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John E. Willard
Trapped Electrons in Organic Glasses‘ John E. Willard Department of Chemistry, University of Wisconsin,Madison, Wisconsin 53706
(Received July 23, 1975)
Publication costs assisted by the U.S. Energy Research and Development Administration
The experimental observations dealing with trapped electrons in organic glasses which are most revealing as to the nature of the trapping process are discussed, and a model of trapping which they suggest is outlined. Data from optical and ESR spectrometry, differential thermal analysis, bleaching, decay, and scavenger studies are cited. It appears that after mobile electrons produced by y irradiation or photoionization of solutes are thermalized they first become stabilized in weak traps through polarization and dipole interactions and then deepen these traps by molecular orientation at rates dependent on the polarity of the matrix molecules and the temperature. The data suggest that the stabilized condition at any temperature involves a continuum of trap depths in which the electrons give optical spectra of different A,, which add up to give the broad observed spectrum. The energy of a photon absorbed by an electron in excess of the detrapping threshold for that electron determines whether the electron can migrate far enough to encounter a capturing entity. If the energy is too low the electron is retrapped rather than being bleached. Evidence for capture of epithermal subexcitation electrons by some scavengers and on the heats of solvation of electrons and cations in organic glasses is also noted.
Introduction Starting in 1962 it was demonstrated2 that electrons liberated by ionizing radiation in several glassy matrices at cryogenic temperatures can be stabilized in chemically uncombined states observable by optical and ESR spectra. Such trapping has now been observed in such widely different glasses as alkaline ices (e.g., 10 M NaOH), aqueous sugar solutions, alcohols, ethers, amines, alkenes, and alkanes. By contrast, significant yields of trapped electrons have not been found in similar crystalline ~ y s t e r n s . ~ This paper evaluates the current understanding of the electron trapping process in glasses, as deduced from experiments in many laboratories, including the author’s. 11lustrations will be taken largely from pure hydrocarbon and methyltetrahydrofuran matrices. Electron spin resonance and optical absorption spectrometry are the most direct methods of detecting trapped electrons (et-) in glasses and give some of the most revealing evidence as’to the nature of the interaction of electrons with the matrix molecules. Significant corollary evidence has been obtained from luminescence, electrical conductivity, and differential thermal analysis studies; from investigations of photobleaching and thermal decay; and from comparative studies with different matrices and different electron scavengers. Endeavors to provide a theoretical understanding of the observed phenomena are in progress in several groups.* Among the questions raised by the trapping of electrons in the glasses are the following. Does the stabilization occur a t preexisting sites or are the traps formed by electronic polarization and bond dipole interaction with the coulomb field of the electron (i.e., does the electron “dig its own hole”)? Are all electrons in a given matrix trapped with the same energy? What accounts for the broad optical spectra of the trapped electrons? What are the distances between cations and electrons? Does photoexcitation promote to a bound state of the trap or to the conduction band? How far do mobilized electrons travel? Do they inevitably combine The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
with the geminate cation? Can trapped electrons tunnel to deeper traps, cations, and scavengers? What are the heats of solvation of trapped ion pairs? Some of these questions are now answered and others are under continuing investigation. The step-by-step evolution of understanding of the phenomena may be traced in review articles dealing with irradiated glassy solid^.^
Physical Properties of Organic Glasses In general glasses used in the study of trapped electrons are formed by immersing a tube of the liquid a t room temperature in liquid nitrogen. Typically this results in a density increase of ~ 3 0 %As . ~the viscosity increases on cooling, the glass transition temperature (T,) is reached (typically a t 10I2 to 1013 P), below which the rate of molecular relaxation becomes too slow for the enthalpy and free volume to keep up with the rate of cooling in maintaining their equilibrium value (Figure 1).Glasses formed by rapid cooling to below T , anneal toward the equilibrium state with time. This is evidenced by an increase in the endothermic differential thermal analysis (DTA) peak which appears on warming the sample8 and by a decrease in the decay rate of trapped electron^.^ Annealing is much slower a t temperatures considerably below T , than near Tg.8 Partial orientation of the molecules of 3-methylpentane (3MP), methylcyclohexane (MCHx), and 2-methyltetrahydrofuran (MTHF) glasses in electric fields as low as lo4 V cm-* has been demonstratedlO a t temperatures near T,, suggesting that the much more intense field in the vicinity of a trapped electron may aid it in producing molecular orientations which result in trapping. The orientation is much greater in MTHF, which has a molecular dipole, than in the hydrocarbons where interaction with bond dipoles must predominate. The glasses are transparent to visible light. If cooled much below the glass transition temperature, they often crack. Some (e.g., MCHx and ethyl alcohol) crystallize on warming while others (e.g., 3MP and MTHF) do not.
