Overlap electrical double layers

The above discussions illustrate that the interactions between overlapping electrical double layers depend on a number of considerations, such as the magnitude of the surface potential, the thickness of the double layer, and the type of electrolyte, among others. Moreover, the expressions that have been obtained here (and others that are available in the literature) depend on additional conditions that are determined by the approximations made in deriving the expressions. 

In Eq. (15), the electrostatic potential, iJ/, is for the overlapping electric double layer of the interacting particles. Numerous models have been created to predict the overlapping field electrostatic potential between parallel plates. However, calculation of the EDL interaction for the common geometry of two spheres has not been satisfactorily resolved, due mainly to the nonlinear partial differential terms in Eq. (13) arising because of the three-dimensional geometry of the system. As a consequence, a number of approximate and numerical models have been developed for the calculation of the EDL interaction between two spheres. These models are briefly described below. 

Instead of using the middle potential F(o) and the potential (l), it is useful to perform the calculations with the dimensionless potentials u and u, and a dimensionless surface charge a. A solution to the problem of pressure due to overlapping electrical double layers in a thin liquid film was first given by Langmuir in form of an approximation... 

Chakraborty S, Srivastava AK (2007) A generalized model for time periodic electroosmotic flows with overlapping electrical double layers. Langmuir 23 12421-12428... 

Fabrication of ID Nanochannels 2D nanochaimels provide the platform to study novel effects such as those due to overlapped electric double layers. However, the large lateral dimension (usually over 1 pm) could render the 2D nanochannel incapable of manipulating single macromolecules, so fabrication of ID nanochannels is necessary for some single molecule sensing and manipulation purpose. Because ID nanochannels need to control the size in both lateral and vertical directions, more advanced lithography techniques are needed to shrink the width of the nanochannel to be comparable to the height of the nanochannel. Much less efforts have been carried out to make ID nanochannels, so only a couple of examples and some possible approaches are summarized as follows. 

D nanochannels provide the platform to study novel effects such as those due to overlapped electric double layers. However, the large lateral dimension (usually over 1 p,m) could render the 2D nanocharmel incapable of manipulating single macromolecules, so fabrication of ID nanochannels is necessary for some single molecule sensing and manipulation purpose. Because ID nanochannels... 

The above results are obtained for two overlapping electric double layers inside the film. Such films can appear between two colliding droplets in an oil-in-water emulsion. In the opposite case of water-in-oil emulsion, the double layers are outside the film. Nevertheless, in the latter case, Ilcor is not zero because the ions belonging to the two outer double layers interact across the thin dielectric (oil) film. The theory for such a film [340] predicts that Ilcor is negative (attractive) and strongly dependent on the dielectric permittivity of the oil film. For such films, Ilcor can be comparable by magnitude with IIvw n i = 0 in this case. 

Sprague, 1. B. Dutta, P. Improved kinetics from ion advection through overlapping electric double layers in nano-porous electrodes. Electrochim Acta 2013, 91, 20-29. 

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

Fig. 2. Schematic diagram of the tunnel gap between sample and tip, with the extension of the electric double layers indicated by the outer Helmholtz plane(OHP). (a) No tip interaction at large tip-sample separation, (b) Overlap of the electric double layers at a distance s = 0.6 nm, which can be achieved by conventional imaging conditions (e.g., Uj = 50 mV It = 2 nA Rt = 2.5 x 107 Q). Inset Dependence of the tunnel gap s on the tunnel resistance Rt for a tunnel barrier of 1.5 eV.

For ii) and iii) loosely structured layers are required, and the chains must protrude into the solution over a distance exceeding the thickness of the electrical double layer so that on approach of the surfaces, the adsorbed layers interfere before the electrical double layers overlap. 

Detailed numerical examples of the behaviour of the surface charge and surface potential when the electrical double layer of two identical amphoteric surfaces overlap and interact are available in the literature (8). Examples of the differences between the form of the interaction free energy under constant... 

In Section 15.6, the retention of proteins in ion exchange chromatography is discussed. The ions in the surrounding electrolyte form an electrical double layer around a charged macromolecule, e.g., a protein. The interaction between a protein and an oppositely charged surface can, therefore, be described as taking place between two overlapping double-layer systems. 

Retention of proteins in ion exchange chromatography is mainly caused by electrostatic effects. Because both the protein and the surface have an electrical double layer associated to it, there is an increase in entropy when the two surfaces approach each other. This is due to a release of counter ions from the two double layers when they overlap. The model that is discussed here is based on a solution of the linearized Poisson-Boltzmann for two oppositely charged planar surfaces. We also show the result from a model where the protein is considered as a sphere and the... 

Theories of electrical double layers and forces due to double-layer overlap (Chapter 11)... 

Two charged particles approaching each other sense the presence of each other through the overlap of their electrical double layers. This double-layer overlap results in a repulsive force between similarly charged particles. 

The purpose of this chapter is to introduce the basic ideas concerning electrical double layers and to develop equations for the distribution of charges and potentials in the double layers. We also develop expressions for the potential energies and forces that result from the overlap of double layers of different surfaces and the implication of these to colloid stability. 

This chapter focuses on some of the basic theories of electrical double layers near charged surfaces and develops the expressions for interaction energies when two electrical double layers overlap ( interact ) with each other. 

As we saw in Chapter 11, surfaces of colloidal particles typically acquire charges for a number of reasons. The electrostatic force that results when the electrical double layers of two particles overlap, if repulsive, serves to counteract the attraction due to van der Waals force. The stability in this case is known as electrostatic stability, and our task is to understand how it depends on the relevant parameters. 

In Chapter 5 we learned that, in water, most surfaces bear an electric charge. If two such surfaces approach each other and the electric double layers overlap, an electrostatic double-layer force arises. This electrostatic double-layer force is important in many natural phenomena and technical applications. It for example stabilizes dispersions.7... 

It remains to find ipm. If the electric double layers of the two opposing surfaces overlap only slightly (x XD), then we can approximate... 

Electrostatic forces, acting when the electric double layers of two drops overlap, play an important role. As mentioned above, oil drops are often negatively charged because anions dissolve in oil somewhat better than cations. Thus, the addition of salt increases the negative charge of the oil drops (thus their electrostatic repulsion). At the same time it reduces the Debye length and weakens the electrostatic force. For this reason, emulsion stability can exhibit a maximum depending on the salt concentration. 

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