Dipole relaxation loss

FIGURE 2.37 The general shape of tan 5 as a function of the frequency at 3(X) and 50°K. The frilly drawn curves give the total losses. The sum of four different contributions (1) the conduction losses, (2) the dipole relaxation losses (sometimes called relaxation losses), (3) the vibration losses, (4) the deformation losses. ... 

Dipole Relaxation Losses. Up to about 10 Hz, dipole relaxation losses are important. They result from the energy that is given up by mobile ions as they jump over small distances in the network. Dipole losses are greatest when the frequency of the applied field is equal to the relaxation time of the dipole. At frequencies either far above or far below the resonant frequency, the losses are the least. Because of its random structure, glass has more than one relaxation time. This results in a broad distribution of dipole relaxation losses with frequency, rather than one discrete loss peak (see curve 2 in Fig. 2.37). 

Deformation Losses. Relaxation and deformation losses are similar in that they are associated with small displacements of ions in the glass network. Deformation losses involve smaller ion movements than do either conduction or dipole relaxation loss mechanisms, and they occur in the region of 10 Hz at room temperature (see curve 4 in Fig. 2.37). 

In order to quantify diffiisional effects on curing reactions, kinetic models are proposed in the literature [7,54,88,95,99,127-133]. Special techniques, such as dielectric permittivity, dielectric loss factor, ionic conductivity, and dipole relaxation time, are employed because spectroscopic techniques (e.g., FT i.r. or n.m.r.) are ineffective because of the insolubility of the reaction mixture at high conversions. A simple model, Equation 2.23, is presented by Chem and Poehlein [3], where a diffiisional factor,//, is introduced in the phenomenological equation, Equation 2.1. 

The subexcitation electrons lose their energy in small portions, which are spent on excitation of rovibrational states and in elastic collisions. In polar media there is an additional channel of energy losses, namely, the dipole relaxation of the medium. The rate with which the energy is lost in all these processes is several orders of magnitude smaller than the rate of ionizaton losses (see the estimates presented in Section II), so the thermalization of subexcitation electrons is a relatively slow process and lasts up to 10 13 s or more. By that time the fast chemical reactions, which may involve the slow electrons themselves (for example, the reactions with acceptors), are already in progress in the medium. For this reason, together with ions and excited molecules, the subexcitation electrons are active particles of the primary stage of radiolysis. 

As in the Monte Carlo calculations,252 253 the analytical calculations of Ref. 254 show that the loss rate on dipole relaxation for a curved trajectory is Mtt = 1.26 times higher than for a straight-line motion. 

Such a comparative study has been made by Byakov and his collaborators.29 255 They have shown that in the case of water the main contribution to the loss rate given by formula (6.3) comes from excitation of intramolecular vibrations rather than from dipole relaxation. This is all the more so in nonpolar media where the main channel of continuous losses is not the relaxation of constant dipole moments (which are zero) but the polarization losses due to the electron-inducing dipole moments in molecules. The possible exceptions are the media consisting of molecules with a high degree of symmetry, such as methane and neopentane, which have no active vibrations in the IR region. 

However, the situation becomes already more complicated for ternary single crystals like lanthanum-aluminate (LaAlC>3, er = 23.4). The temperature dependence of the loss tangent depicted in Figure 5.3 exhibits a pronounced peak at about 70 K, which cannot be explained by phonon absorption. Typically, such peaks, which have also been observed at lower frequencies for quartz, can be explained by defect dipole relaxation. The most important relaxation processes with relevance for microwave absorption are local motion of ions on interstitial lattice positions giving rise to double well potentials with activation energies in the 50 to 100 meV range and color-center dipole relaxation with activation energies of about 5 meV. 

Figure 5.3 Measured temperature dependence of the loss tangent of LaAlCH single crystals and a theoretical fit employing the SKM model and defect dipole relaxation (from [22]).

Thus we cannot escape the depressing reality that 7 2 will get shorter and linewidth will get bigger as we increase the size of the protein studied. The reduced T2 is not only a problem for linewidth, but also causes loss of sensitivity as coherence decays during the defocusing and refocusing delays (1/(2J)) required for INEPT transfer in our 2D experiments. The only ray of hope comes in the form of a new technique called TROSY (transverse relaxation optimized spectroscopy), which takes advantage of the cancellation of dipole-dipole relaxation by CSA relaxation to get an effectively much longer 7 2 value we will briefly discuss TROSY at the end of this chapter. 

Both the dipole-relaxation time and the ionic conductivity are related to the glass-transition temperature Fg. As a material is heated through its glass-transition temperature, static dipoles gain mobility and start to oscillate in an electric field. This causes an increase in permittivity and a loss-factor peak is noted. Obviously this motion is affected by frequency (lower frequencies have greater effects). This effect is shown in Figure 3.62 (Prime, 1997a), which shows the peaks in permittivity and loss factor at Tg. 

In the interpretation of the loss factor tg 8, it is not easy to make a distinction between a dipole relaxation and the interfacial polarization. With metallic electrodes, both effects are superposed on the ionic part of the dielectric loss and not necessarily distinguishable from it. With blocking electrodes, the relative intensity of the dipole relaxation and the Maxwell-Wagner effect depends on the ratio of the thickness of the blocking layers and the zeolite pellets (15). 

Solids and dipole relaxation of defects in crystals lattices Molecules which become locked in a solid or rigid lattice cannot contribute to orientational polarization. For polar liquids such as water, an abrupt fall in dielectric permittivity and dielectric loss occur on freezing. Ice is quite transparent at 2.45 GHz. At 273 °K, although the permittivity is very similar (water, 87.9 ice, 91.5) the relaxation times differ by a factor of 10 (water, 18.7 x 10 s ice, 18.7 x 10 s). Molecular behavior in ordinary ice and a feature which may be relevant to a wide variety of solids has been further illuminated by the systematic study of the dielectric properties of the nu-... 

The control of dielectric permittivity and loss of solid polymers, through an understanding of the origins of their dipole relaxation and ionic conduction processes, is essential for their use in electrical insulation, in electrical/electronic circuits, and devices operated over wide power ranges. This article discusses dielectric properties and behavior of pol5uners and briefly describes measurement techniques and applications. 

Here a is the bulk ionic or dc conductivity is the angular frequency (27rf) r is the dipole relaxation time is the relaxed dielectric constant or low frequency/high temperature dielectric constant (relative permittivity due to induced plus static dipoles) is the unrelaxed dielectric constant or high frequency/low temperature dielectric constant (relative permittivity due to induced dipoles only) o is the permitivity of free space E p is the electrode polarization term for permittivity and E"-p is the electrode polarization term for loss factor. The value of E p and E"p is usually unity, except when ionic conduction is very high (75). 

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