Solvent bulk dielectric constants

Table 8-2 lists several physical properties pertinent to our concern with the effects of solvents on rates for 40 common solvents. The dielectric constant e is a measure of the ability of the solvent to separate charges it is defined as the ratio of the electric permittivity of the solvent to the permittivity of the vacuum. (Because physicists use the symbol e for permittivity, some authors use D for dielectric constant.) Evidently e is dimensionless. The dielectric constant is the property most often associated with the polarity of a solvent in Table 8-2 the solvents are listed in order of increasing dielectric constant, and it is evident that, with a few exceptions, this ranking accords fairly well with chemical intuition. The dielectric constant is a bulk property. 

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... 

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 considerable volume of literature has accumulated on conductance measurements in mixtures of solvents. Ion mobilities and association constants have been measured over a range of bulk dielectric constants with the aim of correlating bulk solvent properties with mobilities, ion association, and ion size parameters. An example of a widely used solvent mixture is water and 1,4-dioxane, which are miscible over all concentrations, providing a dielectric constant range of 2 to 78. The data obtained in systems containing two or more solvents must be treated with circumspection, as one solvent may interact more strongly with a given species present in solution than the other, and the re-... 

A great variety of aqueous—organic mixtures can be used. Most of them are listed in Table I with their respective freezing point and the temperature at which their bulk dielectric constant (D) equals that of pure water. These mixtures have physicochemical properties differing from those of an aqueous solution at normal temperature, but some of these differences can be compensated for. For example, the dielectric constant varies upon addition of cosolvent and cooling of the mixture in such a way that cooled mixed solvents can be prepared which keep D at is original value in water and are isodielectric with water at any selected temperature (Travers and Douzou, 1970, 1974). 

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]. 

Most continuum models are properly referred to as equilibrium solvation models. This appellation emphasizes that the design of the model is predicated on equilibrium properties of the solvent, such as the bulk dielectric constant, for instance. The amount of time required for a solvent to equilibrate to the sudden introduction of a solute (i.e., the solvent relaxation time) varies from one solvent to another, but typically is in the range of molecular vibrational and rotational timescales, which is to say on the order of picoseconds. 

Here, T is the absolute temperature, e is the bulk dielectric constant of the solvent, P is the number of phosphate charges, k is the inverse of the Debye screening length, kB is the Boltzmann constant, qna is the renormalized charge, the interaction between the charges is screened Debye-Hiickel potential, and — j b is the distance between a pair of charges labeled i and /... 

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. 

Figures 2 and 3 represent typical plots of E (= Eobs + 2RT/F In m) vs. ra in mixed solvents with a low (8.68%) and a high (89.00%) proportion of organic component (10,11,12,13). The pronounced increase in the curvature of the plots with increased organic component (decreased bulk dielectric constant) is quite obvious.

Incidentally, such plots (Figure 4) may be used to compute approximate values of the bulk dielectric constants of water-organic mixed solvents from the emf measurements provided that the bulk dielectric constant is higher than 40. In fact, for auto-ionizing solvents this may be a convenient method, and our calculations have shown that such computed values are within 5-7% of the experimental values. 

Table II. Standard Potentials (Molal Scale) of Cell I and the Bulk Dielectric Constants of the Solvents"...

The work and results reported in Part I led us to believe that the first-order coulombic interactions among the ions and the ions and the solvent molecules are the significant interactions in solvents of bulk dielectric constant 40 or higher. This in turn led us to believe that a simple electrostatic model might be used for generating functions that would correlate the ionization processes in two solvents both of moderate bulk dielectric constants. 

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... 

Our primary objective was to develop a computational technique which would correlate the ionization constant of a weak electrolyte (e.g., weak acid, ionic complexes) in water and the ionization constant of the same electrolyte in a mixed-aqueous solvent. Consideration of Equations 8, 22, and 28 suggested that plots of experimental pKa vs. some linear combination of the reciprocals of bulk dielectric constants of the two solvents might yield the desirable functions. However, an acceptable plot should have the following properties it should be continuous without any maximum or minimum the plot should include the pKa values of an acid for as many systems as possible and the plot should be preferably linear. The empirical equation that fits this plot would be the function sought. Furthermore, the function should be analogous to some theoretical model so that a physical interpretation of the ionization process is still possible. 

Through a series of parametrization, the most suitable linear combination was (1/c — 1/c") where c = c + (c — corg), = 2c — c0rg, = bulk dielectric constant of the mixed solvent, corg = bulk dielectric constant of the pure organic component, and c = bulk dielectric constant of water. (The dielectric constant data were obtained from literature these references are not being cited in order to save space. Some of the c values were obtained by these authors by interpolation. For the convenience of the reader we have compiled the values of bulk... 

Table V. Bulk Dielectric Constants of Some Pure Solvents at 25°C...

D = bulk dielectric constant of the solvent in the first part of the chapter DH — Debye-Hiickel... 

The difference between the electrostatic effect calculated using the bulk dielectric constant and that calculated taking account of local structural factors is sometimes called dielectric saturation, although it has been suggested that a better phrase would be inhomogeneous dielectric constant. We refer to the sum of these first-hydration-shell effects as the CDS term, representing structural rearrangements that entail cavitation, dispersion, and solvent disposition. 

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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