Attraction, of charged particles

A. WUrger, Capillary attraction of charged particles at a curved liquid interface, Eumphys. Lett., 75,978, 2006. 

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... 

The electrical double layer is the array of charged particles and/or oriented dipoles that exists at every material interface. In electrochemistry, such a layer reflects the ionic zones formed in the solution to compensate for the excess of charge on the electrode (qe). A positively charged electrode thus attracts a layer of negative ions (and vice versa). Since the interface must be neutral. qe + qs = 0 (where qs is the charge of the ions in the nearby solution). Accordingly, such a counterlayer is made... 

Kunkel (K9) has derived expressions for the collision rate of charged particles allowing for both Coulomb attraction forces and ionic image forces. His final expressions, however, are not readily applied and he concludes only that the rate of growth of a particle over a period of several seconds is small if... 

Calculation of Coagulation Rate. Here we discuss an interaction potential of two charged particles in a liquid within a framework of DLVO theory. Following this theory, the overall interaction potential U, of charged spherical particles of the same radius R and surface distance d is a sum of a coulombic repulsive force of charged particles and a van der Waals attractive force given by the equation (28) ... 

If the collision system can separate asymptotically into a pair of charged particles of opposite signs, the attractive Coulomb tail of the interaction between them supports an infinite number of bound Rydberg states in each closed channel (with a threshold energy Eth). Its coupling with open channels, if any, normally turns these bound states into an infinite series of quasi-bound... 

At the center of the atom is the nucleus, a densely packed area of positively charged protons and neutral neutrons. The positively charged nucleus attracts negatively charged particles called electrons. The electrons can be found in an area that surrounds the nucleus called the electron cloud. Inside the electron cloud are shells and orbitals where electrons are most likely to be found. It is these clouds of moving electrons that allow the atom to form bonds with other atoms. 

Electrophoresis is the motion of charged particles relative to the electrolyte in response to an applied DC-electric field the field causes a shift in the particle counterion cloud, the counterion-diminished end of the particle attracts other counterions from the bulk fluid, counterions from the displaced cloud diffuse out into the bulk fluid, and the particle migrates. The particle velocity is predicted by the Smoluchowski equation. 

Similar analysis can be made for particles with an arbitrary initial charge multiplicity Z. If, in particular, a particle is originally neutral, tunneling will occur in an attractive electric field. It can be readily seen that, in the general case, the activation energy is ET + (Z+ 1)A.FT. The assumption that the molecular affinity EA is independent of the electric field of charged particles is quite reasonable, because at Z < 3 this field is still considerably weaker than the local electric fields associated with the chemisorption process. 

There are two factors that are closely associated with the structure and behavior of atoms. The first of these is known as effective nuclear charge. The nuclear charge is related to the number of charged particles (protons) in the nucleus. As the nuclear charge increases, there is an increase in the attractive force between the nucleus and the electrons. Nuclear charge increases from left to right across a period. 

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