Charge Repulsion Systems

This allows the integrals representing the relationship between structure and macroscopic properties to be simplified to their value at R. This represents a cell model and so for the appropriate property  

We can also develop a zero Kelvin lattice model with slightly different spatial averaging. This gives17 

Also shown is the dimensionless energy density for hard spheres, 3kBTf2 per particle. The viscoelastic liquid zone is difficult to define 

The separation at which this occurs can be taken to be when the pair potential and Brownian energy equate, i.e. V(r0) = 1 kBT. This gives 

This diameter can be used to estimate the viscosity (see Section 3.5.4). Our interest is in determining where the hard sphere boundaries occur  

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We found a way to overcome charge-charge repulsion when activating the nitronium ion when Tewis acids were used instead of strong Bronsted acids. The Friedel-Crafts nitration of deactivated aromatics and some aliphatic hydrocarbons was efficiently carried out with the NO2CI/3AICI3 system. In this case, the nitronium ion is coordinated to AICI3. 

Another important emulsion stabilization is achieved by using polymers. The large polymer molecules adsorbed on solid particles (Figure 9.6) will exhibit repulsion at the surface of the particles. The charged polymers also will give additional charge-charge repulsion. Polymers are used in many pharmaceutical, cosmetics, and other systems (milk). Obviously, the choice of a suitable polymer is specific to each system. 

Unlike TEOS hydrolysis, Si02 particles have been also prepared by hydrolysis of Na2Si02 and Na4Si02 in nonionic reversed micelle systems. Spherical and poly-disperse particles of 31.8 nm mean diameter were produced in polyoxyethylene(9.5) octylphenyl ether-hexanol-cyclohexane systems (25), but more uniform and dense particles were precipitated by hydrochloric acid-catalyzed hydrolysis in a mixture of polyoxyethylene(5) nonylphenyl ether and polyoxyethylene(9) nonylphenyl ether in cyclohexane systems at pH 11 (26). The uniform particle formation at higher pH is attributed to the charge repulsion by OH- adsorbed on particle surface. The particles of specific surface area of 347 m2 g-1 can be obtained by calcination of particles produced at pH 2. 

Other factors (charge repulsion, solvation factors, etc.) could influence the position of the equilibrium in favor of enolate dianion 216. It is also possible that there is a kinetic preference for the formation of dianion 216 and that this species would undergo protonation more rapidly than equilibration. This rule of axial protonation" of 216 has been found to be widely applicable in many cases. However, in systems in which a significant amount of strain must be introduced in order for protonation to occur axially on 216, protonation of conformer 217 (and even conformer 218) becomes important (60). 

Charge-charge repulsive effects increase the importance of the resonance form (35b) having dione-type structure (a 1,4-dication and representing a distonic superelectrophile). Despite the importance of the charge separated structure 35b, the system is included here with other 1,2-ethylene dications and gitonic superelectrophiles. 

Transfer of Cl+ to the arene provides some relief of the Coulombic repulsion in the multiply charged, superelectrophilic system. Under the reaction conditions, it is not yet known to what extent the N-halosuccinimides are protonated in BF3-H2O, but this acid-catalyst has an estimated acidity around IIq —12. 

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