FDMR in Low-Temperature Solids. 2. Observation of Weakly Bound

J. Phys. Chem. 1994, 98, 13262-13279

13262

FDMR in Low-Temperature Solids. 2. Observation of Weakly Bound Electrons? I. A. Shkrob, D. W. Werst, and A. D. Trifunac* Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Received: November 23, 1993; In Final Form: July 6, 1994@

Time-resolved fluorescence-detected magnetic resonance (FDMR) was used to study radiolysis of organic solids at low temperatures (4-30 K). The mobility of charges generated in the primary events of solid-state radiolysis may be accounted for by two mechanisms: single-step tunneling and relatively slow (106-107 s-l) resonant charge transfer involving the solvent hole. Acting together, these mechanisms engender a variety of unusual and previously unknown spectral features. Although the tunneling satisfactorily explains FDMR behavior in general, quantitative agreement is poor, particularly for donor-acceptor systems. It appears that the origin of this discrepancy lays in an underestimation of the tunneling radii in reactions of negative charges. The latter is rationalized in terms of a selectivity of FDMR toward mobile weakly bound electrons and excited radical anions formed after electron scavenging. The possible nature of these weakly bound electronic states is discussed.

1. Introduction In the previous article of this series’ we examined different mechanisms of charge mobility in order to provide a coherent explanation of results of pulsed time-resolved FDMR (fluorescence-detected magnetic resonance) experiments in radiolysis of organic solids at low temperature. Two mechanisms have been considered in detail: single-step electron tunneling and resonant hole transfer. A theoretical framework based on these mechanisms and the Liouville approach for the description of spin and reaction dynamics in the geminate pairs has been developed, and the theoretical predictions were compared with experimental data. This comparison was not conclusive. The tunneling model accounted for many observations (FDMR kinetics: spectral evolution (section 4), narrowness of the reaction zone3) and readily reproduced such complex and specific phenomena as spin coherence transfer from the primary pairs and ensembleaveraged degenerate electron hopping involving the solvent holes.’ Furthermore, for some systems these models correctly simulated the dependence of FDMR on the solute concentration and predicted the magnitude of the effect. However, for the majority of radiolytic systems, including all the examined aromatic donor-acceptor solutes, the theory largely underestimated the charge mobility. Since the magnitude of FDMR correlates with the thermalization distance of electrons in the corresponding liquid solvents, it is unlikely that theories involving delocalized “supermobile” charges, such as pretrapped electrons4 or electronically excited holes? are applicable. While the tunneling theory in our formulation does not work well, there is no obvious alternative. All the theories of charge mobility in frozen dielectric solids assume electron transfer (ET) via tunneling. They differ only in the details of the mechanisms: single-step tunneling$-* jumpwise migration of the electron between traps with progressively decreasing depths (socalled multisite diffu~ion),~ and degenerate electron exchange involving the solvent hole.lOsll The last mechanism is too slow to account for the observed mobility which is (as will be shown)

* Author to whom correspondence should be addressed. Work Derformed under the ausdces of the Office of Basic Energy Sciences, Division of Chemical Sciehe, US-DOE,under contract number W-31-109-ENG-38. Abstract published in Advance ACS Absrrucrs, November 15, 1994. +

@

associated with the negative charge. The fust two mechanisms both postulate that the mobility of a given particle is a function of the potential barrier through which the tunneling occurs, and any higher mobility implies lower barriers. Since there are traps of different depths in the solid, there must be some weakly bound electrons. That cannot be the case with radical anions for which the barrier height is more a function of the molecular orbital rather than a local property of the solvent. On the other hand, there is a significant difference between patterns of FDMR behavior for different classes of solutes. This suggests a link between electronic structure of the radical ions and their rates of recombination. Perhaps tunneling models developed in ref 1 fail to describe the general experimental results because they are too mechanistic and apply only to a small class of systems for which the simplifying assumptions made are a good approximation. In this article we try to improve these models by including mobile excited species produced in the course of successive ET reactions. Although an involvement of these species is by no means established, ow assumption rationalizes some of the most puzzling observations. 2. Reaction and Spin Mechanisms of FDMR Formation The reaction sequence leading to FDMR formation is shown in Figure 1A. For the sake of continuity the reactions are numbered as in ref 1. Radiolysis leads to the ionization of a solvent molecule S and formation of a hole and an electron (1). This primary pair either recombines (7) or transforms into the secondary pair upon attachment of the electron to an acceptor molecule A (2) or through hole scavenging by an electron donor molecule D (4). Most aromatic scintillators behave as donors and acceptors. Due to the high mobility of electrons in nonpolar liquids, reactions 2 and 7 are nearly an order of magnitude faster than reaction 4 at room temperature.12 Scavenging of primary charges follows ET recombination reactions 3, 5, and 6. Due to the very high rate of reaction 6 in nonpolar liquids, the [e,-. .*D+] pairs do not contribute to the FDMR formation in these media. Being very exoergic (-3-4 eV), the recombination reactions yield excited singlet and triplet solute molecules in approximately equal amounts.13 On the microsecond time scale only singlet luminescence is observable. FDMR measures this luminescence as a function of the external magnetic field

0022-3654/94/2098-13262$04.50/0 0 1994 American Chemical Society

FDMR in Low-Temperature Solids

J. Phys. Chem., Vol. 98, No. 50, 1994 13263

fI

2 t

S B+e-

>

radiolysis

IT+P

lLw

I

e'

I

FLUORESCENCE

- A -

Figure 1. (A) Basic electron transfer reactions participating in FDMR formation in the solid; (B) scheme of the spin transitions active in FDMR; (C) general scheme of the pulsed time-resolved FDMR experiment.

under the resonance microwave @w) condition^.'^-'^ Hereafter, we will reference the pw-dependent part AI, of this delayed fluorescence as the FDMR signal; intensity AI, = Ibw-off) Ibw-on) sampled at the center of the spectrum. Reactions 1-8 are not the only ones leading to fluorescence. A certain fraction of the solute molecules are excited via direct radiolysis, in the cross-recombination of radical ions, or by energy transfer from excited solvent molecules. FDMR is selective to the delayed fluorescence resulting from recombination of spin-correlated (geminate) pairs. Therefore, these other three processes are not significant. This distinguishes FDMR from isothermal luminescence, radiothermoluminescence, electron bleaching, and optical absorbance spectroscopies. It is also important to emphasize a crucial difference between FDMR and magnetic resonance spectroscopies based on the measurement of the pw absorption (such as EPR): with FDMR only radical ions may be observed (neutral radicals are not observed), and only reacting species are detected (whereas with EPR only the surviving species are observed). The time window available for FDMR detection is determined by the life span of the spincorrelated pairs.I4 The spin dynamics of FDMR formation were considered in detail elsewhere, e.g., ref 15. A simplified scheme of spin transitions in the p w field is shown in Figure 1B. The resonant pw field accelerates spin transitions between the TOand T*l triplet sublevels of the pair, which are decoupled in the strong magnetic field of the spectrometer. The middle triplet state (TO) is close in energy to the singlet state (S) and is coupled to it by means of the hyperfine interaction (hfi) between the electrons and magnetic nuclei in the radical ions. Due to Zeeman splitting of the triplet states, the hfi-induced spin transitions between the S state and T+I states are forbidden. Radiolysis creates singlet pairs. After a certain period (-0.05 ps) required for STo mixing half of this population is transferred to the To state. If there is no pw field, both of these states decay without further STo conversion. In the pw field the population of To becomes dispersed among the triplet states, two of them being entirely isolated from the S state involved in the fluorescence generation. Thus, the equilibrium between S and To states is shifted toward the triplet state and more singlet pairs are converted to triplet

ones. Due to rapid recombination from all four spin states, this loss in the population of the S state is irreversible, and the fluorescence yield decreases under the pw irradiation (AI, > 0). This simple consideration is correct only if the pw field is weak. When the pw field exceeds the hyperfine interaction in the radical ions, the fluorescence yield increases due to state10cking.l~ Importantly, the FDMR spectrum is a superposition of the EPR lines from both radical ions constituting the pair. In pulse radiolysis (1 -8) we are restricted to observe FDMR through the recombination of the secondary pairs. Although excited solvent molecules are produced in reaction 7, the fluorescence from the solvent excited states is in the far UV, and the quantum yield is small.18 In many instances decomposition of S* may preclude a transfer of the excess energy from the solvent to solute molecules.18 Nevertheless, the resonance in the primary pairs may be observed via spin memory transfer.lJ9 If the primary pairs live sufficiently long, their spin states mix, this mixing being dependent on the resonance conditions in the pair of 2S+ and e-. Due to spin momentum conservation in the course of reactions 2 and 4, the newly formed secondary pairs retain the spin mixing of the primary pairs. If these secondary pairs were short-lived, spin mixing in the pairs would not develop and the only observable resonance lines would be from the primary pairs. Transfers from the primary pairs have never been found in liquids. By contrast, in the solid the coherence transfer is often a major route of the FDMR formation. Formation of FDMR requires some chemical stability of the radical ions. Various side processes, especially ion-molecule reactions,20destroy both the radical ions and the FDMR effect. We excluded these processes from the reaction scheme shown in Figure 1A. Fortunately, most of these reactions are either very slow or do not occur at or near the liquid-helium temperatures.20 A very special side reaction is the resonant charge transfer 9. Though reaction 9 does not destroy the solvent holes physically, a slow exchange between the nuclear subensembles (as illustrated in Figure 1A) reduces and broadens resonance lines from the species. To observe FDMR, the ET reactions 3 and 6 must not be too slow or too fast. If the recombination is too fast (faster than

Shkrob et al.

