Double layer, electric moment

The electrical double layer has been dealt with in countless papers and in a number of reviews, including those published in previous volumes of the Modem Aspects of Electrochemistry series/ The experimental double layer data have been reported and commented on in several important works in which various theories of the structure of the double layer have been postulated. Nevertheless, many double layer-related problems have not been solved yet, mainly because certain important parameters describing the interface cannot be measured. This applies to the electric permittivity, dipole moments, surface density, and other physical quantities that are influenced by the electric field at the interface. It is also often difficult to separate the electrostatic and specific interactions of the solvent and the adsorbate with the electrode. To acquire necessary knowledge about the metal/solution interface, different metals, solvents, and adsorbates have been studied. 

We observe that the sign of A

additional potential jump on the surface of the semiconductor due to the electric double layer, which arises on the surface in adsorption and figures as one of the terms in the experimentally measured work fimction. Such an electric double layer may be the result of the polarization of the chemisorbed particles (when the dipole moments of the chemisorbed particles are directed normally to the surface). This can be the case, for example, in weak chemisorption (when the total charge of the surface remains unchanged). 

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 ... 

Whilst the electric moment so calculated is in reality not an absolute value since it is actually only the alteration in electric moment of the surface produced by substituting the adsorbed solute molecules for solvent molecules, yet it is clear that the ionisable substances possess large values which vary within wide limits as the surface concentration is altered. We must conclude that since the apparent molecular electric moment varies with the concentration that Helmholtz s conception of a rigid double layer must be replaced by some species of boundary layer which varies in structure with the surface concentration. Gouy loo. cit) was the first to consider in detail the mechanism by which the ions are kept away from the charged surface. He put forward the view that the finite value of S is due to their thermal agitation. On this M... 

Thus summarizing, we note that at the leading order the asymptotic solution constructed is merely a combination of the locally electro-neutral solution for the bulk of the domain and of the equilibrium solution for the boundary layer, the latter being identical with that given by the equilibrium electric double layer theory (recall (1.32b)). We stress here the equilibrium structure of the boundary layer. The equilibrium within the boundary layer implies constancy of the electrochemical potential pp = lnp + ip across the boundary layer. We shall see in a moment that this feature is preserved at least up to order 0(e2) of present asymptotics as well. This clarifies the contents of the assumption of local equilibrium as applied in the locally electro-neutral descriptions. Recall that by this assumption the electrochemical potential is continuous at the surfaces of discontinuity of the electric potential and ionic concentrations, present in the locally electro-neutral formulations (see the Introduction and Chapters 3, 4). An implication of the relation between the LEN and the local equilibrium assumptions is that the breakdown of the former parallel to that of the corresponding asymptotic procedure, to be described in the following paragraphs, implies the breakdown of the local equilibrium. 

In the extreme class III behaviour,360-362 two types of structures were envisaged clusters and infinite lattices (Table 17). The latter, class IIIB behaviour, has been known for a number of years in the nonstoichiometric sulfides of copper (see ref. 10, p. 1142), and particularly in the double layer structure of K[Cu4S3],382 which exhibits the electrical conductivity and the reflectivity typical of a metal. The former, class IIIA behaviour, was looked for in the polynuclear clusters of copper(I) Cu gX, species, especially where X = sulfur, but no mixed valence copper(I)/(II) clusters with class IIIA behaviour have been identified to date. Mixed valence copper(I)/(II) complexes of class II behaviour (Table 17) have properties intermediate between those of class I and class III. The local copper(I)/(II) stereochemistry is well defined and the same for all Cu atoms present, and the single odd electron is associated with both Cu atoms, i.e. delocalized between them, but will have a normal spin-only magnetic moment. The complexes will be semiconductors and the d-d spectra of the odd electron will involve a near normal copper(II)-type spectrum (see Section 53.4.4.5), but in addition a unique band may be observed associated with an intervalence CuVCu11 charge transfer band (IVTC) (Table 19). While these requirements are fairly clear,360,362 their realization for specific systems is not so clearly established. 

The opposite effect to electrophoresis is the generation of a sedimentation potential. If a charged particle moves in the gravitational field or in a centrifuge, an electric potential arises — the sedimentation potential. While the particle moves, the ions in the electric double layer lag somewhat behind due to the liquid flow. A dipole moment is generated. The sum of all dipoles causes the sedimentation potential. 

