Historical development of theories of the electrochemical double layer

This review describes the evolution of important concepts related to potential drops at interfaces in electrochemical systems. The role of the thermodynamic theory of electrocapillarity of perfectly polarizable electrodes in the development of interfacial electrochemistry is emphasized. A critical analysis of the phenomenological models of the electrical double layer on ideally polarizable electrodes is given. Certain trends in studying solid electrodes with well-defined surfaces brought into contact with electrolyte solutions are summarized. Attention is drawn to several unsolved problems crucial for the future development of electrochemical surface science. Finally, some recent experimental data are analyzed for selected models.     

Viscoelasticity in the diffuse electric double layer

The electroacoustical impedance of the quartz crystal microbalance (QCM) in contact with aqueous electrolyte solutions was measured using the transfer function method in a flow injection system . Measurements of both components of the impedance of the QCM, the resistance R and the inductive reactance XL, have been performed for modified and bare gold and silver surfaces and for different concentrations of several aqueous electrolyte solutions. For the experimental concentration range of 0-50 mM, unexpectedly the QCM impedance does not follow the Kanazawa equation, as is usual for bulk newtonian liquids. This behavior indicates the presence of a nanometric sized viscoelastic layer between the piezoelectric crystal and the bulk electrolyte solution. This layer can only be identified as the Gouy-Chapman diffuse double layer (DDL). Its elasticity and viscosity have been estimated by the measurement of R and XL. The viscoelasticity of the DDL appears to be independent of the chemical nature of the surface and of the solution viscosity but strongly dependent on the surface charge, the bulk electrolyte concentration and the dielectric constant of the solvent.     

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.     

Ion redistribution in an electric double layer

The structure of a single flat electric double layer (EDL) is studied by grounding a symmetric electrolyte (NaCl), which is in contact with a planar positively corona-treated polypropylene film. Because the profiles of the electrostatic potential distribution and ion distribution in the solution are altered when the solution is grounded, some mobile counterions in the diffuse layer of the electrolyte solution will go into the Helmholtz layer and thus decrease the electric potential psi(a/2) at the Stern plane in order to obtain a new equilibrium. After the system is grounded for a long time, the representation of the electric double layer changes from a Stern model to a Helmholtz model. Theoretical and experimental analyses are given in this study.     

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.     

Recent advances in the electric double layer in colloid science

The interaction between charged colloidal particles is mediated by their electric double layers. Given that pairs of like-charged particles experience a repulsion, why do some dilute colloidal dispersions become unstable and condense at low ionic strengths? This puzzling paradox appears to have been largely resolved over the past year by a careful analysis of all the contributions to the thermodynamic potential of the dispersion. Condensation can be predicted using the traditional pair repulsion of the Poisson–Boltzmann theory without invoking any long-range attractions in the pair potential. However, it has emerged that one has to go beyond the Poisson–Boltzmann theory to account for the instability that occurs in confined colloidal dispersions. Other recent advances in the ubiquitous Poisson–Boltzmann theory have included effective surface charge approaches in calculating the electrokinetic zeta potential, and the modelling of charge regulation in colloidal systems.     

Modelling the electric double layer at electrode/electrolyte interfaces

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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’.     

The electric double layer structure around charged spherical interfaces

We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface potential is determined, and its superiority over the linearized solution is demonstrated.     

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。     

The structure of the electric double layer: Atomistic versus continuum approaches

This article reviews recent forays in theoretical modeling of the double layer structure at electrode/electrolyte interfaces by current atomistic and continuum approaches. We will briefly discuss progress in both approaches and present a perspective on how to better describe the electric double layer by combining the unique advantages of each method. First-principles atomistic approaches provide the most detailed insights into the electronic and geometric structure of electrode/electrolyte interfaces. However, they are numerically too demanding to allow for a systematic investigation of the electric double layers over a wide range of electrochemical conditions. Yet, they can provide valuable input for continuum approaches that can capture the influence of the electrochemical environment on a larger length and time scale due to their numerical efficiency. However, continuum approaches rely on reliable input parameters. Conversely, continuum methods can provide a preselection of interface structures and conditions to be further studied on the atomistic level.     

X-ray study of the electric double layer at the n-hexane/nanocolloidal silica interface

The spatial structure of the transition region between an insulator and an electrolyte solution was studied with x-ray scattering. The electron-density profile across the n-hexane/silica sol interface (solutions with 5, 7, and 12 nm colloidal particles) agrees with the theory of the electrical double layer and shows separation of positive and negative charges. The interface consists of three layers, i.e., a compact layer of Na(+), a loose monolayer of nanocolloidal particles as part of a thick diffuse layer, and a low-density layer sandwiched between them. Its structure is described by a model in which the potential gradient at the interface reflects the difference in the potentials of "image forces" between the cationic Na(+) and anionic nanoparticles and the specific adsorption of surface charge. The density of water in the large electric field (approximately 10(9)-10(10) Vm) of the transition region and the layering of silica in the diffuse layer is discussed.     

Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified Stern layer

A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.