Counterions trivalent

Monovalent cations are compatible with CMC and have Httle effect on solution properties when added in moderate amounts. An exception is sUver ion, which precipitates CMC. Divalent cations show borderline behavior and trivalent cations form insoluble salts or gels. The effects vary with the specific cation and counterion, pH, DS, and manner in which the CMC and salt are brought into contact. High DS (0.9—1.2) CMCs are more tolerant of monovalent salts than lower DS types, and CMC in solution tolerates higher quantities of added salt than dry CMC added to a brine solution. 

Ghromium(III) Compounds. Chromium (ITT) is the most stable and most important oxidation state of the element. The E° values (Table 2) show that both the oxidation of Cr(II) to Cr(III) and the reduction of Cr(VI) to Cr(III) are favored in acidic aqueous solutions. The preparation of trivalent chromium compounds from either state presents few difficulties and does not require special conditions. In basic solutions, the oxidation of Cr(II) to Cr(III) is still favored. However, the oxidation of Cr(III) to Cr(VI) by oxidants such as peroxides and hypohaUtes occurs with ease. The preparation of Cr(III) from Cr(VI) ia basic solutions requires the use of powerful reducing agents such as hydra2ine, hydrosulfite, and borohydrides, but Fe(II), thiosulfate, and sugars can be employed in acid solution. Cr(III) compounds having identical counterions but very different chemical and physical properties can be produced by controlling the conditions of synthesis. 

The theory of counterion condensation is implicit in Oosawa (1957) but the term was coined later (Imai, 1961). The phenomenon was demonstrated by Ikegami (1964), using refractive index measurements of the interaction between sodium and polyacrylate ions. It has since been confirmed for many mono-, di- and trivalent counterions and polyionic species (Manning, 1979). 

Figure 4.10 The effect of monovalent, divalent and trivalent counterions on the hydration state of neutralized poly(acrylic acid). Based on Ikegami (1964).

When the counterion is complex, for example metal-halogen anions such as BF4-, the most electronegative portion of the counterion becomes attached to the silicon center. Because of this attachment, it is natural to consider the intermediacy of a silicenium cation (silylium or silylenium ion) intermediate in such reactions (Eq. 4). Bond energies derived from electron impact studies indicate that Eq. 4 is exothermic in the gas phase by about 8 kcal/mol.26,29 There seems little doubt that trivalent silicon-centered cationic species do exist in the gas phase30,31 or that processes similar to that shown in Eq. 4 do occur there.32,33... 

The actual values of these concentrations depend on a whole array of unknown parameters, but their relative values depend only on the valence of the counterions. The entries outside parentheses in Table 13.1 are the values of the CCC relative to the value for the monovalent electrolyte in the same set of experiments. These are seen to be remarkably consistent for the divalent ions and acceptably close together for trivalent and tetravalent counterions. 

The porous volumes measured by N2 adsorption are listed in Table 3. After the boronation, the total porous volumes (Vt) of the samples increase, corresponding to the increase of benzene adsorption capacity mentioned above. This should be resulted from the following aspects (1) The average mass of zeolite crystallite decrease and the number of crystal particles in unit weight of sample increases after the boronation owing to a limited introduction of trivalent atoms and Na+cations as counterions, as well as a severe dissolution of silicon. Thus, the total porous volume (mL/g) and the adsorption capacity increase. (2) The transformation of pore size occurs during the boronation. As shown in Table 3, the mesoporous volumes increase and the microporous volumes decrease after the boronation, meaning that some micropores are developed into mesopores due to the removal of silicon from the framework. This is also one of the important reasons why the total porous volumes as well as the adsorption capacities increase after the boronation. 

Evidently, more work has to be done for a comprehensive comparison of theory and experiment. Theory and simulations reveal clearly that the PB-cell model should be a poor approximation for divalent counterions and breaks down totally for trivalent counterions [29]. A comprehensive experimental test of these very important conclusions is still missing. 

