Charge-potential relationships electric double layer

It is assumed that the quantity Cc is not a function of the electrolyte concentration c, and changes only with the charge cr, while Cd depends both on o and on c, according to the diffuse layer theory (see below). The validity of this relationship is a necessary condition for the case where the adsorption of ions in the double layer is purely electrostatic in nature. Experiments have demonstrated that the concept of the electrical double layer without specific adsorption is applicable to a very limited number of systems. Specific adsorption apparently does not occur in LiF, NaF and KF solutions (except at high concentrations, where anomalous phenomena occur). At potentials that are appropriately more negative than Epzc, where adsorption of anions is absent, no specific adsorption occurs for the salts of... 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

Equations that describe the relationship between the charge and the potential of the electrical double layer. 

The current density, will be the sum of the faradaic current density, jF, and the charging current density, c, cf. eqn. (8). The latter is related to the interfacial potential indicated in an implicit way by eqn. (20). The theory of the electrical double layer provides no analytical expression for the relation between E and qM and so, rigorously, this part of the problem would have to be solved numerically using the empirical relationship, which is known for many commonly used indifferent electrolytes. If Cd = dqM/dE is the differential double-layer capacity, we have... 

It appears that the data obtained in the above manner prove to be reliable for inferring the charge-potential relationship. Therefore, Fig 3.45 provides convincing evidence that in the case considered double layer repulsive interaction under the conditions of constant charge of the diffuse electric layer is operative. If so, the first integration of Eq. (3.90) predicts that... 

Electrical Double Layer. In order to model the structure of the electrical double layer (EDL) of oxide colloids, it is necessary to formulate 1) the reactions which result in the formation of surface charge (cTq), and 2) the potential and charge relationships in the interfacial region. It has been generally assumed that surface charge (O ), defined experimentally by the net uptake of protons by the surface, results from simple ionization of oxide surface sites (5, 11 12, 13), i.e.. 

The ion and electrical potential distributions in the electrical double layer can be determined by solving the Poisson-Boltzmann equation [2,3]. According to the theory of electrostatics, the relationship between the eleetrieal potential ij/ and the local net charge density per unit volume at any point in the solution is deseribed by the Poisson equation ... 

Standing of surface charge and surface potential, and their relationship to pH, ionic strength, and medium composition. Westall and Hohl (1980) provide an excellent review of alternative models for the electrical double layer, and James and Parks (1982) provide a detailed description zind explanation of the surface chemistry and electrostatics of hydrous metal oxides. Hayes et al. (1988) present an excellent discussion of the effect of the electrical double layer on the adsorption of inorganic anions. A similar approach is used by Zachara et al. (1990) to model the adsorption of aminonaphthalene and quinoline onto amorphous silica. 

The spatial charge distribution in the electrical double layer is exactly what causes the electrokinetic phenomena, namely the mutual displacement of the phases in contact in an applied external electric field (electrophoresis and electroosmosis) or the charge transfer that occurs upon the mutual motion of phases (streaming and sedimentation potentials and currents). The following consideration, the simplest consistent with the Helmholtz model, establishes the relationship between the rate of the phase shift, e.g. that of electroosmosis, and the strength of the external electric field, E, directed along the surface3. 

The quantitative pH shift model [23] combined (1) a proton balance between the surface and bulk liquid with (2) the protonation-deprotonation chemistry of the oxide surface (single amphoteric site), and (3) a surface charge-surface potential relationship assumed for an electric double layer. Given the mass and surface area of oxide, the oxide s PZC, its protonation-deprotonation constants Kj and Kj (Figure 13.2), and the hydroxyl density, these three equations are solved simultaneously and give the surface charge, surface potential, and final solution pH. The mass titration experiment of Figure 13.4 can be quantitatively simulated, but perhaps the most powerful simulation is a comprehensive prediction of final pH versus initial pH, as a function of... 

The electrical double layer in the phase boimdaries produces the -potential as a result of electrostatic and adsorptive interactions. The zeta potential has a very close relationship to the stability of a sol. The zeta potential of a sol can be very effectively reduced ty addition of elec j-olytes. The electrolytes decrease the zeta potential to a critical value, after which neutralization of the charges takes place resulting in the collapse of the double layer. When this happens, flocculation of the colloid takes place. Various other factors which affect zeta potential are surface charge density, dielectric constant of the medium and thickness of the double layer. 

