Electrostatic coulombic forces

The protonation mechanism includes Coulomb electrostatic forces resulting from charged surfaces. The development of surface acidity by the solid phase of the subsurface offers the possibility that solutes having proton-selective organic functional groups can be adsorbed through a protonation reaction. 

The Coulombic electrostatic force is a very long-range force. When the distance is doubled, the force decreases to 50% when a molecule is removed to 10 times the normal distance, the attractive force declines to 10%. 

Ionic crystals are formed by combinations of highly electropositive and highly electronegative elements, such as ordinary salts. Ions rather than atoms occupy positions in the space lattice and are held together by coulomb electrostatic forces. Ionic crystals obey valence rules and are good ionic conductors of electricity when molten. 

Ionic. Ionic materials are those that are brittle and that conduct electricity when molten but not as solids. Melting points range upwards from about 500°C. Examples are CaO (quicklime), Mgp2, and NaCl (common table salt). The electrons are constrained about each atom, some atoms with excess positive charge (cations) and some with excess negative charge (anions). The ions are packed closely together, held by coulomb (electrostatic) forces of attraction. 

The positive and negative ions, of charge q, will experience a Coulombic electrostatic force Fe given by ... 

In the hydrogen atom, the electron is assumed to move in a circle around the nucleus, attracted by the Coulomb electrostatic force. The eigenstate of the electronic motion is therefore determined by the Schrodinger equation for the rotational motion. The Hamiltonian operator is in the same form as that for the rotational motions of molecules mentioned in the last section. Following Eq. (1.57), the Hamiltonian operator is represented as... 

The LR term represents the interactions caused by the Coulomb electrostatic forces, expressed by a modified Debye-Hiickel term. The physical validity of the term is limited to the very dilute region. The purpose of this term is just to provide the true limiting law at infinite dilution. 

Interactions between charged particles are due to Coulomb electrostatic forces that derive from a potential. 

There are tliree important varieties of long-range forces electrostatic, induction and dispersion. Electrostatic forces are due to classical Coulombic interactions between the static charge distributions of the two molecules. They are strictly pairwise additive, highly anisotropic, and can be either repulsive or attractive. 

Since empirical force fields do not accurately estimate the true interatomic forces, it is difficult a priori to say how accurate the fast multipole approximation to the exact Coulomb potential and forces (exact in terms of the sum over partial charges) should be. Probably a good rule is to make sure that at each atom the approximate electrostatic force is within a few percent relative error of the true electrostatic force, obtained by explicitly summing over all atom pairs, i.e., IF — FJ < 0.05 F , for all atoms i, where F is the... 

It is of special interest for many applications to consider adsorption of fiuids in matrices in the framework of models which include electrostatic forces. These systems are relevant, for example, to colloidal chemistry. On the other hand, electrodes made of specially treated carbon particles and impregnated by electrolyte solutions are very promising devices for practical applications. Only a few attempts have been undertaken to solve models with electrostatic forces, those have been restricted, moreover, to ionic fiuids with Coulomb interactions. We would hke to mention in advance that it is clear, at present, how to obtain the structural properties of ionic fiuids adsorbed in disordered charged matrices. Other systems with higher-order multipole interactions have not been studied so far. Thermodynamics of these systems, and, in particular, peculiarities of phase transitions, is the issue which is practically unsolved, in spite of its great importance. This part of our chapter is based on recent works from our laboratory [37,38]. 

The above provides a means of showing how the total excess charge on the solution side of the interface q the excess charge due to cations F+ and the excess charge due to anions F, vary with potential in a solution of fixed concentration of electrolyte. On the basis of this approach to the electrocapillary curves it has been shown that the Gibbs surface excess for cations is due solely to electrostatic forces (long-range coulombic), and this is reflected in the fact that the electrocapillary curves for different cations and... 

Forces Superimposed on the Coulomb Forces. The discussion has been based on the idea that, superimposed on the electrostatic forces between a pair of ions, there are rather short-range forces of other origin, which may be attractive or repulsive. Consider now what the situation will be if these forces cause the mutual potential energy to fall at short distances, below the value — e2/er that is assumed in the Debye-Hlickel theory. In Fig. 74 let the broken curve be a plot of — e2/er, while the full curve gives the actual potential energy between a certain pair of... 

The electrostatic force is given by the coulombic force as e2/r2 while the centrifugal force on the electron is mi /r. Therefore, we can write... 

Consider two stationary point charges, <2i and Q2, separated by a distance R. Let R be the distance vector from Q to Q2. Then Coulomb s law states that the electrostatic force F exerted upon Q2 by <2i is... 

The DLVO theory, a quantitative theory of colloid fastness based on electrostatic forces, was developed simultaneously by Deryaguin and Landau [75] and Verwey and Overbeek [76], These authors view the adsorptive layer as a charge carrier, caused by adsorption of ions, which establishes the same charge on all particles. The resulting Coulombic repulsion between these equally charged particles thus stabilizes the dispersion. This theory lends itself somewhat less to non-aqueous systems. 

Coulombic Force Coulomb s law of electrostatic force is written, in SI units, as... 

For ions and polar molecules, the nature of the solvent is an important factor in solution-phase reactions. Following the derivation of Laidler and Meiser (1982), we first consider the reaction between two ions A and B with charges ZAe and ZL e, respectively, where e is unit electronic charge and ZA and Zu are the number of unit charges on the ions, i.e., are whole positive or negative numbers. The electrostatic force (F) between these two ions separated by a distance r in a vacuum is given by Coulomb s law,... 

Balachandran [23] analyzed the role of electrostatic forces in the adhesion between sohd particles and surfaces. According to the available information this role is not completely clear, the results are contradictory. Electrostatic forces can be significant in the case of polymer and semi-conductor particles. These forces have four main types Coulomb, image charge, space charge and dipole forces. 

---