13264 J. Phys. Chem., Vol. 98, No. 50, 1994 the MIor pw-induced spin transitions, -0.01 pus), then spin states cannot mix. If the reaction is too slow (> 10 pus), then it cannot be observed on a time scale longer than the geminate ion pair lifetime. In the tunneling model the ET rate constant K decreases exponentially with the separation r between the radical ions,

K(r) = KOexp( -rIA)

(10)

where KO = vFC, v is the oscillation frequency s-'), FC is the Franck-Condon factor for ET, and 2 - 1 A.' At lo5 s-l < K < lo8 s-l and FC 0.1-1 we obtain r, 25 f 3 A. This simple calculation indicates that the pairs active in FDMR are narrowly distributed in The width of this distribution depends on A and is independent of KO. However, it may be shown that if FC were OSA. We observed exactly the same spectral pattern up to

-

-

the longest possible delay times of -4 ps. A characteristic timedependent reduction in the M = 0 line relative to the M = &1 lines was observed only when the pulse duration A exceeded 0.4-0.5 ps at the B1 field of 2.4 G (Figure 3B). A reduction in the relative intensity of the M = 0 line was observed for shorter (0.1-0.2 ps) p w pulses or at short t provided that the p w power was sufficiently great (B1 x 7.5 G, Figures 4 and 5). This effect was very similar to that observed with weaker but longer pw pulses, the spectral shape being a function of a flip angle 8, = B1A of the pw pulse. When the pw power was relatively small (B1 x 0.6 G), the spectra remained dominated by a narrow central line up to t 1.5 ps at T = 0 and maximum A of 4.5 ps. In this “continuous-wave” pw regime the decay of AZ(M=O) was faster at higher pw power (Figure 5 ) . The signal obtained with shorter pulses, as shown in Figure 3A, decayed as -t-‘. The spectral shape did not change with temperature (5-30 K) or solute concentration (10-4-10-2 MI. These features seem to be caused by spectral diffusion resulting from resonant charge transfer (9). In order to establish the occurrence of reaction 9, we examined the effect of concentration on the spectral shape. In these experiments a hydrocarbon (whose radical cation was observed) was diluted with another solvent. We succeeded with lo-* M anthracene-& in 1:lO cis-decalin methylcyclohexane-hl4. The methylcyclohexane radical cation gives an extremely broad signal, and the lines with resonance

-

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13266 J. Phys. Chem., Vol. 98, No. 50, 1994

l?b MW,A=O.2ps

i

e-

Figure 3. (A) Variations in the FDMR spectra from M l”D/n-heptane solution at 10 K with the sampling time t upon the action of a “short”pw pulse (T = 0.03 ps, A = 0.02ps, boxcar sampling over 0.2 ps). (B) Effect of the pulse width A on the broadening of spectra (T = 0.05 ps, sampling from 1.5 to 2 ps). The spectral shape did not change much with ‘t (see the diagram) as soon as f’ exceeded 0.2 ps provided that A was short. The broadeningheduction in the M = 0 line rapidly increased with A. (C) Evolution of the FDMR spectra as a function of the pulse delay time T with the pulse sequence shown in the diagram (A = 0.2 ps, sampling within 0.15 ps after the pw pulse, and 200 G spect” width). Spectral shape does not change with T, and the signal decays as -fl. offset exceeding -15 G are not observable. Analysis of FDMR spectra in methylcyclohexane-ht4 and -d14 show either no or very slow hole hopping with kh 5 x lo5 s-l. A quintet from the cis-decalin radical cation (a(4H) = 51 G, a(4H) = 4.8 G20) is readily observable at low temperature. Time evolution of the FDMR signals from anthracene-dlo in neat cis-decalin (Figure 6A) indicates a resonant hole transfer with kh (1 -3) x lo6 s-l (cf. Figure 8B in ref 1). Since the gas-phase ionization potential (IP) of cis-decalin (9.35 eVZ6)is -0.4 eV smaller than the IP of methylcyclohexane-hl4 (9.76 eV, ref 26), the former should rapidly scavenge the holes from the latter.” Indeed, signals from cis-decalin’+ in this binary solution are comparable in magnitude with the signals in neat cis-decalin (Figure 6B). A comparison of FDMR spectra from the binary cis-decalin methylcyclohexane-hl4 solution and the control methylcyclohexane-hl4 and cis-decalin solutions that were obtained with

-

the same integration interval of 1-1.5 ps and under the same pw conditions showed that the broadeningJreduction effect on the M = 0 line is notably smaller upon dilution (Figure 6). Probably, at shorter sampling times (0.1-0.35 ps) an increase in the AZ(M=O)/AZ(M=fl) ratio could have been explained by a contribution from the anthracene’-/methylcyclohexane*+ pairs. However, at t > 0.5 ps the signals from the control anthracene-d~dmethylcyclohexane-h~4 solution were ca. 1020% of the signal in the binary solution. Thus, the spectral changes upon dilution reflect a slower spectral diffusion in the cis-decalin holes. Due to the high IP of n-alkanes (> 10.2 eVz6)the experiments of the previous design are not possible. However, our observations with electron scavengers (section 43.3) showed that the signals from the alkane holes may be observed even at the extreme (up to 80 mol %) dilution of the alkanes with acetone or c&5. In contrast to the previous result with cis-decalin, the

FDMR in Low-Temperature Solids

J. Phys. Chem., Vol. 98, No. 50, 1994 13267

O.Eps

A

Figure 4. Same system as in Figure 3: effects of pw power. Evolution of the FDMR signal with the sampling time t at B1 = 7.5 G (a) and B I = 0.56 G (b) in the continuous-wave fashion of pw pumping. A comparison between the spectra obtained with different p w power and sampled within 0.2-0.4 ,us (c) and 0.4-0.8 ps (d) after the electron beam pulse. The B I fields are, respectively, (i) 0.2 G , (ii) 0.56 G , (iii) 2.4 G, (iv) 4.2 G, (v) 5.9 G, and (vi) 7.5 G (f20%);the curves are shown on top of each other.

1:8 dilution of n-hexane solutions with acetone M anthracene-dlo, T = 100 ns) caused no change in spectral shape. Note, that in neat cis-decalin kh was 3-10 times smaller than in neat n-heptane or n-hexane. We might assume that 1:8 dilution of n-alkanes with acetone was sufficient to slow down the hole transfer. That would imply that reaction 9 in n-alkanes occurs over more than one molecular diameter. The altemative explanation is that hole hopping is not the only mechanism responsible for the spectral diffusion: hindered rotation could cause similar effects.I0 Further work is required to test the latter possibility. In summary, recombination dynamics and spin evolution in the solid are quite different from the liquid. A surprisingly efficient resonant charge transfer involving the solvent holes was observed. 4.2. Signals from the Solutes. 4.2.1. Donor-Acceptor and Acceptor Solutes. All the previous work on solid-state FDMR has been carried out with donor-acceptor scintillators. In these systems two types of signals may be observed: FDMR arising from recombination reactions involving 2A- and from reactions involving 2Af. In the liquid FDMR may be formed in three types of geminate pairs: [2S+. .2A-], [2A+..2A-], and (in polar media) [2A+. .e,-] (Figure 1A). The relative contribution from the [2S+. .2A-] and [2Af. .2A-] pairs is dependent on the solute concentration. Due to coherence transfer, even the signals from the [*Af. .2A-] pairs may carry some spectral features of the h01es.l~ Formation of these pairs may be precluded by addition of large amounts of the second scavenger. In rigid matrices we may also expect the memory transfer from the primary pairs' (section 2). The subject of prime interest is from which pairs are signals observed in the frozen solid.

