Structured ionic cloud

The Structured Ionic Cloud. We base our treatment on the general solution of the linearized Poisson-Boltzmann equation (LPBE, Equation 1). 

Thus the contribution of the structured ionic cloud to the total potential at the surface of the central ion will not be as it is in the DH theory, and because the electrostatic model requires an equipotential surface to be maintained there, a new model is needed. We therefore approximate an ion to a dielectric sphere of radius a, characterized by the dielectric constant of the solvent D, and having a charge Q, residing on an infinitesimally thin conducting surface. This type of model has been exploited by previous workers (17,18) and may be reconciled with a quantum-mechanical description (18). 

From a consideration of the electrostatic free energy alone it is not immediately obvious how the arrangement of ions in the solution as a whole is related to the moving polarized central ion and its structured ionic cloud. It is reasonable to think that the induced multipoles impose restrictions on the mixing of the ions, so that the energy and entropy of configurations described by the structured ionic cloud are lower than in the DH model, as envisaged earlier by Frank and Thompson (16). Such considerations do not lead directly to predictions of the... 

An analogy between the situation just described and those involved in ion-solvent and ion-ion interactions can be drawn. The solvent water, for example, normally has a particular structure, the water network. Near an ion, however, the water dipoles are under the conflicting influences of the water network and the charged central ion. They adopt compromise positions that correspond to primary and secondary solvation (Chapter 2). Similarly, in an electrolytic solution, the presence of the central ion makes the surrounding ions redistribute themselves—an ionic cloud is formed (see Chapter 3). 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

A structure may be imposed on the ionic cloud by supposing that dq in the volume element dv = r2 sin OdOdipdr has a finite number, n, of maxima similarly situated at k 1 from the surface of the central ion (Figure lb). By analogy, this non-radial atmosphere is reducible to a corresponding array of point charges, and this device later enables us to formulate the necessary boundary conditions. 

For 1 1 electrolytes the simplest choice for n is unity (as in Figure lb) and is shown to be appropriate by comparison with experiment. Thus we have n = 1, X = 1 (cos 0i = 1, 0i = 0), and can take any value, since m = 0 and does not depend on (p. Variants of Equation 39 are easily obtained for other than uni-univalent salts by choosing a structure for the reduced ionic atmosphere in the light of symmetry and chemical intuition. This is illustrated with reference to the divalent ion of a 1 2 electrolyte, where it is reasonable as a first approximation to suppose that the ionic cloud will have two diametrically opposed maxima, each at a distance 1 /k from the reference ion. It is easy to see that dipoles induced on the central ion by these two charge centers will cancel, as well all higher terms of odd Z, but that quadrupolar effects (Z = 2) and other terms of even Z will not. For the structure factor the coordinates of the two maxima in dq are 0i = 0 and 02 = 7r, while the atmosphere is still symmetrical with respect to the angular coordinate [Pg.211]

The concept of ionic strength was devised by Debye and Hiickel (47) in order to describe the electric double layer and the general structure of the ionic cloud surrounding a dissolved particle. It is given by... 

What we want to do now is to include the hard core effects into the calculation of the structure of the ionic cloud. Or, what is equivalent, to charge up a system of hard spheres. This is the basic idea of the mean spherical approximation. A convenient treatment of mixtures of neutral hard spheres is provided by the Percus-Yevick(PY) theory,... 

Inside the distorted pseudolattice cell, a force exists associated to the internal electric field associated to the breaking of the symmetry of the equilibrium structure. In the case of the distorted ionic cloud, this field is called the relaxation field and is one of the components responsible for the reduction of the mobility of the ions with respect to the ideal, noninteracting situation (Harned Owen, 1958 Robinson Stokes, 1959). This relaxation force can be proved to be... 

Structural radii, electron cloud radii, ionic radii and solvation. E. C. Baughan, Struct. Bonding (Berlin), 1973,15,53-71 (49). 

Baughan EC (1973) Structural Radii, Electron-cloud Radii, Ionic Radii and Solvation. 15 53-71... 

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

Figure 11.4 Metallic bonding. The atoms of the metal form a regular lattice, the exact nature of which depends on the ionic radius of the metal involved. Each atom donates an electron to the cloud which is free to move throughout the structure and holds the ions together.

Performance Indices Quality Factors Optimum E1LB Critical micelle concentration (CMC) Soil solubilization capacity Krafft point (ionic surfactants only) Cloud point (nonionic surfactants only) Viscosity Calcium binding capacity Surface tension reduction at CMC Dissolution time Material and/or structural attributes... 

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