Electric Double Layer, Perpendicular Fields

At the metal/liquid interphase, the conversion from electronic to ionic conduction occurs. The electrode metal is the source or sink of electrons, and electron transfer is the key process whereby the electrode exchanges charges with the arriving ions, or ionizes neutral substances (a second mechanism of charge transfer is by oxidation of the electrode metal the metal leaves the surface as charged cations and enters the solution). Without electron transfer, there is no chemical electrode reaction, no DC electrode current, and no faradaic current. In the solution at the electrode surface, the electric double layer is formed as soon as the metal is wetted. Electron transfer takes place somewhere in the double layer. 

An electrical potential will be generated across the interphase according to the Poisson Eq. (7.1). This effect is particularly pronounced at the interphase between a solid and a polar medium, as with water, where the surface charges of the solid will attract counterions from the polar medium. When the polar medium is a liquid where the ion mobility is high, the formation of an electric double layer will therefore take place in the liquid phase. 

In this chapter, the double layer charge will be treated as a function of the distance perpendicular to the surface. In the next section, we will treat counterion movements lateral along the surface. 

The double layer can be thought of as a molecular capacitor, where one plate is represented by the charges in the metal and the other plate by the ions at a minimum distance in the solution. The distance between the plates is of molecular dimensions 

In the combined theory of Gouy and Chapman, the exchange of counterions between the double layer and the bulk solution due to thermal motion is taken into account. 

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Clay minerals can polarize in two ways. The first is the permanent dipole moment, which results from the structure and depends on the atomic masses. Its is oriented parallel to the long axis of the clay particles. The second polarity is perpendicular to the first one and is a result of the external electrical field. It depends on the polarization capacity of the electrical double layer. Thus, the mobility of clay particles depends on the combined action of these two moments and is therefore low, varying between 1.10 and 3.1(T m /U-s. 

Under the premise that / should be the same for Pa and Py at the positively charged electrode q ), ion pairs are formed and AGe of DNA (z = -1) enhances AG, and hence B. Conversely, for qo, repulsion of the polyanion occurs and AG, will be diminished for the phosphate backbone. However, within the distance k = 0.3-1 nm, the counterion condensation on the attached side of DNA segments is influenced asymmetrically by q and by the gradient of the electric field > 10 V cm in the double layer. This field polarizes kinked helical parts perpendicular to the surface, on the one... 

An electric dipole Jt in an external electric field E acquires an energy -Ji-E. We take the z-axis as perpendicular to the electrode surface and assume that E is the only nonvanishing component in the electric double layer this implies that the external field is not greatly disturbed by the presence of monoatomic steps and migrating atoms. We therefore need to consider only the z components of the dipole moment. If for a given process the dipole moment in the activated state differs from the moment fio in the initial state, the energy of activation is modified by the presence of the field, and the rate can be written as follows ... 

A common feature of electrokinetic phenomena is a relative motion of the charged surface and the volumetric phase of the solution. The charged surface is affected by the electric field forces, and the movement of such surfaces toward each other induces the electrical field. That is a question of slip plane between the double layer and a medium. The layer bounded by the plane at the distance d from surface (OHP) can be treated as immobile in the direction perpendicular to the surface, because the time of ion residence in the layer is relatively long. Mobilty of ions in the parallel direction to the interfacial surface should also be taken into account. However, it seems that the ions in the double layer and in the medium surrounding it constitute a rigid whole and that the layer from x = 0 to X = d is immobile also in the sense of resistance to the tangent force action. There is no reason why the boundary plane of the solution immobile layer should overlap accurately with the OHP plane. It can be as well placed deeply in the solution. The potential in the boundary plane of the solution immobile layer is called potential (. Strictly speaking it is not a potential of interface because it is created in the liquid phase. It can be considered as the difference of potentials between a point far from the surface (in the bulk solution) and that in the slip plane. 

We may estimate the approximate thickness of the double layer in the one-dimensional picture of Fig. 6.4.1. There, the electric field is taken to be parallel to the x axis, that is, everywhere perpendicular to the plane charged surface. We consider a simple fully dissociated symmetrical salt in solution for which the number of positive and negative ions are equal, so... 

Estimate the thickness of the double layer for the flat case (see Fig. 7.7), when the electric field is perpendicular to the charged plane x = 0. Consider a completely dissociated symmetric salt in a solution with equal positive and negative ion charges, that is,... 

At low degrees of surface heterogeneity (streamline pattern shown in Fig. 6a was obtained. As can be seen a net counter-clockwise flow perpendicular to the applied electric field is present at the first transition plane (i. e. at the initial discontinuity in the heterogeneous surface pattern) and a clockwise flow at the second transition plane. This flow circulation is a pressure induced effect that arises as a result of the transition from the higher local fluid velocity (particularly in the double layer) over the homogeneous surface on the right hand side at the entrance, to the left hand side after the first transition plane (and vice versa at the second transition plane). To satisfy continuity then there must be a net flow from... 

Potential-dependent bands for the OH stretching and HOH bending mode of water have been analyzed and interpreted in terms of the interactions of water molecules with the electric field of the double layer and with the metal surface [46]. In short, the shift of the bending mode in the potential region of 0.4 to 0.9 V indicates 0-adsorbed water molecules being oriented from a tilted to perpendicular position at the surface (Fig. 14). With increasing potential, water dipoles acquire a configuration of minimum interaction... 

Macroscopic electric field Let us consider a slab of equi-distant layers, bearing positive and negative charge densities equal to + cr (Fig. 3.7a). The repeat unit has a dipole moment density equal to aR. As for an association of capacitors. Gauss theorem allows an estimation of the electric field S perpendicular to the layers and of the electrostatic potential V. The field S turns out to be equal to zero between two double-layers and equal to 47rcr inside a double-layer. Its mean value in the slab is, therefore, non-zero ... 

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