The best way to answer this question would be to resolve the hyperfine structure of the signals. Several obstacles prevent this straightforwardtest: inhomogeneous broadening in the rigid matrices, power broadening of the lines, state-locking, and underlying signals from the solvent holes (and, probably, electrons). The f i s t two effects are inherent to the pulsed solidstate FDMR and cannot be eliminated. We failed to resolve the hyperfine structure even for the perfluorinated solute. It is not clear at the present time whether the lack of resolution is due to inhomogeneous broadening, lifetime broadening, or unusual resonance conditions in the anions observed prior to relaxation of the rigid environment. The third problem may be solved either by using a solvent whose holes give very diffuse or very narrow signals, such as methylcyclohexane-hl4, poly(propylene glycol), and deuterated higher n-alkanes, or by sampling the signal within the first 0.05-0.1 ,us when the lines from the solvent holes are relatively weak (section 4.1). The results discussed below were obtained with either the first method or a combination of both. When the protiated scintillators were used, the line from the corresponding radical anions was broad (Figure 7). Although we did not resolve hyperfine structures, often the signals were broad enough to distinguish between the trapped electron et(as these species appear in the donor systems) and 2A*. Despite an extensive search, with the exception of octafluoronaphthalene and benzonitrile (both are the pure acceptor solutes), we have never observed the signals from electrons et-. For some donoracceptor scintillators (PPO,9,lO-&methylanthracene, 4-methoxyanisole, p-dimethoxybenzene) the M i coupling constants in the radical cations are 20-50% higher than in the radical anions. For instance, in the radical cation of p-dimethoxybenzene a(4H)

Shkrob et al.

13268 J. Phys. Chem., Vol. 98, No. 50, 1994

250

1

200

M=O B,=7.5G

\

M-0

ii 150

200

100

50

150 3

g

p‘

g 100

1

2

3

4

50

0.5

1

1.5

2

2.5

3

tlme, pa

Figure 5. Summary of results shown in Figures 2-4 for TMPD in n-heptane. Filled and empty circles: evolution of, respectively, the M = 0 and M = f l lines at the continuous-wave pw pumping with B1 = 2.4 G. The same for the M = 0 line at B1 = 7.5 G (filled squares) and BI = 0.56 G (filled diamonds). For comparison two M = 0 traces obtained with “short” pulses (Figure 3) are shown vide supra. pw pulses are indicated by a white box and the integration window by a blck box.

.. (4

(B)

Figure 6. Effect of dilution on the hopping rate. The spectra are obtained with M anthracene-dlo at 15 K in the continuous-wave mode; numbers indicate the sampling period after the electron beam pulse. (A) Neat cis-decalin; (B) 1:10 (w/w) cis-decalidmethylcyclohexane-h14(i) and neat methylcyclohexane-h14(ii).

-

= 2.6 G and a(6H) = 3.3 G, whereas in the corresponding radical anion a(4H) = 5.1 G and a(6H) 0.28 Another example

is 9,lO-dimethylanthracene.In the radical anion the constants are 2.87 G (4H), 1.5 G (4H), and 3.75 G (6H), and in the radical

FDMR in Low-Temperature Solids

J. Phys. Chem., Vol. 98, No. 50, 1994 13269

(4 (B) (C) Figure 7. FDMR spectra (normalized) from different acceptor and donor-acceptor systems. All traces with the exception of (C, ii) were obtained in methylcyclohexane-hl4 at 10 K, B1 = 2.4 G in the continuous-wave fashion. Numbers in square brackets indicate the sampling interval: (A) signals from (ii) 3 x M 9,lO-dimethylanthracene [0.2-0.6 ps] and (ii) 7 x M PPO [0.1-0.35 ps]; 150 G spectrum width, (B) signal M octafluoronaphthalene sampled within (i) 0.1-0.35 ps and (ii) 0.7-1.2 ps after the electron beam pulse (250 G spectrum width); (c) from M solutions of benzonitrile (5 K) in (i) methylcyclohexane-hl4(BI 0.6 G, T = 0.03 pus, A = 0.26 ps [0.12-0.4 ps], 128 signals from 5 x G) and (ii) n-heptane (6 K, BI 2.4 G, T = 0, A = 0.3 ps [0.05-0.2 ps], 150 G across the spectra).

-

-

.. (A)

Figure 8. FDMR spectra from donor systems (all obtained at 12 K and B1 = 2.5 G, 150 G spectrum width): (A) 1.8 x M TMPD in (i) methylcyclohexane-h14,(ii) squalane, (iii) cis-decalin, (iv) n-octane, (v) 1,4-dioxane, (vi) propan-2-01,(vii) diisopropyl ether (T = 0.03 ps, A = 0.2 ps, sampling within 0.2-0.35 bs);(B) signals from neat triethylamine (continuous-wavepw pumping); (C) signal from 5 x M diethylaniline in n-heptane.

cation the constants are 3.08 G, 1.36 G, and 6.5 1 G, respectively. In the liquid, resonance from the radical cations is readily observable in these systems, forming a broader signal superimposed on the nmower signal from 2A-. We have not observed such signals in solids even at very high concentrations of scintillators (-10-2-10-1 M) and at the longest sampling times (-0.5-5 pus). It appears that in these systems the signal is comprised singularly by 2A- from -50 ns to 5 ps. We observed the [2A+. .2A-] pairs only in neat fluorescers (e.g., 4-metho~yanisole).~It may be concluded that reactions 5 and 6 did not contribute to solid-state FDMR in the usual concentration range. For octafluoronaphthalene (IP % 8.9 eVZ6), which has a diffuse spectrum with a(4F) = 23.2 G and a(4F) = 20 G,29a sharp short-lived feature at the spectral center was observed (Figure 7B). This signal looks very similar to the sharp features in the FDMR spectra in the donor systems, and, probably, the data indicate the spin memory transfer. It is known that in cooled liquids the radical anions (but not the neutral molecules) of octafluoronaphthalene dimeri~e.2~No such process was evident in the solid. With benzonitrile (IP % 9.7 eV,26EA =

-

0.1 eV7) an unexpectedly n m o w signal with fwhm 10 G was observed (cf. a(H) = 8.3 G, a(2H) = 3.9 G, and a(2H) = 0.5 G for the radical anion of benzonitrile,28Figure 7C). Again, this signal may be from the trapped electron rather than the radical anion, although our simulations are not conclusive on that point. It is unlikely that the radical cations of the solutes were produced under the given conditions. For instance, the radical cations of benzonitrile were observed only in radiolysis of CFCL solutions (whose IP is ca 11.9 eV).30 4.2.2. Donor Solutes. If no spin memory transfer is involved, then the FDMR in donor systems must be formed in the [*Df. .e-] pairs and carry no features from the solvent holes. Experimentally, in many solutions (e.g., n-hexane, n-heptane, 2-methyl-n-hexane, n-octane, and cis-decalin) the spectra exhibited well-resolved signals from the corresponding solvent holes (Figures 2-4 and Figure 8). For other solvents studied the signals from the solvent hole were also present but not well resolved (Figure 8A). Similar results where obtained when TMPD was replaced with less efficient scintillators, such as triethylamine and N,N'-diethyl- and dimethylaniline (Figure 8C, Figure 12A).

Shkrob et al.

