Ionic effective dimensions

With this kind of approach, it was also possible to conclude that, in aqueous medium, aU the cations (monovalent or bivalent), as well as the S04 anion, are electroadsorbed in the pores in hydrated state. On the contrary, it seems that the monovalent anions are basically adsorbed in a non-hydrated state. These results enable to establish a scale of ionic effective dimensions in aqueous medium. These dimensions are compared with the ones of the different molecules used for the calibration of the average pore size of carbons by gas phase adsorption (N2, CF4, SFe and methyl tert-butyl ether (MTBE)) ... 

Ionic interactions (repulsive or attractive) can also dramatically alfect HDV. For charged polymers, ionic effects often dominate behavior, especially in aqueous solutions. Theoretical treatments for predicting polyelectrolyte dimensions and phase behavior are discussed by Barrat and Joanny (3) scaling theory for charged polymers is reviewed by Dobrynin, Colby, and Rubinstein (4). 

X-ray diffraction work (11,15) shows that there is an ionomer peak at 4°C which is absent in the acid precursor. This low, broad peak is not affected by annealing or ion type and persists up to 300°C. Since the 4°C peak corresponds to a spacing of about 2.5 nm, it is reasonable to propose a stmctural feature of this dimension in the ionomer. The concept of ionic clusters was initially suggested to explain the large effects on properties of relatively sparse ionic species (1). The exact size of the clusters has been the subject of much debate and has been discussed in a substantial body of Hterature (3,4,18—20). A theoretical treatment has shown that various models can give rise to supramoleculat stmctures containing ionic multiplets which ate about 10 nm in diameter (19). 

Figure 19-4 contrasts the effective sizes of the halide ions. Each of these dimensions is obtained from the examination of crystal structures of many salts involving the particular halide ion. The effective size found for a given halide ion is called its ionic radius. These radii are larger than the covalent radii but close to the van der Waals radii of neutral atoms. 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

The crystal structures of Hf 2 (OH) 2 (S0O 3 (H2O) i, (14) and Ce2(0H)2(S0i,)3 (H20)it (14) also have been determined and found to be isomorphous to the zirconium compound. The cell constants for this series of four isomorphous compounds reflect the effect of the ionic radii on the dimensions of the unit cell. The values for these cell constants are in Table II. Thus, the cell constants for the zirconium and hafnium compounds are nearly identical and smaller than the cell constants for the cerium and plutonium compounds which are also nearly identical. This trend is exactly that followed by the ionic radii of these elements. 

Effect of pH, ionic strength and nonionic surfactemts on polymer dimensions. 

Here we see clearly the large concentration of density around the oxygen nucleus, and the very small concentration around each hydrogen nucleus. The outer contour is an arbitrary choice because the density of a hypothetical isolated molecule extends to infinity. However, it has been found that the O.OOlau contour corresponds rather well to the size of the molecule in the gas phase, as measured by its van der Waal s radius, and the corresponding isodensity surface in three dimensions usually encloses more than 98% of the total electron population of the molecule (Bader, 1990). Thus this outer contour shows the shape of the molecule in the chosen plane. In a condensed phase the effective size of a molecule is a little smaller. Contour maps of some period 2 and 3 chlorides are shown in Figure 8. We see that the electron densities of the atoms in the LiCl molecule are only very little distorted from the spherical shape of free ions consistent with the large ionic character of this molecule. In... 

Covalency effects on cell dimension vs ionic radii plots manifest themselves in a lowering of the line joining the more covalent ions relative to a line joining the Mg and Ca compounds. Thus, in fluorides, Ni... 

In summary, from the above theoretical and experimental results, it is concluded that ionic diffusion towards self-affine fractal electrode should be described in terms of the apparent selfsimilar fractal dimension rather than the self-affine fractal dimension. In addition, the triangulation method is one of the most effective methods to characterize the self-similar scaling property of the self-affine fractal electrode. 

The three metals are chemically similar. The especially close similarity between the Zr and Hf chemistries can be remarked. This may be mainly related to the effect of the lanthanide contraction having made their radii (both atomic and ionic) nearly identical. In comparison with Ti, the larger atomic dimensions of Zr and Hf result in more basic oxides and tendency to achieve higher coordination numbers, etc. 

It is well known that addition of neutral salts to polymer solutions reduces the overall dimensions of polymer chains (the salting-out effect) [43, 44]. In general, the reduction in chain dimensions is reflected in the polymer viscosity. An example of salt effects on water soluble polymer with non-ionic characters has been reported in the literature where the precipitation temperature and the viscosity of polyethylene oxide (PEO) were measured to interpret the unusual... 

The molecular characterization of polyelectrolytes in general, and of DADMAC polymers in particular is complicated for several reasons. First, in aqueous solution the individual properties of the macromolecules are dominated by Coulom-bic interactions. Therefore, the resulting polyelectrolyte effects have to be suppressed through the addition of low molecular electrolyte, such as NaCl. The increase of the ionic strength results in a decrease of the chain stiffness of the polyelectrolyte molecules (see Sect. 5). The chains then revert to the coil dimensions of neutral macromolecules in dilute solutions. However, problems may still arise, particularly since the mode of action of these effects is quite different in various characterization methods [27]. 

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