Ionic distribution curves

Ionic distribution curves (Figures 9 to 17) are plots of the eflFective distribution coeflBcient (or of solute concentration in the solid) against sample length. They are used for evaluating the interface distribution coeflBcient (Equation 2). 

Discussion of Experimental Results. Role of Diffusion. Small differences between cation and anion diffusion coeflBcients (differential diffusion) theoretically can account for the differential ion distribution even if the distribution coeflBcients themselves are assumed to be identical for cations and anions. If ionic distribution curves are determined mainly by differential diffusion, then little information can be obtained from them about the acceptability of different ions in the ice structure. 

Figure 16. Ionic distribution curves for 4.8 X lOr M KF solution frozen at a rate of 5 microns a second with different stirring speeds. The potassium-ion fraction decreases and the hydrogen-ion fraction increases as the stirring rate is increased. This may explain the reduction of the freezing potential by stirring (if the liquid phase is close to 0°C.)...

The smallness of the apparent distribution coeflBcients of ionic solutes in water suggests that all of them impose a considerable distortion on the ice lattice. Ionic distribution curves such as those discussed above show that there are differences in degree. Furthermore, the distortion imposed by a given ion depends also on its counterion. Thus, the ammonium ion in combination with the chloride ion is largely rejected, but in combination with the fluoride ion it is absorbed more readily than any other ion combination investigated. The freezing potential indicates that, even in NH4F, F" is somewhat more readily taken into the ice structure than NH4 ... 

FIG. 4 Induced potential drop S0(x) in the Raleigh model of the ionic distribution, k = 0.2 (curve 1), 0.33 (curve 2), and 0.4 (curve 3). Gray area shows the Raleigh distribution of the induced charge with a = 0.3 nm and /c = 0.33 (see text) which corresponds to curve 2. The total induced charge is normalized... 

Figure 6.4 Distribution curve for ionic conductivity random-walk diffusion in the absence of a field is the dashed line. In the presence of the electric field, the distribution splits into two parts, one for cations and one for anions, each shifted with respect to the origin.

The ordering of the anions in bmimX ionic liquids has also been suggested by our recent large-angle x-ray scattering experiment on liquid bmimi [23]. Figure 13 shows a differential radial distribution function obtained for liquid bmimi at room temperature. Clear peaks in the radial distribution curve are... 

The first satisfactory definition of crystal radius was given by Tosi (1964) In an ideal ionic crystal where every valence electron is supposed to remain localised on its parent ion, to each ion it can be associated a limit at which the wave function vanishes. The radial extension of the ion along the connection with its first neighbour can be considered as a measure of its dimension in the crystal (crystal radius). This concept is clearly displayed in figure 1.7A, in which the radial electron density distribution curves are shown for Na and Cl ions in NaCl. The nucleus of Cl is located at the origin on the abscissa axis and the nucleus of Na is positioned at the interionic distance experimentally observed for neighboring ions in NaCl. The superimposed radial density functions define an electron density minimum that limits the dimensions or crystal radii of the two ions. We also note that the radial distribution functions for the two ions in the crystal (continuous lines) are not identical to the radial distribution functions for the free ions (dashed lines). 

Since an a priori definition of the effective region is hardly possible, each atomic region is usually approximated by a spherical region around the atom, where the radius is taken as its ionic, atomic, or covalent bond radius. The radial distribution of electron density around an atom is also useful to estimate the effective radius of an atom, particularly in ionic crystals. In an ionic crystal, the distance from the metal nucleus to the minimum in the radial distribution curve generally corresponds to the ionic radius. As an example, the radial distribution curves around K in o-KvCrO., (85) are shown in Fig. 19a. The radial distributions of valence electrons (2p electrons) exhibit a minimum at 1.60 A for K(l) and 1.52 A for K(2), respectively. These distances correspond to the ionic radii in crystals (1.52-1.65 A)... 

Figure 2. Freezing potential curves for different ionic species (a) and concentrations (b). Freezing rate was 5 microns a second, Ionic distributions for the 2,5 X lO M solutions (except NHjCl) are shown in Figure 10, Potential of NH.Cl solution is negative with respect to the ice, all others are positive...

