Polarization between charged spheres

Equation (50) may also be used to calculate the attractive force between equal sized, equally and oppositely charged spheres that are perfect insulators. For this condition, the value of ksA and of ksg is taken as unity if polarization possibilities are neglected, and if the charge is initially uniformly distributed. Any polarization will tend toward an approach to the conductor condition (which basically represents a condition of infinite polarization). Figure 8 presents a plot of Eq. (50). Thus, if we assume that the maximum possible field intensity is 200 V/micron, the attractive force between equally but... 

Generally, it is the interaction of a donor (D) and an acceptor (A) involving the transfer of one electron. The probability of one-electron transfer is determined by thermodynamics namely, by the positive difference between the acceptor electron affinity and donor IP. The electron transfer is accompanied by a change in the solvate surroundings—charged particles are formed, and the solvent molecules (the solvent is usually polar) create a sphere around the particles thereby promoting their formation. Elevated temperatures destroy the solvate shell and hinder the conversion. Besides, electron transfer is often preceded by the formation of charge-transfer complexes by the sequence D A D A (D +, A -) (D+, A ) D+ A . ... 

The feeblest type of chemical interaction occurs between neutral atoms, not in their valence state, and is typified by inert-gas crystals. In this case the atoms occur close-packed with a very small accumulation of charge on the interstitial sites. These charges are generated by mutual polarization of vibrating atomic charge spheres. Under high pressure an increased amount of valence density is squeezed into interstitial sites until a metal structure is formed. 

The interaction between two charged particles in a polar media is related to the osmotic pressure created by the increase in ion concentration between the particles where the electrical double-layers overlap. The repulsion can be calculated by solving the Poisson-Boltzmann equation, which describes the potential, or ion concentration, between two overlapping double-layers. The full theory is quite complicated, although a simplified expression for the double-layer interaction energy, V dl( ) between two spheres, can be written as follows ... 

To account for the polarization outside the spheres, we have to add a reaction field that simulates the stabilizing polarization forces from the medium due to the charges created (the Coulomb attraction between the charges is already included in the calculation) ... 

The valence electron that mediates interaction with another atom is considered to be distributed uniformly over the sphere of radius r0 which surrounds the monopositive atomic core. On closer approach the atomic spheres start to overlap and bonding electrons are exchanged between the atoms. This polarization of the system is represented by point charges, related in magnitude... 

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