Simulation of the electrical double layer of a spherical micelle of an anionic substance with regard to the solvent structure

Computer simulation methods are employed to consider the structure of the electrical double layer of a spherical micelle in aqueous surfactant solutions with allowance for the contribution of the solvent. Three micelle models were used in the calculations, namely, a macroion with discretely distributed charges and a continual solvent, a spherical model micelle with a coarse-grained representation of the solvent, and a spherical model micelle in an aqueous phase with an explicit account for water molecules. Based on these three models, the radial profiles of the local densities and electric potentials in the electrical double layer, as well as the degrees of binding single-, double-, and triple-charged counterions by the macroion in aqueous surfactant solutions, are calculated with regard to the Lennard-Jones and electrostatic interactions. The allowance for the molecular structure of the solvent leads to qualitatively different local dependences of the electric potential as compared to both the continual and coarse-grained representation of the solvent.     

Studies on the electrical double layer

Summary The differential double layer capacity of a dropping mercury electrode in contact with 1 N sodium sulphate solutions containing various concentrationsc of nonionic surface active agents is strongly dependent on the timet which has passed after the mercury drop started to grow. The suppression of the capacity value over the zero polarization range increases witht, the time constant of this slow adsorption process being independent of the frequency of the ac bridge and decreasing from 175 msec forc=2.5×10^–5 M to almost zero forc=10^–3 M. It is supposed that the slow diffusion process is the governing factor in this case. The kinetic capacity peaks, both anodic and cathodic, also increase witht in general, the time constants being of the order of msec. These time constants decrease with decreasing frequencyf. The time constants for the anodic peaks decrease, while those for the cathodic peaks increase, with increasing concentrationc. Under certain conditions anomalous behaviours are observed, e. g. the kinetic peaks decrease with increasingt forc=10^–3 atf=3,900 cps. This can be explained by the decrease witht in the fractional interfacial area newly formed, where the kinetic process can take place. If the adsorption exchange process can not take place at the old part of the total interface, the capacity per unit area of the mercury drop decreases witht.

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Zusammenfassung Die differentielle Doppelschichtkapazität einer Quecksilber-Tropf-Elektrode in Kontakt mit In-Natrium-Sulfatlösung, die verschiedene Konzentrationenc von nichtionischen oberflächenaktiven Substanzen enthält, hängt stark von der Zeitt ab, die vergangen ist, nachdem der Tropfen sein Wachstum begonnen hat. Die Herabdrückung des Kapazitätswertes im Null-Polarisationsbereich wächst mitt. Die Zeitkonstante dieses langsamen Adsorptionsprozesses ist unabhängig von der Frequenz der Wechselstrombrücke und nimmt von 175 msec fürc=2,5 · 10^–5 M auf beinahe Null fürc=10^–3 M ab. Es ist zu vermuten, daß die langsame Diffusion in diesem Fall der maßgebende Faktor ist. Die kinetischen Kapazitätsspitzen, anodisch und kathodisch, wachsen ebenfalls mitt, die Zeitkonstanten liegen in der Größenordnung von msec. Diese Zeitkonstanten nehmen mit sinkender Frequenzf ab. Die Zeitkonstanten für die anodischen Maxima nehmen ab, während jene für die kathodischen Maxima anwachsen, wenn man die Konzentrationc erhöht. Unter bestimmten Bedingungen wird anomales Verhalten beobachtet. Z. B. nehmen die kinetischen Maxima mit wachsender Zeit fürc=10^–3 beif=3900 Hz ab. Das kann durch die Abnahme erklärt werden, mit der der Bruchteil an Grenzfläche neu gebildet wird, während der kinetische Prozeß stattfindet. Wenn der Adsorptions-Austauschprozeß in den älteren Teilen der Gesamtoberfläche nicht mehr stattfinden kann, sinkt die Kapazität pro Flächeneinheit des Quecksilbertropfens mit der Zeitt.

     

Studies on the electrical double layer structure at the water/air interface

Effective dipole moments (calculated from experimental data of surface tension and electric surface potential) of some homologous normal alcohols and carboxylic acid were found to vary linearly with the number of carbon atoms in the hydrocarbon chain. Values of effective dipole moments were used for the determination of the effective dipole moments of water molecules , and the dielectric permittivity of the water subphase (₁), as well as in the vicinity of the hydrophobic part of adsorbed molecule (₂). The latter was found to decrease with the increase of the hydrocarbon chain length. Knowing the effective dipole moment of surface water dipoles, the average orientation angle () of water molecules at the inteface was estimated. The calculated potential drop of water varies within the range –0.038 to –2.38 V for two extreme orientations of water dipoles at the surface.     

