Double-layer overlap, electrostatic

So far, we have used the Maxwell equations of electrostatics to determine the distribution of ions in solution around an isolated, charged, flat surface. This distribution must be the equilibrium one. Hence, when a second snrface, also similarly charged, is brought close, the two surfaces will see each other as soon as their diffuse double-layers overlap. The ion densities aronnd each surface will then be altered from their equilibrinm valne and this will lead to an increase in energy and a repulsive force between the snrfaces. This situation is illustrated schematically in Fignre 6.12 for non-interacting and interacting flat snrfaces. 

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... 

The role of electrostatic repulsion in the stability of suspensions of particles in non-aqueous media is not yet clear. In order to attempt to apply theories such as the DLVO theory (to be introduced in Section 5.2) one must know the electrical potential at the surface, the Hamaker constant, and the ionic strength to be used for the non-aqueous medium these are difficult to estimate. The ionic strength will be low so the electric double layer will be thick, the electric potential will vary slowly with separation distance, and so will the net electric potential as the double layers overlap. For this reason the repulsion between particles can be expected to be weak. A summary of work on the applicability or lack of applicability of DLVO theory to non-aqueous media has been given by Morrison [268],... 

A general scheme, based on a rigorous statistical mechanical formulation, for obtaining the interaction between two colloidal particles in a fluid has been outlined. The implementation of the theory is in its early stages. In the DLVO theory and the theory of HLC, it is assumed that the various contributions can be added together. In the MSA, the hard core and electrostatic terms will be additive. However, it is only at low electrolyte concentration that the effect of dipole orientation and the repulsive contribution of the double layer overlap will be additive. There is no reason to believe (or disbelieve) that the van der Waals term should also be additive. 

Electrostatic. Virtually all colloids in solution acquire a surface charge and hence an electrical double layer. When particles interact in a concentrated region their double layers overlap resulting in a repulsive force which opposes further approach. Any theory of filtration of colloids needs to take into account the multi-particle nature of such interactions. This is best achieved by using a Wigner-Seitz cell approach combined with a numerical solution of the non-linear Poisson-Boltzmann equation, which allows calculation of a configurational force that implicitly includes the multi-body effects of a concentrated dispersion or filter cake. 

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... 

The physical stability of a colloidal system is determined by the balance between the repulsive and attractive forces which is described quantitatively by the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. The electrostatic repulsive force is dependent on the degree of double-layer overlap and the attractive force is provided by the van der Waals interaction the magnitude of both are a function of the separation between the particles. It has long been realized that the zeta potential is a good indicator of the magnitude of the repulsive interaction between colloidal particles. Measurement of zeta potential has therefore been commonly used to assess the stability of colloidal systems. 

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 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 ... 

Electrostatic and Dispersion Forces. Several repulsive and attractive forces operate between colloidal species and determine their stability (7,8,10,25, 31,54). In the simplest example of colloid stability, particles 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, and that will act in opposition to any attempt to decrease the separation distance. One can thus 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 the Bom repulsion. 

Colloidal particles snspended in a solvent can acquire charge by two ways. The surface groups can dissociate or the ions from solution can bind to the particle surface (Israelachvili, 1992 Russel, 1989 Hunter, 1987). The charge boimd to the particle surface is balanced by a diffuse region of ions in solution, called the diffuse double layer. When two like particles (radius a) approach one another, the double layers overlap and the particles feel a repulsion. Exact analytic expressions for the electrostatic potential energy ( Ve) for all values of the particle surface potential are difficult to compute and therefore analytical approximations or numerical solutions are used. Eor interacting particles with low surface potential e fa/kT < 1), can accurately be calculated using the linear superposition approximation (Israelachvili, 1992 Russel, 1989 Hunter, 1987)... 

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 ... 

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. 

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... 

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