Shielded Coulomb potential

The Coulomb potential describes the interaction between two isolated charged particles, i.e., ions. At finite concentrations, a better description is obtained using the so-called (Debye-ffiickel) screened or shielded Coulomb potential. 

Figure 9 Electrostatic interaction energy between two hydrogen atoms represented by the shifted-force Coulomb and shielded Coulomb potentials.

Figure 9 shows the Coulomb potential, the shifted-force Coulomb potential (Eq. [31]), the shielded Coulomb potential (Eq. [32]), and the shielded shifted-force Coulomb potential (Eq. [33]) calculated for interaction between two hydrogen atoms with a charge = + e. ... 

This series arises naturally, when expressing the Coulomb potential of a charge separated by a distance s from the origin in terms of spherical coordinates. The positive powers result when r < s, while for r > s the potential is described by the negative powers. Similarly the solutions of the linearized Poisson-Boltzmann equation are generated by the analogous expansion of the shielded Coulomb potential exp[fix]/r of a non-centered point charge. Now the expansion for r > s involves the modified spherical Bessel-functions fo (x), while lor r < s the functions are the same as for the unshielded Coulomb potential,... 

The shielded Coulomb potential of Equation 1.21 contains two contributions, the electrostatic part determined by the charge of the central ion (p (r) given by Equation 1.25 and the part caused by the ionic cloud (pci(f) given by Equation 1.26. The potential (PciW for r = a, i.e., at the surface of the central ion, yields Equation 1.27, which is used to calculate the activity coefficient Jj as discussed in Section 1.5.4. 

Electrostatic interactions. In order to take into account electrostatic interactions and system polarization effects arising from residual charges on atoms, not least important for consideration of charge transfer processes, interactions are calculated between all pairs of atoms in the system using a shielded Coulomb potential. 

Debye length - In the Debye-Huckel theory of ionic solutions, the effective thickness of the cloud of ions of opposite charge which surrounds each given ion and shields the Coulomb potential produced by that ion. 

However, the radial dependence of the eigenfunctions for an electron in a multielectron atom is not the same as for an electron in an one-electron atom. The reason is that the net potential V(r), which enters the differential equation that determines the functions Rni r), does not have the same r dependence as the Coulomb potential. The innermost electron shells of an atom shield the outermost shells from parts of the nuclear charge + 2 e and reduce it. 

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. 

The Coulombic term in Eq. 6 becomes negligible in polar solvents owing to shielding of the electrostatic interaction between the radical ions generated. Table 5 lists representative redox potentials and free energies for photo-mediated electron transfer between a selected group of amines and photosensitizers such as anthraquinone (AQ) and dicyanoanthracene (DCA). 

Electrostatic Potential. The presence of an excess charge at the interface causes it to have an electrostatic surface potential ij/0. This may cause repulsion between two charged surfaces that are close together. In Section 3.1, Coulombic electrostatic interaction was mentioned [Eq. (3.1)], but the repulsion between charged surfaces separated by an aqueous phase cannot be considered Coulombic. This is because the charge is shielded by ions, as was discussed in Section 2.3.2 see Figure 2.10. Counterions (ions of... 

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