Size-dependent ionic density

In this work we start with the primitive jellium model, as appropriate for alkaline metals. In the jellium model for metal clusters a fundamental input is the size-dependent ionic density. Fortunately, when one of us started this calculation in 1984 [3], some experimental data about the size dependence of the nearest-neighbor distance were available from EXAFS (extended X-ray absorption fine structure) measurements [19]. Except for fine details the size dependence is very weak. This means that in a first approximation the bulk density of the metal can be used as input for a cluster calculation. A second question is the size dependence of the shape. Since electron micrographs very often show a spherical shape, at least for the larger clusters, a spherical shape will be assumed for all cluster sizes. This means that for monovalent systems the radius R of the jellium cluster is determined by its bulk density... 

As is mentioned in Sect. 2.2, a discussion of de-ionization processes in the Earth s atmosphere would be incomplete without a mention of the r le of aerosols. The attachment of ions to aerosols in the stratosphere and troposphere has been considered by several workers213. It is clear that their presence will enhance the loss of ions from the gas phase at a rate dependent on the nature, size and number density of the particles, and so this process, which could be the dominant ionization loss process, must be considered along with gas phase ionic recombination in detailed atmospheric de-ionization rate calculations. 

Complex formation of the alkali ions with murexide in methanol was studied quantitatively by spectrophotometric titration with Li+, Na+, and K+. (For Rb+ and Cs+ only qualitative measurements could be obtained since these complexes tend to precipitate). Fig. 8 shows the shift of the absorption maximum upon titration with Na+. The well defined isosbestic point is a good indication for a simple 1 1 complexation equilibrium. In so much as the spectral shift (upon complexation) is a criterion of the strength of the complexes. Fig. 9 indicates that the absolute complex stability parallels monotonically the sequence of ionic sizes. (Both /lAmax and Ae are largest for the smallest ion). In the alkali ion series Li+ forms the strongest and Cs+ the weakest complexes. This monotonic size dependence of the charge density is also expressed in the energy values for the desolvation (—zlHuydr. for Li+= 120 kcal and for Cs+ 60 kcal) (77). 

Whether oxide particles deform in a pseudo-plastic manner or not depends on a multitude of parameters, such as the yield stress of the particles, the yield stress of the matrix, the particle/matrix bonding strength, the crystallite size, the defect density, or the state of stresses. Most of these parameters are unknown or difficult to measure. Good correlation could be found between the particle deformability, with its effect on the increase of the recrystallization temperature, and the fraction of ionic bonding character of the oxide, following the definition of Pauling [1.143]. Figure 3.1-152 shows that... 

In many biological systems the biological membrane is a type of surface on which hydrophilic molecules can be attached. Then a microenvironment is created in which the ionic composition can be tuned in a controlled way. Such a fluffy polymer layer is sometimes called a slimy layer. Here we report on the first attempt to generate a realistic slimy layer around the bilayer. This is done by grafting a polyelectrolyte chain on the end of a PC lipid molecule. When doing so, it was found that the density in which one can pack such a polyelectrolyte layer depends on the size of the hydrophobic anchor. For this reason, we used stearoyl Ci8 tails. The results of such a calculation are given in Figure 26. 

The mobility depends on both the particle properties (e.g., surface charge density and size) and solution properties (e.g., ionic strength, electric permittivity, and pH). For high ionic strengths, an approximate expression for the electrophoretic mobility, pc, is given by the Smoluchowski equation ... 

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