Thickness of electric double layer

K inverse thickness of electrical double layer (Debye-Hiickel parameter)... 

Coalescence frequency J depends on dimensionless parameters k, p, Sa, Sr, t, y, a. The parameter k characterizes relative sizes of interacting drops p is the viscosity ratio of drops and ambient liquid Sa and Sr are the forces of molecular attraction and electrostatic repulsion of drops r is the relative thickness of electric double layer, which depends, in particular, on concentration of electrolyte in ambient liquid y is the electromagnetic retardation of molecular interaction a is relative potential of surfaces of interacting drops. Let us estimate the values of these parameters. For hydrosols, the Hamaker constant is F 10 ° J. For viscosity and density of external liquid take m /s, 10 kg/m. ... 

Figure 13 schematically illustrates our proposed mechanism for the formation of middle phase microemulsions (13). At low salinities, micelles are formed in the aqueous phase in equilibrium with oil. As the salinity increases, the solubilization of oil within the micelles increases and the thickness of electrical double layer around the micelles decreases. The reduction in repulsive forces allows micelles to approach each other closely and subsequently a micelle-rich phase separates out due to the density difference from the aqueous phase forming the middle phase microemulsion. Hence, the middle phase microemulsion is similar to coacervation process in micellar solution where a micelle-rich phase separates out upon addition of salts. The presence of oil only contributes towards the solubilization of oil within the micelles. Ultimately, at higher salinities, surfactant preferen-... 

Bohinc K, Kralj-Iglic V, Iglic A (2001) Thickness of electrical double layer. Effect of ion size. Eiectrochim Acta 46 3033-3040... 

From Helmholtz s equation it is possible to calculate the equivalent thickness of the double layer, S, as well as the electric moment M, i.e. the distance to which a proton and an electron must be separated, in vacuo, to give the same electric moment. From a knowledge of V and F we are in a position to calculate the electric moment of each adsorbed molecule, a few of these are given in the following table ... 

Fig. 3. The structure of electrical double layer at a semiconductor-electrolyte interface (a) and the distribution of the potential (b) and charge (c) at the interface. The electrode is charged negatively. is the space-charge region thickness, La is the Helmholtz layer thickness, Qlc and Qtl are the charge of the semiconductor and ionic plates of the double layer, respectively (for further notations see the text).

The above discussions illustrate that the interactions between overlapping electrical double layers depend on a number of considerations, such as the magnitude of the surface potential, the thickness of the double layer, and the type of electrolyte, among others. Moreover, the expressions that have been obtained here (and others that are available in the literature) depend on additional conditions that are determined by the approximations made in deriving the expressions. 

Owing to the small thickness of the double layer and the fact that the experiment causes electrochemical reactions by application of a potential, an electrical field is created over the double layer, which can reach a magnitude of 1 x KfVm"1. 

Figure 10.4 shows the results of some measurements on aqueous sodium oleate films. The sensitivity of the equilibrium film thickness to added electrolyte reflects qualitatively the expected positive contribution of electric double layer repulsion to the disjoining pressure. However, this sensitivity to added electrolyte is much less than that predicted from electric double layer theory and at high electrolyte concentration an equilibrium film thickness of c. 12 nm is attained which is almost independent of the magnitude of the disjoining pressure. To account for this observation, Deryagin and Titijevskaya have postulated the existence of hydration layers... 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

The relation between the potential and the net charge on the particle, or charge per unit area in the case of an extended surface, cannot be found without a specific hypothesis as to the distribution of electricity in the double layer. For the idealized, plane parallel double layer, if r is the thickness of the double layer, then would be liror/D. 

Equation 3.7 points out that the variation in the electric field strength (-dy/dx) is related to the second power of the inverse of the thickness of the double layer times /, while Equation 3.8 shows that / decays exponentially with respect to distance (jc) from the surface (Fig. 3.23). A plot of ln( // (/0) versus x produces a straight line with slope k, which is the inverse of the double layer thickness. The assumption ij/0 < 25 mV is not applicable to all soil minerals or all soils. Commonly, clay minerals possess more than 25 mV in surface electrical potential, depending on ionic strength. The purpose of the assumption was to demonstrate the generally expected behavior of charged surfaces. 

A1 hydroxide are known to act as binding agents and induce flocculation [33], In all cases, eluent electrical conductivity values (EC), and therefore ionic strength, remained low (50-100 tS cm-1) during the course of the leaching experiment, suggesting that the electrochemical conditions were not conducive for adequate suppression of the thickness of the double layer that would sufficiently reduce the electrostatic repulsive forces between colloid particles and cause flocculation [34],... 

Adsorbed ions attract oppositely charged ions from the solution and so form an electrical double-layer. The outer part of the double layer is diffuse as the counterions are held by a dynamical balance between diffusion and the electrical force. The thickness of the double layer is of the order of nanometres, but it gets thirmer when the concentration of ions in the bulk solution is increased. 

The treatment of Debye and Hiickel is based on the assumption of an electric field which is constant everywhere and on the supposition that all parts of any spherical shell can move with the same velocity in a given direction. The presence of the particle must, however, distort the electrical field and the hydrodynamic currents, and it is only when the particles are very small in comparison with the thickness of the double layer that the Debyc-Hiickcl result would be expected to hold. Since the value of 1/k increases with increasing dilution, it follows that equation (23) should be applicable to small particles in very dilute solutions. For the case of relatively large particles, Henry has derived the modified equation... 

It is opportune to mention here that some writers prefer to avoid the use of the concept of the zeta-potential it is true that there must be some form of potential across the double layer, but it is so variable in sign and magnitude that its exact significance is regarded as uncertain. The quantity which is called the zeta-potential is, according to equation (1), proportional to the product of the surface charge density and the thickness of the double layer, i.e., to ad it is, therefore, considered preferable to regard it as a measure of the electric moment per sq. cm. of the double layer. 

Due to the amphoteric behavior of the used oxides, the separative properties of these ceramic nanofilters for ionic solutes in aqueous solutions will depend on both sieving and electrical effects. Complex electrokinetic phenomena occur during the forced flow of the ionic solutions through the confined volume of the micropores because the thickness of the double layer formed on the charged pore surface and the pore size have the same order of magnitude. Figure 25.3 illustrates... 

Electronic interaction and synergistic effects between catalysts and the support material have been investigated in the context of fuel-cell electrocatalysts. Electron spin resonance (ESR) has been used to demonstrate the electron donation by Pt to carbon [11] support. This has been further supported by XPS studies [12], which show that the metal acts as an electron donor to the support, their interaction depending on their respective Eermi levels. Bogotsky and Snudkin [13] have shown that the characteristics of the electrical double layer formed between the microdeposit (Pt) and the support depends to a certain extent on the difference in the work function of Pt (5.4 eV) and carbon support (pyrolytic support 4.7 eV), thereby resulting in an increase of the electron density of Pt. However, the rise in the electron density can be significant only when the particle size of the microdeposit is comparable to the thickness of the double layer. 

The outer surface of the Stern layer is the shear surface of the micelle. The core and the Stern layer together constitute what is termed the kinetic micelle. Surrounding the Stern layer is a diffuse layer called the Gouy-Chapman electrical double layer, which contains the aN counterions required to neutralise the charge on the kinetic micelle. The thickness of the double layer is dependent on the ionic strength of the solution and is greatly compressed in the presence of electrolyte. 

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