Double layer, electric overlap

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. 

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. 

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... 

For small electric double layer overlap, such that exp [—kH] < 1, these expressions both reduce to... 

Several repulsive and attractive forces operate between colloidal species and determine their stability [12,13,15,26,152,194], In the simplest example of colloid stability, dispersed species would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their electric double layers overlap. The overlap causes a coulombic repulsive force acting against each surface, which will act in opposition to any attempt to decrease the separation distance (see Figure 5.2). One can express the coulombic repulsive force between plates as a potential energy of repulsion. There is another important repulsive force causing a strong repulsion at very small separation distances where the atomic electron clouds overlap, called Born repulsion. 

In the simplest example of colloid stability, suspension partides would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their electric double layers overlap. The repulsive energy VR for spherical particles, or rigid droplets, is given approximately as ... 

Electroosmotic flow is generally reported to be independent of the size of the packing, and consequently the size of the interstitial voids between the particles, unless this size is so small that the electrical double layers overlap [74]. The ability to independently control both the pore size and level of charged functionalities of the methacrylate ester monolithic capillaries enables the direct investigation of the net effect of transport channel size on flow velocity. Recent results clearly demonstrates a... 

Electrical Double-Layer Overlap and Pore Flow... 

For relatively wide channels with negligible electrical double-layer overlap (r/8 > 10), a nearly flat flow profile is expected. It has often been stated that when the channel size and the Debye length are of similar dimensions (r 8), complete electrical double-layer overlap occurs and the EOF is negligible. However, when r 8, a significant EOF can still be created the EOF velocity in the central part of the channel is approximately 20% of that in an infinitely wide channel. Only at conditions where r/8 1 is the EOF fully inhibited by double-layer overlap [25], It should be noted here that the approximations made by using the Rice and Whitehead theory at r/8 < 10 may lead to significant errors in the calculation of the velocity distribution and magnitude of the EOF [17] compared to more sophisticated models. 

Relevant for the discussion of the effects of pore flow in CEC is the total or average EOF through narrow channels. The effect of electrical double-layer overlap on EOF is usually expressed in an electroosmotic flow screening factor P, which is defined as the ratio of the EOF velocity to that obtained without double-layer overlap, as can be found from the Smoluchowski equation ... 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

The theory states that the forces between droplets can be considered as the sum of an attractive van der Waals part Va and a repulsive electrostatic part Er when identical electrical double layers overlap. As the origin of each force is independent of the other, each is evaluated separately, and the total potential of interaction Vt between the two droplets as a function of their surface-to-surface separation is obtained by summation... 

When the protein approaches the surface the electrical double layers overlap, giving rise to a redistribution of charge. This can have a significant impact on protein adsorption. In some systems, e.g. RNase with a hydrophilic sorbent surface, overall electrostatic repulsion between the protein and the sorbent prevents adsorption. With other proteins, e.g. HPA, interactions between charged groups do not play a decisive role. 

The second electroviscous effect, which occurs when particles collide. Their electric double layers overlap and strong repulsive forces arise. Thi.s also results in a viscosity increase. 

The interaction between two charged particles in a polar media is related to the osmotic pressure created by the increase in ion concentration between the particles where the electrical double-layers overlap. The repulsion can be calculated by solving the Poisson-Boltzmann equation, which describes the potential, or ion concentration, between two overlapping double-layers. The full theory is quite complicated, although a simplified expression for the double-layer interaction energy, V dl( ) between two spheres, can be written as follows ... 

Figure 10.15. Schematic representations of the potential distribution between two approaching surfaces, shown (a) before, and (b) after overlap of the electrical double-layer overlap leads to a higher potential between the planes, thus resulting in repulsion...

The electrostatic interaction between film interfaces becomes operative at distances when the both electric double layers overlap each other. If the particles collide at small velocity of motion the lateral distribution of the ions is approximately uniform and from Eq. (21) an electrostatic disjoining pressure, Ilei, can be defined ... 

The presence of charge influences both inter- and intramolecular interactions. The charged polyelectrolyte molecules are surrounded by a diffuse distribution of counterions (cf. Chapter 9). The molecules repel each other by electrical double layer overlap, so that a polyelectrolyte solution may be colloidally stable even when the solvent quality is poor. Intramolecular electrostatic repulsion causes a more stretched conformation of the chain. This can be accounted for by an electrostatic contribution to the persistence length L ... 

FIGURE 16.4 Gibbs energy of electrical double layer overlap of two identical spheres (a = 500 nm) as a function of their separation distance. (1) = 25 mV, 25 mM ionic strength ... 

Let us first consider the electrostatic (double-layer) interaction between two identical charged plane-parallel surfaces across a solution of a symmetrical Z Z electrolyte. If the separation between the two planes is very large, the number concentration of both counterions and coions would be equal to its btllk value, no, in the middle of the film. However, at finite separation, h, between the surfaces, the two electric double layers overlap and the counterion and coion concentrations in the middle of the film, nio and respectively, are no longer equal. As pointed out by Langmuir [311], the electrostatic disjoining pressure, Del, can be identified with the excess osmotic pressure in the middle of the film ... 

Many expressions exist, as we see later (see also Table 2.2 in Chapter 2), but in the simple case of equal-sized spherical particles of equal and small surface potentials (less than 25 mV for 1 1 electrolytes) and small electric double layer overlap the DLVO theory takes the following form (see also Figure 10.3) ... 

Problem 10.10 Critical Coagulation Concentration The DLVO interaction energy between two equalsized spherical particles with the same surface potentials and rather small electric double layer overlap is given by Equation 10.4. 

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