Saturation dielectric

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

This perturbation method is claimed to be more efficient than the fluctuating dipole method, at least for certain water models [Alper and Levy 1989], but it is important to ensure that the polarisation (P) is linear in the electric field strength to avoid problems with dielectric saturation. 

The value of e ff for A-100 (3 with x = 100) is significantly lower than the dielectric constant of bulk water (e = 78), and it decreases further with decreasing charge density. This behavior is apparently ascribable to the hydrophobicity of the polymer backbone and also to the surface charge (dielectric saturation). 

The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed one-layer model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness b — r) and dielectric constant ej, immersed in the bulk solvent of dielectric constant ),. The thickness (b — r) of the solvent layer is taken as the solvent radius, and its dielectric constant ej is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by... 

Capacitance as a function of charge was calculated.79 The capacitance curves showed a single hump, near qM = 0, and leveled off for qM about 10 /xC/cm2 on either side of the potential of zero charge, due to the dielectric saturation of the dipole system. The limiting values of the capacitance increased with increasing electron density of the metal. The nonideality of the metal was shown to... 

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

Due to the finite size of the ions and the solvent molecules, the solution shows considerable structure at the interface, which is not accounted for in the simple Gouy-Chapman theory. The occurrence of a decrease of C from the maximum near the pzc is caused by dielectric saturation, which lowers the dielectric constant and hence the capacity for high surface-charge densities. 

Certain aspects of the solvent structural changes in regions near to the solute have received specialized attention and even inspired their own nomenclature. Two examples, each with a long and distinguished theoretical history, are the hydrophobic effect and dielectric saturation. ... 

Contributing to Ajj are, in addition to the solvent structural effects explicitly considered, contributions from dielectric saturation, from the liquid structure effects one has even in simple fluids, from solvent-mediated dispersion interactions of the ions, from charge-polarizability interactions of the ions, and so on. It is difficult to tell a-priori which effects are dominant or how big they are. However the collection of A 5 coefficients has characteristics that are consistent with the first named effect being dominant. 

Pore size and dielectric constant s of water in pores exhibit a strong effect on proton distributions, as studied in Eikerling. Model variants that take into account the effect of strongly reduced s near pore walls ° and the phenomenon of dielectric saturation ° 2° lead to nonmonotonous profiles in proton concentration with a maximum in the vicinity of the pore wall. 

Confinement of water into regions with dimensions of only a few nanometers, such as typically those found in PEMs, accompanied by a strong electrostatic field due to the anions, will result in a significantly lower dielectric constant for the water than that observed in bulk water. Measurement of this structural ordering of the water has not been accomplished experimentally to date, and this was the motivation to the recent calculation of the dielectric saturation of the water in PEMs with an equilibrium thermodynamical formulation. " In addition to information concerning the state of the water this modeling has provided information concerning the distribution of the dissociation protons in sulfonic acid-based PEMs. 

Fig. 2.3 A schematic representation of the hydration layer near a small ion (left) and a large ion (right), showing the region where the water is dielectrically saturated (with a low relative permittivity e ), hence electrostricted (squeezed) and immobilized. The thickness of this layer, Ar, depends reciprocally on the size of the ion.

A 20% error must be considered remarkably low considering that at least half the whole solvation energy (of 200 KCals/mole) theoretically comes from the first shell of solvent molecules because of the inverse dependence on distance in this first shell dielectric saturation and the short-range van der Waals forces must be considered even if specific covalent-bonds (as with "reactive solvents (43)) may be excluded. 

The Stern theory is difficult to apply quantitatively because several of the parameters it introduces into the picture of the double layer cannot be evaluated experimentally. For example, the dielectric constant of the water is probably considerably less in the Stern layer than it would be in bulk because the electric field is exceptionally high in this region. This effect is called dielectric saturation and has been measured for macroscopic systems, but it is difficult to know what value of e6 applies in the Stern layer. The constant K is also difficult to estimate quantitatively, principally because of the specific chemical interaction energy . Some calculations have been carried out, however, in which the various parameters in Equation (97) were systematically varied to examine the effect of these variations on the double layer. The following generalizations are based on these calculations ... 

