Triple-Ion Association Constants

Table 5 contains a selection of ion-pair association constants, triple ion formation constants, and limiting conductivities for various electrolytes which have been studied in connection with the optimization of battery electrolytes. It shows... 

Table 5. Association constants, triple ion formation constants and limiting conductivities of some lithium electrolytes.

Aqueous solutions of alkali metal salts exhibit almost no association, in contrast to solutions of 2,2 electrolytes, such as CdS04. Solutions of low permittivity contain ion pairs (equilibrium constant Ka), triple ions (equilibrium constant ATt), and higher associates, such as... 

The conductivity functions of such electrolytes can be evaluated at the level of limiting laws with the help of Equation 17.20, permitting the determination of the triple-ion dissociation constant and the ion-pair association constant Ka. 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

Ion-pair association constants K A determined with the set of conductivity equations (7)—(15) agree with those obtained from Eq. (18) and (19) [100]. Salomon and Uchiyama have shown that it is also possible to extend the directly Fuoss-Hsia equation to include triple-ion formation [104],... 

Xas = 0.7 M for formation of an encounter complex between azide ion and substrate, which then undergoes unassisted ionization to form a triple ion intermediate k[ = ki, Scheme 2.4) or, with a smaller association constant and a small compensating rate increase from a formally bimolecular substitution reaction k[ > k. Scheme 2.4). 

Ionic Association Constants Formation Constants of Triple Ions... 

At a quantitative level, near criticality the FL theory overestimates dissociation largely, and WS theory deviates even more. The same is true for all versions of the PMSA. In WS theory the high ionicity is a consequence of the increase of the dielectric constant induced by dipolar pairs. The direct DD contribution of the free energy favors pair formation [221]. One can expect that an account for neutral (2,2) quadruples, as predicted by the MC studies, will improve the performance of DH-based theories, because the coupled mass action equilibria reduce dissociation. Moreover, quadrupolar ionic clusters yield no direct contribution to the dielectric constant, so that the increase of and the diminution of the association constant becomes less pronounced than estimated from the WS approach. Such an effect is suggested from dielectric constant data for electrolyte solutions at low T [138, 139], but these arguments may be subject to debate [215]. We note that according to all evidence from theory and MC simulations, charged triple ions [260], often assumed to explain conductance minima, do not seem to play a major role in the ion distribution. 

The explanation of these results proposed by Kraus and Fuoss21 in a series of papers, is based on two assumptions. The first of these is that electrolytes that are completely dissociated in water or any other solvents of high dielectric constant will be more or less associated into ion pairs in solvents of low dielectric constants. Ion pairs, AB, are considered to form entirely by electrostatic forces from the charged ions A+ and B , and the complexes are assumed to take no part in the conduction. Though no sharp division has been made experimentally these ion pairs are considered to differ from the undissociated portion of a weak electrolyte in that no electron shift has occurred in their formation. The second assumption is that, as the concentration of the ion pairs increases, a proportion of them will combine with ions by electrostatic forces, to form triple ions. ... 

For very low dielectric constants (sr < 10) it is sometimes observed that association of ions produces species more complex than ion pairs. Obviously in these circumstances the models of ion association and eqn. 5.3.4 break down. In the next section we shall consider the conductance of solutions in which triple ions are formed. 

At concentrations far below the conductivity minimum (c 10 mol dm in Fig. 6), triple-ion formation can be neglected. Data analysis is possible with the help of Eqs. (65), in agreement with pairwise additive potential functions, and yields the values of A in Table III. The ion-pair association constants of these plots agree well with the determined independently at higher concentrations with the help of Eq. (72), which takes into account both ion-pair and triple-ion formation. No method is known for the determination of the values of data analysis yields only the product which the quantity is commonly estimated to be 2 A /3. Both ion-pair... 

This form of analysis has been extended to include an association constant for triple-ion aggregates (K ) [26] - i.e., [C A C ] s and [A C A ] s - and some authors have further extended this to include quadruple-ion formation [27-30]. Even assuming that all of the assumptions made in such an evaluation are valid, ultimately the association constant parameters obtained provide little insight into the solution interactions and fail to describe property variations with concentration, especially for high salt concentrations. 

The activation volumina for the solutions at the lower polarity are lacking because in this region the relaxation time is predominantly determined by triple-ion formation even at the lowest TBAP concentration measurable with the field modulation technique. If the ionisation equilibrium is treated as the association-dissociation of hard, charged, spheres subjected to Brownian motion in a continuous medium of dielectric constant D and viscosity n it is possible to give theoretical expressions for and k ... 

However, such deviations occur in the opposite sense to those obtained with low valency product electrolytes, i.e. observed conductances are now substantially lower than those predicted. Such deviations indicate a drastic reduction in the number of conducting species in solution, i.e. association to form ion-pairs has taken place. Such deviations become more marked in solvents of low dielectric constant. In such cases the conductance versus graph may show a minimum (Fig. 4.7) and this is attributed to the formation of triple ions which, unlike ion-pairs, carry a net charge. The formation of ion pairs removes two charged species from solution for each association which... 

The considered above electrostatic models of ion interaction are, undoubtedly, simplified. Each ion is surrounded by the solvate shell, whose character and sizes are determined by the ion, its charge and radius, and sizes of solvent molecules and such their parameters as the dipole moment of their polar groups, structure and sizes of the molecule. The solvent, its solvating ability, and the influence on the ion interaction are not reduced to the medium with the dielectric constant e only. Similarly, the interaction of ions is not restricted by the formation of only the ion atmosphere ion pairs, triples, and associates of several ions appear in the solution. Ion pairs, which can be separated by the solvate shell or be in contact to form contact pairs, also differ in structure. As a whole, the situation is more complex and diverse than its description by the classical theory of interaction of spherical charges in the liquid medium of dielectrics. The solvating ability of the solvent is determined only in part by its dielectric constant. For aprotic solvents, the ability of their heteroatoms to be donors of a free pair of electrons for cations is very significant. The donating ability of Ihe solvent is characterized by its donor number DN, which for the solvent is equal to the enthalpy of its interaction with SbCls in a solution of 1,2-dichloroethane... 

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