Ionic aggregation, theory

The quantum theory of atoms in molecules (QTAIM) [25, 26] is based on analyses of the electron density distribution. The electron density of such systems such as simple molecules or ions, and also complexes, complex molecular and ionic aggregates, as well as crystals may be analyzed using this approach. QTAIM is a powerful tool that allows characterizing of various interactions covalent bonds, ionic bonds, van der Waals interactions and, what is the most important for this review, also HBs. The analysis of critical points of the electron density is very useful. For the critical points (CPs), the gradient of electron density, p(r), vanishes ... 

A29. A. A. Morton, " Solid Organoalkali Metal Reagents. A New Chemical Theory for Ionic Aggregates. Gordon Breach, New York, 1964. 217 pp. The emphasis is on heterogeneous catalysis. 

There have been relatively few attempts to formulate a theoretical basis for explaining and predicting ionic aggregation in lonomers. These have been recently reviewed by Maurltz (41). Some theories (96-99) are semi-empirical in that they Include experimentally determined parameters. Several others (95, 10, 101) are derived from first principles. Various parameters. Including the size and the ionic density of the cluster, are predicted by these models. Confirmation and. Indeed, further theoretical developments, have been hindered by the lack of quantitative experimental data for the cluster structure and energetics. Furthermore, except for some recent work (102), there have been no experimental observations of the actual clustering or its kinetics. 

The dissociation constant in aprotic organic solvents can be derived from fundamental principles based on Bjerrum s theory for ion pairs. In most organic media, the dissociation constant of ion pairs is very low (of the order of around 10 ) [48]. Brandstrom [87] reported that the ionic aggregation states of quaternary salts existing in the organic phase were of various types, i.e., dissociated ions (Q+ + X ), ion pairs (Q+X ), quadruples [(Q X )2], etc. Hence, the total concentration of quaternary salt in an organic phase can be written as... 

The theoretical treatment of the properties of ionic crystals and molecules has been carried farther than that of other types of atomic aggregates. The Bom theory of crystal energy permits the calculation to within... 

Uf all the different types of atomic aggregates, ionic crystals have been found to be most suited to simple theoretical treatment. The theory of the structure of ionic crystals described briefly in the following sections was developed about 40 years ago by Born, Haber, Land6, Madelung, Ewald, Fajans, and other investigators. The simplicity of the theory is due in part to the importance in the interionic interactions of the well-understood Coulomb terms and in part to the spherical symmetry of the electron distributions of the ions with noble-gas configurations. 

The first of these theories applies the law of mass action to the equilibrium between unassociated molecules or ions and micelles, as illustrated by the following simplified calculation for the micellisation of non-ionic surfactants. If c is the stoichiometric concentration of the solution, x is the fraction of monomer units aggregated and m is the number of monomer units per micelle,... 

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