Self-assembly in the electrical double layer of ionic liquids

We have studied the structure of two ionic liquids confined between negatively charged mica sheets. Both liquids exhibit interfacial layering, however the repeat distance is dramatically different for the two liquids. Our results suggest a transition from alternating cation-anion monolayers to tail-to-tail cation bilayers when the length of the cation hydrocarbon chain is increased.     

The determination of the free energy of an electrical double layer

A well-known charging process is used to obtain the free energy of an electrical double layer, in which the double layer is built up by a transfer of ions from one phase to another. The present study formulates proofs that this charging process cannot determine the free energy of an electrical double layer.     

Geometrical factors in the capacity of the electrical double layer

A method for determination of double layer capacities at silver iodide-solution interfaces is presented. The influence of counterion on capacity is subjected to special study in the present work. Capacities at the silver iodide interface are compared with those at the mercury interface (Grahame) and interpreted in terms of theGouy-Stern double layer model. Some characteristic differences between capacities at mercury and silver iodide interfaces are explained in terms of different structural factors.     

Investigation of electrical properties of the electrical double layer on porous glasses

A series of Controlled Porosity Glasses was employed to investigate their electrical surface properties. Surface charge density and adsorption of electrolyte ions were examined, in order to link initial glass composition and physicochemical properties with its surface electrical double layer characteristics. Results prove the increase of surface boron concentration and consequently growing of negative charge and adsorption properties. Authors find it more complicated to explain characteristics of positive charge changes, which require further investigation.     

Effect of N-doping-derived solvent adsorption on electrochemical double layer structure and performance of porous carbon

N-doped porous carbon has been extensively investigated for broad electrochemical applications. The performance is significantly impacted by the electrochemical double layer(EDL), which is material dependent and hard to characterize. Limited understanding of doping-derived EDL structure hinders insight into the structure–performance relations and the rational design of high-performance materials.Thus, we analyzed the mass and chemical composition variation of EDL within electrochemical operation...     

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.     

Surface-bound molecular rulers for probing the electrical double layer

Herein, we report the first experimental investigation on the effect of varying the position of redox-active moieties, within the electrical double layer, on the apparent formal potential and on the electron transfer rate constant. This was achieved using a rigid class of molecules, norbornylogous bridges, to place redox species (ferrocene) at a fixed position above the surface of the electrode. Cyclic voltammetry and alternating current voltammetry were used to calculate the apparent formal potential and the electron transfer rate constant for the electron transfer between the ferrocene and the gold electrode. We use the effect of electric field on the apparent formal potential measurement of the surface-bound redox species to calculate the potential drop from the initiation of the electrical double layer to different distances above it. It was found that self-assembled monolayers formed from ω-hydroxyalkanethiol have a potential profile very similar to that described by classical theories for bare metal electrodes. A steep drop in potential in the Stern layer was observed followed by a smaller potential drop in the Gouy-Chapman layer. The electron transfer rate constant was found to decrease as the distance between the ferrocene moiety and the initiation of the double layer is increased. Thus, the electron transfer rate constant appears to be dependent on ion concentration.     

Structure and dynamics of nanoscale electrical double layer

Electrical double layer (EDL) at substrate–solution interface plays essential roles in basic electrochemistry, energy conversion, desalination and separation, stochastic single-entity sensing, and other applications. The EDL structure generally refers to the inhomogeneous distribution of solution ions at the interfacial region. Dynamic changes in the EDL structure due to the transport of charges at the nanometer scale are the physicochemical origin of recently resolved novel nanotransport phenomena. High surface area materials and devices are potentially advantageous for better applications by providing more accessible interfaces. It is of high importance to emphasize that interfacial structures are indications of capacity, while the efficiency is often related to dynamics. This review discusses emerging transport phenomena under steady-state conditions and the transient deviations in prototype channel-type nanopores as unit elements for porous electrodes/membranes. The fundamental governing mechanism and structure–function correlations will be discussed in the context of energy harvesting and storage, desalination and phase transition, and resistive pulse sensing at the nanometer scale toward single-event/entity resolutions.     

The electrical double layer in LiCl and KF methanol + acetone systems

Differential capacity and interfacial tension measurements were carried out on mercury at 25°C for LiCl and KF in methanol+acetone mixtures, the acetone mole fraction being increased up to 0.8. The Gibbs surface excess of acetone ₂¹ and Guggenheim's model surface mole fraction ₂(₁+₂) were compared at the zero charge potential in saturated and diluted (0.01 M) LiCl solutions. The effect of binary solvent composition on some ionic double-layer properties was observed and described in detail.     

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.     

Contact conditions for the charge in the theory of the electrical double layer

In this paper, from the Born-Green-Yvon equations of the liquid-state theory, we derive a general expression for the charge-density contact value at charged interfaces. This relation is discussed, in particular, for symmetrical electrolytes. We emphasize an essential coupling between the electric properties and the density profile. Limiting behavior at small and large charges at the interface is discussed.