Solvent longitudinal relaxation time

The pre-exponential factor in this case includes the solvent longitudinal relaxation time tl, which will be discussed further on when the recent works concerned with the role of the solvent will be considered. This longitudinal relaxation time is related to the usual Debye relaxation time according to... 

Jaworski et al. [186] found that the reaction constants from the Hammett equation, in the case of the irreversible electroreduction of substituted chloro- and bromo-benzenes in a number of organic solvents, are linearly dependent on the logarithms of the solvent longitudinal relaxation times. 

Fig. 18. Values of the kc jk-i ratio (evaluated from the experimental efficiencies of formation of the excited state) as a function of the solvent longitudinal relaxation time Ti. Data for 4-(9-anthryl)-V,V,3,5-tetra-methylaniline in acetonitrile (ACN), pro-pionitrile (PN), butyronitrile (BN), propylene carbonate (PC), sulfolane (TMS) and 7-butyrolactone (BL) solutions. Adapted from [153].

Solvent Longitudinal Relaxation Time Cl/PS Average Relaxation Time from TDSS ts/PS... 

The effect of solvent in an electron transfer is larger than simply through its energetic contribution to A. There is evidence that the dynamics of solvent reorganization, often represented in terms of a solvent longitudinal relaxation time, tl, contribute to the preexponential factor in (3.6.2) (47, 62-65), e.g., Since tl is roughly proportional... 

Xi Solvent longitudinal relaxation time Tffi Apparent lifetime calculated from the modulation at a single frequenty... 

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

Experiments in the picosecond time range show that C(t) is non-exponential in most solvents with an average spectral relaxation time greater than the longitudinal relaxation time tl and smaller than the Debye time td-... 

The compound bis-(4,4 -dimethylaminophenyl)-sulfone (DMAPS) and related compounds show multiple fluorescences in polar solvents due to excited state charge transfer (Rettig and Chandross [144]). Su and Simon [84,85] have examined the intramolecular electron transfer reaction in DMAPS, in alcohol solution over the temperature range from — 50°C to + 30°C. They observe that the decay of the local excited state is nonexponential and significantly faster than the longitudinal relaxation time of the solvent. In addition, they observed that the emission spectrum of the TICT state... 

In the original Marcus-Hush model, the role of the solvent is described by the static equation of reorganization, Eq. 13 b. The time scale of the reorganization does not appear explicitly and this has been included in more recent treatments of e.t. processes. There are indeed several reports of e.t. reactions of which the rates seem to be controlled by solvent relaxation, related to the longitudinal relaxation time [72]. 

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]. 

Fig. 5. Plot of the logarithm of the standard rate constant for electroreduction of Mn(AcAc)3 (A) and Fe(AcAc)3 ( ) in a given solvent against the logarithm of the longitudinal relaxation time of the solvent [177], The left-hand ordinate scale applies of the Mn system and the right-hand scale of the Fe system. BTN, butyronitrile for definition of the other solvents see Table 1.

Fig. 6. Dependence of the logarithm of the standard rate constant of phenothiazine oxidation on a Ft electrode on the logarithm of the solvent s longitudinal relaxation time. NE, nitroethane TMS, sulfolane. For other abbreviations see 1k-blel.

System Longitudinal relaxation time coefficient, a No. of solvents Regression coefficient... 

Recently Jaworski and coworkers [303] have analyzed mixed solvent influence on surface intramolecular reactions. The authors tried to explain the change in the rate constant with the H2O-DMF mixed solvent composition in terms of the change in the estimated longitudinal relaxation time. A linear correlation was found between k for various H2O-DMF compositions and Tl . 

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... 

As is evident from Eq. (1), the radiation damping effect is particularly severe for large solvent peaks and can make the solvent return to equilibrium many times faster than the intrinsic longitudinal relaxation time (see Fig. 2). Thus, the effects of radiation damping are a major source of difficulties in manipulating solvent magnetization and need to be considered in the... 

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. 

The temperature dependence of the longitudinal relaxation time tl is also an important quantity. For a Debye solvent, tl is given by the relationship... 

Estimation of the longitudinal relaxation time in solvents with multiple Debye relaxation processes is not straightforward. In fact, tl is a function of time in these systems [33, 34], and varies between two limiting values. For a solvent with two relaxation processes, the low-frequency limit for xl is... 

It is clear from these results that there is an approximate correlation between the value of the average relaxation time Xs and the longitudinal relaxation time Xl (see section 4.7). However, careful examination of the time-dependent Stokes shift (TDSS) data reveals that C(t) is described by more than one relaxation process. This is not difficult to understand, considering that many aprotic solvents are found to have more than one relaxation process. This can be attributed to the formation of dimers and other aggregates in these liquids. This is especially the case in aprotic solvents such as DMSO and PC, which have very high dipole moments. Alcohols also have multiple relaxation processes due to the presence... 

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