In the following sections, the relationship between surface charge and electrokinetic phenomena is expounded in terms of classical theory. First, a few possible mechanisms and models for the development of charge at a surface in contact with an aqueous solution are described in order to form a basis for the formation of an electrical double-layer at an interface. Secondly, the electrical double-layer is discussed in terms of an equilibrium charge distribution and electrostatic potential near the interface. With an adequate description of the interface, the discussion turns to explication of electrokinetic phenomena according to the charge distribution in the electrical double-layer and the Navier-Stokes equation. A section then follows which describes common methods and experimental requirements for the measurement of electrokinetic phenomena. The discussion closes with a few examples of the use of measurement of the pH dependence of electroosmosis as an analytical characterization technique from this present author s own experience. The intention is to provide... 

Keep in mind that Eqs. (8-14) are only valid for small Kr, when the electrophoresis retardation (electric-field-induced movement of ions in the electric double layer, which is opposite to the direction of particle movement) is unimportant [41J. This limitation is inherent to the Hiickel equation. Practically, a colloidal suspension always contains charged particles dispersed in a medium with surfactants (or electrolytes) of both polarities. In this case the Poisson s equation must be used for deriving the surface charge density and Zeta potential relationship. Under the Dcbyc-Hiickel approximation, i.c., the small value of potential, zey/ kgT, where v is the potential and z is the valency of ion, a simple relationship between the surface charge density and Zeta potential can be easily obtained [7], The Poisson s equation simply says that the potential flux per unit volume of a potential field is equal to the charge density in that area divided by the dielectric constant of the medium. It can be mathematically expressed as ... 

An electrically charged wall in contact with a liquid gives rise to an electric double layer in its immediate neighborhood. If the thickness of the double layer is very small compared with the average diameter of open spaces in the membrane, simple relationships exist between the electro-kinetic potential and the electroosmotic flow and other electrokinetic phenomena. The electrokinetic potential can then be determined experimentally and used for the characterization of the membrane. In most practical cases, however, the electric double layer occupies a considerable portion of the free spaces, and the approximations made in the simple theory are not justified. If the electrokinetic potential is determined for such a membrane and calculated with Smoluchowski s equation, one finds that it varies with the average pore radius (Zhukov, 1943). For a more detailed discussion of this problem, the reader is referred to Mane-gold and Solf (1931). 

The relationship between the over-potential and Ig U will deviate from the Tafel linear area due to the medium affecting the diffusion layer. The effect will gradually disappear and the polarization curves separate each other obviously when the potential is far from zero electric charge potential. This is the reason that COj and Ca(OH) ions have some surfactant action compared with OH ion to form characteristic adsorption more easily and to bring about the change of the capacitance of the double electric charge layer. 

Based on the previous description of the double layer, it is logical to assume that a direct relationship between the absolute charge at the interface and the concentration of ions in the vicinity of the interface exists. Indeed, several models have been developed in the past that describe the ion concentration as a function of the actual surface charge at a specific distance jc from the interface. Furthermore, the famous Nemst equation, which is the basis for understanding many electrochemical reactions, proves to be helpful as it relates the ion concentration to a quantity called the electrical potential ( j/). The electrical potential is the work (W) required to move a unit charge (q) through the electrical field ... 

The Debye-Huckel theory was developed to extend the capacitor model and is based on a simplified solution of the Poisson equation. It assumes that the double layer is really a diffuse cloud in which the potential is not a discontinuous function. Again, the interest is in deriving an expression for the electrical potential function. This model states that there is an exponential relationship between the charge and the potential. The distribution of the potential is ... 

A persistent question regarding carbon capacitance is related to the relative contributions of Faradaic ( pseudocapacitance ) and non-Faradaic (i.e., double-layer) processes [85,87,95,187], A practical issue that may help resolve the uncertainties regarding DL- and pseudo-capacitance is the relationship between the PZC (or the point of zero potential) [150] and the point of zero charge (or isoelectric point) of carbons [4], The former corresponds to the electrode potential at which the surface charge density is zero. The latter is the pH value for which the zeta potential (or electrophoretic mobility) and the net surface charge is zero. At a more fundamental level (see Figure 5.6), the discussion here focuses on the coupling of an externally imposed double layer (an electrically polarized interface) and a double layer formed spontaneously by preferential adsorp-tion/desorption of ions (an electrically relaxed interface). This issue has been discussed extensively (and authoritatively ) by Lyklema and coworkers [188-191] for amphifunctionally electrified... 

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