Co-sphere overlap

Since we have reason to believe that the order-disorder situation in ionic co-spheres, overlapping and merging as in Fig. 69, could give rise to forces of attraction or repulsion, superimposed on the Coulomb forces, we may inquire whether the observed facts as to activity coefficients may be correlated with the known behavior of the ions as regards viscosity and entropy. 

The explanation given here seems more feasible than that using the concepts of co-sphere overlap (29), and the structure-making or structure-breaking characteristics of ions (SO). This is unsatisfactory because the order shown by the curves does not depend on concentration, and is evident at very low concentrations where the co-spheres would have to be enormous in order to have any overlap. Moreover, the physical nature of the forces arising from such overlap is rather intangible. 

The concept of a solvent co-sphere surrounding a solute particle leads to the consideration of what happens in real solutions where these co-spheres may overlap. Consider two solute particles, i and , in solution which approach so that their co-spheres overlap (Fig. 14 ... 

Figure 14. Diagrammatic representation of the process of co-sphere overlap as two solute species, i and /, come together (a) mutually destructive co-sphere interaction where the co-sphere of solute j dominates the process leading to the solvent reaction shown in (b) in process (c) the interaction is mutually constructive, additional solvent being incorporated into the co-sphere as shown in reaction (d) assuming solute j dominates (Friedman and Krishnan, 1973).

The quantity A++ for Li+ is positive but decreases with increasing ion size. Thus for small ions, water molecules tightly bound to the ion are released as the co-spheres overlap (cf. electrostrictive structure formers). The more negative values for Na+, K+, Rb+ and Cs+ show also that a water molecule in the co-sphere, i.e. in the B-zone, is in a higher energy state than one in bulk water. However, one must be... 

This modification is applicable to distances between r = r, + rj and r = r, -I- rj + d and the upper limit corresponds to when the Gurney co-spheres cease to overlap (see Figure 10.15). Any value of r between the lower limit r, + rj and the upper limit n + rj + d corresponds to overlap of the co-spheres. Overlap of the co-spheres contributes a constant term, no matter how extensive the overlap is. 

Fig. 19. Illustrating the effect of co-sphere overlap as the interionic distance gets small. The solvent displace by overlap is assumed to return to the normal bulk water state. The free energy change per mole in this process is Ay. (After Ramanathan and Friedman. )...

The term Brownian motion was originally introduced to refer to the random thermal motion of visible particles. There is no reason why we should not extend its use to the random motion of the molecules and ions themselves. Even if the ion itself were stationary, the solvent molecules in the outer regions of the co-sphere would be continually changing furthermore, the ion itself executes a Brownian motion. We must use the term co-sphere to refer to the molecules which at any time are momentarily in that region of solvent which is appreciably modified by the ion. In this book we are primarily interested in solutions that are so dilute that the co-spheres of the ions do not overlap, and we are little concerned with the size of the co-spheres. In studying any property... 

Ion Association. One feature of the model is that it requires no vaguely defined breakdown of the DH ionic cloud at some critical concentration, but predicts an even gradation of properties over the whole concentration range, or at least up to concentrations where the co-spheres start to overlap. 

Above 0.1m the values of aqueous salts flatten out and may become negative except where small ions are involved. In 90% acetonitrile, the 0l curve becomes steeper with increasing concentration. This is probably caused by depletion of the free water in the solvent, so that ion solvation by acetonitrile becomes significant. It is also possible that, because ionic electric fields are significant at greater distances in a solvent of lower dielectric constant, the overlapping of ionic co-spheres has a much more drastic effect on the enthalpy than it does in water for this salt. 

Friedman and Krishnan, 1973b). As a result of overlap, some of the solvent co-sphere is displaced and if, for example, the effect of solute j on the solvent dominates the process of overlap, then the overlap can be represented as in Fig. 14(a), the change in the solvent being summarized by the reaction in Fig. 14(b). This mutually destructive overlap can be characterized by the free energy change, Aijt for the solvent reaction, where Ay is related to the thermodynamic energy, and entropy, by the expression A-, - — T. SSj. 

In real solutions, the properties of these solutes can be examined in terms of what happens as the solvent co-spheres approach and overlap. This aspect will be discussed in a later section except for a particular aspect of solute-solute interaction called hydrophobic association. 

Friedman and Krishnan (1973c) using the HNC method (p. 245) calculate that Ay for the hydrophobic interaction between the alkyl groups of alcohols ROH in water (R = Me to t-Bu) is around —418 J mol-1. In general, for overlap between solvent co-spheres of methylene groups, 4Xx — —360 J mol-1, which characterizes hydrophobic association. 

In Passynski s theory, the basic assumption is that the compressibility of water sufficiently bound to an ion to travel with it is zero. Onori thought this assumption questionable and decided to test it. He used more concentrated solutions (1-4 mol dm ) than had been used by earlier workers because he wanted to find the concentration at which there was the beginning of an overlap of the primary solvation spheres (alternatively called Gurney co-spheres) of the ion and its attached primary sheath of solvent molecules. 

The interaction of the transition state with oriented solvent molecules in the inner layer is dependent on the charge density of anions adsorbed through the co-sphere/solvent co-plane overlap and resulting interaction effect (Conway ). 

Gurney introduced the idea of a co-sphere around each ion, which can loosely be identified with a region of hydration. Outside each co-sphere the water is treated as unmodified bulk water with aU the properties of pure water. However, within the co-sphere the water is no longer treated as unmodified bulk water. Allowance is also made for the possibility that the individual co-spheres of ions could overlap with water being squeezed out (see Figures 10.14(a) and 10.14(b)). 

In this model the hard core term is as before, but the Gumey term is different. Instead of adding or subtracting a constant term for the region between r = r, + rj and r = r, + rj + d, this term is allowed to vary and to depend on the extent to which the co-spheres of the two ions overlap. The new term which is used is taken to be proportional to the volume of the overlapping part of the co-spheres, and again the magnitude will depend on the identities of the ions. 

This involves a modified core term where the hard core or hard sphere repulsion is replaced by a non-hard sphere short range repulsion which is proportional to This replaces the Debye-Hiickel core term. The Gurney term remains proportional to the volume of overlap of the co-spheres. 

I- (the Gurney term which is proportional to the volume of overlap of the co-spheres ... 

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