EDLs

Tuckerman DB, Pease REW (1981) High-performance heat sinking for VLSI. IEEE Electron Devise Lett EDL-2 126-129... 

The above form of the Arrhenius equation takes into account the high degree of correlation that exists between the kinetic parameters. This pivoting method solves a convergence problem that can occur during parameter fitting if all six parameters (Fm, Em, Fdl, Edl, Fd2, and Ed2) are allowed to vary. 

An MRL of 0.1 ppm was derived for intermediate inhalation exposure (15-364 days) to trichloroethylene. This MRL was based on a study by Arito et al. (1994a) in which male JCL-Wistar rats were exposed to 0, 50, 100, or 300 ppm trichloroethylene for 6 weeks, 5 days/week, 8 hours/day. A LOAEL of 50 ppm was observed for decreased wakefulness during exposure, and decreased postexposure heart rate and slow wave sleep. Another study with rats found an increase in sleep-apneic episodes and cardiac arrhythmias after exposure to trichloroethylene (Arito et al. 1993). These results corroborate similar effects observed in humans exposed to trichloroethylene, as described in the previous paragraph, as well as evidence of organic solvent-induced sleep apnea in humans (Edling et al. 1993 Monstad et al. 1987, 1992 Wise et al. 1983). 

Edling C, Lindberg A, Ulfberg J. 1993. Occupational exposure to organic solvents as a cause of sleep apnoea. Br J Ind Med 50 276-279. 

We have given defect-equations for edl nine types of defects, and the Equilibrium Constants thereby associated. However, calculation of these equilibria would require values in terms of energy at each site, values which are difficult to determine. A better method is to convert these EC equations to those involving numbers of each Qrpe of intrinsic defect, as a ratio to an intrinsic cation or einion. This would allow us to calculate the actual number of intrinsic defects present in the crystal, at a specified temperature. 

The EDL charge distribution can be modeled by a Poisson-Boltzmann equation (see, e.g., [46]). In many practical cases values for the layer thickness between 1 and 100 nm are obtained [47]. 

The existence of Galvani potentials between two different conducting phases is connected with the formation of an electric double layer (EDL) at the phase boundary (i.e., of two parallel layers of charges with opposite signs, each on the surface of one of the contacting phases). It is a special feature of such an EDL that the two layers forming the double layer are a very small (molecular) distance apart, between 0.1 and 0.4nm. For this reason EDL capacitances are very high (i.e., tenths of pF/cm ). 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

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. 

When an electrode is in contact with an electrolyte, the interphase as a whole is electroneutral. However, electric double layers (EDLs) with a characteristic potential distribution are formed in the interphase because of a nonuniform distribution of the charged particles. 

Two types of EDL are distinguished superficial and interfacial. Superficial EDLs are located wholly within the surface layer of a single phase (e.g., an EDL caused by a nonuniform distribution of electrons in the metal, an EDL caused by orientation of the bipolar solvent molecules in the electrolyte solution, an EDL caused by specific adsorption of ions). Tfie potential drops developing in tfiese cases (the potential inside the phase relative to a point just outside) is called the surface potential of the given phase k. Interfacial EDLs have their two parts in dilferent phases the inner layer with the charge density in the metal (because of an excess or deficit of electrons in the surface layer), and the outer layer of counterions with the charge density = -Qs m in the solution (an excess of cations or anions) the potential drop caused by this double layer is called the interfacial potential... 

Hermann von Helmholtz put the concept of EDL formation at electrode surfaces forward in 1853. For a long time only the interfacial EDLs were taken into account. The considerable importance of various kinds of superficial EDLs was pointed out by Alexander N. Frumkin in 1919. 

The formation of any kind of EDL implies the development of strong electrostatic fields in the interphase. The distance between the two sides of an EDL as a rule is... 

Each type of EDL and the potential drop produced by it contribute to the total Galvani potential, (pg, at the interface considered ... 

Some of the components of the EDL, such as a nonuniform electron distribution in the metal s surface layer and the layer of oriented dipolar solvent molecules in the solution surface layer adjacent to the electrode, depend on external parameters (potential, electrolyte concentration, etc.) to only a minor extent. Usually, the contribution of these layers is regarded as constant, and it is only in individual cases that we must take into account any change in these surface potentials, and which occurs as a result of changes in the experimental conditions. 

Changes in the parameters listed above influence primarily the interfacial EDL that is, the excess charge densities and the distribution of electrostati-... 

Because of mutual repulsion forces and of attraction forces arising on the other side of the EDL, the excess charges in the metal are always tightly packed against the interface. The excess charges in the solution (i.e., the ions) are subject to thermal... 

Different structural models of the ionic EDL have been suggested in order to describe the electrical properties of interfaces. Consider the distribution of electrostatic potential j/ at the solution side of the ionic EDL as a function of distance X from the surface. By convention we locate the point of reference in the solution interior (i.e., we shall assume that / = 0 when x->°°). The potential at X = 0 will be designated as rj/g. The sign of parameter /o corresponds to that of Qs,m-... 

Following the concepts of H. Helmholtz (1853), the EDL has a rigid structnre, and all excess charges on the solntion side are packed against the interface. Thus, the EDL is likened to a capacitor with plates separated by a distance 5, which is that of the closest approach of an ion s center to the surface. The EDL capacitance depends on 5 and on the value of the dielectric constant s for the medium between the plates. Adopting a value of 5 of 10 to 20 nm and a value of s = 4.5 (the water molecules in the layer between the plates are oriented, and the value of e is much lower than that in the bulk solution), we obtain C = 20 to 40 jjE/cm, which corresponds to the values observed. However, this model has a defect, in that the values of capacitance calculated depend neither on concentration nor on potential, which is at variance with experience (the model disregards thermal motion of the ions). 

Thermal motion of the ions in the EDL was included in the theories developed independently by Georges Gouy in Erance (1910) and David L. Chapman in England (1913). The combined elfects of the electrostatic forces and of the thermal motion in the solution near the electrode surface give rise to a diffuse distribution of the excess ions, and a diffuse EDL part or diffuse ionic layer with a space charge Qy x) (depending on the distance x from the electrode s surface) is formed. The total excess charge in the solution per unit surface area is determined by the expression... 

Grahame introdnced the idea that electrostatic and chemical adsorption of ions are different in character. In the former, the adsorption forces are weak, and the ions are not deformed dnring adsorption and continne to participate in thermal motion. Their distance of closest approach to the electrode surface is called the outer Helmholtz plane (coordinate x, potential /2, charge of the diffuse EDL part When the more intense (and localized) chemical forces are operative, the ions are deformed, undergo partial dehydration, and lose mobility. The centers of the specifically adsorbed ions constituting the charge are at the inner Helmholtz plane with the potential /i and coordinate JCj < Xj. 

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