For molecules with no net free charge the measured dipole moment corresponds directly to the internal dipole moment of the molecule [615], With charged molecules, an additional dipole has to be considered which is formed in the subphase due to the electrical double layer. 

Figure 2 Conventional representation of micelles formed by an ionic surfactant, such as sodium dodecyl sulfate. The inner core region consists of the methylene tails of the surfactants. The Stem layer consists of surfactant headgroups and bound counterion species. The diffuse double layer consists of unbound counterions and coions which preserve the electrical neutrality of the overall solution. Also pictured are the transition moment vectors for the S-O stretching modes of sodium dodecyl sulfate.

We may assume this polarization to be caused by an electric double layer formed by an electron distribution over the surface of the conducting adsorbent and corresponding positive charges in the metal. The dipole moment induced in the adsorbed molecules by the field of this double layer may be calculated from the difference between the theoretical value of a2 and the actual value which is found. This difference forms the a2 contribution caused by the dipole and is given by the expression... 

The principle behind this investigation is electrochromism or Stark-effect spectroscopy. The electronic transition energy of the adsorbed chromophore is perturbed by the electric field at the electric double layer. This is due to interactions of the molecular dipole moment, in the ground and excited states, with the interfacial electric field induced by the applied potential. The change in transition frequency Av, is related to the change in the interfacial electric field, AE, according to the following ... 

In the traditional double layer theory, the average dipole moment of a water molecule is proportional to the macroscopic field (the derivative of the electrical potential)... 

FIGURE 11.4 Dipole moments generated on charged particles in response to an applied field. Inset location of CVI current, In, external to the electric double layer. 

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. 

It must be stressed that the polarizability gradient da/dQk also appears in the equation for Raman intensities [175], as indicated also by Lambert [176]. Thus, in view of Eq. (25), we can extend the consequences of the static electric field to vibrations which are forbidden by the surface selection rule the high electric field in the double layer can induce a dipole moment component in the direction of the field on permanent dipoles which are parallel to the surface. Thus the effect of orientation due to the electric field is just a manifestation of the Stark effect. 

Dispersion Technology DT-1200 combines the DT-100 with the DT-200 to give both size and zeta potential. Ultrasound induces a motion of particles relative to the liquid. This motion disturbs the double layer shifting a screening cloud of counter-ions. This displacement creates a dipole moment the sum of which creates an electric field that is measured by two electrode sensors. This field depends upon the value of the zeta potential which can be calculated using the appropriate theory. 

At the surface, the electron density dies off gradually, the electrons spilling over the positive-ion lattice. The charge density is negative on the outer side and predominantly positive just inside the metal (when there is a deficiency of electrons) an electric double layer is created. The dipole moment of this double layer will vary with the nature of the metal and with the co for a given metal. 

In electro-optics, the optical effect of the colloid is measured in the presence of an electric field. The optical effect is related to the electrical moment orientational mechanism, which in turn reflects the electrical double layer features of the particles through its electrical polarizability [1-3]. 

From an analysis of the a dependence on the field frequency v (dispersion curve) for different colloids, it has been shown that the orientation of particles in the kHz range originates solely from their induced dipole moments [2,3,51]. It is generally accepted now that the induced dipole moment of a colloid particle in this region is mainly due to movement of ions in the diffuse part of the particle electrical double layer [51-54], What is the origin of the effect observed in a suspension containing polyelectrolyte molecules ... 

Consider the simple diffusion of an electrolyte in the absence of an external electric field. The diffusion occurs because of a concentration gradient. The situation shown in Fig. 31.12(a) illustrates the initial condition of an electrolytic solution over which there is a layer of pure water. We assume that initially the boundary between the two layers is sharp. Suppose that the ion moves more rapidly than the ion. Then we soon have the situation illustrated in Fig. 31.12(b). In the first few moments of the process the positive ions outdistance the negative ions. An electrical double layer forms, with an associated electric field. The effect of this electric field is to speed up the slower ion and to slow down the faster ion. The system quickly adjusts so that both ions move, in the same direction with the same velocity. If this adjustment did not occur, large departures from electrical neutrality would occur because of the difference in velocity between the positive and negative ions. Correspondingly enormous electric potential differences would develop in the direction of diffusion. In fact, the potential difference that develops and that equalizes the velocities of the ions is rather small (< 100 mV) it is the diffusion potential and is responsible for the liquid junction potential that was described in Section 17.18. 

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. 

---