Primary solvation shell

In our simple model, the expression in A2.4.135 corresponds to the activation energy for a redox process in which only the interaction between the central ion and the ligands in the primary solvation shell is considered, and this only in the fonn of the totally synnnetrical vibration. In reality, the rate of the electron transfer reaction is also infiuenced by the motion of molecules in the outer solvation shell, as well as by other... 

The coordination number is the number of solvent molecules in the primary solvation shell. This quantity can be estimated (for ions) by conductance measurements and by... 

Microsolvation approaches have also been considered toward understanding the role of the primary solvation shell of a carbonium ion (18,90,91,97,98). These ions tend to become transition states whenever strong solvation is taking place (Figure 27). 

There is no quantitative model yet describing the observed electro-osmotic drag coefficients as a function of the degree of hydration and temperature. However, the available data provide strong evidence for a mechanism that is (i) hydrodynamic in the high solvation limit, with the dimensions of the solvated hydrophilic domain and the solvent—polymer interaction as the major parameters and (ii) diffusive at low degrees of solvation, where the excess proton essentially drags its primary solvation shell (e.g., H3O+). 

The rate at which solvent molecules are exchanged between the primary solvation shell of a cation and the bulk solvent is of primary importance in the kinetics of complex formation from aquocations. In both water exchange and complex formation, a solvent molecule in the solvated cation is replaced with a new molecule (another water molecule or a ligand). Therefore, strong correlations exist between the kinetics and mechanisms of the two types of reactions. 

In solvent-separated ion pairs, the primary solvation shells of the cation and the anion actually remain intact. In solvent-shared ion pairs, a single solvent molecule exists in the space between the... 

A Primary solvation shell B Secondary solvation shell C Disordered region D Bulk solvent... 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

Since anions are much less solvated in dipolar aprotic solvents (23) than in water, the hydrogen ion will be more highly solvated in the mixed solvent because it is preferentially solvated by monoglyme in the monoglyme-water mixtures rather than in the pure aqueous medium. The selective solvation is an important factor in an understanding of solute-solvent interactions in mixed solvent systems. Unfortunately, the detailed compositions of the primary solvation shell and the secondary mode of solvation (ion-dipole interaction) in mixed solvents are not yet clearly understood. 

Dissolution of alkali metal cations such as Cs+ results in short-range liquid order in water as a primary solvation shell of about eight water molecules is established about the metal cation. Lithium, however, exerts a much greater polarising power and is capable of organising a first- and second-coordination sphere of about 12 water molecules about itself, resulting in a much larger hydrated radius for the ion and hence decreased ionic mobility. 

In dilute electrolyte solutions ion-ion interaction as function of electrolyte concentration is fully explained by the Debye-Hiickel-Onsager theory and its further development. The contribution of ion solvation is noticed, if, for instance, the mobilities at infinite dilution of an ion in different solvent media or as function of ionic radii as considered. Up till now the calculation of that dependence has been only rather approximateAn improvement is quite probable, though, theoretically very involved if the solvent is not regarded as a continuum, but the number and arrangement of solvent molecules in the primary solvation shell of an ion is taken into consideration. Also the lifetime of molecules in the solvation shell must be known. Beyond this region a continuum model of ion-solvent interaction may be sufficient to account for the contributions of solvent molecules in the second or third sphere. 

While in the methods treated before ion solvation represents the sum of various terms of ion-solvent interaction, spectroscopic methods are mainly, if at all, sensitive to the immediate environment of an ion. Due to this the coordination model, representing the primary solvation shell, is not only used for highly charged ions but also for univalent ions. The precise results of the direct ion-solvent interactions made it possible to evaluate equilibrium constants describing the composition in the solvation shell of an ion in mixed solvents. Therefore, the estimation of single ion free ener es of transfer from spectroscopic measurements is the subject of several recent efforts and is theme of Part III. 

On treating ion solvation it is useful to differentiate between primary and secondary solvation shell or between chemical and physical solvation, respectively The electrostatic calculation of ion solvation is quite often less accurate because specific ion-solvent interactions have to be considered. In the primary solvation shell specific ion-solvent interactions are of much more importance than those with solvent molecules... 

