The solvent holes

Another crucial finding was the realization that rapid spin-lattice (Ti) relaxation in the high-symmetry cycloalkane radical cations precludes their detection with optically-detected magnetic resonance (ODMR) [39-48], the technique which was routinely used to study radical cations in radiolysis of hydrocarbons [38, 50]. For example, trans-decalin + isolated in room-temperature cyclohexane has Tj 7 ns [50] while typical solute radical cations have Ti 1 ps. Since it takes several tens of nanoseconds to flip the electron spin with the microwave radiation (which is required for the magnetic resonance detection) radical cations of some cycloalkanes cannot be detected by ODMR. 

RadiolyticaUy-generated solvent holes have initial excess energy of several electron-volts. It is generally believed that these excited species relax to the ground state on a picosecond time scale or even faster [37,38,53]. Nevertheless, some authors suggest that certain excited cycloalkane holes have lifetimes in nanoseconds [54,55]. Such suggestions are not completely 

It is difficult to assess the plausibility of this scenario because the data allow for more than one interpretation. N2O rapidly scavenges thermalized electrons and quenches the solvent excited states thus reducing the yield of olefins (that form by the fragmentation of these excited states) [1]. Since in some hydrocarbons the olefin radical cations may be formed in reactions of the solvent holes with the olefins in spurs (see below), the yield of these cations will decrease in the presence of N2O. Therefore, the changes observed upon the addition of N2O are not a clear-cut evidence for the involvement of the excited solvent holes. 

The optical absorption spectra of the high mobility solvent holes resemble those for the radical cations isolated in freon matrices [20,22-25]. All of these spectra are bell-shaped featureless curves with maxima in the visible and/or near IR regions. In pulse radiolysis studies, the absorption signal from the solvent hole always overlaps with the signals from the fragment (and/or secondary) radical cations ( satellite ions ), even at the earliest observation times [22-25,57]. Therefore, complex deconvolutions are needed to extract the spectra of the solvent holes. This leaves large uncertainty as for the exact shape of the absorption spectra and the extinction coefficients. 

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The reader may notice that only saturated hydrocarbons (with a possible exception of CCI4) have been observed to yield rapidly migrating solvent holes. As mentioned above, part of this bias is explained by the fact that the holes are usually short-lived, so their dynamic properties are difficult to study. However, in many liquids (such as aromatic hydrocarbons and sc CO2), the solvent holes are relatively stable, yet no rapid hole hopping is observed. In such liquids, the solvent hole has a well-defined dimer cation core with strong binding between the two halves (in the first place, it is this dimerization that... 

Class (3) reactions include proton-transfer reactions of solvent holes in cyclohexane and methylcyclohexane [71,74,75]. The corresponding rate constants are 10-30% of the fastest class (1) reactions. Class (4) reactions include proton-transfer reactions in trans-decalin and cis-trans decalin mixtures [77]. Proton transfer from the decalin hole to aliphatic alcohol results in the formation of a C-centered decalyl radical. The proton affinity of this radical is comparable to that of a single alcohol molecule. However, it is less than the proton affinity of an alcohol dimer. Consequently, a complex of the radical cation and alcohol monomer is relatively stable toward proton transfer when such a complex encounters a second alcohol molecule, the radical cation rapidly deprotonates. Metastable complexes with natural lifetimes between 24 nsec (2-propanol) and 90 nsec (tert-butanol) were observed in liquid cis- and tra 5-decalins at 25°C [77]. The rate of the complexation is one-half of that for class (1) reactions the overall decay rate is limited by slow proton transfer in the 1 1 complex. The rate constant of unimolecular decay is (5-10) x 10 sec for primary alcohols, bimolecular decay via proton transfer to the alcohol dimer prevails. Only for secondary and ternary alcohols is the equilibrium reached sufficiently slowly that it can be observed at 25 °C on a time scale of > 10 nsec. There is a striking similarity between the formation of alcohol complexes with the solvent holes (in decalins) and solvent anions (in sc CO2). 

Lifetime of the solvent hole estimated assuming exponential recombination kinetics, ns. 

Since the formation of the secondary D. ..A pairs occurs with some delay, this can cause a phase shift in quantum oscillations. The spread of phase shifts also leads to a decrease in oscillation amplitude. The delay results mainly from the finite time of the solvent hole trapping by an acceptor molecule D. Due to high electron mobility, its capture by acceptor A is much faster. Under these conditions, the phase shift is related to the concentration [D] of the hole acceptor via a simple relationship... 

Similarly short lifetimes are expected for branched alkanes, such as isooctane [22]. Due to these lifetime limitations, the chemical behavior of cycloalkane holes is understood in more detail than that of the solvent holes in other hydrocarbon liquids. 