13270 J. Phys. Chem., Vol. 98, No. 50, 1994 TABLE 1: Relative Magnitudes of the FDMR Signals (Me M Anthracene410 Solutio& (10-30 in Arb Units) from K, B1 = 2.4 G , T = 0, A = 0.2 gs, Sampling Period of 0.2-0.3 as) no signal

iso-C5 (76b) iSO-CS

(93)

weak (5-25)

medium (25-150)

C - c 6 (66) n-C12 (60)

n-C5 (7 1.5)

n-C6 (67.4)

n-Clo (61.6) n-Clr (60.7)

n-C7 (66) n-Cs (64.2)

2,2-Me2-C4(92)

Me-c-Cs 2,3-Mez-C4 (75) dioxane (42) Et, Me-OH (18-20) Et20 (44) (2-WzO(45) hexene-1 (49) c-c5 hexene-2 (55) pentene-1

n-Cli c-C7

3-Me-Cs (69.6) 2-Me-Cs (70.6)

(a)

strong (> 150)

n-Cg (62.2) 2-Me-C7 2-Me-Clo

3-Me-c~

2.4-Me& (75.3) Me-c-c6 Cis- 1,4-Mez-C-C6 bicyclohexyl cis-decalin squalane (59)

For convenience aliphatic chains with x carbons denoted as C,; n at 295 K.12.22,50

= normal; c = cyclo. b&q)/8,

4.3. Variations of FDMR with b~ and Solute Concentration. 4.3.1. Donor-Acceptor and Acceptor Systems. As was demonstrated in section 4.2.1, in the donor-acceptor systems the FDMR signals are formed primarily in the [2Sf. .2A-] pairs. The magnitude AZc of these signals changes dramatically with the solvent nature. To study these variations we measured AIc in some organic solutions and polymers using M anthracene-& as a scintillator. In this concentration range AIc are maximum, and we may expect that the hole-anion distributions closely resemble pe(r). We divided the solvents in four classes: those giving virtually no signal (A& < 5 arb units), weak signals (5-25), medium signals (25-150), and strong signals (> 150). As Table 1 shows, the solvents of the first group are composed of either polar molecules (with the liquid-phase thermalization range parameter bG < 30 A) or spherically shaped (bG > 75 A) molecules. With the single exception of 2,4-dimethylpentane (74.3 A) the thermalization range parameters of the solvents demonstrating medium and strong FDMR are between 59 and 72 A. Ethers (-42-45 A) and n-alkenes (-45-50 A) gave rather weak signals. This bG dependence is incompatible with the concept of reactive pretrapped (“dry” or “mobile”) electrons suggested by Hamill and others! Indeed, if the electrons react prior to localization, then why does FDMR correlate with bG? These data also rule out any involvement of the mobile excited solvent holes suggested in ref 5. A reduction in the FDMR efficiency with both the decrease and increase in bG is expected in single-step tunneling (section 2).l The tunneling scheme predicts that on the longer time scales even the systems in which FDMR is “bo-forbidden” will exhibit the signal due to a broadening of the reaction zone (Figure 4a in ref 1). Indeed, while no signals were found for the high-mobility liquids on the 0.1-1 ps time scale, weak signals from these systems were obtained on the millisecond time scale.lOJ1 Despite this qualitative agreement, the optimum bG (-65 & 5 A) found experimentally relates poorly to the expected values bG r, 25 A. Furthermore, in the spirit of the tunneling model, the variations in AZc should follow variations in pe(rm) = r,* for the solvents with close bG. Ratios of the signals in such solvents are sometimes as high as 20-50. Assuming that the tunneling parameter A is approximately the same in all these systems (A 1.2 & 0.2 A6-8,31), we find that FC in the corresponding ET reactions varies within a few orders of magnitude. This cannot be correct. Firstly, such a variation would result in an extreme dipolar broadening for the solvents with “small” FC factors, which was not observed.’ Secondly, reactions 2 and 3 are so exothermic that it is highly unlikely that small variations in the alkane structure would produce such a remarkable difference in the FC factors.

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Figure 9. Effect of deuterio substitution in the solvent on the FDMR spectra obtained from M solutions of anthracene-& in methylcyclohexane-h14at 10 K (traces a) as compared with the simulated curves calculated in the assumption of equal FC factors for reactions 2 and 3 (traces b). Numbers at the curves indicate (i) methylcyclohexane-h14and (ii) methylcyclohexane-dl4,respectively. The experimental FDMR spectra were obtained at narrower spectral width, and one does not observe the broader spectral features evident in the simulated traces. The Mi constants for the methylcyclohexane-hl4hole are taken from ref 20. To explore the role of FC factors, we compared signals from lop3M anthracene-dldmethylcyclohexane-dl4and -h14 solutions (Figure 9). According to Willard et al., the G-values of trapped electrons in the protiated solvent is m0.23, while for the deuterated compound it is ~ 0 . 3 (77 8 K, EPR and IR detection); that is, the prompt recombination in the former case is 1.65 times more efficient. This difference becomes larger upon an addition of e- scavengers (biphenyl-hlo) or 2S+ scavengers ( t r i e t h y l a m i ~ ~ e )These . ~ ~ , ~data ~ indicate 2-5 times smaller FC factors in reaction 7 with the deuterated solvent. A difficulty with the FDMR experiments on the isotope effect is the narrowing of the signals from 2S+ upon deuterio substitution due to the smaller spin momentum of 2H. This narrowing and the subsequent difference in the state-locking and exchange broadening (reaction 9) must be taken into account when comparing the signals. To correct the data, we simulated spectra from the pairs assuming no difference in the FC factors in reaction 3 (Figure 9b). According to this simulation, the signal from the methylcyclohexane-hl4holes is very diffuse and forms a field-independent background within 200 G. By contrast, the holes from methylcyclohexanedl4 give a broad (fwhm 30 G) yet rather strong unresolved signal. This simulation is consistent with the experimental spectra in Figure 9a. A comparison between the calculated and observed spectra shows very little isotope effect on FDMR. The difference in the signal intensities is caused by a difference in the resonance conditions. In fact, the tunneling theory is compatible with this observation. A 2- to 3-fold variation in KO would give a relatively small variation of r, and, consequently, similar weights of the FDMR-active pairs.’ At r, bG the weights are practically independent of variations in the FC factors. Since methylcyclohexane is a “good” solvent (Table l), that is, its bG is optimum, the absence of an isotope effect in FDMR regardless of a strong effect on the G-values is not inconsistent with the tunneling nature of charge mobility.’ As this example demonstrates, although the FC factors of ET did affect the tunneling, it is unlikely that the variations of AIc with media were caused by a large-scale variation in the FC factors of ET.

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FDMR in Low-Temperature Solids

J. Phys. Chem., Vol. 98, No. SO, 1994 13271

200

160 Series1

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Series3

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-.

a

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Figure 10. Concentration dependences of AIc obtained at BI = 2.5 G, T = 0, A = 0.2 G , and boxcar sampling from 0.2 to 0.35 ps after the electron beam pulse. Series: (1) anthracene-dlo in methylcyclohexane-hl4, 15 K; (2) biphenyl-& in methylcyclohexane-hl4, 15 K; (3) TMPD in methylcyclohexane-hl4, 15 K; (4)benzonitrile in n-hexane, 15 K; ( 5 ) octafluoronaphthalene in n-hexane, 18 K; (6) anthracene-& in 2.2 x lo-* M solution of naphthdene-hs in n-heptane, 12 K, (7) triethylamine in n-hexane, 6 K; (8) anthracene-dlo in cis-decalin, 6 K. Figure 10 shows concentration (C) dependences of the signals from anthracene-dlo and biphenyl-dlo in methylcyclonexaneh14 and benzonitrile and octafluoronaphthalene in n-hexane at 15 K. In accordance with the qualitative picture drawn in ref 1, the signal grows until C approaches some critical value M) and then stays the same or decreases. A reduction in the signal with dilution is much less than expected on the basis of the tunneling model. With the single exception of benzonitrile, the decrease is linear with C only in very dilute solutions (C < M for anthracene-dlo) in which the average closest distance between the solute molecules and other species is - C 1 I 3 > 80 A. In more concentrated solutions AIc was proportional to log(C). Since the nonlinearity in our model may be achieved only at V,C 1, the result is a serious discrepancy with the tunneling model. As Figure 10 indicates, anthracene is not alone in this behavior. All but one donor-acceptor scintillator gave a similar pattern. These flattened C-dependences resulted from the specific ET kinetics in the donor-acceptor systems. Experiments described below corroborate this conclusion. 4.3.2. Concentration and be-Dependences in the Donor Systems. FDMR behavior observed in the donor systems is very different from that in the donor-acceptor systems. First, the signals were detected only at rather high concentrations of amines, and the increase in AZ, was linear with the solute concentration up to C 0.1 M (Figure 10). Second, while practically all the solvents which gave strong FDMR signals in the donor-acceptor systems gave strong signals with the amines, many other solutions previously categorized as “weak” become “medium”. This includes polar solvents, such as alcohols and ethers. For instance, the signal from TMPD in 1Q-dioxane is 1.5 times greater than the signal in methylcyclohexane-hl4 solutions, whereas with anthracene-dlo it is 10 times smaller (Table 2 ) . In some media (water, alcohols, tetraethylorthosilicate, poly(dimethylsi1oxane)) TMPD gives a sizable signal, while the donor-acceptor systems do not give any. This and other results indicate that the instability of the

