Charges in a medium

Ion pairing is due to electrostatic forces between ions of opposite charges in a medium of moderate to low relative permittivities. It should be distinguished from complex formation between metal cations and anionic ligands, in which coordinative bonds (donation of an electron pair) takes place. One distingnishing feature is that, contrary to complex formation, the association is nondirectional in space. The association of a cation and an anion to form an ion pair can, however, be represented as an equilibrium reaction by analogy to complex formation with an equilibrium constant A)ass [3,5]. If a is the fraction of the electrolyte that is dissociating into ions and therefore (1 - a) is the fraction that is associated, then... 

The potential (j>A (r, t) produced by these charged in a medium with dielectric constant e is obtained from the Poisson equation... 

This summarises the results of experiments on bringing two charged spheres together. It is found that the force of electrostatic interaction between two charges in a medium of relative permittivity, Cr, at a distance, r, apart is given by ... 

For estimating the forces between dipoles of the enzyme and that of the substrate a simplified approach is to use partial charges on the individual atoms, and to calculate the electrostatic interaction by Coulomb s law (Eqn. 65) as a function of the distance, r A, between the partial charges, q expressed in terms of the electronic charge, in a medium of dielectric constant D. 

The model is identical with that discussed in Section IV-A we consider a spherical ion of charge in a medium of spherical particles of polarizability a. It can be shown that the direct contribution of the polarizability of the ion vanishes owing to the spherical symmetry of the problem. We have... 

When two opposite charges in a medium of relative permittivity approach one another, the Coulombic energy of attraction between them equals kT at a critical distance so that ... 

The permittivity of a medium, denoted e, expressed in farad per meter (F.m ), is defined by Coulomb s law applied to the medium. Actually, the modulus of the electrostatic force, in newtons (N) between two point electric charges in a medium q or q, in coulombs (C), separated by a distance in meters (m), is given by the following equation ... 

The electrostatic screening length, also called the Debye length fo, is the key measure of the range of electrostatic interaction among charges in a medium. It is defined as the reciprocal of k, as mentioned above... 

The situation is of course more complicated when the charge assembly resides in a material medium. Materials may be classified as conductors or insulators. For a conductor (e.g., most metals), all net charge resides on the surface of the conductor and distributes itself such that the electric field is zero inside the material. For insulators, or dielectrics (e.g., glass, water. ..), the medium modifies Coulomb s law in a simple way. For two point charges in a medium characterized by dielectric constant s the Coulomb potential is reduced by a factor of g (g = 1 in vacuum and g > 1 in a material medium) ... 

The separation of charges in a medium with a low dielectric constant is less advantageous in comparison with the jaqueous medium. The losses in solvation energies of Im H+ and -C-0 connected with this may be estimated in the same way as described above (by taking into account the electrostatic and specific components of the solvation energy). Further, we must take into account the intraglobular field as well as the interaction energy of ions in the ion pair... 

Namely this value has to be introduced into the Coulomb s law (4.1.1) in order to determine a force acting between two point charges in a medium with dielectric permeability s. 

The Poisson equation relates spatial variation of the potential 4> at position r to the density of the charge distribution, p, in a medium with a dielectric constant e... 

The interaction between two charges qi and qj separated by the distance rij in a medium with a dielectric constant e is given by Coulomb s law, which sums the energetic contributions over all pairs ij of point charges within a molecule (Eq. (25)). 

Another way of calculating the electrostatic component of solvation uses the Poisson-Boltzmann equations [22, 23]. This formalism, which is also frequently applied to biological macromolecules, treats the solvent as a high-dielectric continuum, whereas the solute is considered as an array of point charges in a constant, low-dielectric medium. Changes of the potential within a medium with the dielectric constant e can be related to the charge density p according to the Poisson equation (Eq. (41)). 

To go from experimental observations of solvent effects to an understanding of them requires a conceptual basis that, in one approach, is provided by physical models such as theories of molecular structure or of the liquid state. As a very simple example consider the electrostatic potential energy of a system consisting of two ions of charges Za and Zb in a medium of dielectric constant e. 

The simplest reaction field model is a spherical cavity, where only the net charge and dipole moment of the molecule are taken into account, and cavity/dispersion effects are neglected. For a net charge in a cavity of radius a, the difference in energy between vacuum and a medium with a dielectric constant of e is given by the Bom model. ... 

Zone electrophoresis is defined as the differential migration of a molecule having a net charge through a medium under the influence of an electric field (1). This technique was first used in the 1930s, when it was discovered that moving boundary electrophoresis yielded incomplete separations of analytes (2). The separations were incomplete due to Joule heating within the system, which caused convection which was detrimental to the separation. 

The aqueous diffusivities of charged permeants are equivalent to those of uncharged species in a medium of sufficiently high ionic strength. The product DF(r/R) is the effective diffusion coefficient for the pore. It is implicit in k that adsorption of the cations does not occur, so that the fixed surface charges on the wall of the pore are not neutralized. Adsorption is more likely to occur with multivalent cations than with univalent ones. 

In addition to the nonelectrostatic adsorptive force, there is an image force between a dipole and a metal, which will be present whenever charged or dipolar particles in a medium of one dielectric constant are near a region of another dielectric constant. If the metal is treated as an ideal conductor, the image-force contribution to the energy of a dipole in the electrolyte is proportional to p2j z3, where z is the distance of the dipole from the plane boundary of the metal (considered ideal, with no surface structure), and to 1 + cos2 0. This ideal term is, of course, the same for all metals. If... 

Linear energy transfer (LET) A function of the capacity of the radiation to produce ionization. LET is the rate at which charged particles transfer their energies to the atoms in a medium and a function of the energy and velocity of the charged particle. See Radiation dose. 

The Debye-FIuckel theory for association of spherical ions in a medium of dielectric constant Dr posits that the electrostatic potential energy of interaction between oppositely charged ions is... 

Amis proposed Equation (3)18 for the reaction rate constant involving a limiting case of head-on approach of an ion to a neutral dipolar molecule from electrostatic considerations, as would be the case for metal ion catalysts and neutral C = 0 or P = O substrates. This expression relates the natural log of the rate constant in a medium of dielectric constant (D) to the charge on the ion (Ze), the dipole moment... 

An early continuum treatment of solvation, associated with Born,17 comes out of the analysis of the electrostatic work involved in building up a charge Q on a conducting sphere of radius R in a medium with dielectric constant e. From Poisson s equation, it follows that the potential outside of the sphere is Q/eR. Thus the work of charging is the result of each additional element dq interacting with the charge q already present 87... 

The electrostatic component of the free energy of solvation of the sphere is then the difference between doing this charging in a vacuum (e = 1) and in the medium ... 

This gives the electrostatic contribution to the free energy of solvation of a conducting sphere with charge Q and radius R in a medium with dielectric constant e. 

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