Free counterions

Fig. 4 Slight deformation of the lattice in coordination polymers after removal of the guests, (a) The 4,6-di(l-imidazolyl) l,3,5-triazin-2-one [9] can form a counterion-free framework with channels of a cross section of 9.5 x 5.5 (b) In...

The Gibbs equation was used with n = 1 for the analysis of the surface tension data for surfactants [P], Indeed, these surfactants are counterion free and therefore considered as neutral molecules. The surface areas per molecule have been obtained to be around 30 [59]. These values are much lower than... 

As an example, we discuss here an aqueous solution of one polyelectrolyte P and one strong electrolyte S (=Mv Xv ), where P and S share a common counterion X. Some of the counterions that originate from the polyelectrolyte are assumed to be located in a small volume Vp around the polyelectrolyte backbone (the phenomenon is called counterion condensation ). The polyelectrolyte, condensed counterions, free counterions, free coions, and water contribute to the Gibbs energy of the solution ... 

The concentration of free surfactant, counterions, and micelles as a function of overall surfactant concentration is shown in Fig. XIII-13. Above the CMC, the concentration of free surfactant is essentially constant while the counterion concentration increases and... 

Primitive silver halide microcrystals free of counterions... 

Studies have shown that, in marked contrast to carbanionic polymerisation, the reactivity of the free oxonium ion is of the same order of magnitude as that of its ion pair with the counterion (6). On the other hand, in the case of those counterions that can undergo an equiUbrium with the corresponding covalent ester species, the reactivity of the ionic species is so much greater than that of the ester that chain growth by external attack of monomer on covalent ester makes a negligible contribution to the polymerisation process. The relative concentration of the two species depends on the dielectric constant of the polymerisation medium, ie, on the choice of solvent. 

Winstein suggested that two intermediates preceding the dissociated caibocation were required to reconcile data on kinetics, salt effects, and stereochemistry of solvolysis reactions. The process of ionization initially generates a caibocation and counterion in proximity to each other. This species is called an intimate ion pair (or contact ion pair). This species can proceed to a solvent-separated ion pair, in which one or more solvent molecules have inserted between the caibocation and the leaving group but in which the ions have not diffused apart. The free caibocation is formed by diffusion away from the anion, which is called dissociation. 

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

Compare atomic charges for sodium borohydride and lithium aluminum hydride. Which ion contains the most electron-rich hydride The least electron-rich hydride Based on these results alone, which hydride reagent should be the better reducing agent Explain. Obtain atomic charges for free borohydride and aluminum hydride anions. What changes, if any, does the counterion produce ... 

For isolation of the fully protonated macrocycle, with known counterion composition, the CH,C12 soln of the free-base macrocycle was washed with an equal volume of a 1 M solution of the desired acid before briefly drying (Na2S04) and removing the solvent on the rotary evaporator yield 460 mg (44%) of 56 2HC1 (following treatment with 1 M HC1). The macrocyclic product and its diprotonated salts can be further purified by crystallization (CHCl3/hexane). 

In some cases, an alternative explanation is possible. It may be assumed that any very complex organic counterion can also interact with the CP matrix with the formation of weak non-ionic bonds, e.g., dipole-dipole bonds or other types of weak interactions. If the energy of these weak additional interactions is on the level of the energy of the thermal motion, a set of microstates appears for counterions and the surrounding CP matrix, which leads to an increase in the entropy of the system. The changes in Gibbs free energy of this interaction may be evaluated in a semiquantitative way [15]. 

MeBr is a strong poison only with Et2 All coinitiator. Since Et2 All forms the least nucleophilic counterion, Et2AHXe, it is expected to produce a relatively free carbenium ion, facilitating bromonium ion formation by interaction with MeBr solvent. With more nucleophilic counteranions, like Me3 AlXe or Et2 AlXf (X = Cl, Br), bromonium ion formation is more difficult and poisoning is modest. Evidently, the less stable bromonium ions form only with weakly nucleophilic counterions. MeCl is the weakest poison or may be inert, since chloronium ions are highly unstable. 

