Electric double-layer thickness

The air gas-diffusion electrode developed in this laboratory [5] is a double-layer tablet (thickness ca.1.5 mm), which separates the electrolyte in the cell from the surrounding air. The electrode comprises two layers a porous, from highly hydrophobic, electrically conductive gas layer (from the side of the air) and a catalytic layer (from the side of the electrolyte). The gas layer consists of a carbon-based hydrophobic material produced from acetylene black and PTFE by a special technology [6], The high porosity of the gas layer ensures effective oxygen supply into the reaction zone of the electrode simultaneously the leakage of the electrolyte through the electrode... 

FIGURE 1.1 Electrical double layer around a positively charged colloidal particle. The particle is surrounded by an ionic cloud, forming the electrical double layer of thickness 1/k, in which the concentration of counterions is greater than that of coions. 

Figure 2 A very simple model of electrostatic adsorption on a negatively charged oxide surface with formation of a "double layer" (surface + diffuse layer). Small dosed drcles are cations, larger open drcles are anions, oq" surface charge density x distance from the surface into the solution k thickness of double layer < ) electric potential c ix) and c (x) local concentrations in cations and anions, respectively. The shaded area represents the excess of cations over anions in the diffuse layer, and therefore the amount of cations that are electrostatically adsorbed.

Near each plane an electrical double layer of thickness Id is formed. If the distance between planes is such that the double layers are superimposed, there is interaction between the planes. Due to symmetry, the minimum value of the potential distribution between the planes is achieved at the symmetry axis of the planes (x = hl2), where d(j)/dx = 0, that is, the electric field is absent. At the axis, there is an excess of ions of the same sign as the charge on the planes, which results in increase of osmotic pressure trying to force the planes apart. 

In the small nanochaimels (from a few to about 100 nm), the electric double layer (EDL) thickness becomes larger or at least comparable with the nanochaimels lateral dimensions. It affects the balance of bulk ionic concentrations of co-ions and counterions in the nanochannels. Thus, many conventional approaches such as the Poisson—Boltzmann equation and the Helmholtz-Smoluchowski slip velocity, which are based on the thin EDL assumption and equal number of co-ions and counterions, lose their credibility and cannot be utilized to model the electrokinetic effects through these nanoscale channels. The Poisson equation, the Navier-Stokes equations, and the Nemst-Planck equation should be solved directly to model the electrokinetic effects and find the electric... 

A charged particle immersed in a liquid containing an electrolyte is surrounded by the electrical diffuse double layer. The thickness of the electrical double layer is given by the Debye length 1/k (k = Debye-Hiickel parameter). For a general electrolyte composed of N ionic mobile... 

This chapter is concerned with the mechanisms of formation of the electrical double layer at a dielectric solid/electrolytic solution interface. When such a contact occurs, the solid s surface acquires a certain charge due to the dissociation of surface ionizable groups and adsorption of ions from solution. Since the whole system is assumed to be electroneutral, the solution has to bear an equal charge of opposite sign. This charge is effectively confined to a thin layer near the dividing surface, termed the diffuse double layer. Its thickness is characterized by the reciprocal Debye length. 

Figure 17 Schematic representation of a diffuse electrical double layer, of thickness 1/K, in contact with a positively charged surface. (From Ref. 33.)...

For electrode polarization, the relaxation time should be controlled by the time of building up the elcetrical double layer. Suppose that the cations and anions have a same diffusion coeillcient D ol the dimension area/second, the ion velocity vi in an electrical double layer of thickness k can be expressed as ... 

Figure 13.4. Interparticular forces between two particles of equal radius a, dispersed in a fluid geometrical notations. Minus signs represent negative electrical charges on the surface of the particles and plus signs denote positive ions within the fluid, hich gather on the surface of the particle as a double layer of thickness Kg...

A charged fractal grain is surrounded by the diffuse electrical double layer. The thickness of the double layer is controlled by the Debye length... 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

For originally non-charged particles dispersed in polar media, the surface preferential adsorption of ions, surface molecular group dissociation, isomorphic substitution, adsorption of polyelectrolytes, and even surface polarization will make them behave similarly to charged particles. The Stem layer and diffuse layer comprise what is commonly known as the electrical double layer, the thickness of which depends on the type and concentration of the ions in the suspension as well as on the particle surface. A parameter, called the Debye-Huckel parameter k, is used to characterize electrical double layer thickness. K has the dimension of reciprocal length. For smooth surfaces in simple electrolytes. 

Colloidal particles are electrically charged by fixed or adsorbed ions and are surrounded by small counterioirs. That results in the formation of an electrical double layer of thickness A.j, ByE particle, analogous to the elec-... 

Equation 46 suggests that, maintaining pi constant, q, must depend linearly on if only a first-order electroviscous effect exists, and an increase in the electrolyte concentration implies a decrease in the thickness, 1/k, of the electrical double layer. 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

Previously, we have proposed that SFG intensity due to interfacial water at quartz/ water interfaces reflects the number of oriented water molecules within the electric double layer and, in turn, the double layer thickness based on the p H dependence of the SFG intensity [10] and a linear relation between the SFG intensity and (ionic strength) [12]. In the case of the Pt/electrolyte solution interface the drop in the potential profile in the vicinity ofelectrode become precipitous as the electrode becomes more highly charged. Thus, the ordered water layer in the vicinity of the electrode surface becomes thiimer as the electrode is more highly charged. Since the number of ordered water molecules becomes smaller, the SFG intensity should become weaker at potentials away from the pzc. This is contrary to the experimental result. 

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