Electrostatic mechanism

Before discussing the actual semi-infinite geometry which is relevant for surface effects, let us first consider a system in which all atoms are equally coordinated - a bulk material or some regular clusters, such as a square, a cube, etc., - and let us prove that the equilibrium inter-atomic distance Rq is an increasing function of the coordination number Z. 

Preliminary approach In Bom s model (Section 1.1), the total energy per formula unit is the sum of an electrostatic term, proportional to the Madelung constant a, and of a contribution from the short-range repulsion between neighbouring atoms. We will express the latter in a Lennard-Jones form (n 1)  

When comparing various geometries, it turns out that the Madelung constant a increases with Z, less quickly than Z itself. For example, in the rocksalt stmcture for a diatomic molecule, Z = 1 and a = 1 for a square, Z = 2 and a = 1.29 for a cube, Z = 3 and a = 1.46 and in the bulk, Z = 6 and a = 1.75. The equilibrium inter-atomic distance Ro is thus an increasing function of Z. In NaCl, a simple estimate for these four geometries gives Rq = 2.36 A, 2.51 A, 2.60 A and 2.79 A, respectively. 

This result supports the qualitative arguments, given in Section 1.1, which states that inter-atomic distances are equal to the sum of ionic radii, and that the latter increase with the coordination number (Shannon, 1976). It also supports the bond-length rules for adsorption processes which will be mentioned in Chapter 6 (Gutmann, 1978). 

The compactness of the structure thus favours larger inter-atomic distances. A similar result is obtained whenever the attractive forces, responsible for the cohesion, vary with Z and R less quickly than the repulsive ones. 

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In some systems, such as lake and river waters, the suspended inorganic particles may be coated by biological polymers, termed humic substances, which prevent flocculation by either steric or electrostatic mechanisms. These can also interact with added inorganic salts (31) that can neutralize charged functional groups on these polymers. 

The above discussion has tacitly assumed that it is only molecular interactions which lead to adhesion, and these have been assumed to occur across relatively smooth interfaces between materials in intimate contact. As described in typical textbooks, however, there are a number of disparate mechanisms that may be responsible for adhesion [9-11,32]. The list includes (1) the adsorption mechanism (2) the diffusion mechanism (3) the mechanical interlocking mechanism and (4) the electrostatic mechanism. These are pictured schematically in Fig. 6 and described briefly below, because the various semi-empirical prediction schemes apply differently depending on which mechanisms are relevant in a given case. Any given real case often entails a combination of mechanisms. 

Fig. 6. Four mechanisms of adhesion, (a) The adsorption mechanism (contact adhesion), (b) The diffusion mechanism (diffusion interphase adhesion), (c) The mechanical interlocking mechanism. (d) The electrostatic mechanism.

Ripoll, D.R., Faerman, C.H., Axelson, P.H., Silman, I. and Sussman, J.L. (1993) An electrostatic mechanism for substrate guidance down the aromatic gorge of acetylcholinesterase. Proceedings of the National Academy of Sciences USA 90, 5128-5132. 

In such systems the requirement of the electrostatic contribution to colloidal stability is quite different than when no steric barrier is present. In the latter case an energy barrier of about 30 kT is desirable, with a Debye length 1/k of not more than 1000 X. This is attainable in non-aqueous systems (5), but not by most dispersants. However when the steric barrier is present, the only requirement for the electrostatic repulsion is to eliminate the secondary minimum and this is easily achieved with zeta-potentials far below those required to operate entirely by the electrostatic mechanism. 

In this chapter, the historical development of the above-mentioned electrostatic mechanism will be reviewed and its current application to Pt/silica, Pt/alumina, and Pt/carbon catalysts will be demonstrated. Additionally, its extension to new catalyst systems including bimetallics will be discussed. The method of SEA is in principle applicable to a large number of catalyst systems it is hoped that readers are able to glean enough from this chapter to be able to employ the SEA approach themselves. 

On the other hand, a simpler and purely physical (electrostatic) mechanism might go toward describing the uptake of common noble metal precursors onto common oxide supports. The first model of Agashe and Regalbuto [26] was patterned after that of James and Healy [17] from colloid science literature. In the original James and Healy s model, a Langmuir isotherm was employed and... 

