Hydration sheath

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

The secondary hydration sheath has also been studied using vibrational spectroscopy. In the presence of... 

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

At each interface the interfacial potential will depend upon the chemical potentials of the species involved in the equilibrium. Thus at the Zn/Zn electrode there will be a tendency for zinc ions in the lattice to lose electrons and to pass across the interface and form hydrated ions in solution this tendency is given by the chemical potential of zinc which for pure zinc will be a constant. Similarly, there will be a tendency for hydrated Zn ions in solution to lose their hydration sheaths, to gain electrons and to enter the lattice of the metal this tendency is given by the chemical potential of the Zn ions, which is related to their activity. (See equation 20.155.) Thermodynamically... 

It has been suggested by Ikegami (1968) that the carboxylate groups of a polyacrylate chain are each surrounded by a primary local sphere of oriented water molecules, and that the polyacrylate chain itself is surrounded by a secondary sheath of water molecules. This secondary sheath is maintained as a result of the cooperative action of the charged functional groups on the backbone of the molecule. The monovalent ions Li", Na and are able to penetrate only this secondary hydration sheath, and thereby form a solvent-separated ion-pair, rather than a contact ion-pair. Divalent ions, such as Mg " or Ba +, cause a much greater disruption to the secondary hydration sheath. 

At the molecular level, a number of features are associated with the phenomenon of gelation or precipitation. In particular the disruption of the secondary hydration sheaths around the polyacrylate chains appears... 

Fig. 1.5 A scheme of hydration (1) cation, (2) primary hydration sheath (water molecules form a tetrahedron), (3) secondary hydration shell, (4) disorganized water, (5) normal water... 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

In general, complexation of an aquometal ion occurs when the ligand is a stronger base than H20, and analogously may be considered an acid-base reaction. The stability (or formation) constant, KMl, is used to describe the interaction of the metal ion (Mz+, shown here with the hydration sheath surrounding the metal ion omitted for reasons of clarity) with a complexant (L" ) ... 

Uptake measurements were made [16] at several oxide/solution ratios, reported as surface loading (SL) or m2 oxide surface/liter of solution, as PdCl, 2 concentration was increased and pH was held constant at the optimal value (Figure 6.10a). Each SL indeed indicated a plateau near the steric value [16], For Pt and Pd ammine cations, the maximum surface density over many oxides appears to be a close-packed layer, which retains two hydration sheaths representative results for PTA uptake over silica from a recent paper [19] are shown in Figure 6.10b. The physical limit of cationic ammine surface density thus appears to be 0.84 pmol/m2, or about 1 cationic complex/2 nm2. Cationic uptake, therefore, is inherently half of anion uptake in many cases. 

The retention of hydration sheaths upon adsorption is more consistent with an electrostatic view of adsorption than a chemical one, since by remaining a relatively large distance away from the surface, the metal complexes are less likely to participate in surface-ligand exchange. 

Figure 6.9 A depiction of CPA complexes retaining one hydration sheath adsorbing at a density of about one complex per nm2. (From Spieker, W.A., and Regalbuto, J.R., Chem. Eng. Sci. 56, 2000, 2365.)...

Electron density profile of the quartz-PTA interface. (From Park, C., Fenter, P, Sturchio, N., and Regalbuto, J.R., Phys. Rev. Lett. 94, 2005, 076104.) A schematic of PTA adsorbed with one or two hydration sheaths. 

The measured uptake of CPA and PTA over the three activated carbons [55] is shown in Figure 6.28, and the trends predicted by the RPA model in Figure 6.27 are at least qualitatively observed. However, at high pH, over the two highest-surface-area carbons (CA and KB), uptake is about half of that predicted by the RPA model. The discrepancy was explained [55] by steric exclusion of the large Pt ammine complexes, believed to retain two hydration sheaths [15,19], from the smallest micropores of the high-surface-area activated carbon. 

What would the maximum uptake density of (a) CPA and (b) PTA be if they adsorbed with no hydration sheath ... 

