Solvent relaxation times

To more fully appreciate the equilibrium models, like SCRF theories, and their usefulness and limitations for dynamics calculations we must consider three relevant times, the solvent relaxation time, the characteristic time for solute nuclear motion in the absence of coupling to the solvent, and the characteristic time scale of electronic motion. We treat each of these in turn. 

A fully realistic picture of solvation would recognize that there is a distribution of solvent relaxation times (for several reasons, in particular because a second dispersion is often observable in the macroscopic dielectric loss spectra [353-355], because the friction constant for various types or modes of solute motion may be quite different, and because there is a fast electronic component to the solvent response along with the slower components due to vibration and reorientation of solvent molecules) and a distribution of solute electronic relaxation times (in the orbital picture, we recognize different lowest excitation energies for different orbitals). Nevertheless we can elucidate the essential physical issues by considering the three time scales Xp, xs, and Xelec-... 

Most of the theoretical works concerning dynamical aspects of chemical reactions are treated within the adiabatic approximation, which is based on the assumption that the solvent instantaneously adjusts itself to any change in the solute charge distribution. However, in certain conditions, such as sudden perturbations or long solvent relaxation times, the total polarization of the solvent is no longer equilibrated with the actual solute charge distribution and cannot be properly described by the adiabatic approximation. In such a case, the reacting system is better described by nonequilibrium dynamics. 

An improved and direct correlation between the experimental rate constant and [obtained using Eq. (49)] is observed if v = /zd is used instead of v = 1/Tt, the solvent-dependent tunneling factor is utilized, and only AG (het) of Eq. (8) is used in Eq. (49) (see triangles in Fig. 18). Furthermore, the inverse of the longitudinal solvent relaxation time Xi is not necessarily the relevant one to use as the frequency factor v (see empty circles in Fig. 18). Similar conclusions were reached by Barbara and Jerzeba for the electron transfer reaction in homogeneous solutions. Barbara and Jerzeba measured the electron transfer time... 

In Figure 7 Is shown the solvent relaxation time as a function of temperature and polymer concentration. Analogous to the results, the proton relaxation Is affected by addition of only a small amount of polymer. Further addition of polymer decreases Tj systematically. 

Most continuum models are properly referred to as equilibrium solvation models. This appellation emphasizes that the design of the model is predicated on equilibrium properties of the solvent, such as the bulk dielectric constant, for instance. The amount of time required for a solvent to equilibrate to the sudden introduction of a solute (i.e., the solvent relaxation time) varies from one solvent to another, but typically is in the range of molecular vibrational and rotational timescales, which is to say on the order of picoseconds. 

SDS micelles [188-190]. These results may be a consequence of a lack of template-induced orientation or of the orientational forces being too weak to overcome the orientational preferences between an excited and a ground state molecule. It is certainly the case in all of the micellar examples cited that the solvent relaxation times should allow molecules to reorient themselves at the interface (should they so choose) on timescales which are comparable to those necessary for an excited molecule to form its photoproducts. 

Solvent Relaxation time t (ps) Dipole moment (debye) Loss tangent at 2.45 GHz... 

Fits to single (one floating parameter) and double (three floating parameters) exponential decay laws are always poorer as judged by the x2 and residual traces. In the case where we assume that there is some type of excited-state process (e.g., solvent relaxation) we find that the spectral relaxation time is > 20 ns. This is much, much greater than any reasonable solvent relaxation process in supercritical CF3H. For example, in liquid water, the solvent relaxation times are near 1 ps (56). 

Mg(DOPMR)2-H2(DOP) [Mg(DOP )+-(R)2-[H2(DOP )] - Solvent acetone, CH2C12, DMF or alkyl-acetates X, = 532 or 588 nm the charge-recombination rate constant correlates with the reverse of the solvent relaxation times [196]... 

In the adiabatic regime, the solvent relaxation time rc reaction coordinate. This limit corresponds to (t) = 5(t), so the power spectrum (Eq. (11.87)) is equal to , that is, to white noise . The GLE is reduced to the simple Langevin equation with a time-local friction force — x. Xr is found from Eq. (11.85) ... 

The concept of adiabacity in e.t. processes has gained importance in recent years, and the question does arise to what extent it may influence the observation of the M.I.R. In principle, the occurence of the M.I.R. is related only to the quadratic form of the activation energy, not to the form of the pre-exponential factor. The M.I.R. should therefore be observed for both adiabatic and nonadiabatic reactions. However, if the observable rate of an adiabatic process is controlled by the solvent relaxation time, the influence of the exponential factor may be negligible [18]. 

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. 

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]... 

An elegant alternative is to use the NMR relaxation rate of the solvent. The method relies on the fact that, when there is rapid exchange between solvent molecules on the solid surface and In the bulk solution, the contributions of these two populations to the (average) relaxation rate are additive. In a colloidal dispersion, mobile solvent In the bulk (b) and less mobile adsorbed solvent (a) have widely different relaxation rates, indicated by and T. respectively. The average solvent relaxation time is then given by )... 

We have performed picosecond time resolved absorption spectroscopy for organic dyes in alcoholic solution and have shown the following results. The recXral shape of the difference spectrum before and after the excitation is expressed as the superposition of the absorption and fluorescence spectra detected under steady state condition when the solvent relaxation time is sufficiently short compared with the time resolution of the experimental equipment and the excited state lifetime. On the other hand, the spectrum in the viscous solvent at low temperature shows slightly sharp in initial and broadens its shape with time. 

A. Solvent relaxation times of electron donating solvents... 

As expected from examinations of the individual fluorescence transients, the peak of the reconstructed spectrum shifts to red with time. In Figure 3, the spectral shift correlation functions C(t) are shown with the results of bi-exponential fitting. The observed solvent relaxation times are 7.9 ps (19 %) and 18.7 ps (81 %) for DMA and 6.7 ps (81 %) and 13.3 ps (19 %) for AN. These are much longer than the fluorescence lifetimes of NB, i.e., 0.1 ps... 

Invoking the model assumption that slow variation of 7- relative to the relaxation time associated with Z (t — t) (the latter being essentially the characteristic solvent relaxation time), and averaging the product x (t)xj,(T) over all initial phases, assuming further that the averaged product x (t)X, (t) depends only on t — t, we get... 

It should be kept in mind that increasing the solvent viscosity does not necessarily imply stronger damping, because it may be accompanied with slower solvent motion (longer solvent relaxation time) and smaller elTective friction due to the larger non-Markovian nature of the solvent molecule interaction. See, for example, Bagchi and Oxtoby. ... 

Solvent Relaxation Time Half-Time Value... 

Figure 5.6 Graph of the relation between exchange time estimated by lineshape analysis of IR-SEC data for 1-3 and solvent relaxation time, tie-...

A semiquantitative explanation of the 2-ns component may be as follows The static polarity or the dielectric constant of the water pool of the AOT microemulsions can be obtained from the position of the emission maximum of the probes (C480 and 4-AP) [165,166]. For both probes, the water pool resembles an alcohol-like environment with an effective dielectric constant of 30-40. If one makes a reasonable assumption that the infinite frequency dielectric constant of water in the water pool of the microemulsions is the same as that of ordinary water, i.e., 5, and that the dielectric relaxation time is 10 ns as obtained for the biological systems [18b], then the solvent relaxation time should be about 1.67 ns, which is close to the observed solvation time in AOT microemulsions. 

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