Colloids Coulombic repulsion

Scheme 9.1 Schematic representation of electrostatic stabilization a coulombic repulsion between metal colloid particles.

The DLVO theory, a quantitative theory of colloid fastness based on electrostatic forces, was developed simultaneously by Deryaguin and Landau [75] and Verwey and Overbeek [76], These authors view the adsorptive layer as a charge carrier, caused by adsorption of ions, which establishes the same charge on all particles. The resulting Coulombic repulsion between these equally charged particles thus stabilizes the dispersion. This theory lends itself somewhat less to non-aqueous systems. 

The Huggins coefficient kn is of order unity for neutral chains and for polyelectrolyte chains at high salt concentrations. In low salt concentrations, the value of kn is expected to be an order of magnitude larger, due to the strong Coulomb repulsion between two polyelectrolyte chains, as seen in the case of colloidal solutions of charged spheres. While it is in principle possible to calculate the leading virial coefficients in Eq. (332) for different salt concentrations, the essential feature of the concentration dependence of t can be approximated by... 

In aqueous suspension, the stability is discussed in reference to the DLVO (Deryaguin-Landau-Verway-Overbeek) theory. Within this framework, all solid substances have a tendency to coagulate due to their large van der Waals attractive force. The coulombic repulsive force among colloidal particles more or less prevents this tendency. These two opposite tendencies determine the stability of suspensions. What kind of parameters are concerned in the present nonaqueous system, for which little is known about the stability This is an interest in this section. 

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. 

Overbeek s stricture noted above focuses attention on the principal reason why the current methods of imparting colloid stability are so few in number. The paramount difficulty resides in the projection of the repulsion over distances comparable to that of the attraction (5-10 nm). One way to accomplish this is to use Coulombic repulsion. In the electrostatic stabilization of aerosols, the Coulombic repulsion between the colloidal particles is of a long ran character and can impart stabUity. In liquid dispersion media, however, the principle of electroneutrality demands that the net charge in the dispersion medium be equal, but opposite in sign, to that of the particles. This leads to a more rapid fall-off in the potential. The coimterions in the dispersion medium, however, give rise to the electrical double layers that surround the colloidal particles. It is the mutual repulsion of these double layers that provides stability in electrostatic stabilization (see Fig. 1.2). 

In contrast to this, the scaling theory of the PE star collapse developed in [27] suggested that, instead of the formation of a collapsed core, a decrease in the solvent strength may provoke the formation of bundles by the sticking of individual branches to each other. The bundle formation reduces the excess interfacial free energy of the collapsed domains, without a significant penalty in terms of the intramolecular Coulomb repulsion. More recently, the formation of bundles was theoretically predicted in colloidal PE brushes [42]. 

The crucial importance of the double layer when dealing with colloidal particles dispersed in a solution is due to the repulsion of one particle by another. While overall the particles are neutral, because the diffuse layer can extend into the solution, the unbalanced charge in the diffuse layer of one particle experiences a repulsion by that of another particle. Normally, from the Coulomb law of electrostatics, the force between two equal (in charge and in sign) particles is given by... 

The DLVO theory [1,2], which describes the interaction in colloidal dispersions, is widely used now when studying behavior of colloidal systems. According to the theory, the pair interaction potential of a couple of macroscopic particles is calculated on the basis of additivity of the repulsive and attractive components. For truly electrostatic systems, a repulsive part is due to the electrostatic interaction of likely charged macroscopic objects. If colloidal particles are immersed into an electrolyte solution, this repulsive, Coulombic interaction is shielded by counterions, which are forming the diffuse layer around particles. A significant interaction occurs only when two double layers are sufficiently overlapping during approach of those particles. 

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