Solvation sheaths

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

There is, or may be, an iimer layer of specifically adsorbed anions on the surface these anions have displaced one or more solvent molecules and have lost part of their iimer solvation sheath. An imaginary plane can be drawn tlirough the centres of these anions to fomi the inner Helmholtz plane (IHP). 

The layer of solvent molecules not directly adjacent to the metal is the closest distance of approach of solvated cations. Since the enthalpy of solvation of cations is nomially substantially larger than that of anions, it is nomially expected that tiiere will be insufBcient energy to strip the cations of their iimer solvation sheaths, and a second imaginary plane can be drawn tlirough the centres of the solvated cations. This second plane is temied the outer Helmholtz plane (OHP). 

Within this framework, by considering the physical situation of the electrode double layer, the free energy of activation of an electron transfer reaction can be identified with the reorganization energy of the solvation sheath around the ion. This idea will be carried through in detail for the simple case of the strongly solvated... 

Solvated ions have a complicated structure. The solvent molecules nearest to the ion form the primary, or nearest, solvation sheath (Fig. 7.2). Owing to the small distances, ion-dipole interaction in this sheath is strong and the sheath is stable. It is unaffected by thermal motion of the ion or solvent molecules, and when an ion moves it carries along its entire primary shell. In the secondary, or farther shells, interactions are weaker one notices an orientation of the solvent molecules under the effect of the ion. The disturbance among the solvent molecules caused by the ions becomes weaker with increasing distance and with increasing temperature. 

Various methods are available for determining the solvation number hj and (or) the radius of the primary solvation sheath (1) by comparing the values of the true and apparent ionic transport numbers, (2) by determining the Stokes radii of the ions, or (3) by measuring the compressibility of the solution [the compressibility decreases... 

The species HjO is subject to further hydration in the usual manner. Its primary sheath contains three water molecules linked through electrostatic forces, and in part through hydrogen bonds (i.e., the ion with its primary solvation sheath can be formulated as H9O4+). 

In practical applications of this equation, one must pick values for constant a. To a first approximation it can be regarded as equal to the sum of the radii of two solvated ions. It is not clear, however, whether the solvation sheaths of approaching ions would not be deformed. Moreover, in deriving Eq. (7.43) it was assnmed without sufficient reasoning that the constant a for a given central ion will be the same for different ions present in the ionic atmosphere. 

Ion-pair formation lowers the concentrations of free ions in solution, and hence the conductivity of the solution. It must be pointed out that ion-pair formation is not equivalent to the formation of undissociated molecules or complexes from the ions. In contrast to such species, ions in an ion pair are linked only by electrostatic and not by chemical forces. During ion-pair formation a common solvation sheath is set up, but between the ions thin solvation interlayers are preserved. The ion pair will break up during strong collisions with other particles (i.e., not in all collisions). Therefore, ion pairs have a finite lifetime, which is longer than the mean time between individual collisions. 

Ion-pair formation (or the formation of triplets, etc.) is a very simple kind of interaction between ions of opposite charge. As the electrolyte concentration increases and the mean distance between ions decreases, electrostatic forces are no longer the only interaction forces. Aggregates within which the ions are held together by chemical forces have certain special features (i.e., shorter interatomic distances and a higher degree of desolvation than found in ion pairs) and can form a common solvation sheath instead of the individual sheaths. These aggregates are seen distinctly in spectra, and in a number of cases their concentrations can be measured spectroscopically. 

The conductivities of melts, in contrast to those of aqueous solutions, increase with decreasing crystal radius of the anions and cations, since the leveling effect of the solvation sheaths is absent and ion jumps are easier when the radius is small. In melts constituting mixtures of two salts, positive or negative deviations from additivity are often observed for the values of conductivity (and also for many other properties). These deviations arise for two reasons a change in hole size and the formation of new types of mixed ionic aggregates. 

In the simple case of electrostatic attraction alone, electrolyte ions can approach to a distance given by their primary solvation sheaths, where a monomolecular solvent layer remains between the electrode and the solvated ions. The plane through the centres of the ions at maximum approach under the influence of electrostatic forces is called the outer Helmholtz plane and the solution region between the outer Helmholtz plane and the electrode surface is called the Helmholtz or compact layer. Quantities related to the outer Helmholtz plane are mostly denoted by symbols with the subscript 2. 

The expulsion of cations and/or protons with their associated large solvation sheath. 

Whenever the concentration of a species at the interface is greater than can be accounted for by electrostatic interactions, we speak of specific adsorption. It is usually caused by chemical interactions between the adsorbate and the electrode, and is then denoted as chemisorption. In some cases adsorption is caused by weaker interactions such as van der Waals forces we then speak of physisorption. Of course, the solvent is always present at the interface so the interaction of a species with the electrode has to be greater than that of the solvent if it is to be adsorbed on the electrode surface. Adsorption involves a partial desolvation. Cations tend to have a firmer solvation sheath than anions, and are therefore less likely to be adsorbed. 

Every segment in the polymer chain is solvated by two solvent molecules. Those molecules of solvents 1 and 3 in the solvated sheath which correspond to the bulk composition of 1 1 are disregarded. Only those molecules of solvent 1 in the solvated sheath in excess of this 1 1 ratio constitute what may be regarded as the complex with the polymer. In this particular example the value of is 1 mol of solvent-1 per mol of segment. If the molar volumes of liquid-1 and polymer segment were equal, the coefficient of selective adsorption could also be expressed here as 1 ml of liquid-1 per ml of monomer units. 

Before we consider substitution processes in detail, the nature of the metal ion in solution will be briefly reviewed.A metal ion has a primary, highly structured, solvation sheath which comprises solvent molecules near to the metal ion. These have lost their translational degrees of freedom and move as one entity with the metal ion in solution. There is a secondary solvation shell around the metal ion, but the solvent molecules here have essentially bulk dielectric properties. The (primary) solvation number n in M(S)"+ of many of the labile and inert metal ions has been determined, directly by x-ray or neutron diffraction of concentrated solutions, from spectral and other considerations and by examining the exchange process... 

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