Surface complexation models attempt to represent on a molecular level realistic surface complexes e.g., models attempt to distinguish between inner- or outer-sphere surface complexes, i.e., those that lose portions of or retain their primary hydration sheath, respectively, in forming surface complexes. The type of bonding is also used to characterize different types of surface complexes e.g., a distinction between coordinative (sharing of electrons) or ionic bonding is often made. While surface coordination complexes are always inner-sphere, ion-pair complexes can be either inner- or outer-sphere. Representing model analogues to surface complexes has two parts stoichiometry and closeness of approach of metal ion to... 

The folding of proteins into their characteristic three-dimensional shape is governed primarily by noncovalent interactions. Hydrogen bonding governs the formation of a helices and [) sheets and bends, while hydrophobic effects tend to drive the association of nonpolar side chains. Hydrophobicity also helps to stabilize the overall compact native structure of a protein over its extended conformation in the denatured state, because of the release of water from the chain s hydration sheath as the protein... 

Huq, electrode kinetics, 1087 Hydration sheath. 871, 964, 1512 Hydrocarbon, electrooxydation, mechanism determination. 1152... 

The metal surface can be compared to a stage occupied by this excess-charge density qM. The particles of the solution constitute the audience that responds to the scene on the stage. The first row is largely occupied by water dipoles (Fig. 6.61). The excess charge on the metal produces a preferential orientation of the water dipoles. This is the hydration sheath of the electrode (see Chapter 2). The net orientation of the dipoles varies with the charge on the metal, and the dipoles can even turn around and look away from the electrode. 

The second row is largely reserved for solvated ions. The locus of centers of these solvated ions is called, for historical reasons, the outer Helmholtz plane, hereafter referred to as OHP (Fig. 6.61). On top of the first-row water (the primary water layer) and in between the solvated ions are other water molecules, a sort of secondaty hydration sheath, feebly bound to the electrode. 

Section 6.7.7 ended with an encouraging statement The contribution of the water dipoles constituting the hydration sheath of the electrode can be ignored in the understanding of the differential capacity of the electrified interface. Thus, if water molecules, in spite of their large number in the interfacial region, are not responsible for this property of the double layer, what is We also said that the total differential capacity of the interface could be divided into two contributions... 

The ion, wrapped in a primary hydration sheath, migrates up to the electrode. How close to the electrode can such a hydrated ion approach On its way to the electrode, the ion proceeds until its water molecules collide with the water molecules of the hydrated electrode. At this point, the electron shells of the water molecules of both sides start overlapping and repelling. The ions cannot pass over the guarding water molecules of the electrode and they have to remain in the second layer. The ions are not able to contact the electrode [Fig. 6.88(a)]. The plane drawn through the locus of centers of these hydrated ions is called the outer Helmholtz plane. 

One of these, electron transfer, actually occurs in the ideal definitional sense. It applies to the few overworked redox reactions where there is no adsorbed intermediate. The ion in a cathodic transfer is located in the interfacial region and receives an electron (ferric becomes ferrous) without the nucleus of the ion moving. Later (perhaps as much as 10-9 s later), a rearrangement of the hydration sheath completes itself because that for the newly produced ferrous ion in equilibrium differs (in equilibrium) substantially from that for the ferric. Now (even in the electron transfer case) the ion moves, but the definition remains intact because it moves after electron transfer. The amounts of such small movements (changes in the ion-solvent distance for Fe2+ and Fe3+ ions in equilibrium) are now known from EXAFS measurements. 

Next, let the focus be on one of the chosen ions, say, Fe3, and its hydration sheath (somewhat distorted by adsorption in the double layer). The energy levels in this ion at 300 K are predominantly in the ground state. Because the tunneling of the electron to the ion is taken to occur from the Fermi level of the metal and to be radiationless, the energy states in the ion are the ones of interest for electron transfer. This means that the electrons will be likely to find a home only in electronic states of the hydrated Fe3 ion, well above the ground state. 

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