Mean dipole moment, dielectric relaxation

Equations (7.6) and (7.7) provide a means of determining excited dipole moments together with dipole vector angles, but they are valid only if (i) the dipole moments in the FC and relaxed states are identical, (ii) the cavity radius remains unchanged upon excitation, (iii) the solvent shifts are measured in solvents of the same refractive index but of different dielectric constants. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

The dielectric relaxation strength of the polymers follows the same trends as the mean-square dipole moments per repeating unit. Thus P26DFBM and P25DFBM which have the higher and lower values of (/x2)/x, 5.00 and 1.92 D2 at 25°C, respectively. 

Table 7-4. Change of the natural bond order (NBO) charges and of the dipole moment of pNA in the ICT state. The label (Un)relax/(Un)relax means that we do (not) have allowe for solute geometry relaxation/solvent dielectric relaxation. Charges are in a.u. and dipole moments in Debye...

With local information given by INM analysis in mind, we next see the character of rotational relaxation in liquid water. The most familiar way to see this, not only for numerical simulations [76-78] but for laboratory experiments, is to measure dielectric relaxation, by means of which total or individual dipole moments can be probed [79,80]. Figure 10 gives power spectra of the total dipole moment fluctuation of liquid water, together with the case of water cluster, (H20)io8- The spectral profile for liquid water is nearly fitted to the Lorentzian, which is consistent with a direct calculation of the correlation function of rotational motions. The exponential decaying behavior of dielectric relaxation was actually verified in laboratory experiments [79,80]. On the other hand, the profile for water cluster deviates from the Lorentzian function. As stated in Section III, the dynamics of finite systems may be more difficult to be understood. 

The principal result of our calculation is that the Debye theory (based on the Smoluchowski equation), when extended to fractional dynamics via a onedimensional noninertial fractional Fourier-Planck equation in configuration space, can explain the Cole-Cole anomalous dielectric relaxation that appears in some complex systems and disordered materials. A further result of our calculation is that the aftereffect solution [Eq. (66)] is, with slight modifications, the moment generating function of the configuration space distribution function. Hence the mean-square angular displacement of a dipole, and so on, may be easily calculated by differentiation. We must remark, however, that the fractional Debye theory can be used only at low frequencies (got < 1) just as... 

For polymers, dielectric spectroscopy is sensitive to fluctuations of dipoles, which are related to the molecular mobility of groups, segments, or the polymer chain as well [38]. The molecular mobility is taken as a probe for structure. The basic quantity is the complex dielectric function e f) = t (f) - it"(f) as a function of the frequency/and the temperature T. s (/) is the real whereas e"(/) is the loss part i = >f ). A relaxation process is indicated by a step-like decrease of s (/) with increasing frequency and a peak in e"(/). From the maximum position of the peak a mean relaxation rate can be deduced, which corresponds to the relaxation time of the fluctuation of the dipole moment of a given structural imit. For details see reference [49]. All shown measurements were carried out isothermally in the frequency range from 10 to 10 Hz by an ALPHA analyzer (NovocontroF). The temperature of the sample is controlled by a Quatro Novocontrol system with stability better than 0.1 K. 

Table 3 Comparison of Predicted Root-Mean-Square, dipole moments (debye units) and Corresponding Reduced Limiting Dichroisms, i with Experimental Results Obtained from Electrooptical Relaxation Data and Dielectric Relaxation for a-Chymotrypsin and Sperm Whale Oxymyoglobin ...

Dielectric studies on type-A polymers readily yield four sorts of information. First, the strength of the dielectric relaxation reveals the polymer s mean-square end-to-end distance (r ). Second, the relaxation time of the longest-Uved mode corresponds to the correlation time for reorientation of the end-to-end vector. Third, the detailed lineshape of the dielectric relaxation gives information about more complex relaxations. Fourth, by examining copolymers in which all monomers do not have the same dipole moment, one can in principle gain information on polymer internal modes. 

The intramolecular motions which relax the total dielectric increment, As = So — b oo, or in other words the mean square dipole moment , can generally be divided into two classes (i) fast local motions and (ii) large-scale, slower Brownian motions of chains. The former are responsible for the jS-process, and the latter for the a-process. The mean square dipole moment, = l, where the sum is taken over... 

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