Dielectric constant molecular interpretation

We outline experimental results and provide theoretical interpretation of effect of adsorption of molecular oxygen and alkyl radicals in condensed media (water, proton-donor and aproton solvents) having different values of dielectric constant on electric conductivity of sensors. We have established that above parameter substantially affects the reversible changes of electric conductivity of a sensor in above media which are rigorously dependent on concentration of dissolved oxygen. 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

The next question to be discussed was already mentioned in Section 2.1, namely, since the electrostatic problem, with its sharp boundary and its homogeneous solvent dielectric constant, already represents a somewhat unrealistic idealization of the true molecular situation, how important is it to solve that problem by exact electrostatics We would answer that this is not essential. Although it presumably can t hurt to solve the electrostatics accurately, except perhaps by raising the computer time, it may be unnecessary to do so in order to represent the most essential physics, and a simpler model may be more manageable, more numerically stable, and even more interpretable. This is the motivation for the GB approximation and COSMO. 

When structural and dynamical information about the solvent molecules themselves is not of primary interest, the solute-solvent system may be made simpler by modeling the secondary subsystem as an infinite (usually isotropic) medium characterized by the same dielecttic constant as the bulk solvent, that is, a dielectric continuum. Theoretical interpretation of chemical reaction rates has a long history already. Until recently, however, only the chemical reactions of systems containing a few atoms in the gas phase could be studied using molecular quantum mechanics due to computational expense. Fortunately, very important advances have been made in the power of computer-simulation techniques for chemical reactions in the condensed phase, accompanied by an impressive progress in computer speed (Gonzalez-Lafont et al., 1996). 

The most familiar method of evaluating is by dielectric dispersion experiments, in which the real and imaginary parts of the complex dielectric constant over those of the solvent are determined as functions of frequency. It is the value of referring to the state of vacuum that can be correlated with the molecular structure of the solute. Polymers cannot be dispersed in the gaseous state. Furthermore, solvents effective for polypeptides are usually polar, and only approximate theories are presently available for the estimate of vacuum < 2> from dielectric measurements with polar solvents. Therefore the dipolar information about polypeptides is always beset with ambiguity in absolute magnitude as well as in interpretation. 

The proper choice of a solvent for a particular application depends on several factors, among which its physical properties are of prime importance. The solvent should first of all be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapour pressure, and their temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity also need to be considered. Electrical, optical and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant too. Furthermore, molecular characteristics, such as the size, surface area and volume, as well as orientational relaxation times have appreciable bearing on the applicability of a solvent or on the interpretation of solvent effects. These properties are discussed and presented in this Chapter. 

The structural interpretation of dielectric relaxation is a difficult problem in statistical thermodynamics. It can for many materials be approached by considering dipoles of molecular size whose orientation or magnitude fluctuates spontaneously, in thermal motion. The dielectric constant of the material as a whole is arrived at by way of these fluctuations but the theory is very difficult because of the electrostatic interaction between dipoles. In some ionic crystals the analysis in terms of dipoles is less fruitful than an analysis in terms of thermal vibrations. This also is a theoretically difficult task forming part of lattice dynamics. In still other materials relaxation is due to electrical conduction over paths of limited length. Here dielectric relaxation borders on semiconductor physics. 

Evaluation of solvent-sensitive properties requires well-defined referena i ran eis. A macroscopic parameter, dielectric constant, does not always give interpretable correlations of data. The first microscopic measure of solvent polarity, the Y-value, based on the solvolysis rate of t-butyl chloride, is particularly valuable for correlating solvolysis rates. Y-values are tedious to measure, somewhat complicated in physical basis, and characterizable for a limited number of solvents. The Z-value, based on the charge-transfer electronic transition of l-ethyl-4-carbomethoxy-pyridinium iodide , is easy to measure and had a readily understandable physical origin. However, non-polar solvent Z-values are difficult to obtain b use of low salt solubility. The Et(30)-value , is based on an intramolecular charge-transfer transition in a pyridinium phenol b ne which dissolves in almost all solvents. We have used the Er(30)-value in the studies of ANS derivatives as the measure of solvent polarity. Solvent polarity is what is measured by a particular technique and may refer to different summations of molecular properties in different cases. For this reason, only simple reference processes should be used to derive solvent parameters. 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

The assignment of the 610 nm absorption was based on the apphcation of continuum models of the F and Fj center [18]. In the continuum model of the F center the electron is bound to the vacancy by a potential of the form e jKr, where K is an effective dielectric constant for the material. The continuum model of the F2 center is based on the analogous assumption that the transitions of the Fj center can be interpreted in terms of transitions of a hydrogen molecular ion immersed in a dielectric medium. The energy levels of the center in this model are the eigenvalues of the Hamiltonian... 

Figure 5.1 is a graph illustrating the relative importance of the flux correction term G with respect to the free-molecular flux term Gq. It is graphed for ej[ = 2 and = 1 which correspond to 13.9 nm particles with dielectric constants k = < and K = 1.67, respectively. The argument e e is simply a measure of the Coulomb interaction which is independent of k. For a constant Coulomb potential e e, an increase in k corresponds to an increase in the turnover distances. Since collisions with neutrals increase in importance as the capture distance increases, the flux correction G must increase. The fact that, e.g., ( i/%)e =i ( l o e =2 but both have the same functional dependence upon can be interpreted o mean... 

An example of this type of approach is the recent study performed by Chialvo et al. [264], on the water local environment around species in the archetypal infinitely dilute NaCl aqueous solution i.e., Cl and H2O) at supercritical conditions. These authors determined the water properties within the ion s hydration shells, and compared them with the corresponding to the average local environment around any water molecule. These properties included the radial profiles for the water local density (and the resulting coordination numbers), the local pressure, the local electric field, and a measure of the local dielectric constant around the species Na, Cl and H2O, respectively. Their simulation results provide compelling evidence for the pronounced distortion of the water properties around the species in solution and suggest the need for unambiguous molecular-based interpretation of the local properties. 

The density difference between H2O and D2O can be used for the determination of the deuterium content of heavy water (Schatenstein 1960). It is interesting to note that the 10% difference in density is within 0.5% entirely due to the molecular weight difference. The molar volume of D2O is larger only by 0.34% and that of H2 0 is smaller by 0.15% than the molar volume of H2 0. The isotope effect on the dielectric constant and dipole moment is very small, which plays an important role in the interpretation of solvent isotope effects in aqueous systems (Van Hook 1975). 

In this expression e is the equilibrium dielectric constant while V is the volume of the sphere. The theoretical objective is to relate M to some molecular quantity. The earliest interpretation was in terms of molecular polarizability of the individual molecules in the sphere. This polarizability is due to the mobility of the electronic cloud that surrounds all atoms or molecules and is given by the Clausius-Mosotti equation ... 

As with the dynamic mechanical relaxations, it is also possible to check the dielectric behavior of the sample. In this case the thermal analysis is carried out measuring the dielectric constant, dissipation factor, loss index, and phase angle as a function of temperature and frequency. In order to see a dielectric effect, a dipole must be connected with the molecular motion. In this way dielectric relaxation may be more specific than DMA. A combination of DMA, dielectric measurements, and DSC is often needed for a detailed interpretation of the properties of the materials. ... 

A number of dielectric constant studies of organolithium compounds have been reported and interpreted without cognizance of the hexameric character of the lower molecular weight -alkyllithium compounds. Table VIII (35, 36, 37) lists the results of a number of dielectric constant studies the... 

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