Ion size

Fig. V-1. Variation of m / o and n /wo with distance for = 51.38 mV and 0.01 M uni-univalent electrolyte solution at 23°C. The areas under the full lines give an excess of 0.90 X 10 mol of anions in a column of solution of 1-cm cross section and a deficiency of 0.32 x 10 mol of cations. There is, correspondingly, a compensating positive surface charge of 1.22 x 10 " mol of electronic charge per cm. The dashed line indicates the effect of recognizing a finite ion size.

In the limit of zero ion size, i.e. as o —> 0, the distribution functions and themiodynamic fiinctions in the MS approximation become identical to the Debye-Htickel limiting law. 

Figure A2.3.16. Theoretical HNC osmotic coefTicients for a range of ion size parameters in the primitive model compared with experimental data for the osmotic coefficients of several 1-1 electrolytes at 25°C. The curves are labelled according to the assumed value of a+- = r+ + r-...

Soluble Salt Flotation. KCl separation from NaCl and media containing other soluble salts such as MgCl (eg, The Dead Sea works in Israel and Jordan) or insoluble materials such as clays is accompHshed by the flotation of crystals using amines as coUectors. The mechanism of adsorption of amines on soluble salts such as KCl has been shown to be due to the matching of coUector ion size and lattice vacancies (in KCl flotation) as well as surface charges carried by the soflds floated (22). Although cation-type coUectors (eg, amines) are commonly used, the utUity of sulfonates and carboxylates has also been demonstrated in laboratory experiments. 

The physical and chemical properties of silicate glasses depend on the composition of the material, ion size, and cation coordination number (9). A melt or glass having a Si02/Na20 ratio of 1, ie, sodium metasiUcate [1344-09-8] is expected to possess a high proportion of (SiO ) chains. At a ratio of 2, sheets might predominate. However, litde direct evidence has been shown for a clear predominance of any of these stmctures. The potential stmctures of sihcate melts of different ratios are discussed in detail elsewhere (10—12). 

Thus, it has been shown that calix[4]aryl esters exhibit remarkably high selectivity toward Na [11-14]. This is attributable to the inner size of the ionophoric cavity composed of four 0CH2C=0 groups, which is comparable to the ion size of Na, and to the cone conformation that is firmly constructed on the rigid ca-lix[4]arene platform (Scheme 2). 

The experimentally noionic accessible limiting conductivities A — A — A of the triple ion must be estimated with consideration of ion sizes yielding Ai =A0/3 [101,102] or 2A0/3 [103], with preference for the latter value. 

Kagawa, I. Gregor, H. P. (1957). Theory of the effect of counter ion size upon titration behavior of polycarboxylic acids. Journal of Polymer Science, 23, 477-84. 

The great success of DH theory provoked numerous attempts at improvement and extension to more concentrated solutions, hi the equations reported in Section 7.4.2, known as the first approximation, ion size was disregarded all ions were treated as point charges. This is reflected in Eq. (7.30), where the integration was started from r = 0 (i.e., it was assumed that other ions can, however, closely approach the central ion and that all these ions have zero radius). 

In the second approximation, Debye and Hiickel introduced the idea that the centers of the ions cannot come closer than a certain minimum distance a, which depends on ion size the ions were now treated as entities with a finite radius. The mathematical result of this assumption are charge densities Qy, which are zero for r[Pg.120]

It may seem that the prospeets are bleak for the GvdW approach to electrolytes but, in fact, the reverse is the ease. We need only follow Debye and Hiickel [18] into their analysis of the sereening meehanism, almost as successful as the van der Waals analysis of short-range fluids, to see that the mean-field approximation can be applied to the correlation mechanism with great advantage. In fact, we can then add finite ion size effects to the analysis and thereby unify these two most successful traditional theories. 

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

Fig. 25. The effect of metal ion size on porphyrin ruffling. Very small metal ions [P(V) with an ideal P-N bond length of 1.84 A and low-spin Ni(II) with an ideal Ni-N length of 1.90 A in (a) and (b)) cause extensive S4 ruffling. Metal ions close to the right size (M-N = 2.035 A) give planar structures [Zn(II) in (c)]. Metal ions that are too large [Pb(II) at (d) with ideal Pb-N of 2.39 A] are extruded from the plane of the porphyrin and cause it to dome. For clarity, substituents on the porphyrins such as phenyl or ethyl groups have been omitted. Modified after Ref. (77).

The common disadvantage of both the free volume and configuration entropy models is their quasi-thermodynamic approach. The ion transport is better described on a microscopic level in terms of ion size, charge, and interactions with other ions and the host matrix. This makes a basis of the percolation theory, which describes formally the ion conductor as a random mixture of conductive islands (concentration c) interconnected by an essentially non-conductive matrix. (The mentioned formalism is applicable not only for ion conductors, but also for any insulator/conductor mixtures.)... 

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