From conductivity studies, it is known that the cycloalkane holes rapidly react with various solutes, typically by electron or proton transfer [7-19]. These scavenging reactions establish the identity of the high-mobility cations as the solvent holes Rapid generation of aromatic radical cations (A +) in reactions of the holes with aromatic solutes (A) was observed using pulse radiolysis - transient absorption spectroscopy [4,5,6,20,23-25] and, more recently, using pulse-probe laser-induced dc conductivity [26]. Rapid decay of the conductivity and transient absorbance signals from the cycloalkane holes was also observed [4-25]. 

The formation of high-mobility holes and "satellite ions". As was briefly mentioned above, radiolysis of hydrocarbons results in the formation of several types of cationic species besides the solvent holes. Most of these "satellite ions" are generated within the first nanosecond after the radiolytic pulse. 

In some cases, the identity of paramagnetic "satellite ions" was established by ODMR [42,44,48]. For example, 9,10-octalin + was identified in decalins and their solutions [42]. ODMR spectra of "satellite ions" in cyclohexane were related to EPR spectra of matrix-isolated cyclohexene + (Note that in the liquid cyclohexane, cyclohexene + undergoes a fast ring-puckering motion that averages hyperfine coupling constants for equatorial and axial protons, so the the EPR spectra of cyclohexene + in liquid and solid matrices are different) [42,44,48]. In both of these cases, the olefin radical cations were formed in spurs rather than in a reaction of the solvent hole with the olefin in the solvent bulk [42] (octalins gradually accumulate as radiolytic products). Olefin "satellite ions" were also observed in squalane [24]. 

Second, the "satellite ions" could be generated in scavenging reactions of the solvent holes with radiolytic products in multiple-pair spurs [25,61-65]. The olefins are formed upon the fragmentation of excited solvent molecules generated in recombination of short-lived electron-hole pairs [1]... 

This mechanism would also account for rapid generation of carbonium ions in reactions of the solvent holes with radicals [65]... 

Knowing the absolute values of f/, is important since using the previous estimates for /ih led to unrealistically large reaction radii for reactions of cyclohexane and methylcyclohexane holes with low-IP solutes (2-3 nm ) [8, 14]. These radii suggested extreme delocalization of the solvent hole. Using the correct mobilities reduces these radii to ca. 1 nm which is close to a typical electron-transfer radius in a non-viscous hydrocarbon. 

Rate constants for cyclohexane holes may be found in references [7,8,11,13,14,17], for decalin holes - in references [8,9,12,14,26], for methyl-cyclohexane holes - in references [12,122], for squalane holes - in references [24,30]. The data on the temperature dependence of rate constants of scavenging for the four cycloalkane holes are in reference [10]. For these holes, most of the rate constants were measured by determining the decay kinetics of the transient conductivity signals as a function of the solute concentration. The preferable way of studying the scavenging reactions is by detection of the excess dc conductivity following the "hole injection" reactions (10) and (11) [10-13,26]. In cyclohexane, the determination of the rate constants is complicated by the fact that the solvent hole is in equilibrium with an impurity in the solvent [11]. 

Class (ii) reactions were directly observed for the solvent holes in cyclohexane [11] and methylcyclohexane [122]. For some solutes (SH), the equilibrium... 

The corresponding rate constants are 10-30% of the fastest class (i) reactions and exhibit short reaction radii of 0.15-0.4 nm. Unlike the electron-transfer reactions (that may occur through space), the proton transfer requires close proximity of the donor and acceptor. Thus, short reaction radii of class (iii) reactions suggest a low degree of the solvent hole delocedization. 

Therefore, while in the fluorescence studies the solvent holes were observed before the equilibrium (12) was reached (ca. 7 ns in 3 mM solution), in the conductivity studies the solvent holes were observed well after this equilibrium... 

The only reliable data were obtained for scavenging the solvent hole in cyclohexane by cyclopropane [8,17] and for scavenging the solvent holes of cyclohexane and decalins by oxygen [14,19]. For the latter reactions, the reaction constants are (l-3)xl0 M-l s-l [14], more than two orders of magnitude lower than those for class (i) reactions. Our thermochemical analysis suggests that this reaction is initiated by the H atom transfer to O2 [14]. 

Measurement of the effect of electron scavengers on the RH yield show that scavengers are more effective in reducing this yield than they are in scavenging electrons. A kinetic mechanism was proposed in which a fraction of the solvent holes are initially in an excited state that does not yield the solvent Si state upon recombination [53]. The relaxation and fragmentation of the pre-... 

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