External field, dipolar systems

In some cases of highly condensed media, the fact that the molecular electric fields F largely exceed the externally applied field E and can induce not only linear electric dipoles (199) but also non-linear ones has to be taken into consideration. We thus write quite generally, for dipolar systems ... 

Dielectric relaxation (DR) experiments measure the collective polarization response of all the polar molecules present in a given system. The DR time provides a measure of the time taken by a system to reach the final (equilibrium) polarization after an external field is suddenly switched on (or off). DR measures the complex dielectric fimction, s(w), that can be decomposed into real and imaginary parts as efca) = s (o) — is" (o) where s (co) and s fo ) are the real (permittivity factor) and imaginary (dielectric loss) parts, respectively. The total dipole moment of the system, at any given time t, M(t) = fift) where N is the total number of dipolar molecules and /Af is the dipole moment vector of the ith molecule. The complex dielectric function e((w) is given by the following relation. 

The most obvious application of the Jeener echo is to measure T by plotting echo amplitude vs. time spent in a state of dipolar order. If the system under study is homogeneously broadened, then the location on the echo where the amplitude is measured, provided it is chosen consistently, is immaterial for the measurement of T - In an inhomogeneously broadened system, such as a poly crystalline material, the Jeener echo may be a superposition of Jeener echoes with different shapes and different T- s. If so, it may matter where the echo amplitude is sampled. The most obvious test is to plot relaxation curves from different parts of the echo to determine whether the echo is relaxing uniformly. For a crystalline material, one expects that the dipolar relaxation time T p will be independent of the crystal orientation in the external field because the state of dipolar order is independent of this external field. 

Pereverzev, Y.V., O.V. Prezhdo, and L.R. Dalton. 2002. Sample shape influence on the anti-ferroelectric phase transitions in dipolar systems subject to an external field. Phys Rev B 65 053104-1/4. 

At frequencies higher than the ion motion, the e and M spectra are dominated by the dipolar motions (a-process in this case). In this case, the charaaetistic frequency of the a-processes is approximately the same in the e and M representations because of the small dielectric strength of the a-process for this particular system. Notice that this process, though well resolved in the s and M representations, is not so evident in the cr representation because of different weight. On the other hand, the a representation emphasizes the transition from the high frequency ac conduaivity (that strongly depends on the frequency of the external -field) to the dc conductivity (that is static i.e., independent of the frequency) at lower frequencies. 

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

Let us add a few comments on boundaries between phases in nonmetals. Since the boundary in a nonmetallic heterogeneous system is chemically unsymmetric, its electric charge distribution is dipolar, in contrast to a (symmetric) grain boundary. A force can therefore be exerted on this interface by an externally applied electric field. 

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