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TABLE 2: Relative Magnitudes of FDMR Signals (AZcin Arb Units)from 1.8 x lo-* M TMPD Solutions (15 K, B1 = 2.4 G , T = 0.03 ns, A = 0.2 gs, Sampling over 0.2-0.35 ~ s ) no signal weak” ( 15 mol % the signal decreases as in other systems (Figure 11A). Micro-heterogeneity of the binary solution may be responsible for this peculiar behavior. 4.4.4. Solvent Hole Scavenging. This type of double scavenging experimental has been reported by the Novosibirsk group, which applied the steady-state FDMR technique to glassy hydrocarbons at 77 K." It was found that addition of various solutes (diethyl ether, 1-hexene, benzene, tetramethylethylene, and triethylamine) to the naphthalene-d$squalane and naphthalened$cis-decalin solutions reduced the signals from %+ in the systems. For the most efficient (hole) scavenger, triethylamine, a c50 2 x M was found. We repeated this experiment with 1.5 x low2M anthracene-d&-heptane solution. The outcome of this experiment was opposite to the results reported in ref 11. As previously mentioned, FDMR signals from the alkane solutions of triethylamine may be readily observed with no second solute added. Signals from the solvent holes are well resolved -0.3 ps after the pw pulse; the relative weight of M = f l lines increases with the delay time (section 4.1, Figure

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12A). Due to the spin memory transfer, the signals from 2S+ cannot be eliminated from the spectra even at high concentration of triethylamine. We simulated the experiments performed in ref 11, sampling the fluorescence signal at a short delay time, -0.1-0.3 ps, when the M = &1 lines from the 2S+ were not detectable without the second solute added. In this control experiment we added 10-2-2 M triethylamine, and M anthracene-dlo was constant. It was found that the spectral shapes were identical even when 1.5 M triethylamine was added (Figure 12B), although the signal linearly decreased with concentration of triethylamine (by 15% per mol/L). A similar result was obtained upon addition of another scavenger used in ref 11,tetramethylethylene. The shape of FDMR spectra did not change even with the molar concentration of this solute added though AI, decreased more rapidly than in the previous system. Our results are consistent with other data indicating that reaction 4 (contrary to reaction 2) is a relatively shortrange ET tunneling reaction. Striking differences between our results and those obtained with steady-state FDMR indicate a difference in the mechanisms of the FDMR formation over lo-' s (at 4-20 K) and s (at 77-240 K) time scales.

5. Discussion 5.1. Time Evolution of FDMR Signals: Spin-Locking vs Resonant Charge Transfer. The observed effects resemble but are not totally consistent with state-10cking.l~ First of all, the isolation of S- and T-terms is not complete; the singlettriplet transitions in the high pw field are just slow. Consequently, at longer observation times the states mix and the locking is less pronounced.16 Note that the flip angles of the applied pw pulses, including the short ones (0.1-0.2 ps), exceeded 50-300"; that is, the spin states were sufficiently locked even with these short pw pulses. A further increase in the pulse duration could only weaken the isolation of the spin states by causing weakly forbidden spin transitions. This behavior has been observed in the liquid-state FDMR: l6 under the continuous-wave pw irradiation the state-locking effects were stronger at shorter sampling time t. In the solid the

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Shkrob et al.

opposite picture was observed: the reduction and broadening in the central lines were more efficient at longer sampling times. Furthermore, a progressive decrease in the AZ(M=O)lAZ(M=&l) ratio was observed even when the pw pulses were delayed 0.10.5 ps relative to the electron beam pulse. Theoretically, if the delay time of the pw pulse is longer than the period of the STo mixing, the state-locking cannot fully develop. During the “onpulse” period the spin states are isolated and the singlet-triplet transitions are stopped, so a loss in the population transferred from the S-states to the To-states during the “off-pulse” period cannot be reversed afterwards. Recently, one of us reported experimental observation of this p h e n ~ m e n o n : ’ as ~ , ~soon ~ as the pw pulses were 0.05-0.2 ps delayed, the FDMR traces did not exhibit a sign change up to B1= 30 G. On the contrary, in low-temperature solids the pulse delays did not affect the efficiency of the state-locking. Even a rather slow spectral diffusion due to degenerate electron exchange (reaction 9) would destroy the state-locking. Because of this exchange, nuclear configurations with small local magnetic fields are randomly mixed with configurations with large local fields, this inhibiting the state-locking. Experiments with the exciplex systems reported in ref 15 demonstrated that even at the moderate rate of reaction 9, kh IO6 s-’, the state-locking is completely suppressed (see also ref 17). Note that the state-locking is very dependent on the Mi constants in the radical ions. Very similar broadening effects were observed with anthracene-dlo, 9,10-dimethylanthracene,and octafluoronaphthalene, where the mean Mi constant in the correspondent radical anions increases as 2,20, and 60 G, respectively. These results contradict the attribution of the observed features to statelocking. One can also neglect the exchange effects involving the negative charges: firstly, this process is impossible in the TMPD system, while the spectral evolution in both the systems was similar. Secondly, the spectral shape was independent of the acceptor concentration. The pw-induced, low-frequency quantum must be excluded also. The corresponding frequency would be close to the Rabi frequency,25which gives an oscillation period of -0.2 ps at B1 = 2 G. This period is reduced to 0.04 ps at our maximum p w field of 7.5 G. Both periods are too short to account for the observed features. Attempts to rationalize the observed spectral evolution in terms of dipolar broadening, spin exchange, and the spin memory transfer were equally unsuccessful. However, a good qualitative agreement with the experiment was achieved when the resonant charge transfer reaction 9 was included in the calculations (Figure 8 in ref 1). The rate constant kh of this exchange was estimated as -10’ s-l, which reasonably agrees with the independent estimates made in refs 10 and 11. Resonant hole transfer readily explains the main features of the spectra: (i) broadening of the spectral lines and reduction in the AZ(M=O)IAZ(M=&l) ratio with delay time after the pw pulse; (ii) higher rates of this reduction in the higher pw fields; (iii) forestalling broadening in the M = 0 line; sensitivity of the spectral shape to the pw pulse delay; (iv) concentration dependence. 5.2. Electron Donor Solutes: the Spin Memory Transfer. It must be stressed that while the aromatic amines are much more efficient as electron donors than acceptors, under some experimental conditions (e.g., at UV irradiation of the cooled potassiuddimethoxyethane solutions) they did produce radical anions.34 Although the reaction of electron attachment to amines is very endothermic and, therefore, must not occur at very low temperatures, the process is a potential source of ambiguity in the interpretation of our results. However, we can conclusively exclude this possibility:

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(1) According to ref 34, the hfi constants in 2TMPD- are a(4H) = 5.4 G and a(2N) lG, while in the *TMPD+ these are much larger: a(4H) = 1.99 G, a(4CH) = 6.8 G, and a(2N) = 7.1 G.28,35Simulations of the FDMR spectrum from the IO-* M TMPD solution in methylcyclohexane-hl4 showed that it may be well rationalized as a superposition of the signals from 2TMPD+ and a Gaussian line with fwhm N 8 G (state-locking distortions were included in these computations). As the numbers show, the signal from the radical anion would be broader than the sharp feature obtained. (2) 2TMPD- has never been detected in alcohol and alkane glasses with steady-state EPR. The only observed species were the radical cations 2TMPD+. (3) We observed the very same sharp line in neat triethyland tributylamines (Figure 8). In frozen triethylamine the narrow (fwhm 12 G) signal entirely dominated the spectrum at t 5 1.5 ps; at longer times a very broad unresolved signal from the radical cations was superimposed on the sharp line. The same sharp features were found in the pure acceptor systems (see above). (4) The sharp feature persists upon addition of molar quantities of acetone, C&, and nitrobenzene. It is very unlikely that TMPD radical anions would be formed with many better electron acceptors present. We conclude that a sharp feature in the FDMR spectra is from the trapped electrons, and the signals from the solvent holes were observed due to spin memory transfer from the primary pairs. It appears that the transfer is a general feature for both the pure donor and pure acceptor systems. The appearance of excess electrons in magnetic resonance spectra is w e l l - d o ~ u m e n t e d . ~ ~ EPR, - ~ ~ spin-echo EPR, and ENDOR observations of et- in glasses were a subject of many studies and A good half of these studies were performed on the TMPD solutions studied here. So far, the EPR signals were observed from either glassy matrices or some very specific crystalline polyols (such as sucrose). In the latter the electrons are trapped in either microcavities (cyclodextrine) or specific sites where 2-3 OH dipoles are fortuitously oriented.36b Polycrystalline hydrocarbons-with no reference to their structure-gave no signals from et-. The line width of the signals from e- is known to be controlled by inhomogeneous broadening and reflects dipole-dipole hfi interactions with the surrounding protons of the solvent molecules. This interaction is strong for polar molecules (fwhm 10-15 G) and relatively weak for nonpolar hydrocarbons or deuterated alcohols (3.54.0 G).36a The sharp feature in the FDMR spectra in the nonpolar protic solvents is ca. 8 G wide. This estimate is consistent with a narrowing of the central line from fwhm 12.5 to -9.5 G upon lowering B1 from 2.5 to 0.56 G (TMPD/ methylcyclohexane-hl4, 12 K). It is clear that the signal from et- is unusually wide. As expected, in the polar media (e.g., dioxane, propan-2-01, diisopropyl ether, Figure 8A) the spectral width was greater than in the methylcyclohexane glass, even at the earliest detection times, when the signals from the solvent holes were expected not to interfere. We found that the FDMR signals were qualitatively similar in the glassy and polycrystalline samples; moreover, in methylcyclohexane (which may be solidified in both ways) the spectra were found to be identical. Apparently, the electrons probed with our time-resolved FDMR techniques were not electrons probed by the steady-state EPR or spin-echo EPR spectroscopy of irradiated frozen samples. In the liquid (e.g., in photoionization of TMPD in propan-2-oP5), time-resolved FDMR spectra exhibited a common sharp feature from the solvated electron.

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FDMR in Low-Temperature Solids

J. Phys. Chem., Vol. 98, No. SO, 1994 13275

Steady-state FDMR from the excess electrons trapped in glassy hydrocarbons (at 77- 120 K) has been previously studied with the continuous-wave FDMR method by the Novosibirsk gr0up.~~9* It was found that line widths of these spectra fairly well agree with the numbers obtained with the continuous-wave pw-detected EPR (although the former ones are ca. 0.2 G higher).37 It is noteworthy that no spin memory transfer from the primary pairs was observed in these steady-state FDMR studies. 5.3. Nonlinearity in the C-Dependence. One can interpret the observed nonlinearity in two ways: (i) as a decrease in AIc at higher C relative to the values extrapolated from the lowconcentration region or (ii) unexpectedly high mobility at low concentration. Certainly, the results on the donor and acceptor systems advocate in favor of the latter interpretation. Let us, however, consider the opposite assumption fist. A decrease in the fluorescence yield at higher solute concentration may be due to a self-quenching of luminescence, formation of the [2A-. .2A+] and [e,-. .2A+]pairs, aggregation of A at high concentrations of the solute, degenerate hopping between 2A- and A, dimerization of A and 2A+, and morphological changes in the solids. We can reliably exclude contributions from other than [2S+. .2A-] pairs. Any involvement of [2A+..2A-] pairs would influence the ratio of signals from 2S+ and 2A-. Experimentally, the spectra from 10-4-2 x lo-* M solutions of anthracene-dlo in 1: 10 v/v cis-decalidmethylcyclohexane-hl4had the same shape to the highest concentration. Furthermore, we may exclude degenerate electron exchange 2A- A A 2Adue to its slowness at the low temperature and (in contrast to reaction 9) low concentration of the neutral molecule^.^^ As for the proposed aggregation of the species, the propeller-like biphenyl molecules do not cluster and the radical cation of biphenyl does not dimerize (with the exception of freon solution^.^^). The C-dependence obtained with this scintillator was similar to that for anthracene-dlo, and the range of nonlinearity for biphenyl-dlo is even broader than for anthracenedlo. Radical anions of octafluoronaphthalene are known to dimerize in the cooled liquid solutions.29 This circumstance did not alter the logarithmical character of the C-dependence for this scintillator. The alcohol solutions of biphenyl exhibited a signal growing linearly with C up to 0.3 M.3 Signals in TMPD and benzonitrile systems grow linearly up to 0.05 M. Thus, the fluorescence self-quenching was not responsible for the nonlinearity. Moreover, this nonlinearity was quite apparent in the dilute solutions of scintillators for which no structure-breaking effects were expected. Generally, hydrocarbon structure did not affect the shape of the C-dependence for a given solute. As illustrated in Figure 10, for anthracene-dlo the normalized C-dependences were found to be nearly identical in methylcyclohexane-hl4, cisdecalin, n-hexane, and 2 x M naphthalene-h$n-heptane solution. Since the rate of reaction 9 in these solutions varies at least 3-10 times, the hole hopping was not responsible for the observed nonlinearity. 5.4. Double Scavenging in the Presence of Strong Electron Acceptors. According to Miller and Beitz, the FC factors in the ET reaction 2 for 9-methylanthracene (EA 0.78 eV), hexafluorobenzene (1.75 eV), and p-dinitrobenzene (1.96 eV) in methyltetrahydrofuran at 77 K are close to the same value of 10-2.7 Their result suggests that inefficiency of the scavengers with high electron affinity to suppress FDMR should not be due to slow electron scavenging. However, if that were right, nearly all the electrons would be scavenged at high solute concentration. That was not observed. Moreover, in the TMPD solutions the solutes with electron affinity did not compete for

+

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+

the electron with the scintillator. Nevertheless, C50 in these systems were still in the molar range. Apparently, the scintillators with lower EA were much better electron scavengers than these high-EA compounds. Contrary to the results reported in ref 7, reaction 2 was very inefficient provided that EA exceeded ca. 1.2 eV. Miller and Beitz observed a decrease in the FC factors for reaction 2 with increasing EA when the latter exceeded ca. 2-3 eV? In terms of the tunneling model this could mean only one thing: the inverted region of the Marcus bell-shaped dependence of FC on the driving force for ET. Frequently, the exothermicity is sufficient to excite the radical anions electronically; in this case there is no decrease in the FC factor.’ For the electron affinic solutes used this excitation energy is quite high, and a decrease in FC factor with EA is expected. Our data can be easily explained in terms of the tunneling model if the electrons observed with FDMR are higher in energy than those observed by optical absorption spectroscopy. If the exothermicity of ET reaction 2 were higher for the FDMRprobed electrons, then the increase in the FC factors would be observed at lower EA. From the correlation of the ET rate constants and EA obtained in ref 7, one may estimate the excess energy needed to provide a difference of -300 times in the FC factors upon a given increase in the EA. This estimate is ~ 0 . 8 - 1 eV. Since for the “normal” electrons the binding energy B 1- 1.6 eV, we obtain that for the FDMR-probed electrons, B 0.2-0.4 eV. Once more we reach the conclusion that the FDMR-detected electrons have rather unique properties. 5.5. Single-Step Tunneling. Let us summarize the observations. Resonant hole transfer 9 is a relatively slow reaction that has little effect on charge mobility. The tunneling model works fairly well for the pure donor and pure acceptor systems, but fails to account for FDMR formation in donor-acceptor systems. For the latter, reaction path 2 is preferred to 4. In all the systems studied optimum r, exceeded the expected values by 2-3 times. Electrons observed with FDMR have rather broad magnetic resonance spectra and are very energetic. ET reactions involving radical anions have rates very similar to reaction 2, unlike ET reactions involving the solvent holes. As emphasized in ref 1, single-step tunneling explains many findings and cannot be easily rejected. Consequently, let us assume that the single-step tunneling model is valid but the tunneling parameters used were not appropriate. Now the problem is reduced to answering (i) what parameters were wrong and (ii) why were these parameters wrong? 5.5.1. Tunneling Parameters. If the tunneling model is correct, then the observed discrepancy could be due to (i) an overestimation of bo or (ii) an underestimation of r, in reactions 3 and 6 . (i) An overestimation of the 2S+-to-e,- separations could be caused by a shortening of bo in solid hydrocarbons relative to the values in the liquids. However, it is unlikely that this shortening is sufficient to account for the observed difference of 2-3 times. On the other hand, we have indications that the electrons which we have observed were weakly bound. Electrons in the solids are believed to be trapped in preformed traps: clusters with fortuitous orientation of the solvent molecules,40caves, and crystalline lattice defects.41 The density of a given type of site may differ. Quite possibly, the shallow traps are more abundant than the deep ones, and the bG values for the weakly bound electrons are different from those for the solvated electrons in liquids. There are some grounds for these speculations. According to the spectroscopic and photobleaching experiments (reviewed in refs 3 1, 42, and 43) the trapped electrons are indeed located in potential wells of different depths. Due to the slow site-to-

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Shkrob et al.