The first term on the right hand side refers to the bare ion and disappears because we are engaged in differences of free energies. The second term refers to the coordination model of ion-solvent interaction in the primary solvation shell and the third term takes into account long range interactions. The last contribution may be approximated by the electrostatic interaction of a charged species with the solvent. The radius of the charged species is equal to that of the solvated ion e.g., ionic radius + diameter of the solvent molecules in the primary solvation shell). 

When each ion maintains its own primary solvation shell, the new chemical species is a solvent separated ion-pair (SSIP). If a single solvent layer is shared by ion partners, the species is a solvent shared ion-pair (SIP). If the cation and the anion are in contact and no solvent molecules are present between them, the form is contact ion-pair (CIP) or intimate ion-pair. Figure 2.1 illustrates multistep ion-pair formation equilibrium. What sets ion-pairing apart from complex formation is the absence of directional covalent coordinative bonds resulting from a Lewis base-acid interaction and a special geometrical arrangement. 

When the Boltzmann factor was not linearized and dielectric saturation effects, important near the ion, were considered, better results could be obtained also because the specificity of ion-solvent interaction was accounted for via the introduction of a parameter that measured an effective radius of the primary solvation shell where dielectric saturation occurs [42]. Subsequently, the discontinuous nature of the solvent near the ion was successfully taken into account [43]. 

Fig. 2-11. NMR chemical shift of Na as a function of the mole fraction of dimethyl sulfoxide (DMSO) in a binary mixture of DMSO and acetone (according to [295]). Straight line ideal case without preferential solvation, primary solvation shell of the same composition as the bulk solvent mixture. Curved line real case with preferential solvation of Na by DMSO and isosolvation point at xoMso/(cmol mol ) 0.21, that is, the mole fraction of the bulk solvent for which the solvated ion chemical shift is the average of the shifts obtained in the pure solvents (A<5 = <5dmsO - Acetone)-...

Fig. 2-14. Schematic representation of the equilibrium between (a) a solvated contact ion pair, (b) a solvent-shared ion pair, (c) a solvent-separated ion pair, and (d) unpaired solvated ions of a 1 1 ionophore in solution, according to reference [241]. Hatched circles represent solvent molecules of the primary solvation shell.

First, immediately after ionization, contact ion pairs are formed, in which no solvent molecules intervene between the two ions that are in close contact. The contact ion pair constitutes an electric dipole having only one common primary solvation shell. The ion pair separated by the thickness of only one solvent molecule is called a solvent-shared ion pair In solvent-shared ion pairs, the two ions already have their own primary solvation shells. These, however, interpenetrate each other. Contact and solvent-shared ion pairs are separated by an energy barrier which corresponds to the necessity of creating a void between the ions that grows to molecular size before a solvent molecule can occupy it. Further dissociation leads to solvent-separated ion pairs Here, the primary solvation shells of the two ions are in contact, so that some overlap of secondary and further solvation shells takes place. Increase in ion-solvating power and relative permittivity of the solvent favours solvent-shared and solvent-separated ion pairs. However, a clear experimental distinction between solvent-shared and solvent-separated ion pairs is not easily obtainable. Therefore, the designations solvent-shared and solvent-separated ion pairs are sometimes interchangeable. Eventually, further dissociation of the two ions leads to free, i.e. unpaired solvated ions with independent primary and secondary solvation shells. The circumstances under which contact, solvent-shared, and solvent-separated ion pairs can exist as thermodynamically distinct species in solution have been reviewed by Swarcz [138] and by Marcus [241],... 

Thus, whether molecules move off with an ion is determined by the stmggle between the thermal energy of the solution, which tends to take the water molecule away from the ion into the solvent bulk, and the attractive ion-dipole force. The larger the ion, the less hkely it is that the water molecule will remain with the ion during its darting hither and thither in solution. A sufficiently large ion doesn t have an adherent (i.e., primary) solvation shell, i.e.,= 0. 

Another matter concerns the time of reaction between a set of water molecules after an ion has just pushed its way into the middle of them. Thus, if the lifetime of molecules in the primary solvation shell is sufficiently short, there must be somejumps in which the ion is bare or at least only minimally clothed. How is the hydration number affected by the time needed for the solvent molecules buried in the solvent layer to break out of that attachment and rotate so that their dipoles are oriented toward the ion to maximize the energy of interaction (cos 0 = 1) ... 

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