Solvation time for

Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid-liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62-64]. 

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-... 

In this nonadiabatic limit, the transmission coefficient is determined, via (2.8) by the ratio of the nonadiabatic and equilibrium barrier frequencies, and is in full agreement with the MD results [5a-5c]. (By contrast, the Kramers theory prediction based on the zero frequency friction constant is far too low. Recall that we emphasized for example the importance of the tail to the full time area of the SN2 (t). In the language of (3.14), the solvation time xs is not directly relevant in determining... 

But the entire conception here is that of equilibrium solvation of the transition state by the Debye ionic atmosphere, and closer inspection [51] indicates that this assumption can hardly be justified indeed, time scale considerations reveal that it will nearly always be violated. The characteristic time for the system to cross the reaction barrier is cot, 0.1 ps say. On the other hand, the time required for equilibration of the atmosphere is something like the time for an ion to diffuse over the atmosphere dimension, the Debye length K- this time is = 1 ns for a salt concentration C= 0.1M and only drops to lOps for C 1M. Thus the ionic atmosphere is perforce out of equilibrium during the barrier passage, and in analogy with ionic transport problems, there should be an ionic atmosphere friction operative on the reaction coordinate which can influence the reaction rate. 

At the beginning of this decade, Zewail and coworkers reported a fundamental work of solvation effect on a proton transfer reaction [195]. a-naphthol and n-ammonia molecules were studied in real-time for the reaction dynamics on the number of solvent molecules involved in the proton transfer reaction from alcohol towards the ammonia base. Nanosecond dynamics was observed for n=l and 2, while no evidence for proton transfer was found. For n=3 and 4, proton transfer reaction was measured at pisosecond time scale. The nanosecond dynamics appears to be related to the global cluster behavior. The idea of a critical solvation number required to onset proton transfer... 

Fast librational motions of the fluorophore within the solvation shell should also be consideredd). The estimated characteristic time for perylene in paraffin is about 1 ps, which is not detectable by time-resolved anisotropy decay measurement. An apparent value of the emission anisotropy is thus measured, which is smaller than in the absence of libration. Such an explanation is consistent with the fact that fluorescein bound to a large molecule (e.g. polyacrylamide or monoglucoronide) exhibits a larger limiting anisotropy than free fluorescein in aqueous glycerolic solutions. However, the absorption and fluorescence spectra are different for free and bound fluorescein the question then arises as to whether r0 could be an intrinsic property of the fluorophore. 

Fig. 3 displays the solvation time of the electron (using open symbols) plotted against the longitudinal relaxation time. The results were plotted against the longitudinal relaxation time because that is the time scale that some continuum models would have suggested. Note that the rates are comparable to those seen for the solvation of an anion, and considerably faster than those measured for dipole solvation. The anion data will be discussed below. 

Simulations were done where the dipole is reversed in the solvent molecule. This is equivalent to making measurements in acetonitrile. The calculations suggested that there would only be weak solvation in acetonitrile, despite the fact that acetonitrile is far more polar than any of the alcohols that we have measured. This fact is indeed borne out experimentally. The spectrum of the benzophenone anion is considerably to the red of the spectrum of the benzophenone anion in any of the alcohols that we have measured. In addition, there is no evidence for any shift of the spectrum in the time scale that we observe. This lack of shift may not be surprising, because experiments in acetonitrile suggest that the solvation time is very fast. Thus, any relaxation that is going to take place will have occurred on the time scale of the present experiments. 

An early application of this type of analysis was to decompose Pio/v( ) into its rotational, translational and their cross-correlation subspectra. It was shown through this decomposition that electrostatic solvation spectra for dipole and charge perturbations are dominated by rotational dynamics. More generally, it was shown how the range and symmetry of AP and molecular properties such as masses and moments of inertia are related to the relative contributions of rotational and translational degrees of freedom to SD. INM analysis has also proved useful in comparing the molecular mechaitisms contributing to short-time dynamics observed in different experiments,such as SD, optical Kerr ef-... 

Fig. 2.8 Experimentally obtained solvation time correlation function, S(t), for the solvation of coumarin 343 in water (taken from Ref. [19 a]).

The solvation time t is considerably shorter than td for many solvents. For example for water ex = 4.84, 0 = 79.2 and tD = 8.72 ps [33]. Thus in water t, = 0.59 ps. Why is the time scale for solvation of a dipole so much shorter than td Why are there apparently two characteristic times (ti and rD) for a dielectric medium Friedman [55] suggested two simple thought experiments to resolve the paradox of two times. The relevant theory of dielectrics was described in the 1940s by Frohlich [89],... 

The second thought experiment resembles transient solvation. At t = 0, a certain amount of charge is put on the capacitor plates. This charge jump (D field jump) is analogous to the photon induced change of the dipole moment in the fluorescence solvation experiment. Subsequently (t > 0), the decay of the voltage on the capacitor due to dielectric relaxation of the medium is measured. Note the capacitor in this experiment is not connected to an external power supply for t > 0. The characteristic relaxation time for the decay of the voltage (and electric field E) is t,. 

Ignoring the potential limitations of the dielectric data, we can evaluate the Debye-Onsager model for a number of apparently roughly Debye solvents, like propylene carbonate, the alkyl nitriles, the alkyl acetates, and other solvents. First of all, C( ) is often strongly nonmonoexponential, in contradiction to the theoretical prediction. Second, the observed average solvation time is often much different from xt. 

TABLE 4 Comparison of Experimental and Theoretical Values for Solvation Times in Aqueous Solutions ... 

For other molecules, simulations and theory show a different behavior. If the barrier is comparable or greater than k%T the rate is of course partly controlled by thermal activation (Eq. (41)). On the other hand, if the barrier is zero and the reaction is very exoergic, then the average relaxation time can be much shorter than the average solvation time [139], as is the case for the molecule ADMA, which is discussed in Section III.D. 

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