Diffuse electrical double-layer interaction between

The generation of colloidal charges in water.The theory of the diffuse electrical double-layer. The zeta potential. The flocculation of charged colloids. The interaction between two charged surfaces in water. Laboratory project on the use of microelectrophoresis to measure the zeta potential of a colloid. 

The discussion of the relative stability of solutions with inverse micelles and of liquid crystals containing electrolytes may be limited to the enthalpic contributions to the total free energy. The experimentally determined entropy differences between an inverse micellar phase and a lamellar liquid crystalline phase are small (12). The interparticle interaction from the Van der Waals forces is small (5) it is obvious that changes in them owing to added electrolyte may be neglected. The contribution from the compression of the diffuse electric double layer is also small in a nonaqueous medium (II) and their modification owing to added electrolyte may be considered less important. It appears justified to limit the discussion to modifications of the intramicellar forces. 

By using the above equations, Derjaguin and Landau, and Verwey and Overbeek (DLVO) proposed a system for the process of adhesion. According to the work of Derjaguin and Landau, the interaction of two diffused electrical double layers would cause the formation of an energy barrier between the two interacting particles. This energy barrier would lie between two minima. 

This layer, which is termed the diffuse electrical double layer, can be described mathematically by the Poisson-Boltzmann equation. Within this layer, the shear plane of the particles is located. The potential at this distance from the surface is particularly important as it is the experimentally accessible zeta-potential. When two different colloidal particles that are electrically charged at their surfaces with ions of the same sign approach each other, they wiU experience a net repulsion force as a result of the interaction between the ions located at their diffuse layers. If the net interaction potential between the particles is repulsive and larger than the kinetic energy of the collision, they wiU not coagulate. 

It should be noted that the above discussion only dealt with the electrostatic interaction between an isolated pair of particles. It is reasonable to neglect the effect of the particle concentration for the dilute colloidal dispersion because the distance of separation between the particles is much larger than the thickness of the electrical double layer. Nevertheless, the counterions associated with other particles (macroions) have an appreciable influence on the pair of interactive particles when the particle concentration is so high that the distance of separation between the particles becomes comparable to the thickness of the diffuse electrical double layer. The following equation, which takes into consideration the effect of the particle concentration, was proposed to calculate k [2] ... 

The interaction between two double layers was first considered by Voropaeva et a/.145 These concepts were used to measure the friction between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at Eam0, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. 

At a semiconductor-electrolyte interface, if there is no specific interaction between the charge species and the surface an electrical double layer will form with a diffuse space-charge region on the semiconductor side and a plate-like counter ionic charge on the electrolyte side resulting in a potential difference (j) across the interface. The total potential difference across the interface can be given by... 

What is the Gibbs free energy of an electric double layer The energy of an electric double layer plays a central role in colloid science, for instance to describe the properties of charged polymers (polyelectrolytes) or the interaction between colloidal particles. Here, we only give results for diffuse layers because it is simpler and in most applications only the diffuse layer is relevant. The formalism is, however, applicable to other double layers as well. 

What happens when the dimensions are furthermore reduced Initially, an enhanced diffusive mass transport would be expected. That is true, until the critical dimension is comparable to the thickness of the electrical double layer or the molecular size (a few nanometers) [7,8]. In this case, diffusive mass transport occurs mainly across the electrical double layer where the characteristics (electrical field, ion solvent interaction, viscosity, density, etc.) are different from those of the bulk solution. An important change is that the assumption of electroneutrality and lack of electromigration mass transport is not appropriate, regardless of the electrolyte concentration [9]. Therefore, there are subtle differences between the microelectrodic and nanoelectrodic behaviour. 

Gouy1 and Chapman,2 who were the first to predict the distribution of electrolyte ions in water around a charged flat surface, demonstrated that the ions form a diffuse layer (the electric double layer) in the liquid near the interface. The interaction between two charged surfaces, due to the overlapping of the double layers, was calculated much later by Deryaguin and Landau3 and Verwey and Overbeek.4 The stability of the colloids was successfully explained by them in terms of a balance between the double layer and van der Waals interactions (the DLVO theory).3 4... 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

Several mechanisms of interaction between particles of solids are known [3]. Mechanical adhesion is achieved by flowing a metal into the support pores. The molecular mechanism of adhesion is based on the Van der Waals forces or hydrogen bonds, and the chemical mechanism on the chemical interaction of the metal particles with the support. The electric theory relates adhesion to the formation of an electric double layer (EDL) at the adhesive-substrate interface. Finally, the diffusion mechanism implies interpenetration of the molecules and atoms of the interacting phases, which results in the interface blurring. These insights into the nature of adhesion can be revealed in the papers about the interaction of transition metal... 

Many properties of disperse systems are related to the distribution of charges in the vicinity of the interface due to the adsorption of electrolytes. The adsorption of molecules is driven by the van der Waals attraction, while the driving force for the adsorption of electrolytes is the longer-range electrostatic (Coulomb) interaction. Because of this, the adsorption layers in the latter case are less compact than in the case of molecular adsorption (i.e., they are somewhat extended into the bulk of the solution), and the discontinuity surface acquires noticeable, and sometimes even macroscopic thickness. This diffuse nature of the ionized adsorption layer is responsible for such important features of disperse systems as the appearance of electrokinetic phenomena (see Chapter V) and colloid stability (Chapters VII, VIII). Another peculiar feature of the adsorption phenomena in electrolyte solutions is the competitive nature of the adsorption in addition to the solvent there are at least two types of ions (even three or four, if one considers the dissociation of the solvent) present in the system. Competition between these ions predetermines the structure of the discontinuity surface in such systems -i.e. the formation of spatial charge distribution, which is referred to as the electrical double layer (EDL). The structure and theory of the electrical double layer is described in detail in textbooks on electrochemistry. Below we will primarily focus on those features of the EDL, which are important in colloid... 

When a metal electrode is placed in an electrolyte solution, an equilibrium difference usually becomes established between the metal and solution. Equilibrium is reached when the electrons left in the metal contribute to the formation of a layer of ions whose charge is equal and opposite to that of the cations in solution at the interface. The positive charges of cations in the solution and the negative charges of electrons in the metal electrode form the electrical double layer [4]. The solution side of the double layer is made up of several layers as shown in Fig. 2.7. The inner layer, which is closest to the electrode, consists of solvent and other ions, which are called specifically adsorbed ions. This inner layer is called the compact Helmholtz layer, and the locus of the electrical centers of this inner layer is called the inner Helmholtz plane, which is at a distance of di from the metal electrode surface. The solvated ion can approach the electrode only to a distance d2. The locus of the centers of the nearest solvated ion is called the outer Helmholtz plane. The interaction of the solvated ion with metal electrode only involves electrostatic force and is independent of the chemical properties of the ions. These ions are called non-specifically adsorbed ions. These ions are distributed in the 3D region called diffusion layer whose thickness depends on the ionic concentration in the electrolyte. The structure of the double layer affects the rate of electrode reactions. 

To obtain Eqs. 11, 12, 13, and 14, it was assumed that the concentration of each ionic species within the electric double layer is related to the electric potential energy by a Boltzmann distribution. A comparison of Eq. 11 with the numerical results obtained by Prieve and Roman [2] shows that the thin-layer polarization model is quite good over a wide range of zeta potentials when Ka > 20. If 1(1 is small and Ka is large, the interaction between the diffuse counterions and the particle surface is weak and the polarization of the double layer is also weak. In the limit of... 

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