Relaxation time ionic polarization

A case of solvent-driven electronic relaxation has been observed [76] for [Re(Etpy)(CO)3(bpy)]+ in ionic liquids TRIR spectra have shown at early times a weak signal due to the II. state, in addition to much stronger bands of the 3MLCT state. Although no accurate kinetic data are available, the II. state converts to MI.CT with a rate that is commensurate with the solvent relaxation time. Fluorescence up-conversion provided an evidence [10] for population of an upper II. state in MeCN, which converts to CT with a much faster lifetime of 870 fs (Table 1). The solvent dynamic effect on the 3IL—>3CT internal conversion can be rationalized by different polarities of the II. and JCT states, Fig. 11. The solvent relaxation stabilizes the 3CT state relative to II., driving the conversion. 

It is an important aspect that block-copolymer micelles are characterized by much longer relaxation times than compared to low molecular surfactants. Non-equilibrium morphologies can easily be obtained in a vitrified state due to the efficient suppression of structural reorganization, because of the corresponding very slow response of the micelles to changes of temperature, solvent and concentration. In the case of a block-ionomer, i.e. a diblock copolymer where one block consists of ionic units, it was observed that micelles which formed in non-polar solution needed weeks to re-equilibrate after dilution of the solvent [226-228]. 

Elliott (1987, 1988 and 1989) approached the relaxation problem differently. In his diffusion controlled relaxation (DCR) model, Elliott, like Charles (1961) considers ionic motion to occur by an interstitialcy mechanism. There is a local motion of cations (for example Li ion in a silicate glass) among equivalent positions located around a NBO ion. Motions of cations among these positions causes the primary relaxational event and it occurs with a characteristic microscopic relaxation time t. The process gives rise to a polarization current. However, when another Li ion hops into one of the nearby equivalent positions with a probability P(/), a double occupancy results around the anion and this makes the relaxation instantaneous. Since the latter process involves the diffusion of a Li ion, the process as a whole involves both polarization and diffusion currents. Thus the relaxation function can be written as [l-P(/)]exp(-t/r). [1-P(0] is a function of the jump distance and the diffusion constant. Making use of the Glarum-Bordewijk relation (Glarum, 1960 Bordewijk, 1975) for [1-/ (/)] Elliott (1987) has shown that... 

Complementary to the electronic polarization, a charge carrier created in a molecnlar solid also polarizes the intramolecular vibration modes of the molecule on which it is located as well as dipole active modes of the neighboring molecules, thus forming an extended ionic state. As already mentioned, the corresponding relaxation time is comparable to the residence time The new quasiparticle associated with this... 

The dielectric di persion of DNA solutions was measured with various samples. The dielectric increment and the relaxation time of helical DNA are proportional to the square of the length of the molecule, hut values for coil DNA are distinctly smaller than for helical DNA. The rotary diffusion constant is measured simultaneously with the dielectric measurement. The agreement of both relaxation times is fair in a region of low molecular weight, hut the disparity becomes pronounced when DNA is larger. Theories on the mechanism of ionic electric polarization are reviewed. Currently, counter ion polarization for a cylindrical model seems to account most reasonably for the dielectric relaxation of DNA. 

Finally, attempts are made on a theoretical basis to explain the unusually large dielectric increments and relaxation times of DNA. The discussion is limited to ionic-type polarizations in this report. The available theories, such as the Maxwell-Wagner theory 29) and the surface conductivity treatment, are reviewed and analyzed. These theories do not explain the dielectric relaxation of DNA satisfactorily. Finally, the counter ion polarization theory is described, and it is demonstrated that it explains most reasonably the dielectric relaxation of DNA. 

Interpreting the experimental data in this form nowadays is a commonly employed method to obtain information about the relaxation processes in ionic conductive materials and polymer-conductivity nanoparticles composites. In this representation, interfacial polarization and electrode contributions are essentially suppressed [44, 45]. The peak in the imaginary part of M" depends on temperature, which can be related to the translational ionic motions. The corresponding relaxation time = l/(27r/p), where /p is the peak frequency, therefore is called conductivity relaxation time. 

Solvation dynamics (SD) studies of micellar solutions have reported a timescale which does not match with the dynamics either when the probe is inside the bulk water or when it is inside the bulk hydrocarbon (core). This indicates that the probe used resided neither in the bulk water nor in the dry core region, but was located in the Stem layer. Bhattacharyya and co-workers have studied SD in several micelles and found that the SD in the Stem layer of the micelles is three orders of magnitude slower than that in bulk water (in bulk the relaxation time is on the sub-picoseond timescale) [6]. The components that could cause solvation in the Stem layer of micelles are the polar or ionic headgroups of the surficants, the counterions, and the water molecules. In such an environment water motion could be severely restricted, giving rise to the slow component of SD. 

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). 

Many polymeric materials consist of dipoles (chemical bonds which have an unbalanced distribution of charge in a molecule) and traces of ionic impurities. If a polymer containing polar groups is heated so that an immobile dipole becomes mobile, an increase in permittivity is observed as the dipole starts to oscillate in the alternating electric field. This effect is referred to as a dipole transition and has a characteristic relaxation time (t) associated with it (76). When exposed to an electric field, the dipoles tend to orient parallel to the field direction and the ions move toward the electrodes, where they form layers. The dipole relaxation time... 

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