Dielectrics, Onsager theory

Dielectrics, Onsager theory of, 103 Dienophile, oxygen as a, 248, 252 Diffusion, coefficient, 170... 

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

Figure 7 shows the temperature dependence of the dissociation yield of geminate pairs with an initial separation distance rQ = 24 A and a = 0.10 eV. The dielectric constant was 3.5 and the field 104 V/cm. The dashed line represents predictions of the three-dimensional Onsager (1938) theory. It is obvious that disorder increases 7]/%, particularly at low temperatures. Figure 8 shows the variation of 7j/7j0 with a, assuming e = 3.5 and T = 250 K. The datum for a = 0 is the value obtained from the conventional Onsager theory. 

The Onsager theory was first successfully applied to the static permittivities of electrolyte solutions by Ritson and Hasted, who showed that almost the entire depression of the pemuttiidty arises from the region lying between two spheres, of radius 2 and 4 A, centred on the ion. Dielectric deorements were calculated, and in a subsequent paper plausible hydration numbers were obtained. In their calculation a discontinuous model was used, with the assumption that the first sheath of water molecules was fiilly saturated, i.e. oriented to a (positive) ion. 

The spectral position of absorption and fluorescence are influenced by the dielectric properties of the medium in which observations are made. Figure 5 shows that the vapour phase 0-0 bands in absorption and fluorescence of a molecule are identical, whereas in solution with solvent of static dielectric constant e, refractive index n, the bands are no longer coincident. The differences can be rationalized as follows. From Onsager theory, a solute molecule of dipole moment ju in a spherical cavity of radius a polarizes the dielectric of the solvent, producing a reaction field. This is given for the ground-state of the solute molecule (of dipole moment iiq), by (22). Upon excitation, and invoking the Franck-Condon principle, the electronic excitation is much more rapid than the dielectric relaxation time of... 

In the classical reaction-field model, the solute molecule is considered embedded in a cavity inside a homogeneous dielectric medium. From the Onsager theory (Onsager, 1936) the electronic reaction field at the center of the solute molecule is given by... 

The traditional treatment regarding medium effects is the dielectric continuum model in the Kirkwood-Onsager theory [76]. This simple model assumes that the solvation energy arises from the electrostatic interaction between the solutes and... 

In contrast to diamagnetism where the magnetic interactions between molecules can be neglected, the polarization field in the medium becomes important when discussing dielectric anisotropy (see, e.g., Bottcher< >). Maier and Meier > took this into account by applying the Onsager theory.The effective induced dipole moments per molecule along and... 

The Onsager theory considers two potentials determining the fate of an electron/hole pair the Coulomb potential e /er (e=dielectric constant) and the thermal energy kT. Pairs having a radial distance r larger than tc will escape recombination. At the critical radial distance r, the thermal energy is equal to the Coulomb potential [see Eq. (2-5)]. 

In order to derive equations for the dielectric components, the authors used similar simplifications as in the Onsager theory. 

Maier and Meier [35] worked out these ideas more quantitatively by applying Onsager s theory of static polarization for nematic liquid crystals. The Onsager theory relates the dielectric constant to molecular properties, namely the molecular polarizability a and the permanent electrical dipole moment /i. In the case of nematic liquid crystals, however, the polarizability has to be treated as a tensor with principal values an and a and an angle ]8 has to be introduced to describe the... 

The external static electric field applied to a dielectric material induces fire polarisation P, that is the dipole moment per unit volume. For low fields P is prt rtional to the electric field E [1>3], P = 8o(8s - 1) E, where 8s is the relative dielectric permittivity or dielectric constant and 8o is the dielectric permittivity of free space. All these quantities concom the macroscopic volume of the dielectric medium. In order to relate them to the relevant microscopic param ers (for example dipole moment and polarisability) the local electric field Eioc acting on a molecule must be known. The relation between Eioc and E is the crucial problem of the physics of dielectrics and has not been solved in general. For isotropic fluids the Onsager theory is commonly used [4]. 

In the Onsager theory of isotropic dielectrics as well as in its extension to the nematic phase given by Maier and Meier the short range dipole-dipole correlations w e ignored. Therefore the dipole moment p in EQNS (1) - (3) cannot be identified with its value measured in the state [16]. The dipole-dipole correlations were considered in the theory developed by Frdtdich [17] who generalised the former Kirkwood approach [18]. Frdhlich has introduced the dipole-dipole correlation factor (known as the Frdhlich-Kirkwood g-factor) in the form... 

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). 

The solvent effects on charge-transfer spectra between Me3Sn-NCS and I2 was investigated. Onsager s theory of dielectrics was used to estimate the stabilisation energy of excited states257. 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

Historically, one of the central research areas in physical chemistry has been the study of transport phenomena in electrolyte solutions. A triumph of nonequilibrium statistical mechanics has been the Debye—Hiickel—Onsager—Falkenhagen theory, where ions are treated as Brownian particles in a continuum dielectric solvent interacting through Cou-lombic forces. Because the ions are under continuous motion, the frictional force on a given ion is proportional to its velocity. The proportionality constant is the friction coefficient and has been intensely studied, both experimentally and theoretically, for almost 100... 

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