Molecular dipoles, dielectric

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

At lower frequencies, orientational polarization may occur if the glass contains permanent ionic or molecular dipoles, such as H2O or an Si—OH group, that can rotate or oscillate in the presence of an appHed electric field. Another source of orientational polarization at even lower frequencies is the oscillatory movement of mobile ions such as Na". The higher the amount of alkaH oxide in the glass, the higher the dielectric constant. When the movement of mobile charge carriers is obstmcted by a barrier, the accumulation of carriers at the interface leads to interfacial polarization. Interfacial polarization can occur in phase-separated glasses if the phases have different dielectric constants. 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

There is greatly renewed interest in electron solvation, due to improved laser technology. However it is apparent that a simple theoretical description such as implied by Eq. (9.15) would be inadequate. That equation assumes a continuum dielectric with a unique relaxation mechanism, such as molecular dipole rotation. There is evidence that structural effects are important, and there could be different mechanisms of relaxation operating simultaneously (Bagchi, 1989). Despite a great deal of theoretical work, there is as yet no good understanding of the evolution of free-ion yield in polar media. 

In the Onsager s SCRF model, the solute is placed in a cavity immersed in a continuous medium with a dielectric constant e. The molecular dipole of the solute induces a dipole in the solvent, which in turn interacts with the molecular dipole, leading to a net stabilization effect. 

According to the Kirkwood theory of polar dielectrics, simple relations (23) between molecular dipole moment vectors and the mean-square total dipole moment of water clusters can be used to compute the static dielectric constant of water. As the normalized mean-square total dipole moment increases towards unity, theory predicts decreases in the static dielectric constant. Since MD results indicate that the mean-square total dipole moment of interfacial water is greater than that for bulk water (48), the static dielectric... 

In summary, VH F demonstrates the same pattern of solvent dependence as does 2/h h. However, all the subtleties seem to be enhanced. Usually 2/H F decreases in solvents of higher dielectric strength, but an appropriate dipole orientation with respect to the H—C—F group can lead to the opposite result as is observed in vinyl fluoride. This situation is perhaps most likely to occur in mono-fluoro compounds where the fluorine is the principal contributor to the molecular dipole. In either case the electric field effect as postulated with the Pople expression for the contact term produces the correct prediction. 

An interesting observation should be made concerning the dependence of the physical properties on molecular cyclicity, since it will have a significant effect on the formulation of electrolytes for lithium ion cells. While all of the ethers, cyclic or acyclic, demonstrate similar moderate dielectric constants (2—7) and low viscosities (0.3—0.6 cP), cyclic and acyclic esters behave like two entirely different kinds of compounds in terms of dielectric constant and viscosity that is, all cyclic esters are uniformly polar (c = 40—90) and rather viscous rj = 1.7—2.0 cP), and all acyclic esters are weakly polar ( = 3—6) and fluid (77 = 0.4—0.7 cP). The origin for the effect of molecular cyclicity on the dielectric constant has been attributed to the intramolecular strain of the cyclic structures that favors the conformation of better alignment of molecular dipoles, while the more flexible and open structure of linear carbonates results in the mutual cancellation of these dipoles. 

The macroscopic polarization of the phase is given by equations 1 and 2, where Di is the number density of the ith conformation, jlj is the component of the molecular dipole normal to the tilt plane when the ith conformation of the molecule is oriented in the rotational minimum in the binding site, ROFj is the "rotational orientation factor", a number from zero to one reflecting the degree of rotational order for the ith conformation, and e is a complex and unmeasured dielectric constant of the medium (local field correction). 

The physical picture is now as illustrated in Fig. 9.1.1. The electric field associated with the molecular dipole (/lx) polarizes the dielectric medium (i.e., the solvent). This polarization of the solvent will give rise to an additional electric field (.Er) at the molecular dipole (in addition to the field created by the isolated molecular dipole). The field is called the reaction field of the dipole. The dipole and the field are parallel, i.e.,... 

By analogy with the the Onsager s theory, it is assumed that the response of the molecule to an external probing field can be expressed in terms of an external dipole moment fit, sum of the molecular dipole moment and the dipole moment arising from the molecule-induced dielectric polarization. Following ref. [8] and ref. [47],... 

The dielectric constant of the vaccum c(j is included in the susceptibility definitions as SI units are used throughout this work. The analogous definition can be applied to the microscopic polarization p of a molecule with the molecular dipole moment jli and the polarizabilities a,/3, and y instead of the static polarization P (0) and the susceptibilities y-P. 

Two bulk effects are considered in the following Sections ionic conductivity, and molecular dipole orientation. It is also necessary to introduce the so-called infinite-frequency dielectric polarization which provides the baseline against which to measure the other effects. The permittivity e is written schematically as... 

The situation is much more complicated in solids because the intermolecular effects can no longer be ignored, i.e. the approximation EM = 0 inherent in the simple formula for the local field (2.29) is not generally true. Consequently, although we can predict the molecular dipole moment from known group moments, it is not possible to calculate the molar polarisation and thereby the relative permittivity, without further elaboration of the dielectric model. In the case of a polymer there are further complications which arise from the flexibility of the long chains. 

Onsager derived an improved formula by adopting a better model for the calculation of the local field at a molecule. His model consists of a spherical cavity which is excised in the dielectric material and which is just large enough to accommodate one molecule. The molecular dipole is supposed to be a point dipole fj, at the centre of the sphere, radius a. Onsager then said that the local field operating on the dipole at the centre of the cavity could be resolved into two components, a cavity field G and a reaction field R ... 

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