Dipole motions, relaxation frequency

Freezing of a dipolar liquid is accompanied by a rapid decrease in its electric permittivity [8-10]. Following solidification, dipole rotation ceases and the electric permittivity is almost equal to n, where n is refractive index, as it arises from deformation polarisation only. Investigation of the dynamics of a confined liquid is possible from the frequency dependences of dielectric properties, which allows both the determination of the phase transition temperature of the adsorbed substance and characteristic relaxation frequencies related to molecular motion in particular phases. 

Part of the work performed on a sample will be converted irreversibly into random thermal motion by movement of the molecules or molecule segments. This loss passes through a maximum at the appropriate transition temperature or relaxation frequency in the associated alternating mechanical field (torsion pendulum test). A similar effect is obtained by the delayed response of the dipoles with dielectric measurements. Therefore, dielectric measurements can be made only on polar polymers. According to the... 

Assuming (as it is reasonable) that for conditions in which the approximation ko 5> 1 is valid, the dynamic mobility also contains the (1 — Cq) dependence displayed by the static mobility (Equation (3.37)), one can expect a qualitative dependence of the dynamic mobility on the frequency of the field as shown in Figure 3.14. The first relaxation (the one at lowest frequency) in the modulus of u can be expected at the a-relaxation frequency (Equation (3.55)) as the dipole coefficient increases at such frequency, the mobility should decrease. If the frequency is increased, one finds the Maxwell-Wagner relaxation (Equation (3.54)), where the situation is reversed Re(Cg) decreases and the mobility increases. In addition, it can be shown [19,82] that at frequencies of the order of (rj/o Pp) the inertia of the particle hinders its motion, and the mobility decreases in a monotonic fashion. Depending on the particle size and the conductivity of the medium, the two latter relaxations might superimpose on each other and be impossible to distinguish. 

However for the other cases in Table 2 it is possible that the high frequency process may be of a different character, since the local motions relax such a substantial part of . Warchol and Vaughan (73) proposed a model of small-step diffusion in a cone to account for limited motions in such supercooled systems. Their model has been extended by Wang and Pecora (74). The essential result of this model (73, 74) is that for motions of a dipole vector limited within a cone of cone-angle 0, where 0Q < 40 , we have... 

The dielectric (e" and M") spectra and the relaxation frequencies of the p relaxation are similar to the mechanical spectra (J" and E", respectively) and the corresponding relaxation rate over a wide temperatures range (Muzeau et al. 1991 Perez et al. 1999). These observations suggest that the underlying mechanisms for the local electrical and mechanical relaxation processes in PMMA are similar. Clearly, this is not always the case for polymers, since all modes of motion of a polymer chain are not dielectrically active. When rotational diffusion occurs about a variety of different axes among which only a few reorient a dipole, the shape of the relaxation and the average rates of relaxation in a dielectric measurement may and will differ from those in a mechanical test. Dielectric, dynamic mechanical, and DSC glass transition... 

Careful inspection of the qualitative plots in Fig. 6.30 reveals that the relaxation frequency of the dipole motions moves to lower values as cure proceeds, indicative of the loss of free space and the increase of the effective Tg of the matrix. Also, r decreases and Ae gets smaller, somewhat like ACp. The curing time at which the frequency of the a-relaxation loss peak is approximately 0.1 Hz can be taken as indicative of the vitrification point of the matrix. 

The time t is the relaxation time for dipole reorientation in an electric field of frequency (0 (radians s ). For real systems there may be a number of contributions to the electric permittivity, each relaxing at a different frequency, for example due to internal dipole motion in flexible molecules or collective dipole motion. If these contributions to the electric permittivity are at sufficiently different frequencies, they can be separated in the dielectric spectrum, and it is possible to apply Eq. (9) to each relaxation process. At low frequencies (g)->0), the orientation polarization contribution to... 

