Diffuse electrical double layer thickness

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

Calculate the thickness of the diffuse electric double layer for a negatively charged solid surface in contact with the following... 

Fig. 2 Concentration profile of positive (thick line) and negative (thin line) ions in a diffuse electrical double layer near a negatively charged surface. [NaCl]=0.01 mol 1 ...

Electric Double-Layer Thickness A measure of the decrease of potential with distance in the diffuse part of an electric double layer. It is the distance over which the potential falls to 1 /e, or about one-third, of the value of the surface or Stem layer potential, depending on the model used. Also termed the Debye length. 

Figure 17 Schematic representation of a diffuse electrical double layer, of thickness 1/K, in contact with a positively charged surface. (From Ref. 33.)...

A charged fractal grain is surrounded by the diffuse electrical double layer. The thickness of the double layer is controlled by the Debye length... 

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] ... 

Figure 2.8. A schematic representation for the effect of the particle concentration on the thickness of the diffuse electrical double layer.

For originally non-charged particles dispersed in polar media, the surface preferential adsorption of ions, surface molecular group dissociation, isomorphic substitution, adsorption of polyelectrolytes, and even surface polarization will make them behave similarly to charged particles. The Stem layer and diffuse layer comprise what is commonly known as the electrical double layer, the thickness of which depends on the type and concentration of the ions in the suspension as well as on the particle surface. A parameter, called the Debye-Huckel parameter k, is used to characterize electrical double layer thickness. K has the dimension of reciprocal length. For smooth surfaces in simple electrolytes. 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

The formation of a membrane potential is connected with the presence of an electrical double layer at the surface of the membrane. For a thick, compact membrane, an electrical double layer is formed at both interfaces. The electrical double layer at a porous membrane is formed primarily in the membrane pores (see Section 6.2). The electrical double layer at thin membranes is formed on both membrane surfaces. It is formed by fixed ions on the surface of the membrane and the diffuse layer in the electrolyte. 

As suggested before, the role of the interphasial double layer is insignificant in many transport processes that are involved with the supply of components from the bulk of the medium towards the biosurface. The thickness of the electric double layer is so small compared with that of the diffusion layer 8 that the very local deformation of the concentration profiles does not really alter the flux. Hence, in most analyses of diffusive mass transport one does not find any electric double layer terms. For the kinetics of the interphasial processes, this is completely different. Rate constants for chemical reactions or permeation steps are usually heavily dependent on the local conditions. Like in electrochemical processes, two elements are of great importance the local electric field which affects rates of transfer of charged species (the actual potential comes into play in the case of redox reactions), and the local activities... 

Finally, if the thickness of the electrical double layer (diffuse layer) in the droplet is comparable with r, the r dependence of kqbs will be dependent on the TBA+ concentration in the droplet since the spatial distribution of the inner electric potential of the droplet varies with [TBA+TPB ], However, since results analogous with those in Figure 14a ([TBA+TPB ] = 10 mM) have been obtained even at [TBA+TPB"] = 5mM (Aodiffuse layer effect does not contribute to the r effect on kobs at r > 1 /an. 

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. 

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