Solvation time

Mozumder s (1988) conjecture on electron thermalization, trapping and solvation time scales in liquid water is based on combining the following theoretical and experimental information ... 

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... 

From the above equation it appears convenient to characterize solvation dynamics by means of the solvation time correlation function C(t), defined asa)... 

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. 

Figure 3 Solvation time in alcohols of the electron and the benzophenone anion, plotted versus the longitudinal relaxation time tj. (The dipole data are from Refs. [5,6].)...

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. 

If one compares the log of the solvation time to the log of viscosity, the two primary alcohols fall on the same straight line and this line has a slope of 1. The 2-propanol, while correlated with viscosity, does not show a linear dependence [21]. 

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],... 

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 3 Comparison of Calculated Average Solvation Times from Dielectric Continuum and MSA Models with Experimental Results... 

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. 

TABLE 5 A Comparison of the Average Electron Transfer Times of 9,9 -Bianthryl in Various Polar Solveuts to the Average Solvation Times of Coumarin Probes... 

The reader is also referred to the innovative nonphotochemical electron transfer studies of Weaver et al. [147], These authors have been exploring dynamical solvent effects on ground state self-exchange kinetics for or-ganometallic compounds. This work has explored many aspects of solvent control on intermediate barrier electron transfer reactions, including the effect on a distribution of solvation times. The experimental C(t) data on various solvents have been incorporated into the theoretical modeling of the ground state electron transfer reactions studied by Weaver et al. [147]. 

After thermalization, the electron may recombine with a positive ion or be captured by a molecule forming a negative ion, or it may be locked in a trap the role of which may be played by fluctuation cavities or structural disturbances in the medium, or by polarization pits that the electron digs when it interacts with surrounding molecules. Such captured electrons are called solvated electrons (in water they are sometimes called hydrated electrons).31,32 According to the data obtained in picosecond pulsed-radiolysis sets,33 34 the solvation time of an electron is 2 x 10-12 s in water and —10 11 s in methanol. 

When solvation time is much shorter than the lifetimes, both constructions of c(f) give very similar results because v (f) vsc. However, when solvation dynamics becomes slower, such as in proteins, on a time scale close to the lifetimes, the contribution of v/(f) is significant, and Eq. (6) must be used to construct c(t). For all results reported here, we used Eq. (6). Note that for the molecular dye probe with only single lifetime emission, Vi(t) = vt 0) = vss = v(oo) and Eq. (6) becomes equal to Eq. (1). 

Extensive studies in reverse micelles revealed a similar water distribution [127-130], which is consistent with the distinct water model proposed by Finer [150]. For example, when the molar ratio (wo) of water to the surfactant is 6.8 in lecithin reverse micelles with a corresponding diameter of 37 A, three solvation time scales of 0.57 (13%), 14 (25%), and 320 ps (62%) were observed using coumarin 343 as the molecular probe. At w0 = 4.8 with a 30-A water core diameter, only a single solvation dynamic was observed at 217 ps, which indicates that all water molecules are well ordered inside the aqueous pool. The lecithin in these reverse micelles have charged headgroups, which have much stronger interactions with water than the neutral headgroups of monoolein in the... 

Direct MD simulations of the observed Stokes shifts and corresponding solvation time scales for several proteins were reported recently [188, 199, 202, 203]. Overall, significant discrepancies exist between simulation results and experimental observations, but some general features are promising. Here, we summarize one of our recent MD studies of W7 in apomyoglobin with linear response and direct nonequilibrium calculations and highlight the critical findings, as well as point out extensive improvement required in theoretical model [199]. 

Ab initio and Monte-Carlo calculations. Attempts have appeared in pulse radiolysis to describe the dynamics of free electron production, recombination and solvation on a microscopic scale [31-34]. This requires the knowledge of a number of physical parameters solvated electron and free ion yields, electron and hole mobilities, slowing-down cross-sections, localization and solvation times, etc. The movement and fate of each reactant is examined step by step in a probabilistic way and final results are obtained by averaging a number of calculated individual scenarios. 

In water e solvation time is much shorter (r = 0.3 ps at room temperature [31]) and one may think that e may contribute to Ps formation. At present there is no clear theoretical judgment on such a possibility. However, there is some experimental evidence (see the next section) against participation of e in Ps formation. 

Fig. 5.5 Temperature dependencies for Ps formation probability, electron solvation time and positron lifetime in n-propanol. With changing temperature from 150 K to 300 K the electron solvation time in n-propanol varies within 5 orders of magnitude. At the highest studied temperature r approaches 10 ps. At low temperatures it exceeds e+ lifetime T2 more than 1000 times. If e had really contributed to Ps formation, Ps yield would have to decrease. However, it even slightly increases. This fact favors the presolvated electron as the main precursor of Ps formation.

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