Spheres interactions

The interaction between particles belonging to the same species is a hard sphere interaction... 

Outer-sphere interaction in aqueous solutions of complex compounds. V. E. Mironov, Russ. Chem. Rev. (Engl. Transl), 1966,35, 455-469 (123). 

The formation of a 3D lattice does not need any external forces. It is due to van der Waals attraction forces and to repulsive hard-sphere interactions. These forces are isotropic, and the particle arrangement is achieved by increasing the density of the pseudo-crystal, which tends to have a close-packed structure. This imposes the arrangement in a hexagonal network of the monolayer. The growth in 3D could follow either an HC or FCC struc-... 

R. W. Hedges, and E. Messens, Genetic aspects of rhizo.sphere interactions. The Rhizosphere (J. M. Lynch, ed.). John Wiley, Chichester, 1990, p. 129. 

In the case of the Na+ and K+ complexes of N9-ethyladenine-aza-18-crown-6, the metal ions exhibit different types of interaction at the minor groove site N3 (Fig, 14) (52). The Na+ complex, 6, shows a second-sphere interaction involving the coordinated H20 hydrogen bonding to N3 [Na-OH2 2.327, H0 N3 2.836 A], In contrast, the K+ complex, 7,... 

Fig. 14. Structures of (6), illustrating the second-sphere interaction with A-N3, and (7), showing the K1 A N3 binding. Reproduced with permission from Ref. (52). Copyright 2001, Royal Society of Chemistry.

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

In studies on solvent effects involving variation in the composition of two component mixtures, similar types of outer-sphere interactions yield preferential solvation wherein the solvent composition of the outer-sphere may differ markedly from the bulk solvent composition. Supporting electrolyte species and buffer components may also participate in outer-sphere interactions thereby changing the apparent nature (charge, bulk, lability) of the reacting solvated metal ion or metal complex as perceived by a reacting ligand in the bulk solvent. 

Types of metal adsorption to mineral and organic surfaces (a) outer sphere interactions, (b) adsorption by electron-donor groups, (c) adsorption by negatively charged surface sites, and (d) adsorption to surface groups capable of forming metal-covalent bonds. The only parts of the molecular structure of the particle shown are the atoms engaged in metal adsorption. 

The region of a metal ion complex where hgands make direct binding interactions with the central metal ion. When the ligands do not completely neutralize the positive ionic charge of the central ion, other ions or electron-rich substances will become loosely associated with the complex through so-called outer coordination sphere interactions. 

Subsequent to CO2 association in the hydrophobic pocket, the chemistry of turnover requires the intimate participation of zinc. The role of zinc is to promote a water molecule as a potent nucleophile, and this is a role which the zinc of carbonic anhydrase II shares with the metal ion of the zinc proteases (discussed in the next section). In fact, the zinc of carbonic anhydrase II promotes the ionization of its bound water so that the active enzyme is in the zinc-hydroxide form (Coleman, 1967 Lindskog and Coleman, 1973 Silverman and Lindskog, 1988). Studies of small-molecule complexes yield effective models of the carbonic anhydrase active site which are catalytically active in zinc-hydroxide forms (Woolley, 1975). In addition to its role in promoting a nucleophilic water molecule, the zinc of carbonic anhydrase II is a classical electrophilic catalyst that is, it stabilizes the developing negative charge of the transition state and product bicarbonate anion. This role does not require the inner-sphere interaction of zinc with the substrate C=0 in a precatalytic complex. 

So far, we have only considered the interaction between flat snrfaces, basically becanse of the simplification of the PB eqnation in one dimension. Of conrse, colloidal particles are nsnally spherical and for this geometry the exact nnmerical solntion of the three-dimensional PB eqnation becomes very difficnlt. However, we can obtain an estimate of the sphere-sphere interaction from the planar resnlt if the radins a of the spheres is mnch larger than the Debye length (i.e. Ku 1). This method was developed by Derjagnin. 

FIGURE 4. Typical outer-sphere interaction of [Mg(H20)5] with two GC base pairs in the major groove of a DNA double helix... 

Each of the species mentioned above can be expected to exhibit different interactions with Mg + and the binding situation is even more complex than with carboxylates. In addition to outer-sphere interactions, phosphates, like carboxylates, are capable of... 

We begin by considering an array of spherical particles with motion that is totally governed by Brownian movement. Let us assume that there are particles of two different radii, Rs l and Rs 2- We assume the spheres interact on contact, in which case they adhere, forming a doublet. Although this is a highly oversimplified picture, it provides a model from which more realistic models can be developed in subsequent stages of the presentation. 

Early numerical estimates of ternary moments [402] were based on the empirical exp-4 induced dipole model typical of collision-induced absorption in the fundamental band, which we will consider in Chapter 6, and hard-sphere interaction potentials. While the main conclusions are at least qualitatively supported by more detailed calculations, significant quantitative differences are observed that are related to three improvements that have been possible in recent work [296] improved interaction potentials the quantum corrections of the distribution functions and new, accurate induced dipole functions. The force effect is by no means always positive, nor is it always stronger than the cancellation effect. 

Very little is known about the irreducible ternary dipole components. An early estimate based on classical electrodynamics, hard-sphere interaction and other simplifying assumptions suggests very small, negative contributions to the zeroth spectral moment [402], namely —0.13 x 10-10 cm-1 amagat-3. 

In the simplest approximations, molecules are assumed to be hard spheres. Interactions between molecules only occur instantaneously, with a hard repulsion, when the molecules centers come close enough to overlap. 

Evaluate the Chapman-Enskog expression for the thermal conductivity, Eq. 12.87, for the special case of a hard-sphere interaction. Show that for a pure-species, this gives the result cited earlier as Eq. 12.57. 

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