Dielectric saturation model

Dielectric-saturation models attribute the hydration repulsion to the presence of a layer with lower dielectric constant, e, in the vicinity of the interfaces. Models with a stepwise [584,585] and continuous [586] variation of e have been proposed. 

Jayaram et al. performed a systematic study of the effects of electrostatic interactions on the counterion condensation around DNA. They used a 20-mer of electrically neutral sodium-DNA, with the DNA fixed in its canonical B form. The mobile counterions were placed randomly in a 50 A radius cylinder around the DNA, and the solvent was modeled as a dielectric continuum. Four dielectric treatments, ranging from Coulombic interactions with constant dielectric to a dielectric saturation model with a modified Coulombic potential introducing dielectric discontinuity, were studied. The dielectric saturation model used a modified Hingerty sigmoidal function... 

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 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... 

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. 

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 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. 

In spite of the remarkable difficulty in defining a detailed model, the number of computational codes introducing dielectric nonlinearity, especially in the form of dielectric saturation, is quite abundant. We quote here the main approaches more details can be found in the already quoted review [8],... 

This model has been, and still is, widely used especially for some specific applications. An older use is in the description of dielectric saturation effects around ions. The origin is the Debye model, not completely satisfying and thus subjected over the years to many variants. The spherical symmetry of the problem suggests the use of a distance dependent function s(r). The functions belonging to this family are often called sigmoidal functions because their spatial profile starts from a low value and increases monotonically to reach... 

These theories based on simple electrostatic models, however, do not always predict well the experimental data, because they have some problems regarding the effects of ion solvation on the value a and of the dielectric saturation on e. See also -> association constant. 

Some of the facts that Hasted et al. established are shown in Table 2.11, They found that the lowering of the dieleetrie eonstant of 1 M solutions is in the range of 10-20%. This ean be nieely explained by taking the water in eontaet with the ion as dielectrically saturated (unable to orient on the demand of the external field), but still having a dieleetrie eonstant of only 6, eompared with the value of 80 for bulk water unaffected by ions. The table shows the number of water moleeules pa ion pair that one has to assume are saturated (i.e., irrotationally bound in the vicinity of each ion) to make the above model come out right (i.e., reproduce the measured dieleetrie constants of solutions). This model leads to a very simple equation for the dielectric constant of a solution ... 

Figure 1.6 Variation of the dissociation coefficient Eq. (1.5) of reaction Eq. (1.3) with temperature along the water saturation curve, as described by a dielectric continuum model. R = 1.987 cal moF here is the gas constant. SeePaddison etal. (2001).

Permittivity variations in a strong electric field non-linear and saturation behaviour progress of e gperimental methods molecular behaviour and various theoretical models molecular correlations complete dielectric saturation electrostriction and electrocaloric effect. 

Flgare 20 Graphs of dielectric saturation correlation factors, (i) B Z) calculated from formula (304) for the rotational isomerism model with Z = U/kT Oi) R Z) calculate from formula (307) for internal rotation, with Z = UJkT. In ather case an invasion in sign of is found to occur very rapUily with... 

The electrostatic term GENP is accompanied by a second term GCDS which, as the acronym indicates, collects cavitation, dispersion, and solvent structure contributions, the latter regarding dielectric saturation and other reorganization effects, when present. GCDS is modeled in terms of an interfacial atomic surface tension term, <7fc, and of the parameter Ak giving the solvent-accessible surface area for atom k ... 

The Fuoss estimate of is based on a more reasonable model than that of Bjerrum and therefore is preferred. However, there are also problems with the Fuoss treatment in so far as it considers the solvent to be a dielectric continuum. Dielectric saturation effects are expected to be important, especially near the ions involved in ion pair formation. The second problem relates to the choice of the effective size for the ions. In the calculation made here the value of a for MgS04 was chosen to be much bigger than the crystallographic radius of Mg. This presumably is because the cation is strongly hydrated in aqueous solution. One is then faced with the question whether the ion pair involves contact of the two ions or whether it is better considered to be a species in which the two ions are separated by at least one water molecule. These questions can only be properly resolved using other experimental methods. 

The Born model certainly overestimates the solvation term at static frequencies. Using the MSA to account for the effects of dielectric saturation, equation (7.8.32) can be rewritten as... 

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