Macroscopic dipole moment, dielectric

A dielectric sample, when placed in an external electric field E, acquires a nonzero macroscopic dipole moment indicating that the dielectric is polarized under the influence of the field. The polarization P of the sample, or dipole density, can be presented in a very simple way ... 

The third mechanism has been suggested in [30]. The macroscopic dipole moment results from the gradient of the quadrupolar density. In addition to the usual dielectric term... 

Exposing a dielectric material to an electric field (E, D) always leads to polarization, i. e. a separation of electric charges forming a macroscopic dipole moment (Pe) characteristic to the system and the applied electric field (E, D) applied, cp. Fig. 6.8 ... 

For polymer chains a complicating feature is the presence of cross-correlation terms due to the angular correlations of dipole vectors along a chain (1,6,8). The dielectric increment Ae is a time-averaged (equilibrium) property of a system and may be expressed in terms of the fluctuations of the macroscopic dipole moment TJ(t) of a sphere of volume V according to the Kirkwood-Frohlich relation (1). 

P(co) is an internal field factor and A t) is a time-correlation function which represents the fluctuations of the macroscopic dipole moment of the volume V in time in the absence of an applied electric field. Equations (44) and (45) are a consequence of applying linear-response theory (Kubo-Callen-Green) to the case of dielectric relaxation, as was first described by Glarum in connexion with dipolar liquids. For the special case of flexible polymer chains of high molecular weight having intramolecular correlations between dipoles but no intermolecular correlations between dipoles of different chains we may write... 

However, when placed in an external electric field Eq, all dielectrics regardless of their molecular properties are polarized, i.e., becomes nonzero, the dielectric acquires a macroscopic dipole moment (Figure 4.20b). 

As the metallic particles are assumed to be sufficiently large for macroscopic dielectric theory to be applicable, we can substitute for a the expression for the polarisability of metallic particle immersed in an insulator. The dipole moment is given by the integration of the polarisation over the volume V. Thus, if the polarisation is uniform ... 

A macroscopic model for regular air/solution interfaces has been proposed by Koczorowski et al 1 The model is based on the Helmholtz formula for dipole layers using macroscopic quantities such as dielectric constants and dipole moments. The model quantitatively reproduces Ax values [Eq. (37)], but it needs improvement to account for lateral interaction effects. 

Without specifying the dimensions and spatial configuration of the solvation shell, we will treat it in terms of its macroscopic characteristic, like of other dielectric materials. First, consider a polar solution, in which the solutes possess a constant dipole moment as is shown in Fig. 4. In each solvate of a solution, the immediate surroundings are polarized due to the dipole moment, /[Pg.201]

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.

After these preliminary remarks, the term polarity appears to be used loosely to express the complex interplay of all types of solute-solvent interactions, i.e. nonspecific dielectric solute-solvent interactions and possible specific interactions such as hydrogen bonding. Therefore, polarity cannot be characterized by a single parameter, although the polarity of a solvent (or a microenvironment) is often associated with the static dielectric constant e (macroscopic quantity) or the dipole moment p of the solvent molecules (microscopic quantity). Such an oversimplification is unsatisfactory. 

It seems that there is a need to reexamine, some of the basic quantities used in transport processes, like Thiele numbers, attempting to connect them to more chemical quantities. For example, the macroscopic quantity, e the dielectric constant, can be interpreted in terms of dipole moment distribution, and the dipole moment has immediate structural implications. Now to talk of a dielectric constant in the interaction of two atoms would be a rather useless exercise, since the dilectric constant is a continuous matter concept, not a discrete matter concept. In the same... 

For practical purposes the solvent is described as a continuum, so that the dimensions of the solvent molecules do not appear explicitly in the interaction energy equations the permanent dipole moments and the polarizabilities of the solvent are expressed as functions of macroscopic properties which are the dielectric constant D and the refractive index n the interaction... 

Equations (1.3) and (1.4) describe the mean properties of the dielectric. This macroscopic point of view does not consider the microscopic origin of the polarization [3], The macroscopic polarization P is the sum of all the individual dipole moments pj of the material with the density Nj. 

The response of a medium to a macroscopic field E(t) generated by the superposition of a static and an optical component (E(f) = E° + E cos(< h)) is represented by the dielectric polarization vector (dipole moment per unit of volume) P(t) ... 

The OWB equations obtained in this semiclassical scheme analyse the effective polarizabilities in term of solvent effects on the polarizabilities of the isolated molecules. Three main effects arise due to (a) a contribution from the static reaction field which results in a solute polarizability, different from that of the isolated molecules, (b) a coupling between the induced dipole moments and the dielectric medium, represented by the reaction field factors FR n, (c) the boundary of the cavity which modifies the cavity field with respect the macroscopic field in the medium (the Maxwell field) and this effect is represented by the cavity field factors /c,n. 

The dielectric constant is a macroscopic property of the material and arises from collective effects where each part of the ensemble contributes. In terms of a set of molecules it is necessary to consider the microscopic properties such as the polarizability and the dipole moment. A single molecule can be modeled as a distribution of charges in space or as the spatial distribution of a polarization field. This polarization field can be expanded in its moments, which results in the multipole expansion with dipolar, quadrupolar, octopolar and so on terms. In most cases the expansion can be truncated to the first term, which is known as the dipole approximation. Since the dipole moment is an observable, it can be described mathematically as an operator. The dipole moment operator can describe transitions between states (as the transition dipole moment operator and, as such, is important in spectroscopy) or within a state where it represents the associated dipole moment. This operator describes the interaction between a molecule and its environment and, as a result, our understanding of energy transfer. 

For vapors, the local field vanishes because of the spherical symmetry and eqs A.5 and A.6 provide good agreement with experiment. However, for liquids one can no longer use eq A.6 for the polarizability in the Lorentz— Debye model. Indeed, for liquid water, eq A.5 diverges for values of y about 4 times smaller than the value of y for its vapor, which at 300 K is y = ye 4 yd = 32.3 x 10 40 C2 m2 J "1. One can regard eq A.5 as the definition of the molecular polarizability and calculate y in terms of the macroscopic dielectric constant e. The lower value of the polarizability in liquid than in vapor can be explained in the framework of the Lorentz—Debye model by the hindered rotation of the permanent dipole moment by the neighboring molecules in the condensed state. 

The van der Waals force is ubiquitous in colloidal dispersions and between like materials, always attractive and therefore the most common cause of dispersion destabilization. In its most common form, intermolecular van der Waals attraction originates from the correlation, which arises between the instantaneous dipole moment of any atom and the dipole moment induced in neighbouring atoms. On this macroscopic scale, the interaction becomes a many-body problem where allowed modes of the electromagnetic field are limited to specific frequencies by geometry and the dielectric properties of the system. 

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