Macroscopic polarization, dielectric

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). 

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. 

Since m is related to the macroscopic polarization P via m = Pv, where v is the volume of a water molecule, eqs A.l and A.4 provide the following expression for the macroscopic dielectric constant ... 

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. 

Now within a liquid dielectric all the molecules, at configurations t within the sphere V, have to be dealt with statistically, and the macroscopic polarization is obtained as a result of statistical averaging of the microscopic processes occurring in the sphere ... 

Macroscopic polarization P of a dielectric medium can be expanded to a power series of the applied field strength... 

R. Resta (1994) Macroscopic polarization in crystalline dielectrics the geometric phase approach. Rev. Mod. Phys. 66, pp. 899-915... 

When a dielectric material is submitted to a direct current (DC) field, the constituent permanent dipoles orientate to the field direction, and a macroscopic polarization is established. After an infinite polarization time, the polarization reaches its saturation value, P0, given, at low field, by... 

It has been realized since the mid-1800s that the presence of material interfaces in matter provides discontinuities for the travel of changes, and provides opportunities therefore for the delays in their travel in response to an applied field. This the experimenter would view as an electrical polarization. One would then assign to the system as a whole an apparent dielectric constant containing the effects of these macroscopic polarizations, and in addition to those due to the molecular modes discussed above. 

FIGURE 7.13. (a) Static hysteresis of macroscopic polarization P E) and (b) dielectric susceptibility x E) = dPjdE for an FLC cell. A14 is defined as the hysteresis width. 

Static dielectric constant and refractive index are the common parameters that represent the macroscopic polarity of the solvent medium. The measured static dielectric constants of several ILs are low (e=11.4-12.3 at 298 K) [51,52] and indicate that these media are much less polar than acetonitrile (f = 35.9 at 298 K) [53]. However, the experimental observations with ILs cannot be explained on the basis of the measured dielectric constants [54]. To understand the interaction of the solvent molecules with the solute molecules at the microscopic level in the solution, the solvent polarity is often expressed in terms of the microscopic solvent polarity parameter, . (30) [54], which is defined as... 

Dielectric spectroscopy, in the context of this system, deals with the interaction of an applied alternating electric field with the orientable dipoles in matter that account for polarizability. Macroscopic polarization is microsopically related to the dipole density of N permanent molecular dipoles of moment in a volume F. In low molecular weight molecules, the net dipole moment can... 

In semiconductor nanostructures, local field effects are mostly due to a surface charge polarization contribution, which is essentially a macroscopic classical term, that is very important in optical properties calculations. For instance, surface polarization is responsible for a strong optical anisotropy of elongated nanocrystals [36]. We can say that the one-particle contribution represents the optical properties of an isolated, stand-alone nanocrystal, the intrinsic properties due to the delocalized states and the quantum confinement effects. One-particle contributions do not take into account the influence of the external environment into the optical properties, such as the macroscopic polarization of the surface bonds. On the contrary, the methods beyond one-particle calculations, based on the inversion of the dielectric matrix or, as we will see below, a time-dependent tight-binding formulation, take into account more properly the influence of the external environment, in particular the charge transfer within the nanocrystals and at the surface. 

So-called atomic polarization arises from small displacements of atoms under the influence of the electric field at a frequency of approximately 10 Hz (optical infrared range). The atomic polarizability cannot be determined directly but is normally small compared to the electronic polarizability. Electronic and atomic polarization occur in all types of polymer, even polymers with no permanent dipole moments. Polymers with permanent dipoles show no macroscopic polarization in the absence of an external electric field. If an alternative electric field is applied and if the electric field frequency is sufficiently low with reference to the jump frequency of segments of the polymer, the dipoles orient in the field and the sample shows not only electronic and atomic polarization but also a dipolar polarization. DETA, which operates in a frequency range from 10 to 10 Hz, is used to monitor dipole reorientation induced by conformational changes. These are referred to as dielectric relaxation processes. 

The oscillating electric field of the light wave induces electric dipoles by the passage through a dielectric medium, which leads to a macroscopic electric polarization of the medium. In the case of less intensive light the dipole moments are linear and the resulting macroscopic polarization P is... 

The purpose of this Chapter is to describe the dielectric properties of liquid crystals, and relate them to the relevant molecular properties. In order to do this, account must be taken of the orientational order of liquid crystal molecules, their number density and any interactions between molecules which influence molecular properties. Dielectric properties measure the response of a charge-free system to an applied electric field, and are a probe of molecular polarizability and dipole moment. Interactions between dipoles are of long range, and cannot be discounted in the molecular interpretation of the dielectric properties of condensed fluids, and so the theories for these properties are more complicated than for magnetic or optical properties. The dielectric behavior of liquid crystals reflects the collective response of mesogens as well as their molecular properties, and there is a coupling between the macroscopic polarization and the molecular response through the internal electric field. Consequently, the molecular description of the dielectric properties of liquid crystals phases requires the specification of the internal electric field in anisotropic media which is difficult. 

We now turn to the changes that occur in the macroscopic structure of a liquid crystal due to a destabilization and reorientation of the director under direct action of an electric or magnetic field. The external field might be coupled either to the dielectric (diamagnetic) anisotropy (magnetically or electrically driven uniform Frederiks transition and periodic pattern formation) or to the macroscopic polarization (flexoelectric effect and ferroelectric switching) of the substance. The fluid is considered to be nonconductive. 

The response of an antiferroelectric is shown two diagrams below. The initial macroscopic polarization is zero, just as in a normal dielectric and the P- relation is linear at the beginning until, at a certain thresh-... 

In the meantime Debye, who the year before had been appointed professor of theoretical physics at the University of Zurich, in 1912 introduced the idea of polar molecules , i.e., molecules with a permanent electric dipole moment (at that time a hypothesis) and worked out a theory for the macroscopic polarization in analogy with Langevin s theory of paramagnetic substances. He found, however, that the interactions in condensed matter could lead to a permanent dielectric polarization, corresponding to a susceptibility tending to infinity for a certain temperature, which he... 

The dielectric permittivity is a macroscopic quantity it relates the external electric field E to the macroscopic polarization. 

LCPs are the hottest research topics in the field of liquid crystals because of their unusual properties. Among the LCPs, BCLCPs (Fig. 16.10) possess macroscopic polar order with a variety of useful properties, such as dielectric, piezo, and... 

Unfortunately, it is not always possible to obtain such closed expressions for 8 (a ) and F t), Consequently, a number of phenomenological descriptions of the complex dielectric constant and macroscopic polarization autocorrelation function have been proposed in the past to aid in the analytical description of experimental data. 

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