Solvated electron mobility

The diffusion coefficients of the ion are usually estimated from their mobilities (or conductances), which can be measured independently. Diffusion coefficients (or mobilities) vary over very large ranges for the solvated electron in different solvents (neopentane, D 2 x 10 4 m2 s 1 and n 7 x 10 3 m2 V-1 s 1 hexane, D 2 x 10 7 m2 s 1 and ju 8x 10 6 m2 V-1 s 1) [320]. There is considerable evidence that the mobility of electrons is not constant, but on the contrary, the mobility depends on the applied electric field, increasing approximately proportionately with electric field at high fields in solvents where n is small and decreasing with electric field in solvents where n is large. If the solvated electron mobility depends on the electric field, then the diffusion coefficient may also depend on the electric field. The implications of these complications are discussed in Sect. 2.2 and in Chap. 8, Sect. 2.7. 

Doldissen et al. [348] found that the solvated electron mobility may be increased (or decreased) fourfold at fields 107Vm 1 compared with the mobility at low fields (<105 Vm 1). Such electric fields are small compared with those mutual fields when ions approach to within 2 nm or less of each other (>2xl08 Vm 1). No measurements of drift mobilities have been possible at such electric fields. It is not possible to state that the field dependence extends to these large electric fields, though the trend of the experimental results at moderately large electric fields is often extrapolated to large electric fields (Mozumder [349] and... 

The electron will be solvated in a region where the solvent molecules are appropriately arranged. There must be a cluster of electrons of a size of 4-5 to support the formation of the solvated electron from the results of Gangwer et al., [23], Baxendale [24,25], and Kenney-Wallace and Jonah [16]. This behavior does not depend on the specific alcohol or alkane and even occurs in supercritical solutions, as has been shown in experiments done using mixtures of supercritical ethane-methanol mixtures [19]. Experiments have also shown that the thermodynamically lowest state might not be reached. For example, the experiments of Baxendale that measured the conductivity of the solvated electron in alcohol-alkane mixtures showed that when there was a sufficient concentration of alcohols to form dimers, there was a sharp decrease in the mobility of the electron [24,25]. This result showed that the electron was at least partially solvated. However, the conductivity was not as low as one would expect for the fully solvated electron, and the fully solvated electron was never formed on their time scale (many microseconds), a time scale that was sufficiently long for the electron-alcohol entity to encounter sufficient alcohols to fully solvate the electron. Similarly, the experiments of Weinstein and Firestone, in mixed polar solvents, showed that the electron that was observed depended on the initial mixture and would not relax to form the most fully solvated electron [26]. 

In experiments done by Baxendale [24] and Baxendale and Sharpe [25] in mixed n-propanol-hexane systems, it was found that at low concentrations of alcohol, a solvated species was formed however, it was not the solvated electron. The existence of the solvated species was determined by the decrease in mobility of the electron in the solvent. The mobility never decreased to the level that would be expected for the solvated electron and no evidence of the solvated electron spectrum was detected. 

Carbon disulfide is isovalent to carbon dioxide and it also has a bent monomer anion. While gas-phase CO2 has negative EAg of —0.6 eV [24], for CS2, EAg is +0.8 eV [34]. Despite this very different electron affinity, Gee and Freeman [34] observed long-lived electrons in CS2 (with lifetime > 500 psec) with mobility ca. 8 times greater than that of solvent cations. Over time, these electrons converted to secondary anions whose mobility was within 30% of the cation mobility. Between 163 and 500 K, the two ion mobilities scaled linearly with the solvent viscosity, as would be expected for regular ions. Of course, Gee and Freeman s identification of the long-lived high-mobility solvent anions as electron is just a manner of speech Obviously, quasifree or solvated electrons cannot survive for over a millisecond in a positive-EAg liquid. 

As already stated, the diffusion coefficient and mobility of a solvated electron, though much smaller than that of a free electron in a conduction band, are some 4-5 times larger than for the solvated cation. There is some doubt whether the electron carries along a solvated shell with it, and there has been discussion in the literature of mechanisms by which molecules drift across the cavity, changing their orientation as they do so. 

Up to now, only hydrodynamic repulsion effects (Chap. 8, Sect. 2.5) have caused the diffusion coefficient to be position-dependent. Of course, the diffusion coefficient is dependent on viscosity and temperature [Stokes—Einstein relationship, eqn. (38)] but viscosity and temperature are constant during the duration of most experiments. There have been several studies which have shown that the drift mobility of solvated electrons in alkanes is not constant. On the contrary, as the electric field increases, the solvated electron drift velocity either increases super-linearly (for cases where the mobility is small, < 10 4 m2 V-1 s-1) or sub-linearly (for cases where the mobility is larger than 10 3 m2 V 1 s 1) as shown in Fig. 28. Consequently, the mobility of the solvated electron either increases or decreases, respectively, as the electric field is increased [341— 348]. 

Fig. 28. Electric field dependence of the solvated electron drift mobility in liquid ethane at various temperatures (K). After Doldissen et al. [348].