Structural Significance of ion Distribution Curves. The effect of solutes, ionic and not ionic, on the structure of water has been the object of much research, especially since the fundamental investigations of H. S. Frank and co-workers (52, 53, 54, 88, 132, 133, 135). By contrast, relatively little is known about the way solutes fit into the ice structure. Subsequent sections of this paper review some pertinent evidence. 

Differential ion transfer across the phase boundary is manifest in small differences of distribution coeflBcients for the species of an ion pair. The distribution coeflBcient for a given ion depends also on the other ionic species present in solution and their concentrations. The apparent distribution coeflBcients, determined from experiment, depend on both freezing rate and concentration. Differential diffusion appears to play only a secondary role. The apparent distribution coeflBcients for potassium and cesium fluoride are higher than those for HF solutions of the same concentration. They appear to increase with concentration while those for HF decrease. The increase is perhaps explained by the formation of regions of higher concentration at cell or grain boundaries, or it may be related to the possibility that most cations enter the ice lattice interstitially rather than substitutionally. The interpretation of solute distribution curves in ice is diflBcult. 

With the aid of assumed equilibrium constants, Nagypal and Beck calculated the concentration distributions of the various complexes formed in this assumed system, as functions of the donor solvent concentration and the relative permittivity determined by this. Figure 8.2 presents the distribution curves constructed from these data. It can be seen that the distributions of several ionic species display anomalous behaviour. This is particularly well reflected by the two maxima and one minimum appearing in the distribution curve of the complex MS. In the case of each... 

Regarding the ionic liquid [Ciomim][NTf2], the shape of the distribution curve indicates that the uranium(VI) extraction involves partitioning of the neutral di-oxouranium(VI)-TBP-nitrato complex as observed in alkanes. This is illustrated in Fig. 2.15, where one can notice the dependence of Ku on TBP concentration which resembles that obtained for dodecane. This observation suggests that the... 

With respect to the shape of the pore size distribution curves, figure 3 shows two types of pores the pores around 30-45A in diameter which are the normal size of pores when no additive is used, and the pores around 120 A in diameter, which are the result of the change in structure promoted by the interaction of the NH4 and CO ions with the aluminium in the mixed oxide. The higher diameter pores found in the pure titanium sample may be the result of the generation of CO2 gas fix>m the decomposition, during caldnation, of the free ionic 3 found in this sample, which promotes the formation of a few large pores of more than 200A in diameter and wtuch contribute little to the total surface area (42 mVg) and the cumulative pore volume (0,102 cm /g). 

The preparation and physical properties of oil/water microemulsions containing liquid paraffin, glycerol, water and blends of Tween 60 and Span 80 have been examined [180]. The decrease in micellar size as the surfactant/alcohol ratio was increased is similar to the situation observed with solubilized micellar solutions formed by non-ionic surfactants. Turbidity spectra methods of particle sizing have shown that an increase of temperature of preparation over the range 25 to 80° C led to a gradual decrease in the modal diameter and the half-width of the size distribution curve. Phase diagram studies on micellar solutions prepared at 70° C have indicated a pronounced dependence of the area of existence of microemulsions on the ratio of Tween to Span in the system and on the oil... 

Top typical saturation curve and variation of mean electron energy with applied field. Middle fraction of the electron swarm exceeding the specific energy at each field strength. Calculated assuming constant collision cross-section and Maxwell-Boltzman distribution. Bottom variation of products typical of involvement of ionic precursors (methane) and excited intermediates (ethane) with applied field strength... 

In a similar fashion the bonding in H2 might be formally regarded as a complementary pair of one-electron donor-acceptor interactions, one in the ot (spin up ) and the other in the 3 (spin down ) spin set.8 In the long-range diradical or spin-polarized portion of the potential-energy curve, the electrons of ot and (3 spin are localized on opposite atoms (say, at on HA and 3 on HB), in accordance with the asymptotic dissociation into neutral atoms. However as R diminishes, the ot electron begins to delocalize into the vacant lsB(a) spin-orbital on HB, while (3 simultaneously delocalizes into Isa on HA, until the ot and (3 occupancies on each atom become equalized near R = 1.4 A, as shown in Fig. 3.3. These one-electron delocalizations are formally very similar to the two-electron ( dative ) delocalizations discussed in Chapter 2, and they culminate as before (cf. Fig. 2.9) in an ionic-covalent transition to a completely delocalized two-center spin distribution at... 

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