Overlapping charge clouds, potential

To get the potential energy of two overlapping charge clouds, consider the interaction of small elements of each cloud and then form a double integral over each of them. Calling the clouds 1 and 2, and the volume elements within them dvi and dv2, each of which carries a charge equal to the charge density of each cloud times the element s volume, the potential is ... 

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 many colloidal and micellar systems the asymmetry in size is large enough for the experiment to measure only the macroion-macroion correlation [35], For this reason various approximations, by which macroions are assumed to interact via an effective potential, are often applied. Macroions are assumed to be surrounded by a cloud of an opposite charge and it is assumed that the overlap of two clouds results in the repulsive interaction. In a popular theory, referred to as the one-component fluid (OCF) model, the macroions interact via the repulsive screened Coulomb potential in the form,... 

The 3D quadrupole ion trap suffers from a severe limitation. If the number of trapped ions is too high, the electrical field due to the Vcos iot potential is overlapped by that due to the ion cloud. The result is a drop in instrumental performances, particularly in mass resolution and linear response. To avoid this undesired phenomenon, a preliminary scan (not seen by the ion trap user) is performed and the ionization time (or the ion injection time) is optimized, thus confining the optimum number of ions inside the trap (see Fig. 2.18). This prescan leads to a well-controlled instrumental setup but, of course, it limits the sensitivity of the instrument. To overcome this problem, two different approaches can be employed (1) increase the ion storage capacity of the trap by increasing the electric field strength (2) increase the inner volume of the trap, so as to obtain a less dense ion cloud, which results in a decrease of space charge effects. 

The counterions form a diffuse cloud that shrouds each particle in order to maintain electrical neutrality of the system. When two particles are forced together their counterion clouds begin to overlap and increase the concentration of counterions in the gap between the particles. If both particles have the same charge, this gives rise to a repulsive potential due to the osmotic pressure of the counterions which is known as the electrical double layer (EDL) repulsion. If the particles are of opposite charge an EDL attraction will result. It is important to realize that EDL interactions are not simply determined by the Columbic interaction between the two charged spheres, but are due to the osmotic pressure (concentration) effects of the counterions in the gap between the particles. 

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