Dielectric saturation effects

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 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. 

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...

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... 

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]. 

It may be remarked that large polyatomic ions will exhibit only very small dielectric saturation effects, but will contribute to the dielectric decrement by reason of thdr large volume. Such ions, of volume fraction v and zero dipole moment, have been treated " by the mixture relation of... 

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. 

Paunov, V.N., R.I. Dimova, P.A. Kralchevsky, G. Broze, and A. Mehreteab. 1996. The hydration repulsion between charged surfaces as an interplay of volume exclusion and dielectric saturation effects. J. Colloid Interface Sci. 182 239—248. 

The field dependence of the dielectric constant is known as the dielectric saturation effect (DSE), and in an unassociated medium A e/E2 increases linearly with concentration. Malecki (20) has found that in alcohol solutions considerable nonlinearities occur—positive saturation is obtained at low concentrations and negative at high concentrations. This behavior is interpreted according to the theory of Piekara (22), and for 1-hexanol in hexane Malecki shows that the degree of association increases with increasing concentration. 

When the Born treatments of Gibbs energies and entropies of hydration of ions are modified by taking into consideration these dielectric saturation effects, the agreement with experiment is considerably better. The experimental values in Figure 7,1 are consistent with a dielectric constant of somewhat less than the true value of 78 ... 

In the derivation of this term the solvent distribution is assumed to be uniform (but it is possible to extend the method to non uniform distributions, to describe e.g. dielectric saturation effects for cations [19], and electrostriction effects for supercritical liquids [20, 21]), and the response function is modeled in terms of a matrix partitioning approach to the calculation of intermolecular potentials [22]. With the aid of a formal re-elaboration of the whole model, and by introducing a few reasonable approximations, the related matrix is reduced to the following form ... 

Multivalent Mn ions induce dielectric saturation effects in the polar region of the reaction center of PS II, which reduces the reorganization energy of the medium during charge transfer. 

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