Polarization macroscopic

A paraelectric substance is not polarized macroscopically because the dipoles are oriented randomly. However, they can be oriented by an external electric field (orientation polarization). The orientation is counteracted by thermal motion, i.e. the degree of polarization decreases with increasing temperature. 

For the measurements presented in Fig. 18, the smectic-C material FLCEl.l (see Table 1), was crosslinked inside a commercial EHC glass cell with an electrode gap of 10 pm. Deformation of the cell with a force of 1 N induces a charge of 6 pC/cm [36]. The magnitude of this value should be compared to the macroscopic spontaneous polarization (macroscopic dipole moment) of the FLC under investigation. For the uncrosslinked FLC, P values of 40-60 nC/cm have been observed [36]. Thus, if a full reversal of the orientation of P could be induced by... 

In the previous sections we have described the interaction of the electromagnetic field with matter, that is, tlie way the material is affected by the presence of the field. But there is a second, reciprocal perspective the excitation of the material by the electromagnetic field generates a dipole (polarization) where none existed previously. Over a sample of finite size this dipole is macroscopic, and serves as a new source tenu in Maxwell s equations. For weak fields, the source tenu, P, is linear in the field strength. Thus,... 

For stronger fields the relationship between the macroscopic polarization and the incident field is non-linear. The general relation between P and E is written as... 

As implied by the trace expression for the macroscopic optical polarization, the macroscopic electrical susceptibility tensor at any order can be written in temis of an ensemble average over the microscopic nonlmear polarizability tensors of the individual constituents. 

This is followed by two field actions which again create a vibrational coherence but, now, with opposite phase to the first coherence. Hence one obtains a partial rephasing, or echo, of the macroscopic polarization. The final field action creates the seventh order optical polarization which launches the signal field (the eighth field). Just as for the spin echo in NMR or the electronic echo in 4WM, the degree of rephasing (tlie... 

Another important class of materials which can be successfiilly described by mesoscopic and contimiiim models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different enviromnents. Lipid molecules, for instance, comprise a polar head that likes an aqueous enviromnent and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

An alternative approach to obtaining microwave spectroscopy is Fourier transfonn microwave (FTMW) spectroscopy in a molecular beam [10], This may be considered as the microwave analogue of Fourier transfonn NMR spectroscopy. The molecular beam passes into a Fabry-Perot cavity, where it is subjected to a short microwave pulse (of a few milliseconds duration). This creates a macroscopic polarization of the molecules. After the microwave pulse, the time-domain signal due to coherent emission by the polarized molecules is detected and Fourier transfonned to obtain the microwave spectmm. 

By extending some previous heuristic proposal [238,239], the phase in the polarized state of a ID solid of macroscopic length L was expressed in [240] as... 

Further subclassification of nonlinear optical materials can be explained by the foUowiag two equations of microscopic, ie, atomic or molecular, polarization,, and macroscopic polarization, P, as power series ia the appHed electric field, E (disregarding quadmpolar terms which are unimportant for device appHcations) ... 

The continuum electrostatic approximation is based on the assumption that the solvent polarization density of the solvent at a position r in space is linearly related to the total local electric field at that position. The Poisson equation for macroscopic continuum media... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

The macroscopic optical analysis of these effects requires the introduction of two complex indexes of refraction for the ferromagnetic material, one for lefr-circu-larly polarized light and another for right-circularly polarized light, which to first order, are given by... 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Most modern discussions of solvent effects rely on the concept of solvent polarity. Qualitative ideas of polarity are based on observations such as like dissolves like and are well accepted. However, quantification of polarity has proven to be extraordinarily difficult. Since the macroscopic property polarity arises from a myriad of possible microscopic interactions, this is perhaps unsurprising. Hence, it is important that care is taken when measuring the polarity of any liquid to ensure that it is clearly understood what is actually being measured. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

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