Double layer distortion

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

A relatively constant Tafel slope for reactions not involving adsorption, and those involving adsorption with complete charge transfer across the double layer, distorted by second order effects, may also be explained in terms of a non-Franck-Condon process. Since adsorbed intermediates in charge transfer processes also show adsorption energies depending on potential in the same way as the potential energy barrier maxima, these should also follow the same phenomena. 

Calculation of the Zeta Potential. The conversion of electrophoretic mobility to zeta potential is complicated somewhat by the existence of the electrophoretic relaxation effect. Figure 5 shows a schematic diagram of this effect. As we expose an emulsion droplet and its surrounding double layer to an electric field, the double layer distorts to the shape shown in the figure. This distorted double layer now creates its own electric field that... 

Taking the double-layer distortion from equilibrium as a perturbation, Prieve and Roman [2]... 

Taking the double-layer distortion from equilibrium as a perturbation, Prieve and Roman [2] obtained a numerical calculation for the diffusiophoretic velocity of a dielectric sphere of radius a in concentration gradients of 1 1 electrolytes (KCl or NaCl) which was applicable to arbitrary values of and ku, where k Ms the Debye screening length equal to 2Z e n°°IskT) On the other hand,... 

When an electric field is applied, localization of ionic distribution takes place and electrical dipoles generate static attractive forces. This electric double layer distortion theory [37-39] is supported by the experimental observation that the ER effect is drastically affected by the addition of water or a surfactant, or the difference in the electric conductivity of the suspended particles and the dispersant. 

The mobility curves have this shape because of double layer distortion. The applied field sweeps the double-layer ions back and forth and this leads to a change in the charge distribution around the particle. For highly charged particles, this has a significant effect on the flow field and the electric forces that act on the particle. 

To understand why the double layer distortion affects the mobility in this way, it is useful to consider the representation of the sinusoidal electrical forces on the particle as rotating vectors in Figure 4.10. The force on the particle due to the applied electric field is denoted by Fa in the figure. The actual force is the projection of this vector on the horizontal axis. The vectors rotate with a constant angular velocity ((o), so their horizontal projection will be sinusoidal. The distortion of the double layer leads to the back field Fb. The phase of this force relative to the apphed force is determined by the angle between these two vectors. The net electric force is the horizontal projection of F the vector sum of Fa and Fb. 

The above discussion also applies to the thin double layer systems with surface conductance considered in the previous section. The surface conductance alters the double layer charge distribution, and so it gives rise to double layer distortion. 

The double layer distortion is only significant for particles with moderate to high zeta potentials. The effect is most pronounced for Ka values between 1 and 10. In this range it is significant if zeta is more than 50 mV in magnitude. For Ka values outside this range the effect can still be important, but only at higher zeta potentials. 

Orthorhombic distortion, owing to puckered metal as well as B layers, occurs in the RUB2 type, whereas for monoclinic Ir2B3 (IrB, 35) a sequence of puckered B and metal double layers containing isolated B atoms is established. ... 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The primary electroviscous effect occurs, for a dilute system, when the complex fluid is sheared and the electrical double layers around the particles are distorted by the shear field. The viscosity increases as a result of an extra dissipation of energy, which is taken into account as a correction factor pi" to the Einstein equation ... 

The slopes of the different curves correspond to the fuU electrohydrodynamic effect, ( ) + ( ) pj, where the first term expresses the hydrodynamic effect, and the second is the consequence of the distortion of the electrical double layer that surrounds the particles. To determine this second term and, more exactly, the primary electroviscous coefficient, pi. 

Molybdenum trioxide has a layered structure with orthorhombic symetry [16] (a=3.963, b=ll855, c=3.696 A), this structure consists of double layer sheets parallel to the (010) cleavage plane. The building unit is a distorted M0O6 octahedron, with Mo-0 distances 1.67, 1.73, 1.95 (twice), 2.25 and 2.33 A (Fig.l)... 

The structure of alumina on NiAl(l 1 0) was the subject of a surface X-ray diffraction study by Stierle et al. [46]. The model derived by Stierle et al. from the analysis of the X-ray diffraction data was based on a strongly distorted double layer of hexagonal oxygen ions, where the Al ions are hosted with equal probability on octahedral- and tetrahedral-coordinated sites the resulting film structure was closely related to bulk k-A1203. An attractive feature of Stierle s model was that it provided a natural explanation of the domain structure of the alumina overlayer, which is induced by a periodic row matching between film and substrate lattices. However, as pointed out recently by Kresse et al. [47], this structure model has two bonds with... 

The plug flow profile would only be distorted in very narrow bore capillaries with a diameter smaller than the thickness of two double-layers that then overlap. To achieve an undisturbed flow, Knox suggested that the diameter should be 10-40 times larger than 6 [15]. This can easily be achieved in open capillaries. However, once the capillary is packed with a stationary phase, typically small modified silica beads that carry on their own charged functionalities, the distance between adjacent double-layers is only a fraction of the capillary diameter. However, several studies demonstrated that beads with a submicrometer size can be used safely as packings for CEC columns run in dilute buffer solutions [15,35]. 

The double layers of vanadium oxide found in the xerogel have been described in a number of other vanadium oxides by Galy ° and Oka ° they also form the double sheets described above for VeOis. These oxides, in which the vanadium is found in distorted VOe octahedra, show particularly attractive electrochemical capacities " exceeding 200 mAh/g in some cases, as shown in Figure 9. However, at the present time their rate capability appears somewhat limited. More recently vanadium oxide nanotubes have been synthesized, first by Spahr et these compounds also contain double sheets of vanadium oxide and again have interesting but complex... 

The addition of 0.18 interstitial ions to the formula unit of La2Ni04 requires that the oxidation state of Ni be increased to +2.36. Given that the equatorial Ni-O bonds have a length of 194 pm and therefore a bond valence of 0.46 vu, this increase in the oxidation state of Ni allows the axial bond valences to be increased from 0.08 to 0.26 vu reducing the length of the Ni-Oa iai bonds from 259 pm to the more acceptable value of 215 pm. This in turn reduces the valence required for the axial La-O bond by 0.18 vu which, together with the extra valence contributed by the interstitial 0 , reduces the distortion around La " " to an acceptable level. It is difficult to calculate the BSI and GII for this compound since one needs to know how the interstitial 0 ions are ordered within the LaO double layer, but clearly the BSI will be considerably reduced from the value 0.29 vu that it had before the introduction of the defect and subsequent electronic relaxation. This form of the structure is stable and is the form normally found when the material is prepared in air. 

Next, let the focus be on one of the chosen ions, say, Fe3, and its hydration sheath (somewhat distorted by adsorption in the double layer). The energy levels in this ion at 300 K are predominantly in the ground state. Because the tunneling of the electron to the ion is taken to occur from the Fermi level of the metal and to be radiationless, the energy states in the ion are the ones of interest for electron transfer. This means that the electrons will be likely to find a home only in electronic states of the hydrated Fe3 ion, well above the ground state. 

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