Stability repulsion

One explanation for the alpha effect is ground-state de-stabilization Repulsive electronic interactions between the alpha atom s lone-pair and the nucleophile occur in the ground-state, and such destabilization is expected to be relieved as a covalent bond is forming in the transition-state of a nucleophilic substitution reaction. Reduced solvation in molecules exhibiting the alpha effect may also play a role in the increased nucleophilicity for example, OH2 displays no effect in the gas phase, but a substantial effect is observed in solution. Another factor may be the abihty of the alpha lone-pair to stabilize any partially positive group formed in the transition state. 

Another way to interpret the above observations would be in terms of the general principle that effective steric stabilization of polymer-coated droplets requires that the continuous phase be a good quality solvent for the polymeric stabilizer. Under poor quality solvent conditions (asi-casein at high ionic strength), the required entropic stabilizing repulsion of the adsorbed protein layer is converted into a destabilizing polymer-mediated attraction (Dickinson and Stainsby, 1982 Dickinson, 2006). 

Fig. 5 Polymer chains grafted to particle surfaces provide a stabilizing repulsion as particles approach, the chains overlap and repel.

The next section reviews modeling and simulation approaches for polymers in bulk supercritical solutions. Theoretical and simulation studies of colloids in supercritical fluids are then discussed. These studies describe the relationship between colloid stability and bulk solution phase behavior of the stabilizer as a function of solvent density. Another goal of this section is to describe in detail the causes of the stabilizing repulsive force, and why the force becomes attractive as solvent density is decreased. The theory and simulation results are compared to colloid stability experiments. 

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

If an ionic surfactant is present, the potentials should vary as shown in Fig. XIV-5c, or similarly to the case with nonsurfactant electrolytes. In addition, however, surfactant adsorption decreases the interfacial tension and thus contributes to the stability of the emulsion. As discussed in connection with charged monolayers (see Section XV-6), the mutual repulsion of the charged polar groups tends to make such films expanded and hence of relatively low rr value. Added electrolyte reduces such repulsion by increasing the counterion concentration the film becomes more condensed and its film pressure increases. It thus is possible to explain qualitatively the role of added electrolyte in reducing the interfacial tension and thereby stabilizing emulsions. 

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Themiodynamic stability requires a repulsive core m the interatomic potential of atoms and molecules, which is a manifestation of the Pauli exclusion principle operating at short distances. This means that the Coulomb and dipole interaction potentials between charged and uncharged real atoms or molecules must be supplemented by a hard core or other repulsive interactions. Examples are as follows. 

Ding C F, Wang X B and Wang L S 1998 Photoelectron spectroscopy of doubly charged anions intramolecular Coulomb repulsion and solvent stabilization J. Phys. Chem. A 102 8633... 

For so-called steric stabilization to be effective, tire polymer needs to be attached to tire particles at a sufficiently high surface coverage and a good solvent for tire polymer needs to be used. Under such conditions, a fairly dense polymer bmsh witli tliickness L will be present around the particles. Wlren two particles approach, such tliat r < d + 2L, tire polymer layers may be compressed from tlieir equilibrium configuration, tluis causing a repulsive interaction. 

To see how and under what conditions stability is enhanced or diminished, we need to consider the symmetry of the orbital (9-32), Flectrons in the antisymmetric orbital r r have a 7ero probability of occurring at the node in u where U] = rj. Electron mutual avoidance of the node due to spin correlation reduces the total energy of the system because it reduces electron repulsion energy due to charge... 

The Birch reductions of C C double bonds with alkali metals in liquid ammonia or amines obey other rules than do the catalytic hydrogenations (D. Caine, 1976). In these reactions regio- and stereoselectivities are mainly determined by the stabilities of the intermediate carbanions. If one reduces, for example, the a, -unsaturated decalone below with lithium, a dianion is formed, whereof three different conformations (A), (B), and (C) are conceivable. Conformation (A) is the most stable, because repulsion disfavors the cis-decalin system (B) and in (C) the conjugation of the dianion is interrupted. Thus, protonation yields the trans-decalone system (G. Stork, 1964B). 

The small differences m stability between branched and unbranched alkanes result from an interplay between attractive and repulsive forces within a molecule (intramo lecular forces) These forces are nucleus-nucleus repulsions electron-electron repul sions and nucleus-electron attractions the same set of fundamental forces we met when... 

Of the two conformations of ethane the staggered is 12 kJImol (2 9 heal mol) more stable than the eclipsed The staggered conformation is the most stable conformation the eclipsed is the least stable conformation Two main explanations have been offered for the difference in stability between the two conformations One explanation holds that repulsions between bonds on adjacent atoms destabilize the eclipsed conformation The other suggests that better electron delocalization stabilizes the staggered conformation The latter of these two explanations is now believed to be the correct one... 

The greater stability of an equatorial methyl group compared with an axial one IS another example of a steric effect (Section 3 2) An axial substituent is said to be crowded because of 1,3 diaxial repulsions between itself and the other two axial sub stituents located on the same side of the ring... 

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