Metal-solvent distance

The electrical double layer at Hg, Tl(Ga), In(Ga), and Ga/aliphatic alcohol (MeOH, EtOH) interfaces has been studied by impedance and streaming electrode methods.360,361 In both solvents the value ofis, was independent of cei (0.01 < cucio4 <0.25 M)and v. The Parsons-Zobel plots were linear, with /pz very close to unity. The differential capacity at metal nature, but at a = 0,C,-rises in the order Tl(Ga) < In(Ga) < Ga. Thus, as for other solvents,120 343 the interaction energy of MeOH and EtOH molecules with the surface increases in the given order of metals. The distance of closest approach of solvent molecules and other fundamental characteristics of Ga, In(Ga), Tl(Ga)/MeOH interfaces have been obtained by Emets etal.m... 

This was averaged over the total distribution of ionic and dipolar spheres in the solution phase. Parameters in the calculations were chosen to simulate the Hg/DMSO and Ga/DMSO interfaces, since the mean-spherical approximation, used for the charge and dipole distributions in the solution, is not suited to describe hydrogen-bonded solvents. Some parameters still had to be chosen arbitrarily. It was found that the calculated capacitance depended crucially on d, the metal-solution distance. However, the capacitance was always greater for Ga than for Hg, partly because of the different electron densities on the two metals and partly because d depends on the crystallographic radius. The importance of d is specific to these models, because the solution is supposed (perhaps incorrectly see above) to begin at some distance away from the jellium edge. 

For the metal in the electrochemical interface, one requires a model for the interaction between metal and electrolyte species. Most important in such a model are the terms which are responsible for establishing the metal-electrolyte distance, so that this distance can be calculated as a function of surface charge density. The most important such term is the repulsive pseudopotential interaction of metal electrons with the cores of solvent species, which affects the distribution of these electrons and how this distribution reacts to charging, as well as the metal-electrolyte distance. Although most calculations have used parameterized simple functional forms for this term, it can now be calculated correctly ab initio. 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

Hence, we see that Ch is determined primarily by the quantum-statistical properties of the metal-solvent systems rather than by the distance of solvent approach. The primitive local estimate gives an example when / is, indeed, of minor importance. Take a model of a film with low dielectric constant that separates an ideal metal and the bulk solvent ... 

The aforementioned diffuse-layer and discreteness-of-charge effects have been taken into consideration in the model proposed by Grahame and Parsons [26,250-252]. First, it was assumed (unlike in the Stern model) that the specifically adsorbed ions were located at the distance from the metal surface (in the inner Helmholtz plane ) ensuring their maximum bond strength, owing to the combination of forces of electrostatic and quantum-mechanical origins. It shows the need for the partial or even complete desolvation of the adsorbed species and its deep penetration into the compact layer. The position of this adsorption plane depends on all components of the system, metal, solvent, and adsorbed ion. 

Similar to Sect. 2.1.11.2, let us consider first the interaction of two charged species located at a small distance (atomic scale) from the metal-solvent interface. Once again, it turns out that the functional form of the U(R) dependence is only influenced by the same characteristic length, sLh, which had already appeared in Eq. (79) for the image potential, that is the product of the hulk dielectric constant of the solvent and the inverse value of the compact -layer capacitance, Eq. (80). 

From the results it would suggest that the chloroform-transition metal ion distance is relatively small and that the chloroform molecules is able to penetrate closer to the transition metal ion than any other of the solvents used. This is supported by X-ray studies(17) which show that when iron(III) dithiocarbamates are crystallized from chloroform solution in at least some of the compounds chloroform is complexed, the chloroform protons being bonded to the sulfur atoms of the dithiocarbamate ligands. 

In the treatment of Badiali et al. (1981) the jellium model of the metal electron system is used with the jellium edge being assumed to be a plane passing through the centers of surface atoms of the metal. Solvent molecules then lie in contact with the surface at a distance equal to the radii, T, of surface metal atoms and hence are separated from the jellium edge by a distance T. This is not an altogether realistic model and, in fact, does not take into account the "overspill effect associated with the wave function of the metal s electrons at the surface. Another problem is that the solvent is represented by an electron-repulsive dielectric continuum, little related to the properties of water dipoles which are involved at the Hg surface in aqueous systems that have mostly been experimentally studied in double-layer capacitance works. 

The rate and activation parameters for the intramolecular electron transfers from Os(II)(NH3)5 to Ru(III)(NH3)5 across oligoproline peptide bridges have been determined. The rate constants decrease from 3.1 x 10 s to 50 s as the number of proline units is increase from 1 to 4, and the metal-metal separation distance increases from 12 to 21 A. A time-correlated single photon counting method was employed to investigate the kinetics of the forward [ Ru(II)- Rh(III)] and reverse [Ru(III)<-Rh(II)] intramolecular electron transfer reactions within covalently linked Ru/Rh polypyridine complexes in aqueous, acetonitrile, and methanol solvents. The rate constants for the outer-sphere electron transfer reactions of [Ru(edta)pyz] and... 

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). 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

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