4∶1和活化时间2 h下所得活性炭的比表面积和总孔容分别达到2 540 m2/g和1.65 cm3/g,该活性炭电极在0.5 mol/L TEABF4/PC电解液中的比电容达到最大值46.0 F/g。     

Recent progress in the theory of the electric double layer

Recent progress in the theory of the electric double layer is surveyed briefly. It is concluded that the Gouy-Chapman-Stern treatment of the diffuse double layer, although fairly good, differs significantly from recent computer simulation studies. However, some recent theories, such as the hypernetted chain, the modified Poisson-Boltzmann, and the Born-Green-Yvon approximations, are in satisfactory agreement with the simulations. This survey concludes with a microscopic treatment of the solvent contributions to the double layer.     

Planar electric double layer for a restricted primitive model electrolyte at low temperatures

Monte Carlo simulation and the modified Poisson-Boltzmann theory are used to investigate the planar electric double layer for a restricted primitive model electrolyte at low temperatures. Capacitance as a function of temperature at low surface charge is determined for 1:1, 2:2, 2:1, and 3:1 electrolytes. Negative adsorption can occur for 1:1 electrolytes at low surface charge with low electrolyte concentration. The 1:1 electrolyte diffuse layer potential as a function of surface charge displays a maximum at low densities. At high densities, the diffuse layer potential is negative with a negative slope. The Gouy-Chapman-Stern theory fails in this low-temperature regime, whereas the modified Poisson-Boltzmann theory is fairly successful in this regard.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Differential capacitance of the electric double layer: mean-field modeling approaches

Electrolytes screen the charges carried by an electrode through the formation of a diffuse double layer. The corresponding differential capacitance reflects the change of the surface charge density with the applied surface potential. Mean-field modeling of the differential capacitance is an attempt to qualitatively explain experimental findings such as the camel-to-bell shape transition in terms of physical factors including the ion size and concentration, nonelectrostatic ion–ion interactions, electrostatic ion–ion correlations, and the influence of the electrode curvature. We highlight the central role of the lattice gas model as a conceptual tool to describe concentrated electrolytes and ionic liquids, and we briefly summarize how extensions and generalizations of this model give rise to concepts known as ‘overscreening’ and ‘underscreening’.     

Low-blank digestion of geological samples for platinum-group element analysis using a modified Carius Tube design

We have developed a modified Carius Tube design that permits the low-blank digestion of geological samples prior to platinum-group element analysis. The new Carius Tubes incorporate a liner of high-purity quartz glass that retains the sample and acids during the digestion procedure. This dramatically reduces the comparatively high Pt blank associated with dissolutions in conventional Carius Tubes. Using the new Carius Tube design we are able to achieve total procedural blanks for the determination of the PGE in geological samples that are at the 1–15 pg/g level for Ru, Pd, Ir and Pt. This constitutes a reduction of blank values by a factor of ∼10–100 compared to standard NiS fire assay sample preparation techniques. Received: 23 September 1997 / Revised: 24 October 1997 / Accepted: 31 October 1997     

Low-blank digestion of geological samples for platinum-group element analysis using a modified Carius Tube design

We have developed a modified Carius Tube design that permits the low-blank digestion of geological samples prior to platinum-group element analysis. The new Carius Tubes incorporate a liner of high-purity quartz glass that retains the sample and acids during the digestion procedure. This dramatically reduces the comparatively high Pt blank associated with dissolutions in conventional Carius Tubes. Using the new Carius Tube design we are able to achieve total procedural blanks for the determination of the PGE in geological samples that are at the 1–15 pg/g level for Ru, Pd, Ir and Pt. This constitutes a reduction of blank values by a factor of ～10–100 compared to standard NiS fire assay sample preparation techniques.     

The water-amorphous silica interface: analysis of the Stern layer and surface conduction

To explain why dynamical properties of an aqueous electrolyte near a charged surface seem to be governed by a surface charge less than the actual one, the canonical Stern model supposes an interfacial layer of ions and immobile fluid. However, large ion mobilities within the Stern layer are needed to reconcile the Stern model with surface conduction measurements. Modeling the aqueous electrolyte-amorphous silica interface at typical charge densities, a prototypical double layer system, the flow velocity does not vanish until right at the surface. The Stern model is a good effective model away from the surface, but cannot be taken literally near the surface. Indeed, simulations show no ion mobility where water is immobile, nor is such mobility necessary since the surface conductivity in the simulations is comparable to experimental values.