For D = 3 in., cp = 1000 /(g/liter, Sps = 1 Y/micron, Dp = 10 microns, pp = 1 gm/cm3, and <5 = 1, the ratio GielGig will be 8.25. Thus, even for such a small exposed charged cloud, deposition by electrostatic means will be almost an order of magnitude greater than by gravity. The electrostatic mechanism will also result in deposition on the under side of the surface. 

Blank, T.A. and Becker, P.B. (1995) Electrostatic mechanism of nucleosome spacing. J. Mol. Biol. 

Bennett, E., Urcan, M., Tinkle, S., Koszowski, A., Levinson, S. Contribution of sialic acid to the voltage dependence of sodium channel gating. A possible electrostatic mechanism, J. Gen. Physiol. 

Clearly, proteins can adhere to surfaces by electrostatic mechanisms, particularly at low ionic strength where the electrostatic field of the surface and the protein is much more extended. Indeed, this is the basis of ion exchange chromatography, so widely used for the separation, purification, and characterization of proteins. However, by the time one reaches the 0.15 M salt concentration of the physiologic environment, general electrostatic processes are no longer dominant. 

Matulis, D., Rouzina, I. and Bloomfield, V.A. (2000) Thermodynamics of DNA binding and condensation isothermal titration calorimetry and electrostatic mechanism. J. Mol. Biol., 296, 1053-1063. 

Poisson equation — In mathematics, the Poisson equation is a partial differential equation with broad utility in electrostatics, mechanical engineering, and theoretical physics. It is named after the French mathematician and physicist Simoon-Denis Poisson (1781-1840). In classical electrodynamics the Poisson equation describes the relationship between (electric) charge density and electrostatic potential, while in classical mechanics it describes the relationship between mass density and gravitational field. The Poisson equation in classical electrodynamics is not a basic equation, but follows directly from the Maxwell equations if all time derivatives are zero, i.e., for electrostatic conditions. The corresponding ( first ) Maxwell equation [i] for the electrical field strength E under these conditions is... 

The essential requisite for the present scenario is the unique property of the charged torus, that is, its instability to thicken beyond a certain size. Therefore, its applicability is not limited to the case, in which the torus thickness is limited by the electrostatic mechanism. For example, we expect that surfactant molecules, which are sometimes used as condensing agents, may affect such structural property through the packing inside folded structures. Note also that the presence of the finite-sized bundles is rather ubiquitous in other semiflexible polyelectrolyte systems and biopolymer solutions. Seeking for its consequences would be a yet uncultivated problem. 

Johnson, G., Moore, S.W. (2003). Human acetylcholinesterase binds to mouse laminin-1 and human collagen IV by an electrostatic mechanism at the peripheral anionic site. Neuro-sci. Lett. 337 37-40. 

It appears from these model studies on spectra of phenols that we cannot, by spectral means alone, discriminate between a hydrogen bonding, a hydrophobic bonding, or an electrostatic mechanism for perturbations of protein tyrosyl groups. 

The studies of intermolecular quadnipolar relaxation with MD simulations (and Monte Carlo simulations) was initiated by Engstrom et al. [49] in the beginning of the eighties [50-54]. The problem then concerned the nuclear spin relaxation of ions in water. Very successful and well accepted theoretical models of the electrostatic mechanism had been developed, and with computer simulations it was possible to examine some of the assumptions of these models [37,38]. Furthermore, the performance of the electrostatic models could be compared to that of theoretical models of the collision induced mechanism [36,55]. 

This gave the necessary link to the parameters of the theoretical models. The cross correlation represent the collective motion around the solute and as such are very difficult to incorporate into a model based on molecular properties. In the theoretical models for the electrostatic mechanism, the cross correlation was simply introduced as a scaling factor in front of the self EFG-TCF [37]. This scaling factor, however, contains information which is essential for understanding the relaxation mechanism. 

The specific surface areas depend on the pH (surface charge) and on the nature of the initial AI13 sol (r=2.0 or r=2.5). In the case of pure electrostatic mechanism it should depend on the adsorbate-adsorbent affinities. 

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