Counterions definition

To date, direct asymmetric synthesis of optically active chiral-at-metal complexes, which by definition leads to a mixture of enantiomers in unequal amounts thanks to an external chiral auxiUary, has never been achieved. The most studied strategy is currently indirect asymmetric synthesis, which involves (i) the stereoselective formation of the chiral-at-metal complex thanks to a chiral inductor located either on the ligand or on the counterion and then (ii) removal of this internal chiral auxiliary (Fig. 4). Indeed, when the isomerization of the stereogenic metal center is possible in solution, in-... 

By definition, in a solution all ions belong to the same phase, even though counterions may cluster more or less diffusely around the macroions. When significant amounts of a simple 1 1 electrolyte (such as KCl) are added to a polyelectrolyte solution, dissociation of the polyelectrolyte macromolecule is repressed in an extreme case the polyelectrolyte may be salted out. An undissociated polyacid may be precipitated by generous addition of a simple acid such as HCl. 

While related to its carbon analogs, the existence of the RsSi species as a free ion in condensed phases had been doubted for a long time. However, NMR characterization using bulky aryl substituents has provided evidence for the triply coordinated silicon cation. " However, definitive evidence was recently reported by the groups of Reed and Lambert with a silyl cation species bound to three mesityl groups and a carborane [HCBnMesBrg] counterion (Eig. 7.5). It was suggested that... 

The rate constants for the reaction of a pyridinium Ion with cyanide have been measured in both a cationic and nonlonic oil in water microemulsion as a function of water content. There is no effect of added salt on the reaction rate in the cationic system, but a substantial effect of ionic strength on the rate as observed in the nonionic system. Estimates of the ionic strength in the "Stern layer" of the cationic microemulsion have been employed to correct the rate constants in the nonlonic system and calculate effective surface potentials. The ion-exchange (IE) model, which assumes that reaction occurs in the Stern layer and that the nucleophile concentration is determined by an ion-exchange equilibrium with the surfactant counterion, has been applied to the data. The results, although not definitive because of the ionic strength dependence, indicate that the IE model may not provide the best description of this reaction system. 

Modem work on these and related bare post-transition element clusters began in the 1960s after Corbett and coworkers found ways to obtain crystalline derivatives of these post-transition element clusters by the use of suitable counterions. Thus, crystalline derivatives of the cluster anions had cryptate or polyamine complexed alkali metals as countercations [8]. Similarly, crystalline derivatives of the cluster cations had counteractions, such as AlCLj, derived from metal halide strong Lewis acids [9]. With crystalhne derivatives of these clusters available, their structures could be determined definitively using X-ray diffraction methods. 

Calculated concentrations, using (4.9), for the various components, surfactant monomers, counter-ions and micelles, for the case of CTAB micellization (with a cmc of 0.9mM), is shown in Figure 4.5. Clearly, the micelle concentration increases rapidly at the cmc, which explains the sharp transition in surfactant solution properties referred to earlier. It is also interesting to note that the law of mass action (in the form of equation 4.9) predicts an increase in counterion (Br ions) concentration and a decrease in free monomer concentration above the cmc. It has been proposed that for ionic surfactants, a useful definition of the cmc would be... 

In the most general sense, any anion radical produced by reduction with a metal, or by electrolytic reduction in the presence of a metallic counterion could be considered an organometallic anion radical. Any review based on such a definition would be monumental. To achieve a manageable volume of material, with a content suitable to the context of this series, we have limited this chapter to anion radicals produced from organometallic compounds. Anion radicals for which the metal is present solely as the reducing agent or counterion have, for the most part, been excluded. 

The specific electro-diffusion phenomena, the field and force saturation and counterion condensation, as well as the corresponding features of the solutions to the Dirichlet problem for (2.1.2) to be addressed in this chapter, are closely related to those observed by Keller [7], [8] for the solutions of (2.1.3a) with f tp) positive definite, satisfying a certain growth condition. Keller considered f( 0, satisfying the condition... 

As for the theory of this phenomenon, it was first observed by Onsager [27a] that, since in the limit a — 0 an LCD a is expected to yield a singularity of the type —surface potential, the statistical-mechanical phase integral for counterions should diverge for a greater than some critical value, characteristic of a given valency. Indeed consider a counterion (for definiteness anion) of valency z. The appropriate phase integral is of the form... 

The binding of counterions and van der Waals attraction make further contributions to the association. The heats of formation determined so far, however, are insufficient. More definite knowledge about the nature of the binding has been obtained by spectroscopic investigation. 

In such a case, no conclusion about the mechanisms can be reached from the form of 4(t) and the observed rate will be determined primarily by the fastest process. By extension of the argument, one easily sees that marked deviation of any of the parallel processes from exponential decay will be reflected in the overall rate with possible change in the functional form. Thus, if the rotation is described by exp(-2D t) as in Debye-Perrin theory, and the ion displacements by a non-exponential V(t), one finds from eq 5 that 4(t) = exp(-2D t)V(t) and the frequency response function c(iw) = L4(t) = (iai + 2D ) where iKiw) = LV(t). This kind of argument can be developed further, but suffices to show the difficulties in unambiguous interpretation of observed relaxation processes. Unfortunately, our present knowledge of counterion mobilities and our ability to assess cooperative aspects of their motion are both too meagre to permit any very definitive conclusions for DNA and polypeptides. 

Now, let us consider the fluctuations of a segment of M charges. The segment is located at least one Debye length away from the ends of the polyion. If Ag denotes the deviation of the free energy of the segment from its minimum value, then Ag = MAG. But, the thermal average of AG is, by definition, (AG) = kBT/2. Consequently, the mean-square number fluctuations of condensed counterions, ((A0)2), is [50]... 

By definition, < ) = tdvNa where Na is Avogadro s number, v is the volume per counterion, and vo is the counterion concentration. 

A lower Al content definitely leads to the Si richer Beta phase, that incorporates TEA+ counterions to Al negative charges and TEAOH ionic pairs, that occupy the maximum of the intracrystalline free volume, while Na+ ions partly neutralize the Si-O" framework defect groups. 

In the original Polanyi approach the spaces between the various equlpotential planes correspond to definite volumes 0(z), so that there is a function u = f[characteristic curve, which is typical for each adsorbent-adsorbate combination and independent of temperature. This picture has, except for the specificity of /, a generic nature and is therefore not only applicable to liquid-like adsorbates but also to the enrichment of gas near the surface. Just like nitrogen molecules in the Earth s atmosphere or counterions around a charged colloidal particle. 

The present refinement in linear siloxane polymerization is a monumental achievement resulting from the astute observations and ingenuity of many chemists over the past 120 years. The workers cited in this chapter are only some of the more recent contributors. Still, much work is yet to be done, and the critical reader should be left with many questions. For example, the equilibria 2 and 3 are traditionally the basis for explaining the distribution of molecular sizes and byproducts, but they exclude any role for the reactive chain ends. Yet, the accumulating evidence of the critical role of the counterions at the reactive ends in the mechanism of the process suggests that the equilibria may have to be rewritten to include the reactive ends. Definitive experiments are needed to settle the point. 

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