Relaxation times permanent dipole

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 ... 

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. 

In these equations, D is the appropriate rotational diffusion coefficient and 3 = 1/kT results from thermal averaging. The asymmetry of the two responses, given by the second term of the field on expression, clearly results from permanent dipole torques but involves both dipole relaxation with e 1/2 D and polarizability with relaxation time t = 1/6 D = x /3, botE for rotational diffusion. a r... 

The first, permanent-dipole term is important only at zero frequency in the summation over imaginary sampling frequencies f . The relaxation time r is big enough that for f =i the permanent-dipole term in a is effectively zero this term counts only at zero frequency. In both mks (SI or Systeme International) and cgs ("Gaussian") units, the dipole moment //.dipole = qd for charges q separated by distance d. [See table S.8 and Eq. (L2.171) in Level 2.]... 

Writing this with explicit imaginary frequency dependence and with Debye relaxation of the permanent dipole term of relaxation time r gives... 

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. 

In most other cases the dispersion curves are flattened in comparison with pure Debye functions as presented in (10). This indicates the existence of more than one relaxation time. A rather obvious explanation is based on an ellipsoidal shape of the protein molecule with components of the permanent dipole along each of the three principal axes. In general, this should result in three corresponding relaxation times. Applying this concept to practical examples, it turns out that the assumption of an ellipsoid of revolution with only two relaxation times is quite sufficient for a quantitative fit of the experimental curves. In such a way, the ratio of the axes can be determined. It must be emphasized, however, that the data really do not permit an unambiguous discrimination between two or more individual relaxation times. 

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.

The colloid particle or polyelectrolyte molecule may possess a permanent dipole moment. Considerable influence of this moment on the magnitude and the sign of the electro-optical effect is expected in the range of particle rotation. Discrimination between the induced and the rotational relaxation of the particles can be reached, however, since the electro-optical response to a sinusoidal electric field is the sum of a time-independent term adc and a term a2rjJ that is sensitive to the particle rotation [24,45]. The critical frequency of the alrjJ relaxation depends on the rotational diffusion coefficient Dr of the particle, while the critical frequency of relaxation of the time-independent term adc depends on the translational diffusion coefficient of the ions moving on the particle surface. 

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... 

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-... 

The preceding discussion has to do with induced dipoles whereas, the relaxation studies deal with the motions of parts of polymer chains that have different relaxation times for orientation. Many polymers such as polyvinyl fluoride, polyvinyl chloride and nylons have permanent dipoles that may be reoriented on the application of an applied field. The response of the oriented permanent dipoles will vary with the strength of the applied field. 

The time course of orientational changes induced by electric fields contains information on the orientation mechanism, and on the electrical and geometrical properties (main dipole axis, length) of the aligning and deorienting molecules. For instance, permanent dipole orientation of a given particle type in the presence of a constant electric field builds up with zero slope and has two modes, whereas the build-up of induced dipole orientation starts with maximum slope and is characterized by only one time constant. The deorientation relaxation of a system of identical particles, after termination of the step pulse, is monophasic, independently of the presence of permanent or induced dipoles. Table 3 summarizes the characteristic features of the rotational kinetics indicated by electric dichroism and birefringence for small perturbations. We see that there are a number of specific relationships to differentiate between permanent and induced dipole mechanism. In particular, the technique of field-reversal is a sensitive indicator for the relative contributions of permanent or induced dipoles. 

The dipolar nature of amino acid intervening in molecular structure of collagen implies the existence of a permanent dipole i orientated along the revolution axis of the cylindrical rod. By electrical birefringence measurements, Yoshioka and O Konski have predicted a value of about 15000 Debye for this important permanent dipole and an orientational relaxation time of 0.1-0.2 ms. These results are in agreement with the more recent birefringence experiments of Bemengo et On the other hand,... 

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. 

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