Carbocations are intermediates in several kinds of reactions. The more stable ones have been prepared in solution and in some cases even as solid salts, and X-ray crystallographic structures have been obtained in some cases. An isolable dioxa-stabilized pentadienylium ion was isolated and its structure was determined by h, C NMR, mass spectrometry (MS), and IR. A P-fluoro substituted 4-methoxy-phenethyl cation has been observed directly by laser flash photolysis. In solution, the carbocation may be free (this is more likely in polar solvents, in which it is solvated) or it may exist as an ion pair, which means that it is closely associated with a negative ion, called a counterion or gegenion. Ion pairs are more likely in nonpolar solvents. 

It is unlikely that free carbanions exist in solution. Like carbocations, they usually exist as either ion pairs or they are solvated. " Among experiments that demonstrated this was the treatment of PhCOCHMe with ethyl iodide, where was Li ", Na", or K" . The half-lives of the reaction were for Li, 31 x 10 Na, 0.39 X 10 and K, 0.0045 x 10 , demonstrating that the species involved were not identical. Similar results were obtained with Li, Na, and Cs triphenylmethides (PhsC M Where ion pairs are unimportant, carbanions are solvated. Cram " demonstrated solvation of carbanions in many solvents. There may be a difference in the structure of a carbanion depending on whether it is free (e.g., in the gas phase) or in solution. The negative charge may be more localized in solution in order to maximize the electrostatic attraction to the counterion. ... 

When a charged particle is placed in aqueous media, however, the mobility may no longer be proportional to the intrinsic particle charge, since free counterions in solution will associate and move with the particle and thereby alter the net force exerted on the particle by the electric and fluid flow fields. The region of free or mobile counterions surrounding the particle has been termed the electrical double layer or ionic atmosphere. 

The consequences of these solutions are shown in Figure 4.4. The abscissa is n, the total number of counterions or charged groups on the polyion, and is proportional to Q. Along the ordinate are the numbers of counterions bound, , and free, n equal to n(l — jff) and nP respectively. 

The critical value for Q is 1/z. There is a proportional increase in the number of free counterions, f/z, as Q increases from zero, reaching a plateau when Q = z. Also, below this value the degree of dissociation,) , increases as the concentration decreases, and tends to unity as v tends to zero. When Q> /z, p decreases with 0 and tends to /zQ as 0 tends to zero. The number of free ions caimot exceed njz Q. Note that this number is inversely proportional to the square of the valence. The condensation of ions is thus very sensitive to valence for multivalent counterions it takes place at a lower value of Q and the number of free ions is much smaller... 

When the degree of neutralization is small the charge on the polyion and the number of counterions will also be small and the majority of counterions will be free. As the degree of neutralization, a, increases, the polyion charge, Q, will increase. This observation follows from the following equations ... 

The coulombic force is proportional to the square of the effective charge on the polyion, i.e. n], (The effective charge is equivalent to the number of free counterions, ,.) When the charge along the polyion, Q, is small the extensive forces involved are those of purely coulombic repulsion. 

Osmotic pressure results from the difference in concentration between the boimd but mobile coimterions within the polyion and the free counterions outside it. The concentration of counterions is greater within the polyion so that solvent molecules tend to enter this region. The osmotic force is proportional to the difference n—n where n equals the total number of counterions or the number of ionizable groups on the polyion. 

Repulsive coulombic forces exist between charged polyions. These are attenuated by the bound counterions conversely they are stronger for polyions having a higher concentration of free counterions. When the charge along the polyion, Q, is small the forces involved are purely coulombic repulsion forces. However, when Q exceeds a certain value, counterions condense on the polyions and reduce the repulsive forces. 

Ion binding reduces the repulsive forces between the charged groups on the polyanion but, unless the counterions are site-bound, the repulsive osmotic forces are not affected. At full neutralization the coulombic forces along the polymer chain become zero. However, the polymer does not contract, because the osmotic forces remain unless, of course, all the cations become site-bound. (Of course, in the case of a free weak acid the concentration of mobile hydrogen ions is very small and the polymer adopts a compact form.)... 

---