Classical Stability Theory

Stability (Classical Theory).—In recent years the question of stability has acquired a considerable importance in applications.9 Here we shall discuss briefly the principal points in the two major trends in studies of stability. 

There are two general theories of the stabUity of lyophobic coUoids, or, more precisely, two general mechanisms controlling the dispersion and flocculation of these coUoids. Both theories regard adsorption of dissolved species as a key process in stabilization. However, one theory is based on a consideration of ionic forces near the interface, whereas the other is based on steric forces. The two theories complement each other and are in no sense contradictory. In some systems, one mechanism may be predominant, and in others both mechanisms may operate simultaneously. The fundamental kinetic considerations common to both theories are based on Smoluchowski s classical theory of the coagulation of coUoids. 

An important consequence of quantal charge transfer between ions and ion pairs (dipoles) is the appearance of non-pairwise-additive cooperative or anticooperative contributions that have no counterpart in the classical theory. These nonlinear effects strongly stabilize closed-CT systems in which each site is balanced with respect to charge transfers in and out of the site, and disfavor open-CT systems in which one or more sites serves as an uncompensated donor or acceptor. This CT cooperativity accounts for the surprising stability of cyclic (LiF) clusters, which are strongly favored compared with linear structures. 

The classical theory [50,52,53,55] expresses the change in free enthalpy (A/x) resulting from the nucleation phenomena Equation 1 has a positive contribution from the interface free energy (ySg, which takes into account the generation and stabilization of an interface), and a negative contribution... 

Compared with other 1,1-disubstituted olefins, the captodative olefins do not seem to present abnormal behavior that could be related to the captodative stabilization of the transient growing radical. Both conversions and molecular weights can be rationalized by classical theories linking the polymerizability of these olefins to steric and dipole-dipole repulsions. 

Classical theories of emulsion stability focus on the manner in which the adsorbed emulsifier film influences the processes of flocculation and coalescence by modifying the forces between dispersed emulsion droplets. They do not consider the possibility of Ostwald ripening or creaming nor the influence that the emulsifier may have on continuous phase rheology. As two droplets approach one another, they experience strong van der Waals forces of attraction, which tend to pull them even closer together. The adsorbed emulsifier stabilizes the system by the introduction of additional repulsive forces (e.g., electrostatic or steric) that counteract the attractive van der Waals forces and prevent the close approach of droplets. Electrostatic effects are particularly important with ionic emulsifiers whereas steric effects dominate with non-ionic polymers and surfactants, and in w/o emulsions. The applications of colloid theory to emulsions stabilized by ionic and non-ionic surfactants have been reviewed as have more general aspects of the polymeric stabilization of dispersions. ... 

In the case of the nickel alloys, the stability of the passive layer is a problem. The alloys depend on the oxide films or the passive layers for corrosion resistance and are susceptible to crevice corrosion. The conventional mechanism for crevice corrosion assumes that the sole cause for the localized attack is related to compositional aspects such as the acidification or the migration of the aggressive ions into the crevice solution [146]. These solution composition changes can cause the breakdown of the passive film and promote the acceleration and the autocatalysis of the crevice corrosion. In some cases, the classic theory does not explain the crevice corrosion where no acidification or chloride ion build up occurs [147]. 

We give in conclusion a brief formulation of the ideas which have led to Bohr s atomic theory. There are two observations which are fundamental firstly the stability of atoms, secondly the validity of the classical mechanics and electrodynamics for macroscopic processes. The application of the classical theory to atomic processes... 

The fundamental postulate of the stability of atoms referred to in the introduction is satisfied by the two principles of atomic mechanics given in 10. We now inquire to what extent they are in agreement with the other fundamental postulate, that the classical theory shall appear as a limiting case of the quantum theory. 

In 1908 Thomson proposed a model of the atom the positive charge was uniformly spread throughout a sphere of definite radius to confer electrical neutrality, electrons were imbedded in the sphere. For stability according to classical theory, the electrons had to be at rest. This requirement could be met f or the hydrogen atom by having the electron at the center of the sphere. This model failed the crucial test provided by the scattering of a-rays by thin metal foils. 

These forces originate from entirely different sources and therefore may be evaluated separately. The interplay of (i) and (ii) forms the basis of the classical theory of flocculation of lyophobic dispersions, flrst proposed by Derjaguin and Landau in Russia and independently by Verwey and Overbeek in the Netherlands and hence now known as the DLVO theory. The interplay of (i) and (iii) is commonly termed steric stabilization , and much has been written on this protective mechanism, although a workable understanding has developed only during the last two decades. 

The phosphorus and sulfur ylides are more stable than the nitrogen and oxygen analogs (66). The former species are comprised of carbenes complexed to soft donors, whereas in the latter the carbenes are not stabilized by the adjoining hard bases. The high stability of CH2I compared to that of CHjF is at variance with the classical theory of inductive effect, but it is exactly as predicted on the basis of HSAB principle if regarded as [X complexes. 

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