Repulsive screened Coulomb interactions

Though the theory of Derjaguin-Landau-Verwey-Overbeek (DLVO) [17, 18] was essentially designed for hydrophobic colloids, it is often applied to the analysis of the stability of polyelectrolyte solutions. According to this approach an overlap of the electrical double-layers of two charge-like colloidal spheres in an electrolyte solution always yields a repulsive screened Coulomb interaction, and the van der Waals forces are responsible for the attraction. A number of experiments in the recent decades, however, provide evidence that the effective interparticle potential shows a long-range attraction which cannot be ascribed to the van der Waals forces [15, 88-93], In spite of numerous theoretical attempts to explain this phenomena (for a review see [7, 8, 10, 94,... 

Figure 2. Ion ion dispersion interactions (curve 1) calculated using the Lifshitz approach in ref 4 dominate at small separations the water-screened Coulomb interactions (curve 2, e = 80, A = < >) however, they are negligible compared to the nonscreened Coulomb interactions (e = 10, A = < >) (curve 3), in the presence of a hard wall repulsion at r = 3.6 A.

In conclusion, we suggest that the ion dispersion forces were ignored by most (but by no means all) electrolyte theories mainly because they are important only for separations between ions smaller than about 5 A, and the interactions at these distances are not well-known. It is hard to believe that at these distances the interactions can be accurately described by a sum between a hard-wall repulsion, a Coulomb interaction, and a London attraction. Even if the latter would be true, a correction in the local dielectric constant (because of incomplete screening by water molecules) would render again the van der Waals interactions negligible, up to distances of the order of ion diameters. 

In many colloidal and micellar systems the asymmetry in size is large enough for the experiment to measure only the macroion-macroion correlation [35], For this reason various approximations, by which macroions are assumed to interact via an effective potential, are often applied. Macroions are assumed to be surrounded by a cloud of an opposite charge and it is assumed that the overlap of two clouds results in the repulsive interaction. In a popular theory, referred to as the one-component fluid (OCF) model, the macroions interact via the repulsive screened Coulomb potential in the form,... 

Other known methods that have been used in the study of lanthanides include the OP scheme, the LDA + U approach, where U is the on-site Hubbard repulsion, and the DMFT, being the most recent and also the most advanced development. In particular, when combined with LDA + U, the so-called LDA - - DMFT scheme, it has been rather successful for many complex systems. We note here that both DMFT and LDA + U focus mostly on spectroscopies and excited states (quasiparticles), expressed via the spectral DOS. In a recent review article (Held, 2007), the application of the LDA + DMFT to volume collapse in Ce was discussed. Finally, the GW approximation and method, based on an electron self-energy obtained by calculating the lowest order diagram in the dynamically screened Coulomb interaction, aims mainly at an improved description of excitations, and its most successful applications have been for weakly correlated systems. However, recently, there have been applications of the quasi-particle self-consistent GW method to localized 4f systems (Chantis et al., 2007). 

Large spherical polyions are usually treated as an effective one-component system where the interaction between the polyions is given by a hard sphere potential plus a repulsive screened Coulomb potential (DLVO model) [31]. The screening of the polyion interactions is entirely due to the charges and concentrations of counterions and salt ions. As a result, the polyions interact via an effective charge Zeff or an effective surface potential. The value of z f depends on how the correlations between the polyions themselves and between polyions and counterions are theoretically formulated. All models discussed so far lead to an effective interaction in terms of screening arguments. A more detailed theory is required to consider the small ions in the system explicitly. Different approaches... 

From Eq. (4.37) i/e see that for certain concentractions and q2<(Aj /ky(q) this effective interaction between electrons due to the screened Coulomb interaction and the exchange of virtual dressed excitons can become attractive corresponding to an overscreening of the Coulomb repulsion between the electrons. 

In conclusion, the repulsive interactions arise from both a screened coulomb repulsion between nuclei, and from the overlap of closed inner shells. The former interaction can be effectively described by a bare coulomb repulsion multiplied by a screening function. The Moliere function, Eq. (5), with an adjustable screening length provides an adequate representation for most situations. The latter interaction is well described by an exponential decay of the form of a Bom-Mayer function. Furthermore, due to the spherical nature of the closed atomic orbitals and the coulomb interaction, the repulsive forces can often be well described by pair-additive potentials. Both interactions may be combined either by using functions which reduce to each interaction in the correct limits, or by splining the two forms at an appropriate interatomic distance . 

The potential of mean force due to the solvent structure around the reactants and equilibrium electrolyte screening can also be included (Chap. 2). Chapter 9, Sect. 4 details the theory of (dynamic) hydro-dynamic repulsion and its application to dilute electrolyte solutions. Not only can coulomb interactions be considered, but also the multipolar interactions, charge-dipole and charge-induced dipole, but these are reserved until Chap. 6—8, and in Chaps. 6 and 7 the problems of germinate radical or ion pair recombination (of species formed by photolysis or high-energy radiolysis) are considered. 

Necessarily for any number of particles more than two, eqn. (211) cannot be solved exactly, even if v° = 0 and U = 0. When there are more than two particles, the motion of one particle, say j, causes both k and / to move. Now because k and / are perturbed by j, then the perturbation to the motion of k is felt by /. The motion of j affects / directly and also indirectly through k. These indirect effects are not usually very important, especially in chemical kinetics, because the particles most likely to react are those which are closest together. Under such circumstances, the direct effect is stronger than the transmitted and reflected components. These effects have been considered by Adelman [481], Freed and Muthukumar [482] and Allison et al. [483]. Adelman draws an interesting parallel between the screening of hydrodynamic repulsion and the electrolyte screening of a coulomb interaction [481]. 

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