Solvents longitudinal dielectric relaxation time

This approximation requires that cos. This behavior in fact follows from a Debye dielectric continuum model of the solvent when it is coupled to the solute nuclear motion [21,22] and then xs would be proportional to the longitudinal dielectric relaxation time of the solvent indeed, in the context of time dependent fluorescence (TDF), the Debye model leads to such an exponential dependence of the analogue... 

Before leaving SD applications of the LRA, it is worth stressing that a different approach has often been taken in relating the electrostatic C i) to pine solvent dynamics. In this approach, the connection is made to solvent dielectric relaxation. Early theories made the connection through the longitudinal dielectric relaxation time," while more recent ones use as input the dielectric dispersion s or its generalization to finite wavevectors, e(k, co). 23.24.29,68,89... 

The situation changed dramatically with the application of picosecond and, later, faster techniques. One stimulating study was that of Kosower and Huppert [41]. They found that the reaction time for a particular intramolecular charge transfer in a series of alcoholic solvents was equal to the respective slowest longitudinal dielectric relaxation time of the solvent. It was later pointed out that this equality of the reaction and dielectric relaxation times would apply for barrierless reactions (AG a 0) or, more precisely, for the reactions where the relevant solvent dielectric relaxation, or its fluctuation, are the slow step, i.e., slower than the reaction would be in the absence of any slow solvent relaxational process. 

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

Fig. 16.4 Correlation between the fluorescence lifetime rp and the longitudinal dielectric relaxation time, TL (Eq. (15.19)) of 6-A -(4-methylphenylamino-2-naphthalene-sulfonW,iV-dimethylaniide) (TNSDMA) and 4-N, A-dimethylaminobenzonitrile (DMAB) in linear alcohol solvents. The fluorescence signal is used to monitor an electron transfer process that precedes it. The line is drawn with a slope of 1. (From E. M. Kosower and D. Huppert, Ann. Rev. Phys. Chem. 37,127 (1986) see there for original publications.)...

Below is a table which shows the measured rate constants for the oxidation and the longitudinal dielectric relaxation times (ti) for the solvents [A.D. Clegg et al,. Am. Chem. Soc. 126 (2004) 6185]. 

Forty years after Kramers seminal paper on the effect of solvent dynamics on chemical reaction rates (Kramers, 1940), Zusman (1980) was the first to consider the effect of solvent dynamics on ET reactions, and later treatments have been provided by Friedman and Newton (1982), Calef and Wolynes (1983a, 1983b), Sumi and Marcus (1986), Marcus and Sumi (1986), Onuchic et al. (1986), Rips and Jortner (1987), Jortner and Bixon (1987) and Bixon and Jortner (1993). The response of a solvent to a change in local electric field can be characterised by a relaxation time, r. For a polar solvent, % is the longitudinal or constant charge solvent dielectric relaxation time given by, where is the usual constant field dielectric relaxation time... 

The longitudinal relaxation time tl, rather than the dielectric relaxation time tes- s relevant to the motions of a dipole in the field of a fixed charge (see Section 4.3.4). For these solvent, tl is in the region of 0.2 ps (cf. F. Laerman, T. Elsaesser and W. Kaiser, Chem. Phys. Lett. 156 (1989) 381). 

This longitudinal relaxation time differs from the usual Debye relaxation time by a factor which depends on the static and optical dielectric constants of the solvent this is based on the fact that the first solvent shell is subjected to the unscreened electric field of the ionic or dipolar solute molecule, whereas in a macroscopic measurement the external field is reduced by the screening effect of the dielectric [73]. 

Recent theoretical treatments, however, suggest instead that the dynamics of solvent reorganization can play an important and even dominant role in determining vn, at least when the inner-shell barrier is relatively small [43-45]. The effective value of vos can often be determined by the so-called longitudinal (or "constant charge ) solvent relaxation time, rL [43, 44]. This quantity is related to the experimental Debye relaxation time, rD, obtained from dielectric loss measurements using [43]... 

According to the Debye model there are three parameters associated with dielectric relaxation in a simple solvent, namely, the static permittivity s, the Debye relaxation time td, and the high-frequency permittivity Eoq. The static permittivity has already been discussed in detail in sections 4.3 and 4.4. In this section attention is especially focused on the Debye relaxation time td and the related quantity, the longitudinal relaxation time Tl. The significance of these parameters for solvents with multiple relaxation processes is considered. The high-frequency permittivity and its relationship to the optical permittivity Eop is also discussed. 

Table 7.5 Average Relaxation Times from Time-Dependent Stokes Shifts (TDSS) for Coumarin Cl 52 in Various Solvents Together with the Longitudinal Relaxation Time Determined by Dielectric Relaxation Spectroscopy [20]...

For the present purposes, it is sufficient to note that Xeir in a number of simple polar solvents can be approximated by the longitudinal relaxation time, x, extracted from solvent dielectric loss spectra. Interestingly, substantial (up to ca 50 fold) variations in x, are observed in such media, from ca. 0.25 to 10 ps [12]. Since analytic theories predict commonly that Vn Xj, correspondingly large variations in Vn are anticipated to be achieved by suitable alterations in... 

The solvation process in alcoholic solutions of molecular species has been examined by picosecond measurements on the time-dependence of the Stokes shift , i.e., of the frequency difference between the maxima of the absorption and fluorescence spectra. The time-constant for this quantity for solutions of 1-naphthylamine in propanol is 52 ps, which agrees as regards order of magnitude with the result of an electrostatic calculation from a model in which the solvent is represented by a dielectric continuum and the solute by a spherical cavity of dielectric constant c- This model predicts the relaxation time of the reactive field to be not x but the longitudinal relaxation time tl which equals Ti ( c + 2 oo)/( c -f 2 q), and can be much smaller than td for highly-polar solvents (cf. Section 4.3.4). 

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