Compact structures are also induced by size, shape, and charge of multivalent counterions, such as spermidine3+ and [Co(NH3)6]3+ [31, 108, 109]. The concentrations of trivalent and divalent ions that are necessary to reach the intermediates states are much lower than the corresponding concentrations of monovalent ions [108,109]. To put it differently, the number of multivalent condensed cations that reduce the net charge of RNA is smaller than the number of condensed monovalent ions needed to reach the same charge reduction [31, 108, 109]. 

The influence of counterion valence on the double layer thickness is described by the valency rule of Schulze and Hardy. It basically predicts that if a monovalent counterion is changed to a divalent counterion, the thickness of the double layer decreases by half and if the divalent counterion is changed to a trivalent ion, the thickness of the double layer decreases by three-quarters (Fig. 9.2). The relative amounts of counterions required to induce flocculation are 100 for a monovalent, 2 for a divalent, and 0.04 for a trivalent ion. 

The Schulze-Hardy rule stipulates that the ccc decreases with the chaise of the counterion of mono, di, and trivalent ions in the ratio of (1/z). (But the Schulze-Hardy rule is usually used in a qualitative sense to indicate the significance of the valence of the counterion to bring about destabilization.)... 

Hribar, B., and Vlachy, V. Monte Carlo study of micellar solutions with a mixture of mono- and trivalent counterions. Langmuir, 2001, 17, No. 6, p. 2043-2046. 

Spohr, E., Hribar, B., and Vlachy, V. Mechanism of macroion-macroion clustering induced by the presence of trivalent counterions. Journal of Physical chemistry B, 2002, 106, No. 9, p. 2343-2348. 

A silica-alumina is formed upon isomorphous substitution of a trivalent aluminum atom for a tetrava-lent surface silicon atom in the silica lattice. The commensurate incomplete coordination of the aluminum atom generates charged structural sites that, in the absence of surface hydroxyl groups, behave as Lewis acid and base sites(7). The presence of a proton as a counterion or a hydroxyl group as occurs upon hydrolysis can produce strong Bronsted acid sites(2 15, 16). Removal of the hydroxyl groups may convert Bronsted sites to Lewis sites reversibly(9, 15). Similar complexities as alluded to previously with the alumina surface arise in a detailed discussion of the nature of the active sites on silica-alumina so that several kinds of sites are usually invoked in interpretations of experimental measurements of surface acidity and catalytic activity(14, 15). 

Up to now only monovalent ions have been investigated. For multivalent ions the prediction of the PB theory is that for the distribution function P(r) only the product of the Manning parameter and the counterion valence v matters. Therefore a system of monovalent ions at ln = 3a is claimed to have the same distribution function as a system of trivalent ions at B = lo It will now be shown that this statement is an artifact of the PB approximation. Figure 9 shows examples of systems that are complementary in the described sense. Not only is the condensation enhanced as compared to PB theory, but the enhancement is stronger for the case involving multivalent ions. Two different reasons may be suggested to explain this effect ... 

At first sight this finding might appear inevitable. Nevertheless, since r0A < ve0 for the investigated cases, the inequality from the beginning of this section does in fact hold, albeit not in the strong version. For this specific situation veJA is 1.9 for the divalent systems and 2.9 for the trivalent ones. Observe that the inequality does not specify the density of counterions or rods, at which the three-dimensional Wigner crystal is to appear. Rather, Ref. 47 assumes only that a bundle of rods has formed and... 

FIG. 26 Three-dimensional g(r) for the generic system with trivalent counterions at a density of 0.04247a- 3. Clearly visible is a structure pointing to local arrangements of the ions, for which the position of the first maximum is taken as a characteristic length. 

Figures 7 and 8 show variations in the electric light scattering effect from suspension, stabilized by NaPSS adsorption, with increasing concentration of salts of divalent (Mg2+) and trivalent (Al3+) counterions [18], One observes a steep decrease of the LF effect and some increase of the HF effect at concentration 2.5 X 10 M MgCl2 and 1.6 x 10 5 M A1C13, respectively. These amounts of low molecular salts are sufficient for Na+ to be fully replaced by Mg2+ and Al3+ from the polyion surface. The electro-optical effects vary in a different way when MgCl2 is added to the suspension with no NaPSS adsorbed on the particle surface—Figure 9. This by no means...

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