Electrical diffuse part

In a qualitative way, colloids are stable when they are electrically charged (we will not consider here the stability of hydrophilic colloids - gelatine, starch, proteins, macromolecules, biocolloids - where stability may be enhanced by steric arrangements and the affinity of organic functional groups to water). In a physical model of colloid stability particle repulsion due to electrostatic interaction is counteracted by attraction due to van der Waal interaction. The repulsion energy depends on the surface potential and its decrease in the diffuse part of the double layer the decay of the potential with distance is a function of the ionic strength (Fig. 3.2c and Fig. 

Simple electrolyte ions like Cl, Na+, SO , Mg2+ and Ca2+ destabilize the iron(Hl) oxide colloids by compressing the electric double layer, i.e., by balancing the surface charge of the hematite with "counter ions" in the diffuse part of the double... 

When particles or large molecules make contact with water or an aqueous solution, the polarity of the solvent promotes the formation of an electrically charged interface. The accumulation of charge can result from at least three mechanisms (a) ionization of acid and/or base groups on the particle s surface (b) the adsorption of anions, cations, ampholytes, and/or protons and (c) dissolution of ion-pairs that are discrete subunits of the crystalline particle, such as calcium-oxalate and calcium-phosphate complexes that are building blocks of kidney stone and bone crystal, respectively. The electric charging of the surface also influences how other solutes, ions, and water molecules are attracted to that surface. These interactions and the random thermal motion of ionic and polar solvent molecules establishes a diffuse part of what is termed the electric double layer, with the surface being the other part of this double layer. 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

It is convenient to think of the diffuse part of the double layer as an ionic atmosphere surrounding the particle. Any movement of the particle affects the particle s ionic atmosphere, which can be thought of as being dragged along through bulk motion and diffusional motion of the ions. The resulting electrical contribution to the resistance to particle motion manifests itself as an additional viscous effect, known as the electroviscous effect. Further,... 

Figure 26-20 (a) Electric double layer created by negatively charged silica surface and nearby cations. (fc>) Predominance of cations in diffuse part of the double layer produces net electroosmotic flow toward the cathode when an external field is applied. 

In an electric field, cations are attracted to the cathode and anions are attracted to the anode (Figure 26-20b). Excess cations in the diffuse part of the double layer impart net momentum toward the cathode. This pumping action, called electroosmosis (or electroen-dosmosis), is driven by cations within — lOnm of the walls and creates uniform pluglike electroosmotic flow of the entire solution toward the cathode (Figure 26-21a). This process is in sharp contrast with hydrodynamic flow, which is driven by a pressure difference. In hydro-... 

Cations striking a cathode liberate electrons. A series of dynodes multiplies the number of electrons by 105 before they reach the anode, electroosmosis Bulk flow of fluid in a capillary tube induced by an electric field. Mobile ions in the diffuse part of the double layer at the wall of the capillary serve as the pump. Also called electroendosmosis. electroosmotic flow Uniform, pluglike flow of fluid in a capillary tube under the influence of an electric field. The greater the charge on the wall of the capillary, the greater the number of counterions in the double layer and the stronger the electroosmotic flow. 

The discussion up to this point has been concerned essentially with metal alloys in which the atoms are necessarily electrically neutral. In ionic systems, an electric diffusion potential builds up during the spinodal decomposition process. The local gradient of this potential provides an additional driving force, which acts upon the diffusing species and this has to be taken into account in the derivation of the equivalents of Eqns. (12.28) and (12.30). The formal treatment of this situation has not yet been carried out satisfactorily [A.V. Virkar, M. R. Plichta (1983)]. We can expect that the spinodal process is governed by the slower cation, for example, in a ternary AX-BX crystal. The electrical part of the driving force is generally nonlinear so that linearized kinetic equations cannot immediately be applied. 

The electric double layer can be regarded as consisting of two regions an inner region which may include adsorbed ions, and a diffuse region in which ions are distributed according to the influence of electrical forces and random thermal motion. The diffuse part of the double layer will be considered first. 

Consider the motion of liquid in the diffuse part of the double layer relative to that of a non-conducting flat surface when an electric field... 

The distribution of ions in the diffuse part of the double layer gives rise to a conductivity in this region which is in excess of that in the bulk electrolyte medium. Surface conductance will affect the distribution of electric field near to the surface of a charged particle and so influence its electrokinetic behaviour. The effect of surface conductance on electrophoretic behaviour can be neglected when ka is small, since the applied electric field is hardly affected by the particle in any case. When tea is not small, calculated zeta potentials may be significantly low, on account of surface conductance. 

The calculation of the interaction energy, VR, which results from the overlapping of the diffuse parts of the electric double layers around two spherical particles (as described by Gouy-Chapman theory) is complex. No exact analytical expression can be given and recourse must be had to numerical solutions or to various approximations. 

So far, only non-specific ion adsorption in the diffuse part of the electric double layer has been considered. The broad prediction is that VR should decrease in an approximately exponential fashion with increasing H and that the range of VR should be decreased by... 

The chloride and sodium ions form the diffuse part of the electrical double layer. 

The presence of salt promotes aggregation due to reduction of the diffuse part of the electric double layer. According to a review by Franks and Eagland, 1975 (6) salt effects on the electric double layer are to be found at I 0.1 for univalent ions. 

The authors have adopted the term diffuse electric layer for the diffuse part of the double electric layer other authors prefer to call it double diffuse layer (DDL). 

The key link between ELS experiments and particle electrostatic properties is the theoretical model of colloidal electrohydrodynamics. The required model is considerably more complicated than the one needed in the interpretation of DLS data. DLS relies upon a relatively simple colloidal hydrodynamic model to relate the measured particle diffusivity to particle radius via the Stokes-Einstein Eq. (39). The colloidal electrohydrodynamic model for ELS must account for the complex physical/chemical/electrical structure of the particle surface as well as the distortion of the diffuse part of the electrostatic double layer due to the motion of the particle through the medium. 

At the interface between O and W, the presence of the electrical double layers on both sides of the interface also causes the variation of y with Aq<. In the absence of the specific adsorption of ions at the interface, the Gouy-Chapman theory satisfactorily describes the double-layer structure at the interface between two immiscible electrolyte soultions [20,21]. For the diffuse part of the double layer for a z z electrolyte of concentration c in the phase W whose permittivity is e, the Gouy-Chapman theory [22,23] gives an expression... 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

The stability of inverse micelles has been treated by Eicke (8,9) and by Muller (10) for nonaqueous systems, while Adamson (1) and later Levine (11) calculated the electric field gradient in an inverse micelle for a solution in equilibrium with an aqueous solution. Ruckenstein (5) later gave a more complete treatment of the stability of such systems taking both enthalpic (Van der Waals (VdW) interparticle potential, the first component of the interfacial free energy and the interparticle contribution of the repulsion energy from the compression of the diffuse part of the electric double layer) and entropic contributions into consideration. His calculations also were performed for the equilibrium between two liquid solutions—one aqueous, the other hydrocarbon. 

The electrical charges in the double layer are not actually concentrated in two planes at the interface but have a more or less diffuse part extending into the interior of the phases. 

The model introduced by Stern (2), which is in best agreement with all experimental facts, combines a distribution of charges in a space charge layer (diffuse part of the double layer) and the Helmholtz layer (rigid part of the double layer). Ions are assumed to be adsorbed on the electrode and thus bound to the surface by chemical forces. If strongly adsorbed ions are present at the interface, the rigid double layer predominates in determining the electrical properties of the interface. 

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