Ionic volume, intrinsic

Statistical correlations have been estabUshed by Marcus et al. [49] between y (I , S) and the properties of the ions and those of the solvents, but these cannot be deconvoluted to separate dependences on such properties. For the tetraalkylammo-nium ions (from Et N onwards), there is a linear dependence of F (I, S) on the intrinsic volumes of the ions, meaning that there is a constant volume increment for each -CHj- group, 16cm mol , irrespective of the solvent. For small ions, the dependence of F (1, S) is about equally shared by the intrinsic ionic volumes and their basicities (for anions) and acidities (for cations), the dominant solvent property being their tightness, measured by their solubility parameter. 

The intrinsic ionic volumes Vi j ,r are assumed to be independent of the temperature. For monatomic ions they are given by the Mukeijee expression [74] ... 

Figure 6 suggests that the viscosity of ionic polysaccharides in dilute d-tartaric acid (TA) and of nonionic polysaccharides in water (c, = 0.05-0.07%) are in the same general t),- — ci orbit at 28°C. A sample of CMC (0.05 g) was dispersed in 80-mL water in 100-mL beakers to which TA was afterward added to different molarities TA supplied the H+ counterion intrinsic to an ionic polysaccharide and the nonintrusive tartrate ion. The solutions were transferred to 100-mL Erlenmeyer flasks and brought to volume with water prior to dilution viscometry. Judging from Fig. 7, a molar concentration of TA approximating 0.35 ensures an r sp/ci minimum in a dilute CMC dispersion (ci = 0.05-0.07%). 

The free spaces where Ps can form and o-Ps can have a reasonably long lifetime may be extrinsic defects, as just illustrated, or intrinsic defects, such as created when heating a pure solid compound. More generally, they may correspond to the natural voids present in any solid matrix (e.g., "free volume" in polymers, treated elsewhere in this book). Ps can be formed not only in molecular solids, including frozen liquids, but also in a number of ionic solids, even when the open spaces are rather small. For example, Ps is formed in such a highly packed lattice as KC1 [44, 45] where the largest space available corresponds to the tetrahedral sites circumscribed by 4 Cf anions, with a radius of only 0.0845 nm, resulting in an o-Ps lifetime of about 0.65 ns. 

Partial molal volumes of aqueous ionic species vary considerably with changes in pressure and temperature. The molar volume of an aqueous species can be split into a Coulombic and a non-Coulombic term. The non-Coulombic term consists of the intrinsic volume of the ion. The Coulombic term consists of the volume of solvation and the volume of collapse. The volume of solvation is related to the orientation of water dipoles around the aqueous species, and the volume of collapse is the component of the partial molal volume related to the collapse of the water structure in the vicinity of the aqueous species. The pressure and temperature dependence of the molar volume of aqueous species arises from a similar change in the electrostatic properties of the solvent... 

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