Counterion dissociation equilibrium

Mauritz et al., motivated by these experimental results, developed a statistical mechanical, water content and cation-dependent model for the counterion dissociation equilibrium as pictured in Figure 12. This model was then utilized in a molecular based theory of thermodynamic water activity, aw, for the hydrated clusters, which were treated as microsolutions. determines osmotic pressure, which, in turn, controls membrane swelling subject to the counteractive forces posed by the deformed polymer chains. The reader is directed to the original paper for the concepts and theoretical ingredients. 

Molecular Model of Counterion Dissociation Equilibrium. The following molecular concept is supported, or suggested, by both these spectroscopic observations and past ultrasonic investigations of simple aqueous electrolytes. In particular, a four-state model reminiscent of the multistep ionic dissociation mechanism of Eigen et al., (22, 23) was adopted (24). With regard to Figure 3, tFie states are classified as 1) completely dissociated hydrated ion pairs, 2) ion pairs at the contact of undisturbed primary hydration shells, and 3) outer and 4) inner sphere complexes. The relative populations of these states, (P ... 

Figure 12. Four state model of the hydration-mediated counterion—side chain association—dissociation equilibrium, of Mauritz. (Reprinted with permission from ref 107. Copyright 1982 American Chemical Society.)...

Because the electrical circuit is closed inside the sensor, no external reference electrode is necessary and the Severinghaus-type electrode can be used for measurement in either gaseous or liquid samples. It is important to remember, however, that the potential of the internal reference electrode must remain constant. In principle, it would be possible to use a liquid junction but it would add to the complexity of the design. Because the counterion resulting from the dissociation equilibrium is the only interfering ion, and because it is present in a very low concentration, it is possible to ascertain the constancy of the reference potential by careful choice of the internal electrolyte. Thus, for example, in the CO2 electrode the internal electrolyte is O.lMNaHCOs and 0.1 M NaCl and Ag/AgCl is used as an internal reference element. 

It will be assumed that the surfece charge is due to the dissociation of surface groups (for instance dissociation of surfactant molecules).8 9 In general, the electrolyte counterions are the most abundant ions in the vicinity of the surfece and therefore they can control the surface charge via reassociation. Denoting by cE the concentration (in the reservoir) of an 1 1 electrolyte, by N the number of sites per unit area, and by x the fraction of dissociated sites, the dissociation equilibrium provides the expression... 

As the water uptake proceeds, the increased sidechain-counterion dissociation allows for more complete ionic hydration. The deformation of the polymer chain network upon further incorporation of water molecules also proceeds by a shift in the distribution of rotational isomers to higher energy conformations and changes in other intramolecular, as well as intermolecular interactions. Consequently, the increased overall energy state, for a given membrane water content of n moles, per equivalent of resin, is manifested by polymer chain retractive forces that resist expansion of the network. Accordingly, the configurational entropy decreases as less conformations become available within the matrix. Eventually, an equilibrium water content, nQ, is... 

The retrogradation of the dissociation equilibrium is brought about by addition to the reaction medium of common ion salts whose cation is inert toward the polymerization system. As for the nature of the counterions, those that bring about a certain covalency of the active centers are preferred. Addition of a weak nucleophile is also an efficient means to curb the reactivity of carbocations. The following systems (monomer, initiating system, solvent) qualify, more or less perfectly, for the category of living polymerizations ... 

In contrast, in the cationic polymerization of cyclic ethers (e.g. THF or seven-membered oxepane), the dissociation equilibrium constants have considerably higher values, depending on the solvent polarity Ro-lO molh (CH2CI2) and - 10 molT (CH3NO2, QH5NO2) with SbClg as a counterion (see Table 8 in Ref [3a]). 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

Imai (1961) has observed that multivalent counterions are more strongly bound than are monovalent ones. This phenomenon can be demonstrated theoretically by considering equilibrium conditions for two counterions with valencies z and (Zj > z and degrees of dissociation and P -For a cylindrical model the equilibrium equations are... 

A pseudophase ion exchange model has been applied to reactions in micellar systems with varying success (1-7). According to this model, the distribution of nucleophile is considered to depend on the ion-exchange equilibrium between the nucleophile and the surfactant counterion at the micelle surface. This leads to a dependence on the ion-exchange constant (K g) as well as on the degree of dissociation (a) of the surfactant counterion. The ion exchange (IE) model has recently been extended to oil in water microemulsions (8). 

