Electrical repulsive potential energy

According to the DLVO theory, total potential energy between two particles is expressed by the sum of van der Waals attractive potential energy and electrical repulsive potential energy and the dispersion is stable when the total potential energy is higher than 15 kT (4). 

The electrical repulsive potential energy due to the electrical charge of the particles in aqueous solution can be approximated by ... 

Water droplets in an organic continuous phase show very low electric repulsion potentials. This means that a pure w/o-emulsion cannot be stable, because the total potential energy is only of the attraction mode. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

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. 

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. 

How was the theoretical DLVO curve in Figure 1.12 obtained The DLVO model [18, 19] postulates that the appropriate thermodynamic potential energy of interaction between two parallel flat plates can be described in terms of two components a repulsive term VR, resulting from the overlap of electrical double layers, and an attractive van der Waals interaction, VA. It also assumes that these interactions are additive, so that the total potential energy can be written as... 

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