13276 J. Phys. Chem., Vol. 98, No. 50, 1994 site tunneling, a thermal equilibrium in the system is achieved over a very considerable time. Thus, the binding energies B and the tunneling parameters A = B-I” of trapped electrons are somehow distributed around the mean values -0.75-1.2 eV with a dispersion parameter no less than 0.1-0.2 eV. This distribution is very broad for ethanol glass at 77 K, in which B energies are found to cover an interval from -0.5 to -2 eV?2 For weakly exoergic reaction 2 this distribution causes a variation in the exothermicity and, therefore, ET rates.6 Since the more weakly bound electrons react faster than the electrons in the deeper traps, the endothermicity of ET grows with time (the so-called “deepening of traps”). This mechanism is responsible for the flattening of et- decay curves in the ethanol and methyltetrahydrofuran g l a s s e ~ . ~The . ~ same mechanism is likely to account for the flattened et- decay curves obtained for highly exothermic reactions 2 proceeding via electron excitation of the radical anion^.^ Radiothermoluminescence experiments also indicate the deepening of traps in polar media.I3 When the electrons are strongly bound, exothermicity of reactions 3 and 6 is insufficient for singlet excitation. Frequently, in the afterglow spectra the luminescence is triplet, whereas in the spontaneous radiation-induced spectra, luminescence is both triplet and ~ing1et.I~ Steady-state FDMR at 77200 K also indicates the presence of different sites in hydrocarbons. An analysis of the satellite structure in the et- line performed in ref 38 suggests that on average the excess electrons observed with that technique are located in the caves -3.6 8, in diameter, where they interact with two to three protons (squalane, 120 K; cis-decalin, 77 K). This is quite different from the results on EPR and electron spin-echo spectroscopy rationalized in terms of an electron trapped in a cave -6-7.5 8, in diameter interacting with as many as 18-21 protons (3methylpentane, 77 K).44 (ii) In regard to an underestimation of the reaction radii in reactions 3 and 6, a broad spectrum of binding energies B for ET reaction 6 would increase 1 and r, for the weakly bound electrons and broaden the spherical layer bordering the FDMRactive pairs. Such an increase would cause a substantial increase in the weight of FDMR-active pairs, thus giving more proper estimates of the FDMR intensity. The increased r, would naturally explain the absence of dipolar broadening in the examined geminate radical ion pairs. However, unlike the trap depths of e,- the binding energies of structurally well-defined anions are expected to be fairly similar. According to the photoelectron emission spectroscopy (reviewed in ref 46), bound-continuum transitions from the radical anion 2An- in the ground state occur at the photon energy ’2.2 eV. This energy is only -0.5 eV for the excited state (tetrahydrofuran, 295 K). The former threshold is somewhat smaller for the naphthalene radical anion, 1.7 eV. However, this B is still larger than the average trap depth of et-. Both (i) and (ii) have the same origin: a selectivity of FDMR toward the weakly bound electrons. There are no clues, however, why higher B for the electrons should affect the rate of reaction 3. Let us consider the C-dependences assuming that the electrons involved in the FDMR formation are weakly bound. In the donor systems the C-dependence was linear and mainly reflected efficiency of reaction 4. We know that in the donoracceptor systems the rate of this reaction was much slower than the rate of reaction 2. That would be the case if reaction 4 were an ordinary (short-range) tunneling reaction and reaction 2 were a long-range reaction of the weakly bound electron. In the donor-acceptor systems the C-dependence was controlled by the negative charge scavenging. If reaction 2 is long-range, it would explain the observed increased yield of the radical

anions. However, to observe FDMR there must be reaction 3 generating the fluorescence. If the electron scavenging occurred over a much longer distance than r, in reaction 3, then the latter would be a limiting step, and the C-dependence would be still linear. Thus, qualitatively, the C- and bedependences may be explained if both tunneling reactions 2 and 3 are long-range while reaction 4 is short-range. There is the odd case of benzonitrile. The EA of this solute is quite low (0.1 eV vs 0.09 eV for biphenyl, methyltetrahydrofuran7), so reaction 2 must be a long-range one. Thus, the anomalous behavior was due to a short r, in reaction 3. With the same approach we may explain results on the double scavenging. Radii of ET reactions 2 and 12 were close because their tunneling barriers were close: both were long-range reactions. Strong acceptors did not work since reaction 2 was too slow: the exothermicity of the scavenging was too high to provide matching of the vibrational wave packets? No such obstacle existed for hole scavenging, but this reaction is shortrange and may compete with the reaction path 2,3 only at very high concentrations of the electron donor solute. Now we may answer the first question. Single-step tunneling consistently explains FDMR results if the barrier energy in the FDMR-probed ET reactions 2 and 3 is unusually small. 5.5.2. Electron Transfer Distance. Reaction radii r, would be greater than the “normal” values only if 1 were higher than -1 8, (apparently, KOcannot exceed 1015s-l). This suggestion implies 1 2-3 8, or B 0.1-0.3 eV. The figures are consistent with estimates made in section 5.4. Interestingly, the same small values of B were earlier suggested by Brocklehurst to account for the observed rates of thermal detrapping of electrons in the soft glasses.47 The concept of shallow traps was also applied to interpret the relative yields of the singlet and triplet product^,'^ different yields of trapped electrons at 4 and 77 K,36 etc. We have already mentioned data on photobleaching, kinetics of electron decay, and absorption spectroscopy showing the existence of traps with different depths, at least in the polar media. The fundamental difficulty with our assumption is a striking contradiction between the estimated 1and the values obtained from the results on electron and hole scavenging in glasses.6-8 In some systems (e.g., TMPD/2-chlorobutene) these experiments gave 1 1.2 A,which was referred to as the superexchange mechanism operating in the solvent.8 It is hard to believe that such an exotic mechanism comprises a general rule. Rather, the true mechanism must be applicable to most of the solvents and be intrinsic for the reaction sequence 2 (or 6) and 3. Indeed, as was demonstrated above, we did not observe increase A in reactions 4. There are three major features which are different in ET reactions in the FDMR-detected pairs and in the scavenging reactions studied with transient absorption techniques: both electron donor and electron acceptor were ionic species; the product of the ET reaction was an electronically excited solute molecule; the electron acceptor is 2S+ (this would be important for the superexchange mechanism); reaction 3 is preceded by exoergic reaction 2. The last feature may be crucial for the FDMR formation since highly exothermic ETs frequently lead to the generation of energetic radical anions 2A-* lying -0.7-1.0 eV above the ground state (Figure 13A).7,45,48The first excited states of the radical anions are deactivated within -0.01-0.1 ns. Since these states are closer to the conduction band of the solvent than the ground state, the binding energy of the electron at the state B* must be substantially smaller than B, and the corresponding ET would have a greater A. When the rate of this ET is higher than the rate of deactivation, most of the anions decay through

-

-

-

FDMR in Low-Temperature Solids

+e’+A

J. Phys. Chem., Vol. 98,No. 50, 1994 13277

+

1

*il

% = = + % -

S+’A*

10

20

CS)

30

40

50

r/A-

Figure 13. (A) Proposed scheme of the FDMR formation via rapid reactions initiated by electrons from the shallow traps; (B) effective rate constant of the forward ET as a function of the separation between ’Sf and ’A-.

the forward ET. With increase in the separation distance r, the rate of the forward transfer from 2A-* becomes smaller than the rate of deactivation and ET from +A2 prevails. The radical dependence of the ET “rate constant” in this twolevel system may be expressed in terms of an effective parameter

where K*(r) = KO exp(-r/A*) is the rate constant of ET from 2A-*, K ( r ) = KO exp(-r/A) is that from 2A-(;1*>;1) and

is the yield of 2A- ( k b is the deactivation rate constant). Figure 15 shows a comparison between K(r) and Kedr) calculated with = 1 A, A* = 2 A, KO = loi5S - ’ , and kda = 10” S-’. As the calculation shows, at r > r*, where r* is the radius at which K*(r*) kda, the radical dependence of Kedr) is very similar to K(r). Both have an asymptotic -exp(-r/A) behavior, but Kedr) >> K(r). Therefore, spectroscopic techniques with a time resolution worse than kda-’ 0.1 ns would demonstrate a “normal” decay kinetics. The only correction to the formulas we previously derived is a shift r,,, r,,, r*, which is precisely what was postulated earlier. Involvement of the excited radical anions readily explains the anomalous behavior of benzonitrile. This solute has a rare combination of a very high (’2 eV7) first excited state of its radical anion (similarly to the acceptors with electron affinity that were used) but has a relatively low EA (unlike other acceptors). Without involvement of the