Debye and Falkenhagen [92] also predicted that the permittivity of electrolyte solutions should increase as c,/2 where c is the ionic concentration. According to Hasted [105], such an effect has not been demonstrated experimentally, probably because the high conductivity of such solutions can mask permittivity changes. On the contrary, the permittivity of electrolyte solutions decreases with concentration [106] by 25—50% at lmoldm-3. This is probably associated with the binding of dipolar solvent molecules to ions, thus reducing the solvent orientational contri-butional to the permittivity (dielectric saturation). 

Consequently, while the effect of an electric field dependence of both drift mobility and diffusion coefficient and also hydrodynamic repulsion decreases, the recombination probability, dielectric saturation and relaxation effects increase the recombination probability. 

In equation (23), a and a2 are the molecular radii of the reactants and r the internuclear separation between them. For a self-exchange reaction where there is no change in coordination number, ai a2 = a, and if it is assumed that electron transfer occurs between the reactants in close contact, a1 + a2 = r which leads to equation (24). Equations (23) and (24) neglect specific contributions from individual solvent molecules such as hydrogen bonding and, also, possible dielectric saturation effects that may arise because of restricted rotations of solvent dipoles in the near vicinity of the electrostatic fields of the ions. 

Gavryushov, S. (2008). Electrostatics of B-DNA in NaCl and CaCD solutions Ion size, interionic correlation, and solvent dielectric saturation effects. J. Phys. Chem. B 112, 8955-8965. 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

The Mataga-Kakitani (M-K) theory is based on the rather general observation that e.t. processes which show the M.I.R. are mostly charge recombinations and charge shifts, whereas the photo-induced charge separations which start from neutral reactants follow Rehm-Weller behaviour. It is then suggested that the difference is due to the electric field which acts on the solvent in the field of ions or ion pairs, partial dielectric saturation of polar solvents would be reached, and this would restrict solvent motion. No such dielectric saturation effect would exist in the solvent shell of neutral reactants, so that solvent motion remains unhindered. 

The only evidence for this partial dielectric saturation of polar solvents in the field of ions is the results of some computer simulations of molecular dynamics, following the Monte-Carlo method [87], It is claimed that these show dielectric saturation up to a distance of about 1 A from the solute s molecular envelope. Such a thin shell does not accommodate a single solvent molecule and for this reason the dielectric saturation is called partial. 

The M-K theory of the role of dielectric saturation has led to many discussions and comments. In the first place, the occurrence of dielectric saturation is not established beyond doubt by molecular dynamics simulations even though these are sometimes described as computer experiments , they cannot replace actual observations of the natural world. The results of such simulations depend on the assumptions made in the model itself other authors claim that dielectric saturation becomes important only in the neighborhood of very small ions like Li+ in water, but that it is negligible in the solvent shell of the larger molecular ions involved in e.t. processes [88], At the present time, it appears therefore that no experimental... 

Irrespective of the occurrence of dielectric saturation, it has been questioned whether it would produce the desired result in any case, namely the distortion and displacement of the potential wells as suggested by the M-K theory [89]. Figure 13 shows an outline of the effect of dielectric saturation on the energy wells of an e.t. process, following the M - K model (a) and the objections of other authors. 

Fig. 13. Configuration coordinate diagram for the donor. The free energies E of the donor before and after electron transfer are shown as functions of the polarization P. The free energies of the neutral donor and the ion are shown by the parabolas denoted by X and Y, respectively. If one takes into account the dielectric saturation effect, these parabolas are modified as the curves denoted by X and Y, respectively. The parabola denoted by Y" is the free energy curve of the ion used in the Kakitani-Ma-taga model...

From an experimental standpoint, there is a further complication which does not seem to have been discussed within the framework of the M-K theory, namely the observations of the M.I.R. in nonpolar solvents. To take one example, the bell-shaped rate constant vs energy plot shown in Fig. 11 contains points which represent observations of the same e.t. processes in a nonpolar solvent (toluene) as well as a highly polar solvent. Dielectric saturation is usually described as being only of the orientational kind and no suggestion has been made that induction saturation in a nonpolar solvent could also take place. It is then difficult to see, following the M-K model, why a saturable polar solvent and a nonsaturable solvent should lead to similar behaviors with respect to the presence, or the absence, of the M.I.R. 

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