Dielectric relaxation permanent dipole

The remaining types of polarization are absorptive types with characteristic relaxation times corresponding to relaxation frequencies. Debye, in 1912, suggested that the high dielectric constants of water, ethanol, and other highly polar molecules were due to the presence of permanent dipoles within each individual molecule and that there is a tendency... 

There is no oscillation the polarization merely relaxes toward zero with a time constant t. In the following paragraphs, we shall use (9.35), the basic assumption of the Debye theory, to derive an expression for the dielectric function of a collection of permanent dipoles. 

On physical grounds, relaxation of permanent dipoles is expected to be highly dependent on temperature this is in contrast with Lorentz oscillators, the dielectric behavior of which is relatively insensitive to changes in temperature. Debye (1929, Chap. 5) derived a simple classical expression for the relaxation time of a sphere of radius a in a fluid of viscosity tj ... 

P. J. W. Debye, Polar Molecules (Dover, New York, reprint of 1929 edition) presents the fundamental theory with stunning clarity. See also, e.g., H. Frohlich, "Theory of dielectrics Dielectric constant and dielectric loss," in Monographs on the Physics and Chemistry of Materials Series, 2nd ed. (Clarendon, Oxford University Press, Oxford, June 1987). Here I have taken the zero-frequency response and multiplied it by the frequency dependence of the simplest dipolar relaxation. I have also put a> = if and taken the sign to follow the convention for poles consistent with the form of derivation of the general Lifshitz formula. This last detail is of no practical importance because in the summation Jf over frequencies fn only the first, n = 0, term counts. The relaxation time r is such that permanent-dipole response is dead by fi anyway. The permanent-dipole response is derived in many standard texts. 

Helical polypeptides constitute a sinqjler biopolym syst which also displays a distinct rotational mechanism of dielectric dispersion. The a-helix structure implies an appreciable permanent dipole moment parallel to its long axis and a relaxation frequency whidi may become very low because of the considerable length of the particles. Since the latter cannot be made uniform for synthetically prepared samples a more or less extended relaxation spectrum is inevitable. 

Owing to their definite structures, most biomolecules have an appreciable permanent dipole moment which must lead to dielectric polarization via the rotational mechanism of preferential orientation. Thus pertinent experimental investigation permits a direct determination of the molecular dipole moments and rotational relaxation times (or rotational diffusion coefficients, respectively). These are characteristic factors for many macro-molecules and give valuable information regarding structural properties such as length, shape, and mass. 

The dielectric behaviour of proteins in aqueous solutions was first extensively studied by Ondey and co-workers. They interpreted the data in terms of rotational polarization of permanent dipole moments. The latter were found to be in the range of 100—1000 D (1 D = 10- e.s.u.) while the relaxation times came out at ca. 10" s. Despite some ta-itidsm, the preferential-orientation effect must still be considered the prindpal dielectric-polarization mechanism of proteins. - This view is also supported by dieledric dispersion studies of various proteins in solvents of different viscosity. The measured relaxation times were indeed proportional to rj as predided by (29) and (30). Nevertheless, for very large molecules (M, > 10 ) indications of other mechanisms, whose relaxation does not depend on the bulk viscosity of the solvent, have been observed. ... 

The dielectric, structural, relaxation time is related to the linear regime. It reflects the evolution of the average permanent dipole moment, linked to the given molecule. The dielectric relaxation time detects heterogeneities indirectly, via changes of the average surrounding of a molecule. It was shown in ref. that dielectric relaxation can be well portrayed, with small distortion only close to Tp, by the MCT critical-like dependence ... 

Figure 17. Time-resolved fluorescence spectra of a solute with one vibrational mode in ethanol at 247 K.68 The various frames show the fluorescence spectrum measured at successively later times after the application of a 1 ps excitation pulse. Each spectrum is labeled with the observation time. The steady-state fluorescence spectrum is given by the dashed curve in the bottom frame. In the electronic ground state, the solute vibrational frequency is400cm 1, and in the excited state, the frequency is 380 cm 1. The dimensionless displacement is 1.4. The permanent dipole moment changes by 10 Debye upon electronic excitation. The Onsager radius is 3A. The longitudinal dielectric relaxation time, xL, is 150 ps.

V. The curves in Figure 1 were calculated by using the static value of the dielectric constant for each liquid. However, the dielectric constant of a medium is time dependent, because it requires a certain amount of time for the medium to attain its new polarization equilibrium after the sudden application of an electric field. In a polar liquid the permanent molecular dipoles require a certain time to rotate to line up with the electric field. When the value of tgn is in the vicinity of or smaller than that of the dielectric relaxation time t of the liquid—i.e., when tgn S 10t,— then a time-averaged complex dielectric constant should be used in Equations II, IV, and V. At a time t after the instantaneous application of a d.c. electric field, the dielectric constant of the medium in the field is given approximately by... 

The first mechanism (a) refers to dielectric relaxation pertinent to a permanent dipole influenced by a rather narrow hat intermolecular potential the next two (b, c) refer to the complex permittivity generated by two elastically vibrating hydrogen-bonded (HB) molecules. The last mechanism (d) refers to a nonrigid dipole vibrating in direction perpendicular to that of the undisturbed H-bond. 

This state describes (i) dielectric response arising from libration of a permanent dipole p in a hat-like potential well [the relevant librational band is located near the border of the infrared region (at 700 cm-1)] and (ii) the nonresonance relaxation band, whose loss peak is located at microwaves. The lifetime Tor of the LIB state is much less than a picosecond. 

The hat-like potential model evolved from consideration of rotation of a permanent dipole between two perfectly reflecting plates inclined one with respect to the other through the angle 2f. The history of the hat potential is described in detail in the context of dielectric relaxation in liquids in GT2. 

However, the relaxation time they observed was widely different from the relaxation time of rotary diffusion (rro.) of about 10-3 second observed by Edsall (4). If dielectric polarization is caused by the orientation of a permanent dipole, the relaxation time must be similar to that for rotary diffusion. The rotary diffusion of elongated particles usually represents the rotary motion of the whole body around the short axis. If DNA has a permanent dipole in the transverse direction, the whole molecule would rotate around the major axis and the dielectric relaxation time would not necessarily be the same as that of rotary diffusion. Thus they concluded that the difference between the rotary and dielectric relaxation times ob-... 

Dielectric relaxation u, unit vector along permanent dipole (o) Um(t)y l,m... 

We have also demonstrated that it was possible to throw light on the orientation fluctuations of polar macromolecules like collagen, by measuring the noise emission conductivity (t versus frequency. The critical time of orientation fluctuations of the collagen permanent dipoles cannot be assimilated to the classical dielectric relaxation time T , but the numerical value of is very near to the reorientation time measured by electrical birefringence. 

The mechanism of dielectric effects of interest to DETA involves permanent dipoles which exist within the sample and try to follow an alternating electric field, but may be hindered to do so when attached to segments of molecules with limited mobility. The fundamental analogy of dielectric and mechanical relaxation has been pointed out... 

Dielectric relaxation spectroscopy is widely used to study molecular dynamics of conventional and liquid crystal polymers. Since the mesogenic groups of a side-chain liquid crystal polymer contain strong permanent dipoles, the technique may be utilized to study the reorientation and, as Attard et have shown, the level of... 

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