A common technique for measuring the values has been to employ species that produce anions with useful ultraviolet (UV) or visible (vis) absorbances and then determine the concentrations of these species spectropho tome trie ally. Alternatively, NMR measurements could be employed, but generally they require higher concentrations than the spectrophotometric methods. A hidden assumption in Eq. 5 is that the carbanion is fully dissociated in solution to give a free anion. Of course, most simple salts do fully dissociate in aqueous solution, but this is not necessarily true in the less polar solvents that are typical employed with carbanion salts. For example, dissociation is commonly observed for potassium salts of carbanions in DMSO because the solvent has an exceptionally large dielectric constant (s = 46.7) and solvates cations very well, whereas dissociation occurs to a small extent in common solvents such as DME and THE (dielectric constants of 7.2 and 7.6, respectively). In these situations, the counterion, M+, plays a role in the measurements because it is the relative stability of the ion pairs that determines the position of the equilibrium constant (Eq. 6). 

Conductivity measurements for solutions of living poly-pPL with DBCK+ counterion in CH2CI2/8PL mixture indicated that macroions and macroion-pairs are present in the system. In Fig.l, taken from Ref. 2 the Vant Hoff>s plots are given for dissociation constants of poly-ePL macroion-pairs with DBCK+ counterion (Kp) and similar plot for dissociation constants of Ph4B DBCK+ (Kpi). Dissociation of Ph4B"DBCK+ was investigated because this salt was further used in the kinetic measurements to shift the equilibrium between macroions and macroion-pairs towards the latter ones. 

An alternative suggestion is that the coordinated monomer dissociates to give an oxyanion stabilized by the nucleophile s counterion, most commonly, tetrabutylammonium or cesium ions,69 by analogy to the mechanism proposed for activation of tributylstannyl ethers by nucleophiles.57 This proposal is summarized in Fig. 14, which also shows the product mixture obtained for methyl (2S,3R)-2,3-dihydroxybutanoate. For this compound, reaction on the oxygen atom of the inherently less acidic hydroxyl is favored. Both anions, E and F, are in equilibrium with the coordinated monomer, and the less populated (but more reactive) anion E reacts to a greater extent, or in other words, the difference in the rate constants for trapping is greater than the difference in equilibrium constants. 

Figure 9 shows evolution of molecular weights with conversion for a hypothetical system, in which ions and ion pairs have the same reactivities (kp+ = kp = 10s mol L sec-1), covalent species are inactive, the ionization equilibrium constant is Ki = 10 5 mol-, L, and the dissociation constant is Kd = 10 7 mol/L. Kf is defined by the ratio of the rate constant of ionization to that of recombination of counterions within the ion pair (Kj = kj/kr). Kd is defined by the ratio of the rate constants of the dissociation of ion pair and that of the association of free ions (Kd... 

It is possible to distinguish between free ions from associated and covalently bonded species by conductivity measurements, because only free ions are responsible for electrical conductivity in solution [136, 399], Spectrophotometric measurements distinguish between free ions and ion pairs on the one hand, and covalent molecules on the other, because in a first approximation the spectroscopic properties of ions are independent of the degree of association with the counterion [141], The experimental equilibrium constant. Kexp, obtained from conductance data, may then be related to the ionization and dissociation constants by Eq. (2-16). 

The propagating anion and its counterion exist in relatively nonpolar solvents mainly in the form of associated ion pairs. Different kinds of ion pairs can be envisaged, depending on the extent of solvation of the ions. As a minimum, an equilibrium can be conceived between intimate (contact) ion pairs, solvent-separated ion pairs, and solvated unassociated ions. The nature of the reaction medium and counterion strongly influences the intimacy of ion association and the course of the polymerization. In some cases the niicrostructure of the polymer that is produced from a given monomer is also influenced by these variables. In hydrocarbon solvents, ion pairs are not solvated but they may exist as aggregates. Such inter-molecular association is not important in more polar media where the ion pairs can be solvated and perhaps even dissociated to some extent. 

In the model it is proposed that during the exchange RA + B O RB + A involving a chemical reaction of the counterions, B and A, with the resin site, R, they exist in the exchanger in two states, namely free and as the species formed by their combination with R. Counterions B and A are considered to be immobile vdiile bound and to move unimpeded while free. Ideally, ion concentrations in the free and bound states (c, and a respectively) are related to the dissociation constants, K, of the complexes Ri by the equilibrium relations for the complexation reactions. These dissociation-association equilibria have the form... 

In Merle s examination of carboxymethyldextran, polyvinyl sulfate (a fully dissociated polyelectrolyte) was used in place of a simple salt to control the ionic strength. Invasion of the gel phase by coion X was thus avoided. The electrochemical potential of the mobile counterions are equal throughout such a system at equilibrium and Equation 7 transforms to... 

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