Association of counterion

In summary, ASAXS has the potential to provide information both about the association of counterions to a macroion, as well as about the... 

Here, c3 and cd are the concentrations of salt and polyion, respectively. The difference in association of counterions between the products and the reactants is given by (1 + 2T3d) [65-73]. Consequently, counterions associated with the polyion will be released into the bulk solution if the (1 + 2T3D) is negative. The release of counterions leads to density changes in the condensed layer and provides an additional driving force, except that it is entropic in nature [65-73]. 

Effective surface charge is reduced by association of counterions with charged surface groups. If the amphoteric (2-pK) concept is applied, the association of counterions, i.e. anions (A ) and cations (K+) is represented as ... 

From the stoichiometric point of view, reaction equations describing association of counterions do not depend on the choice of the model binding of one counterion to the oppositely charged surface site always occurs. 

When treating the association of counterions one may also apply the association statistics (AS) model which is equivalent to the Bjerrum theory for ion pairing in an electrolyte solution [29,30]. However, in the case of surface association spaee is available only on the side of the liquid. Another difference is due to the critical distance which depends on direction and is a function of the surface potential. This theory explains why two ionic species may associate at the surface despite the fact that they do not undergo ion pairing in the bulk of solution. According to the Bjerrum theory, ions of large effective size cannot approach the critical distance and such an electrolyte is completely dissociated. At the surface the critical distance extends by increasing surface potential and once the surface potential exceeds the critical value, at which the critical distance matches the minimum separation, association at the interface proceeds. 

In order to better understand the equilibria in the interfacial layer, it is desirable to obtain the thermodynamic parameters of the reactions involved in the surface charging processes. It is not a simple task to determine the enthalpy of specified surface reactions. At first the mechanisms of the reactions are not always clear, and secondly the situation is often so complicated that several contributions can hardly be distinguished. In the most simple case, when association of counterions does not take place (low ionic strength), one can use measurements of the temperature dependency of the point of zero charge [48-56]. The slope of the pHp c vs. reciprocal thermodynamic temperature yields the enthalpy value dependent on the assumed stoichiometry of the processes. Application of the adsorption or amphotheric or coordination concept yield [22]... 

It has been reported that surfactants form mixed micelles with the drugs (Rodriguez et al, 2004, Alam et al, 2007). Mixed micelles are known to possess quite different physicochemical properties from those of pure micelles of the individual components. The micellar aggregation number and the association of counterions with micelles change dramatically with composition in mixed micelles. The degree of counterion association of an ionic micelle is about 0.7 for monovalent counterions. However, when an ionic surfactant is mixed with a non-ionic surfactant, the degree of the association falls to zero as the mole fraction of the non-ionic surfactant in the micelle increases (Meyer Sepulveda, 1984, Jansson Rymden,... 

The measured heat Q is a sum of products of extents of reactions (1), (2) and (9) and corresponding reaction enthalpies since the extents of association of counterions are negligible in the vicinity of p.z.c. at low ionic strength ... 

The phase separation model is restricted to micellization which produces micelles with a very large association number, p. In addition, it can only describe the association process into micelles and not the association and dissociation described by the eqnilibria, npon which closed association models are based. However, the main problem with the model is that micelles cannot rigorously be considered to constitute a separate phase, since they are not uniform and homogeneous throughout. However, it is a simple model which works quite well for micelles with large association numbers. As with the closed association model, the phase separation model can be applied to ionic surfactants, provided that allowance is made for the association of counterions with the micelle. 

Oosawa (1971) developed a simple mathematical model, using an approximate treatment, to describe the distribution of counterions. We shall use it here as it offers a clear qualitative description of the phenomenon, uncluttered by heavy mathematics associated with the Poisson-Boltzmann equation. Oosawa assumed that there were two phases, one occupied by the polyions, and the other external to them. He also assumed that each contained a uniform distribution of counterions. This is an approximation to the situation where distribution is governed by the Poisson distribution (Atkins, 1978). If the proportion of site-bound ions is negligible, the distribution of counterions between these phases is then given by the Boltzmann distribution, which relates the population ratio of two groups of atoms or ions to the energy difference between them. Thus, for monovalent counterions... 

Ionization of the carboxyl groups is accompanied by binding of the cations. But if counterions are site-bound the charge on the carboxyl groups is neutralized and chain contraction results. A special case is that of the polyacid which adopts a contracted form because the close association of hydrogen ions with carboxyl groups results in a neutral chain. 

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

Unlike solid state -stacks, however, double helical DNA is a molecular structure. Here CT processes are considered in terms of electron or hole transfer and transport, rather than in terms of material conductivity. Moreover, the 7r-stack of DNA is constructed of four distinct bases and is therefore heterogeneous and generally non-periodic. This establishes differences in redox energetics and electronic coupling along the w-stack. The intimate association of DNA with the water and counterions of its environment further defines its structure and contributes to inhomogeneity along the mole-... 

Although the exact nature of the active center in polymerizations of butadiene with these Ba-Mg-Al catalysts is not known, we believe that the preference for trans-1,4 addition is a direct consequence of two aspects of this polymerization system, namely (1) the formation of a specific organobarium structure in a highly complexed state with Mg and A1 species, and (2) the association of the polybutadiene chain end with a dipositive barium counterion which is highly electropositive. 

These reactions comprise nucleophilic SN2 substitutions, -eliminations, and nucleophilic additions to carbonyl compounds or activated double bonds, etc. They involve the reactivity of anionic species Nu associated with counterions M+ to form ion-pairs with several possible structures [52] (Scheme 3.4). 

The classical model, as shown in Figure 1, assumes that the micelle adopts a spherical structure [2, 15-17], In aqueous solution the hydrocarbon chains or the hydrophobic part of the surfactants from the core of the micelle, while the ionic or polar groups face toward the exterior of the same, and together with a certain amount of counterions form what is known as the Stern layer. The remainder of the counterions, which are more or less associated with the micelle, make up the Gouy-Chapman layer. For the nonionic polyoxyethylene surfactants the structure is essentially the same except that the external region does not contain counterions but rather rings of hydrated polyoxyethylene chains. A micelle of... 

The nature of the counterion has had a profound impact on catalysis, as will be seen. Structurally, it was of considerable interest to delineate the factors that influence selectivity and to examine whether the counterion plays a role in the solid-state geometry of these catalysts. While the hexafluoroantimonate copper complexes of bis(oxazoline) 55c are completely dissociated in the solid state, analogous triflate complexes exhibit weak bonding to one counterion in the apical position (2.62 A from the metal), Fig. 23. Association of the triflates in the solid state was also noted for Complex 266d. The water molecules are distorted toward the phenyl substituents, similar to the SbF6 complex 265d. 

Thus kp for lithium counterion is 1/300 of kp for potassium counterion. The low reactivity and association of lithium alkoxide was reported in the anionic polymerization of epoxides.We have found that two fold increase of the lithium initiator concentration has led to a decrease of the kp nearly to one half. This indicates that the kinetic order with respect to the initiator would be near to zero, suggesting a very high degree of association of the active species. Thus the propagation reaction appears to proceed in practice through a very minor fraction of monomeric active species in case of lithium catalyst. 

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