Hummel and Luthjens [398] formed electron—cation pairs in cyclohexane by pulse radiolysis. With biphenyl added to the solvent, biphenyl cations and anions were formed rapidly on radiolysis as deduced from the optical spectra of the solutions. The optical absorption of these species decreased approximately as t 1/2 during the 500 ns or so after an 11ns pulse of electrons. The much lower mobility of the molecular biphenyl anion (or cation) than the solvated electron, es, (solvent or cation) increases the timescale over which ion recombination occurs. Reaction of the solvated electron with biphenyl (present in a large excess over the ions) produces a biphenyl anion near to the site of the solvated electron localisation. The biphenyl anion can recombine with the solvent cation or a biphenyl cation. From the relative rates of ion-pair reactions (electron-cation, electron—biphenyl cation, cation—biphenyl anion etc.), Hummel and Luthjens deduced that the cation (or hole) in cyclohexane was more mobile than the solvated electron (cf. Sect. 2.2 [352, 353]). 

Any analysis of the recombination probability of the solvated electron with a cation may be further complicated by the possibility that there are two states of the solvated electron, loosely described as a localised and a delocalised state. These are believed [399] to be associated with lower and higher drift mobilities of the solvated electron, respectively. The consequences of such a complex transport behaviour on the recombination probability of solvated electrons has been discussed by Tachiya and Mozumder [328]. 

In suggesting an increased effort on the experimental study of reaction rates, it is to be hoped that the systems studied will be those whose properties are rather better defined than many have been. By far and away more information is known about the rate of reactions of the solvated electron in various solvents from hydrocarbons to water. Yet of all reactants, few can be so poorly understood. The radius and solvent structure are certainly not well known, and even its energetics are imprecisely known. The mobility and importance of long-range electron transfer are not always well characterised, either. Iodine atom recombination is probably the next most frequently studied reaction. Not only are the excited states and electronic relaxation processes of iodine molecules complex [266, 293], but also the vibrational relaxation rate of vibrationally excited recombined iodine molecules may be at least as slow as the recombination rate [57], Again, the iodine atom recombination process is hardly ideal. 

Let us use the obtained values of the diffusion coefficients D in water-alkaline glasses to estimate the contribution of diffusion to the decay of etr by reaction with acceptors at low temperatures. Let us estimate, for example, the temperature at which, for a typical concentration of acceptor additive N = 10 2M and for a maximal time of observation t = 106s, the condition 4nRDDNt = 0.01 [or, which is the same thing, exp( —4nRDDNt) = 0.99] will be fulfilled, i.e. the decay of et by the diffusion channel will amount to 1%. Taking into account the abnormally high mobility of solvated electrons [114] it is reasonable to assume that the main contribution to D is made by the diffusion of elr rather than by that of the acceptor. In this case, all the values of D obtained above must be related to the same process, the diffusion of e. ... 

The metallic nature of concentrated metal-ammonia solutions is usually called "well known." However, few detailed studies of this system have been aimed at correlating the properties of the solution with theories of the liquid metallic state. The role of the solvated electron in the metallic conduction processes is not yet established. Recent measurements of optical reflectivity and Hall coefficient provide direct determinations of electron density and mobility. Electronic properties of the solution, including electrical and thermal conductivities, Hall effect, thermoelectric power, and magnetic susceptibility, can be compared with recent models of the metallic state. 

SCHEME 4.1 Schematics of radiolysis and reducing species. As a result of ionization of the water molecule, hydroxyl radicals and hydrated electrons are formed. The final radiolytic yield depends on the secondary reactions in spurs and on the presence of other compounds. See Refs 25,26,190, and 191 for the detailed discussion and references. Solvated electrons are mobile enough to escape spurs and to react with the heme protein complexes even at 77K. All other reactive products of radiolysis are immobilized in the solid solvent matrix, or trapped by radical quenchers. 

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. 

The metals, and to a lesser extent Ca, Sr, Ba, Eu, and Yb, are soluble in liquid ammonia and certain other solvents, giving solutions that are blue when dilute. These solutions conduct electricity electrolytically and measurements of transport numbers suggest that the main current carrier, which has an extraordinarily high mobility, is the solvated electron. Solvated electrons are also formed in aqueous or other polar media by photolysis, radiolysis with ionizing radiations such as X rays, electrolysis, and probably some chemical reactions. The high reactivity of the electron and its short lifetime (in 0.75 M HC104, 6 x 10"11 s in neutral water, tm ca. 10-4 s) make detection of such low concentrations difficult. Electrons can also be trapped in ionic lattices or in frozen water or alcohol when irradiated and again blue colors are observed. In very pure liquid ammonia, the lifetime of the... 

Most methods for determining the electron mobility use pulse radiolysis techniques in which the concentration of electrons is followed during or after the ionizing pulse, either by the time-of-flight method or by measurement of the change in conductivity. However, due to the inherent conductance of polar liquids, direct conductivity measurements of solvated electrons are generally difficult in these media. Therefore, the diffusion coefficient and the mobility of the solvated... 

Delaire JA, Delcourt M-O, Belloni J. (1980) Mobilities of solvated electrons in polar solvents from scavenging rate constants. /Phys Chem 84 1186-1189. 

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