Solvent sheath

Arrangement 1, in which ions stripped of their solvent sheath are in direct contact with the metal. 

Most authors have accounted for the mutual influence of ions and solvent molecules only by assuming a firmly bound solvent sheath around the ion. The structure of the bulk solvent and the influence of electrolyte concentration on this structure are not taken into consideration. 

The number of such independent terms in a metal hexacarbonyl is 13 (10 if we discard quartic terms containing the distortion of some CO group raised to an odd power), in addition to the three harmonic force and interaction constants. Thus the number of physical quantities exceeds the number of parameters that may, with the available data, be fitted to Eq. (18). There is the further possibihty that the observed frequencies are distorted by interaction with solvent in a way that is not adequately compensated for by Eq. (18). The classical amplitude of a triply excited oscillator is greater than that for one that is only singly excited, and so jostling of solvent and solute molecules, and variability and asymmetry in the solvent sheath, may become important. This may explain the observation that binary and more especially ternary i.r. bands are considerably broader than are fundamentals in the same solvents. 

Just as the central ion can perturb and cause a rearrangement of the surrounding solvent molecules and ions, the electrode itself can cause the surrounding particles to assume abnormal, compromise positions (relative to the bulk of the electrolyte). It will be seen later that an electrode also can get enveloped by a solvent sheath and an ionic cloud. There are, however, many other interesting, phenomena arising from the fact that one can connect an external potential source (e.g., a battery) to the electrode by a metallic wire and thus control the electrode charge. New possibilities emerge that do not exist in the case of the central ion. 

What happens when the metal is charged Would other types of forces be involved The forces of attraction between the metal and the water molecules still operate, but in addition, the charge on the metal will stimulate the water molecules to orient themselves. The process is similar to the orientation of dipoles in the solvent sheath around an ion (see Chapter 2). 

The contribution of the metal to the double layer was discussed in Sections 6.6.7 to 6.6.9. However, we have said little about the ions in solution adsorbed on the electrode and how they affect the properties of the double layer. For example, when presenting the Stem model of the double layer (Section 6.6.6), we talked about ions sticking to the electrode. How does an interface look with ions stuck on the metal What is the distance of closest approach Are hydrated ions held on a hydrated electrode i.e., is an electrode covered with a sheet of water molecules Or are ions stripped of their solvent sheaths and in intimate contact with a bare electrode What are the forces that influence the sticking of ions to electrodes ... 

The process of contact adsorption can be viewed in the following way (Fig. 6.90) First, a hole of area of at least 1U —where r, is the radius of the bare ion—is swept free of water molecules in order to make room for the ion. At the same time, the ion strips itself of part of its solvent sheath and then jumps into the hole. During this process, the involved particles—electrode, ion, water molecules—break old attachments and make new ones (change of enthalpy, AH) and also exchange freedoms and restrictions for new freedoms (change of entropy, AS). 

One possibility is for the ion to wander about on the solution side of the interface, say, in the OHP, till it comes face to face with a hole site. Then, in one shot, the ion could get electronated, divest itself of its solvent sheath, and dive into the lattice. This would be a direct one-step deposition reaction (Fig. 7.129). 

The necessary reorientation or reorganization of solvent dipoles also creates a barrier to electron transfer. An attempt is made to illustrate the point schematically in Figure 2. Rather than try to show individual solvent molecules and their dipole orientations, the decrease in ion-solvent interaction between a +3 and a +2 ion is illustrated by the more tightly drawn circle around the +3 ion. The circles are a schematic attempt to illustrate the interactions between the surrounding solvent sheath and the ionic charges. 

The fact that only naked molecules are refined is based on the problem that for crystal lattices at least 27 unit cells would have to be included (with at least one unit per cell, including counter ions and solvents of crystallization), and in solution at least 200 molecules of water must be refined in the solvent sheath interacting with the compound to be modeled. Since CPU time f(m2), where m is the number of nuclei, the time required for a single optimization cycle increases dramatically under these conditions. Even more importantly, the initial configuration of the molecule and its environment is not easy to predict since the intermolecular contacts (crystal lattice, ion-pairing and solvation) of a compound to be modeled are not known beforehand. Thus, inclusion of environmental effects in modeling studies has necessitated the use of some severe approximations176-781. 

In this simple form of the Marcus theory, two terms, the reorganization of the inner coordination shell (AG m) and that of the solvent sheath (AG 0Ut), both describing the degenerate transition-state geometry, contribute to AG. While molecular mechanics might also be used to model the encounter complex, force field calculations have mainly been applied to the estimation of the inner coordination shell reorganization term (AGt,)19,143 1445. 

Another factor that affects the reduction of hydronium ion is its solvent sheath (solvation energy). By convention the pXa of H30(tq) in water is defined... 

Owing to the operation of these ion-dipole forces, a number of water molecules in the immediate vicinity of the ion (the number will be discussed later) may be trapped and oriented in the ionic field. Such water molecules cease to associate with the water molecules that remain part of the network characteristic of water (Section 2.4.3). They are immobilized except insofar as the ion moves, in which case the sheath of immobilized water molecules moves with the ion. The ion and its water sheath then become a single kinetic entity (there is more discussion of this in Section 2.4.3). Thus, the picture (Fig. 2.11) of a hydrated ion is one of an ion enveloped by a solvent sheath of oriented, immobilized water molecules. 

Thus, one must consider the contribution to the heat of formation of the primary solvated ion (i.e., step 3 of the cycle used in the theoretical calculation presmted earlier), which arises from interactions between the ion and the dipoles induced in the water molecules of the primary solvent sheath. The interaction energy between a dipole and an infinitesimal charge dq is -p dq/P, or, since dq/P is the field dX due to this charge, the interaction energy can be expressed as -p dX. Thus, the interaction energy between the dipole and an ion of charge ZjCo. exerting a field zf /P, can be found by. 

Conversely, spectroscopic methods (particularly NMR and neutron diffraction) can be used to sense the residence time of the water molecules within the solvent sheaths around the ion. Thus, they could offer the most important data still required—a clean quantitative determination of the number of molecules that move with the ion. Unfortunately they only work in concentration regions far higher than those of the other methods. A summary of results from these methods is given in Tables 2.23 and 2.24. 

A model has been given for the breaking up of an ionic crystal into free ions which stabilize themselves in solution with solvent sheaths. One central theme guided the account, the interaction of an ion with its neighboring water molecules. 

Fig. 3.38. The distinction between free water and hydration water that is locked up in the solvent sheaths of ions.

The (1 - ( )p Na)np term is used to account for the difference in the equilibrium of simple salt with a linear polyelectrolyte and its cross-linked gel analog [60]. The release of territorially bound counterion from the polyion domain to the solution leads to a gain of negative and positive charges, respectively, by the solvent sheath of the polyelectrolyte and the salt solution. Whereas the two separate phases in the gei/salt system remain electroneutral, this is not the case with the linear polyelectrolyte/salt system. This difference is resolved, however, in the development of the... 

Figure 1.1 (a) Solvent sheaths of individual ions in contact (b) bare ions in contact (c) partial... 

---