Electrical double layer region

According to the model proposed by Verwey and Niessen (1939), an electric double layer is formed at an ITIES, which consists of two ionic space charge regions. As a whole the electric double layer is electrically neutral, so for the excess charge density in the part of the double layer in the aqueous phase, and for the part in the organic phase,... 

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

The state of stability under these conditions can be qualitatively described as follows. As two oil droplets approach each other, the negative charge gives rise to a repulsive effect (Figure 7.4). The repulsion will take place within the electrical double-layer (EDL) region. It can thus be seen that the magnitude of double-layer distance will decrease if the concentration of ions in the water phase increases. This is because the electrical double layer region decreases. However, in all such cases in which two bodies come closer, there exists two different kinds of forces that must be considered ... 

The region extending from the phase boundary out to about 3 nm is quite unlike the solution beyond. Generalizations valid elsewhere in the solution do not necessarily apply here. In this inner zone, the so-called double-layer region [9], we may encounter a violation of the electroneutrality condition (see Sect. 4.1) and large electric fields. Concentrations may be enhanced or depleted compared with the adjacent solution. 

This electrokinetically driven micro mixer uses localized capacitance effects to induce zeta potential variations along the surface of silica-based micro channels [92], The zeta potential variations are given near the electrical double layer region of the electroosmotic flow utilized for species transport. Shielded ( buried ) electrodes are placed underneath the channel structures for the fluid flow in separate channels, i.e. they are not exposed to the liquid. The potential variations induce flow velocity changes in the fluid and thus promote mixing [92],... 

There remain some experimental problems. Since the conductivity of the mobile electric double layer region is higher than in bulk solution, the surface conductance alters the electric field distribution somewhat, hence the zeta potential. This is usually not significant for small values of Ka and/or ionic strengths greater than about 0.01 M. In the presence of the applied electric field, the electric double layer... 

In an analysis of a rigid, charged surface, Stokes [28] proposed a perturbation method in which the derivative of electrical potential with respect to position variable is expanded in a negative power series in the position variable. Following a similar approach [23], we assume, for the double-layer region ( = 0),... 

The electrical potential in the membrane phase is obtained by substituting (39)-(42) with i — 1 into (37). Similarly, substituting (38)-(40) and (43) into (37) with i — 0 gives the electrical potential in the double-layer region. Here, jcp, and xq are defined as... 

However, there is no corresponding increase in the average velocity with increased hydraulic diameter. This is because the nature of electroosmotic flow—the flow is generated by the motion of the net charge in the electrical double layer region driven by an applied electrical field. When the double layer thickness 1/k) is small, an analytical solution of the electroosmotic velocity can be derived from a one-dimensional channel system such as a cylindrical capillary with a circular cross section, given by... 

FIGURE 7.3 Distribution of electrical potential in the double layer region surrounding a charged particle showing the position of zeta potential and the reciprocal Debye length. (From Williams, R.A., in Colloid and Surface Engineering Applications in the Process Industries, Butterworth-Heinemann, Oxford, 1992. With permission.)... 

All solid surfaces acquire electrostatic charges when they are in contact with an aqueous solution. The surface charge in turn attracts the counterions in the liquid to the region close to the surface, forming the electric double layer. Under a tangentially applied electrical field, the excess counter-ions in the double layer region will move, resulting in a bulk liquid... 

In the LE the local dielectric constant at the interface may be significantly modified as a result of orientation of the water-molecule dipole in the electric field of the double layer. Furthermore, ions can flow to the interface and be adsorbed there, in the double-layer region. 

Some of the illustrative examples for the application of EQCN technique are collected in [157]. The electrical double-layer region of optically polished gold in 0.1-M NaF, KF, RbF, and CsF solutions in the absence and with addition of specifically adsorbing anions S04 , OH , Cl , and Br was studied, arriving at the conclusion that EQCN can be used to investigate the electrical double-layer phenomena on metal electrodes. 

Inside the silicon semiconductor, electrons diffuse from the n-type side (with a high electron concentration) in the direction of thep-type side. Holes diffuse from the p-side in the opposite direction. This results in a region where all charge carriers are depleted (space charge region). At thep-n junction both electrons and holes accumulate electrons on one side of the junction, and holes at the other side. Thus, a double layer of electric charges is formed, which leads to a potential difference of about 0.6-0.7 V. This is the solar cell s open-circuit voltage (OCV). When both sides of the... 

Fig. 1 Electroosmotic flow near the double layer region for (a) a homogeneous surface (C = -ICol)and(b) a homogeneous surface with a heterogeneous patch (C = + ICoD- Over the heterogeneous patch, the excess cations are attracted to the positive electrode resulting in an electroosmotic flow in the opposite direction to that over the homogeneous regions with an excess anion concentration. Arrows represent streamlines and 1/k refers to the characteristic thickness of the electrical double layer...

The surface conduction is the excess electric conduction tangential to a charged surface and originates from the excess counterions concentrations in the electrical double layer region near the solid-liquid interface. The corresponding electric conductivity is called the surface conductivity, /is, that is considered as the electric conductivity of a sheet of material of negligible thickness, with a unit m Specific surface conductivity values are of the order 10 10 for water in glass capillaries. 

Hence, pressure varies with position in the electrical double-layer region, where an electrical body force exists, just as it varies with position in a static pool of liquid, where gravitational body force exists. In the latter case, pressure increases with depth in accordance with the familiar rules of hydrostatics. Substitution of Equation 3.19 into Equation 3.23 yields... 

We shall restrict our consideration here to the simplest electrochemical case the electrical double layer, which is not complicated by charge transfer or by specific adsorption. At first glance it would seem that, if there is no change in mass and nothing happens in the bulk of the solution in which the electrode is immersed, the EQCM response should be zero. However, essentially all measurements show that in the double-layer region the frequency of the EQCM depends on potential. The effect is rather small—a few Hz for crystals with fundamental frequencies of 5-10 MHz. 

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