-

-

-

+

energetic states reaction 3 exhibits a “normal” range and the C-dependence was linear, At high concentration of the solute the self-quenching

+

2~-* A

4

2

~

+A -

(15)

must compete with the forward ET, which (as much as an overlap of the reaction zones’) explains the observed decrease in the FDMR signal at C > M. A mechanism of increase in the mobility of radical anion upon an attachment of the very energetic electron may be quite different (Rydberg states, collective states with the solvent, etc.). Any such mechanism, however, should provide an overall lifetime of the radical anion(s) not less than 20-30 ns (judging from the broad resonance lines in the FDMR spectra of the species) and not more than 1-2 ,us. The exothermicity required for population of the 2A-* states significantly exceeds the expected electron affinities of aromatic scintillators, which are not greater than 0.2-0.3 eV in the solid. To provide the proposed downhill transfer, the binding energy B of electrons should be rather small. This assumption unifies both of our proposals. Within this general scheme, pulsed time-resolved FDMR follows a sequence of chemical events initiated by the weakly bound electrons, leaving the reactions initiated by more strongly trapped electrons undetected due to the time window limitations. In the first step the excess energy of electrons in shallow traps is transferred to the radical anions. Low binding energy of these

13278 J. Phys. Chem., Vol. 98, No. 50, 1994 electrons increases the reaction radius of scavenging which causes more effective generation of the radical anions over a shorter period. The energy transferred to the radical anions dissipates in two ways: via the forward ET to the solvent hole and via a nonradiative deactivation. Interplay between these reactions increases the ET radius r, for reaction 3 without changes in the parameter A at t > 10 ns. Both these long-range reactions may have escaped the earlier observation precisely because they cause a rapid loss of the negative charges via geminate recombination. A fraction of the strongly bound electrons would react on the sub-microsecond scale. However, their scavenging would not lead to the production of the excited radical anion, so the following reaction 3 would have a “normal” radius, and FDMR would be inhibited at the low solute concentrations (as in the benzonitrile solutions). Thus, the reactions initiated by these electrons are doubly inefficient: their scavenging is too slow and the second ET is short-range. Within this scheme, the observation of unusually broad signals from the electrons in TMPD solutions illuminates the transitory nature of these electrons: they are short-lived species located in the shallow traps. The same assumption explains why no electron EPR signal was observed in the polycrystalline samples while observed with FDMR: all these electrons rapidly recombine. Since in the electron donor systems the scavenging of the holes is a reaction with “normal” radius, the FDMR has linear concentration dependence (though an “abnormal” bG-dependence due to an involvement of the weakly bound electrons). 5.6. Nature of the FDMR-Probed Electrons. The binding energy B of the FDMR-probed electrons estimated from the reaction radii and exothermicity of reaction 2 is -0.1-0.3 eV. Photoexcitation of these electrons would cause their ejection into the conduction band. This explains why the species could not be observed optically: the corresponding transitions lie in the region of the IR fundamentals, so the solvent would absorb most of the incident light. The exact mechanism of trapping in the nonpolar solids is still unknown. Common wisdom is that the electron is trapped in some preformed defects. Electrons are bound to these structures by means of electrostatic interaction with individual C-H bond dipoles.40 This concept may be suitable to account for the properties of strongly bound electrons detected with EPR, UV/vis, and IR spectroscopies but is not applicable to the electrons detected with FDMR. First of all, the number of these defects seems to be too high. Their density is practically independent of the solid being crystalline or vitreous, addition of the molar quantities of solutes, and so on. Furthermore, the trapped electrons in alkane glasses have fairly narrow EPR lines, while the lines of the FDMR-probed electrons are 2-3 times broader. This inhomogeneous broadening indicates that the latter species were much more spin-delocalized than the EPRdetected electrons. On the other hand, the reaction dynamics of the FDMR-detected electrons can be described by a singlestep tunneling model. Interestingly, calculations based on the microdipole model suggested in ref 40 predicted B 0.5 eV even for the most fortuitous orientations of the bond dipoles, as well as a considerable charge delocalization over more than two or three solvent shells. This model, however, poorly reproduced absorption spectra. The alternative 3D-well model proposed to Yoshida41satisfactorily reproduced these spectra but postulated the existence of spherical cavities of -5 A in diameter. There should not be many such caves in the tightly packed crystals, and, indeed, G(e,-) values in the crystalline solids are much smaller than in the g l a s s e ~ . ~ Both ~ . ~calculations ~ indicate that the electrons detected with FDMR were not trapped in the usual sense.

-

Shkrob et al. It is suggested here that one should visualize the FDMRprobed electron as a strongly scattered p ~ l a r o n . ~A~“hot” .~~ electron formed in reaction 1 rapidly loses energy in collisions with the solvent molecules. Velocity of this loss depends on the elasticity of electron-molecule collisions and intermolecular forces (i.e., properties of the lattice to absorb the impacts as a whole). Both these factors affect thermalization of electrons in liquids, so it is not unreasonable that there is a correlation between the distribution of “cooled” electrons in the solid and in the liquid. At a certain point the relaxed excess electrons propagate as polarons via a band-type motion. However, prior to this moment the electron colliding with molecules could impose structural defects from which it cannot freely e s ~ a p e . ~ ~ . ~ ~ Properties of these electrons must be intermediate to the quasifree electrons and the ones localized in the deep preformed traps. Substantial spin delocalization and small binding energies are explained within this concept. The weakly bound electrons in our model are not as localized as the strongly bound ones. However, they are somehow distributed around the solvent holes. These electrons propagation via single-step tunneling and not by thermally activated band motion and the subsequent retrapping.

6. Conclusion This work provides insights into the mechanism of lowtemperature radiolysis of solids. We found that the results on pulsed sub-microsecond-resolved FDMR may be explained in terms of two mechanisms of charge mobility: slow (106-107 s-l) hopping of the solvent holes and single-step electron tunneling. Acting simultaneously, these mechanisms provide a variety of spectral features, many of them previously unknown. The unexpectedly rapid resonant hole transfer could result from the superexchange in the solvents. Although the tunneling mechanisms account for the results in general, tunneling models in their original formulation poorly reproduced the scale of ET reactions. Analysis of discrepancies between theoretical and experimental results showed that the concept of tunneling is consistent with the data. However, the ET parameters which we put into the models must be readjusted. Qualitative agreement may be achieved by rescaling the decrease parameters A in ET reactions 2 and 3. This suggests that FDMR detects chemical transformations of weakly bound electrons, while slow reactions of more strongly trapped electrons are not detected on this time scale. The weakly bound electrons decay via a long-range and rapid ET to acceptor molecules. The high exothermicity of this transfer leads to the population of an excited state of the radical anion. This causes a competition between a long-range forward ET to the solvent holes and deactivation into the ground state (which follows a short-range transfer to the holes). As a result, the radial dependence of the recombination constant is biexponential, with a steep decrease (A 2-3 %.)within the first -20 A, succeeded by a rapid decrease (with common A- 1 A) at higher separations between the partners. When reaction 2 involves more strongly bound electrons, only the ground state of the radical anion is produced, and the short-range reaction 3 is statistically disfavored. The involvement of electrons with unusual properties is proven by the FDMR spectra obtained in donor systems: the observed electrons have much broader lines than the EPR-detected species. We estimate binding energies of the FDMR-probed electrons as -0.10-0.3 eV. The electrons are quite dissimilar to those observed with optical techniques. Rather, they resemble a state intermediate to quasi-free electrons and the electrons trapped in clusters or cavities formed by the solvent molecules. It may be assumed that in frozen solids the electrons are trapped in

-

FDMR in Low-Temperature Solids two distinctive steps: firstly, these intermediate states are formed; secondly, the electrons are further trapped via a longrange ET to the preformed sites.

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