Bulk dielectric media

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

The hydration energy of the ion can be treated in terms of the ion s self-energy in the bulk dielectric medium diminished by the energy that would have been associated with the region of bulk solvent unavailable to the ion beyond the nearby surface of liquid, but to which is added the charging energy associated with the same volume in the free space above the liquid where c = 1. 

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

If the solute were simply a collection of point charges surrounded by a continuous dielectric medium with the bulk dielectric constant of the solvent, the self-energy and the strength of charge-charge interactions in the solute would be reduced by a factor of . This is called dielectric screening. However, the solute itself occupies a finite volume, and solvent is excluded from this volume. This reduces the dielectric screening and is called... 

A subject not treated here is the use of distance-dependent effective dielectric constants as a way to take account of the structure in the dielectric medium when a solute is present. This subject has recently been reviewed [120], In the approaches covered in the present chapter, deviations of the effective dielectric constant from the bulk value may be included in terms of physical effects in the first solvation shell, as discussed in Section 2.2. 

Theoretical treatment of the femtosecond pulse propagation in a bulk Kerr medium with the dispersion of dielectric permittivity was based on the... 

It is well known that a solvent can canse dramatic changes in rates and even mechanisms of chemical reactions. Modem theoretical chemistry makes it possible to incorporate solvent effects into calcnlations of the potential energy surface in the framework of the continnnm and explicit solvent models. In the former, a solvent is represented by a homogeneous medium with a bulk dielectric constant. The second model reflects specific molecule-solvent interactions. Finally, calculations of the potential energy surface in the presence or absence of solvents can be performed at various theory levels that have been considered in detail by Zieger and Autschbach [10]. 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

In more recent work, Johnston and co-workers (17,18,20,27,32) showed quantitatively that the local fluid density about the solute is greater than the bulk density. In these papers, results were presented for CQ2, C2H4, CF3H, and CF3C1. Local densities were recovered by comparison of the observed spectral shift (or position) to that expected for a homogeneous polarizable dielectric medium. Clustering manifests itself in deviation from the expected linear McRae continuum model (17,18,20,27,32,56,57). These data were subsequently interpreted using an expression derived from Kirkwood-Buff solution theory (20). Detailed theoretical... 

Figure 3.1 shows a simplified picture of an interface. It consists of a multilayer geometry where the surface layer of thickness d lies between two centrosymmetric media (1 and 2) which have two different linear dielectric constants e, and e2, respectively. When a monochromatic plane wave at frequency co is incident from medium 1, it induces a nonlinear source polarization in the surface layer and in the bulk of medium 2. This source polarization then radiates, and harmonic waves at 2 to emanate from the boundary in both the reflected and transmitted directions. In this model, medium 1 is assumed to be linear. 

Electrostatics is certainly the most important interaction between a dielectric medium and a molecular species. Therefore, it has also been investigated extensively for interfaces as shown in the previous section. Nonelectrostatic forces are often neglected in the bulk solution since their contribution to the solvation energy is often limited because of reciprocal cancellation and their effect on molecular properties is small [16] (repulsion and particularly dispersion) or zero (the present understanding of cavitation is strictly empirical). 

The solvation free energy calculated by considering only the bulk electrostatics is somewhat arbitrary because the boundary between the dielectric medium and the solute is not well defined, and in fact the treatment of the solvent as a homogeneous, isotropic, linear medium right up to a definite boundary is not valid. To obtain an accurate solvation... 

While the field produced by remote dipoles can be treated as screened by a medium with a large dielectric constant (e = 80), the screening of the neighboring dipoles is much weaker. In the present treatment, we will simply assume that Elocal is produced only by the dipoles located within a radius 21 from the given site and that the dielectric constant for them is a constant e". The electric field caused by a neighboring molecule is given by eq 17 (with e" replacing e ). It is important to emphasize that the local dielectric constant e" is smaller than e, the bulk dielectric constant of water. 

Not to be forgotten is the assumption that neither the presence of the electrolyte nor the interface itself changes the dielectric medium properties of the aqueous phase. It is assumed to behave as a dielectric continuum with a constant relative dielectric permittivity equal to the value of the bulk phase. The electrolyte is presumed to be made up of point charges, i.e. ions with no size, and responds to the presence of the charged interface in a competitive way described by statistical mechanics. Counterions are drawn to the surface by electrostatic attraction while thermal fluctuations tend to disperse them into solution, surface co-ions are repelled electrostatically and also tend to be dispersed by thermal motion, but are attracted to the accumulated cluster of counterions found near the surface. The end result of this electrical-thermodynamic conflict is an ion distribution which can be represented (approximately) by a Boltzmann distribution dependent on the average electrostatic potential at an arbitrary point multiplied by the valency of individual species, v/. 

For a homogeneous dielectric medium, in the absence of interface effects (see Sect. 3.2), the experimental quantities sx and e" are equal to the bulk properties e and e", and the experimental loss tangent becomes... 

Current efforts in quantum-chemical modeling of the influence of solvents may be divided into two distinct approaches. The first, the supermolecular approximation, involves the explicit consideration of solvent molecules in quantum-chemical calculations. Another possibility for simulating solvent influence is to replace the explicit solvent molecules with a continuous medium having a bulk dielectric constant. Models of this type are usually referred to as polarized continuum models (PCMs). 

The reactivity ratios observed are markedly different in polar and nonpolar solvents. These differences appear to be determined mainly by the nature of the solvation at the active chain end. Most of the change occurs at quite low concentrations of polar solvent in a primarily hydrocarbon medium hence, the bulk dielectric constant of the solution is not an important factor under conditions where most of the reaction is carried by ion pairs. In solvents such as tetrahydrofuran it might be possible to detect changes in reactivity ratios at different concentrations of active polymer chains as the proportion of free anions increases with dilution. No experiments have been reported yet to check this point. 

Several theoretical models have been proposed (31) to rationalize the ionization process in a dielectric medium and to interpret the experimental data (32). Despite serious criticisms (32), the so-called Bom electrostatic model, in the opinion of these authors, is perhaps still the best model. According to this model the free energy change for the ionization of a weak acid in a solvent of bulk dielectric constant c is given by the equation... 

The solvent also acts as a dielectric medium, which determines the field diji/dx and the energy of Interaction between charges. Now, the dielectric constant e depends on the inherent properties of the molecules (mainly their permanent dipole moment and polarizability) and on the structure of the solvent as a whole. Water is unique in this sense. It is highly associated in the liquid phase and so has a dielectric constant of 78 (at 25 C), which is much higher than that expected from the properties of the individual molecules. When it is adsorbed on the surface of an electrode, inside the compact double layer, the structure of bulk water is destroyed and the molecules are essentially immobilized... 

An alternative simulation procedure is to replace the explicit solvent molecules with a continuous medium having the bulk dielectric constant. - " Once the solvent has been simplified, it is much easier to employ quantum mechanical techniques for the ENP relaxation of electronic and molecular structure in solution thus this approach is complementary to simulation insofar as it typically focuses on the response of the solute to the solvent. Since the properties of the continuum solvent must represent an average over solvent configurations, such approaches are most accurately described as quantum statistical models. 

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