Dielectric constant, in the double layer

The adsorption of an inhibitor affects the dielectric constant since the double layer structure is affected. This effect is exemplified by the corrosion of iron in 10% HC1 by quinolinium compounds.49 The inhibition by quinolinuim compounds has been attributed to the ordering effect by the re-electron system of the inhibitor molecules on the water molecules located at the metal interface. 

The concept of constant dielectric permittivity in the double layer is also of concern. Different factors such as high ionic concentration or strong electric fields can affect the dielectric permittivity. In addition, description of the dielectric properties of solutions by a single parameter - the dielectric permittivity - also came under criticism and led to the development of nonlocal electrostatics. 

The double-layer capacity of an electrode immersed in a lO M aqueous solution is found to be 50 /tF/cm. The potential difference at the interphase is 0.1 V. Assume that the dielectric constant e in the double layer is 5.9. 

An ion adsorbed on the surface of a suspension will draw near to it an ion of opposite sign in the solution these ions in the double layer are thus hound and can only escape if their kinetic energy exceeds a definite critical value W. If the chemically adsorbed ions have a valency % and n is the valency of the opposite charged ions in the liquid of dielectric constant K in contact with the solid and separated from the former by a distance x, we obtain... 

The first theoretical description of the double layers assumed that the ions interact via a mean potential, which obeys the Poisson equation.2 Such a simple theory is clearly only approximate and sometimes predicts ionic concentrations in the vicinity of the surface that exceed the available volume.3 There were a number of attempts to improve the model, by accounting for the variation of the dielectric constant in the vicinity of the surface,4 for the volume-exclusion effects of the ions,5 or for additional interactions between ions and surfaces, due to the screened image force potential,6 to the van der Waals interactions of the ions7 with the system, or to the change in hydration energy when an ion approaches the interface.8... 

Polymer molecules are often employed to stabilize colloids [1]. In most theoretical treatments of the effect of polymer adsorption [2-5], only the steric force is taken into account, and the steric force and the traditional double-layer force for particles devoid of hairs are assumed to be additive. The steric force is a short-range interaction which acts only when the chains on the surfaces of the two particles interpenetrate [6-8]. However, in addition to this short-range interaction, a hairy surface can also generate another effect, because it can change the dielectric constant in the vicinity of the surface. 

As the dielectric constant of region I increases, the concentrations of ions near the surface increase, the magnitude of the surface charge density decreases, and the force between the two plates decreases (Fig. 17). Compared to the constant surface charge case, for which only the ion concentrations in the double layer increased with increasing dielec-... 

The dielectric constant of the solvent is assumed to be of the same value in the bulk and in the double layer, and it is the only influence that the solvent has on the double layer. 

Could this be behavior in terms of the Maxwell-Wagner dispersion, which would arise through conductivity in the double layer near the polyanion. In support of this, the dielectric constant falls as the frequency increases (Fig. 2.79). 

The second type, of more importance, is a force due to surface-induced liquid structure. At a conceptual level we have already encountered such a force in the double-layer. There the electrolyte can be regarded as the "liquid", with the suspending water a continuum backgroimd that affects the problem only through its dielectric constant. The bulk "liquid" electrolyte has a uniform distribution of cations and anions. In the presence of the charged surface, that uniform distribution changes. The overlap in profile of the surface induced liquid structure causes the force. 

Sass J. K., Schott J. and Lackey D. (1990), Prospects for the direct determination of the dielectric constant of water in the double layer using model adsorption experiments in UHV co-adsorption of Cs and H20 on Cu(llO) , J. Electroanal. Chem. 283, 441-448. 

The determination of the real surface area of the electrocatalysts is an important factor for the calculation of the important parameters in the electrochemical reactors. It has been noticed that the real surface area determined by the electrochemical methods depends on the method used and on the experimental conditions. The STM and similar techniques are quite expensive for this single purpose. It is possible to determine the real surface area by means of different electrochemical methods in the aqueous and non-aqueous solutions in the presence of a non-adsorbing electrolyte. The values of the roughness factor using the methods based on the Gouy-Chapman theory are dependent on the diffuse layer thickness via the electrolyte concentration or the solvent dielectric constant. In general, the methods for the determination of the real area are based on either the mass transfer processes under diffusion control, or the adsorption processes at the surface or the measurements of the differential capacitance in the double layer region [56],... 

In order to integrate the above expression, one needs to know how the viscosity, q, and the dielectric constant, e, change within the double layer. Had these two quantities maintained their bulk values all the way up to the x=0 surface, the macroscopic phase displacement velocity, o0, would have been determined solely by the surface thermodynamic potential, (p0, regardless of the potential distribution in the double layer. Experimental results... 

As seen from Equation 1.7, the electro-osmotic flow depends on the dielectric constant and viscosity of pore fluid, as well as the surface charge of the solid matrix represented by the zeta potential (the electric potential at the junction between the fixed and mobile parts in the double layer). The zeta potential is a function of many parameters, including the types of clay minerals and ionic species that are present, as well as the pH, ionic strength, and temperature. If the cations and anions are evenly distributed, an equal and opposite flow occurs, causing the net flow to be zero. However, when the momentum transferred to the fluid in one direction exceeds the momentum of the fluid traveling in the other direction, electro-osmotic flow is produced. 

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. 

In the integration of Eq. (4.31) it has been assumed that 77 and e are independent of d(()/dx, the local field strength at any point in the double layer. This assumption may be incorrect, since the local electrical field in the double layer would be very high (of the order of 10 Vcm ), if there is a fall of 100 mV in a distance of 100 A. Such a high field would tend to reduce the dielectric constant. More rigorously, we should write... 

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