Contributions to the permittivity from fluctuations in the amplitude of the tilt angle are expected to be small away from phase transitions, but this process is strongly temperature dependent, and the relaxation frequency tends to zero at a phase transition this relaxation is known as the soft mode in common with similar behaviour in crystals. Both the Goldstone mode and the soft mode relaxation processes are a result of the cooperative motion of molecular dipoles, and there is no proper molecular theory for them. The real and imaginary parts of the permittivity fit semicircular Cole-Cole plots, and so each mode can be characterized by a single relaxation frequency, although the dielectric absorptions for the... 

In the mcLPC chain all permanent dipoles are located on the backbone chain and as such they take part in the inter- and intramolecular motions. In the light of what was mentioned above, we should not expect a DR picture significantly different from that observed for ordinary semi flexible chains. In particular, observation of the influence of orientational order on the dynamics would be problematic, since the end-over-end reorientation of a mesogenic unit is excluded, and other modes of motion should have comparable relaxation frequencies (cf. Section 4.3). 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

A.A. Jones, Clark Univ., Mass. I would tend to agree with the dynamic picture you presoited. The idea that the high frequency motion in the sulfone hexene type polymers doesn t cause a net relaxation of dipoles but moves the magnetic dipole-dipole interaction around to cause nuclear relaxation is, I think, the crux of the matter. 

Dielectric relaxation study is a powerful technique for obtaining molecular dipolar relaxation as a function of temperature and frequency. By studying the relaxation spectra, the intermolecular cooperative motion and hindered dipolar rotation can be deduced. Due to the presence of an electric field, the composites undergo ionic, interfacial, and dipole polarization, and this polarization mechanism largely depends on the time scales and length scales. As a result, this technique allowed us to shed light on the dynamics of the macromolecular chains of the rubber matrix. The temperature as well as the frequency window can also be varied over a wide... 

Both Ti and T2 relaxations of water protons are mainly due to fluctuating dipole-dipole interactions between intra- and inter-molecular protons [62]. The fluctuating magnetic noise from all the magnetic moments in the sample (these moments are collectively tamed the lattice) includes a specific range of frequency components which depends on the rate of molecular motion. The molecular motion is usually represented by the correlation time, xc, i.e., the average lifetime staying in a certain state. A reciprocal of the correlation time corresponds to the relative frequency (or rate) of the molecular motion. The distribution of the motional frequencies is known as the spectral density function. 

The frequencies of rotational transitions are much smaller than vibrational frequencies, which means that the rotational motion is slower than the vibrational one. For a free molecule, the period of rotational motion is within 10 12-10 9 s. In condensed media the rotational motion is even slower, its period being respectively greater. At this stage it is more correct to speak of the relaxation time of the molecules. The latter essentially depends on the phase state of the medium. For example, in liquid water the relaxation time of molecular dipoles in an external electric field is about 10 11 s, whereas in ice (at 0°C) it is — 1 () 5 s. 

In our early work33 [50] the constant field model was applied to liquid water, where the harmonic law of particles motion, corresponding to a parabolic potential, was actually employed in the final calculations of the complex permittivity. In this work, qualitative description of only the libration band was obtained, while neither the R-band nor the low-frequency (Debye) relaxation band was described. Moreover, the fitted mean lifetime x of the dipoles, moving in the potential well, is unreasonably short ( ().02 ps)—that is, about an order of magnitude less than in more accurate calculations, which will be made here. 

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. 

The nuclear Overhauser effect (NOE) is a consequence of the modulation of the dipole-dipole interactions (through space) between different nuclei and is correlated with the inverse sixth power of the internuclear distance. Experimentally, the NOE is the fractional change in intensity of one resonance when another resonance is irradiated in a double-irradiation experiment. The NOE phenomenon is intimately related to spin relaxation. The NOE varies as a function of the product of the Larmor frequency, co0, and the rotational correlation time, tc. In small molecules, tc is short relative to uo"1. In this extreme motional narrowing situation, the frequency... 

---