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Trapped Electrons in Organic Glasses Production of Electrons in Glassy Solids Free electrons may be produced in glassy solids by exposure to high energy electrons from accelerators or the high energy electrons ejected by y rays or x rays. These electrons (e.g., >0.1 MeV) eject secondary electrons every 1000 8, or so along their tracks and each secondary electron ejects some two to four electrons which are trapped within “spurs” of some 150 8, or less radius in the glasses. Electrons may also be formed in glasses by photoionization of solutes (e.g., N,N,N’,N’-tetramethyl-p-phenylenediamine (TMPD)5g or sodium metalll). In contrast to y irradiation, this method gives random distribution, the nature of the cation is definitively known, and if monochromatic light is used the energy given to the electron is known. Also, if the ionization potential of the solute is less than that of the solvent, it may be assumed that the positive charge does not migrate. A chemical method hm proved effective for generating electrons in water and alcohols deposited from the vapor phase on a rotating metal drum in vacuo. When sodium or potassium vapor is allowed to condense on such a deposit a t 77 K, trapped electrons are produced.12 Trapped Electron Yields as a Function of Matrix and Dose Hydrocarbon glasses typically give G values for trapped electrons (number of electrons trapped per 100 eV of ionizing radiation absorbed) of 2.13 These values are lower than the values of 3 to 414 for the yield of primary ionization events determined by charge collection in the gas phase, but higher than the G(free electrons) detectable by charge collection in the liquid phase (e.g., G(et-) in glassy 3MP at 77 K is 0.65 while G(free electron) in the liquid at 300 K is 0.1515). In the gas, the long mean free path of the electron precludes geminate recombination with the parent cation following thermalization; in the much more dense liquid, thermalization occurs within a relatively short distance and geminate recombination is probable. In glasses the densities, and hence the thermalization distances, are similar to the liquid case (unless the probability of energy loss per collision is less in the glass because of fewer vibrational and rotational degrees of freedom), but return of the electron to the cation is often prevented by trapping. Similar traps in the liquid are mobile, allowing rapid neutralization, and are also less stable to thermal destruction. Although the yields of trapped electrons are uniformly higher in polar compounds than hydrocarbons, molecular structure plays a role independent of polarity. For example, the G(et-) values in 3-methylheptane (3MHp), 3-methylhexane (3MHx), and 3MP glasses are about 0.5, 0.7, and 0.7, whereas in 2,4-dimethylpentane (2,4-DMP) and 2,4dimethylhexane (2,4-DMHx) they are 0.09 and 0.17, and in polycrystalline hydrocarbons negligible trapping of e- occurs. In hydrocarbon glasses some of the electrons produced by ionizing radiation are chemically trapped by radicals, forming carbanions.16Since no method has yet been developed for determining the yields of either the carbanions or cations, it is possible that G(tota1 charged pairs) is similar for all hydrocarbon matrices. In this case the differences in G (et-) between different hydrocarbons would be accounted for by the effect of differences in the pathlength for thermalization of the electrons on the competition between
TP
T.
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TEMPERATURE
Figure 1. Schematic diagram of enthalpy and volume changes dur-
ing cooling, heating, and annealing of glasses near the glass transition temperature: (curve A) rapid cooling; (curve B) slower cooling; (line C) equilibrium enthalpy and volume achieved after prolonged annealing from A or B; (- - -) direction of change on anneallng; .) changes on warming after different extents of annealing; (- - -) extrapolated behavior of liquid.
-
-
(.a
physical trapping and carbanion formation. Large differences in thermalization distances are suggested by the observation that electron mobilities in liquids of spherical molecular structure (e.g., CH4 and neopentane) are as much as lo3 greater than for molecules of linear structure (e.g., n -pentane).17 In principle an attractive method for determining the relative electron trapping efficiency of different matrices without interference from electron capture by radicals would be to determine the quantum yields for production of et- in glasses by photoionization of solutes. However, factors such as bleaching of the et- by the photoionizing light, absorption of activating light by the cation product and radical formation by photosensitized mechanisms complicate the interpretation of such studies. With increasing y dose to organic glasses at 77 K, the concentration of et- passes through a maximum (at about 1020 eV g-l for hydrocarbons and higher for polar glasses) and then decreases.16aJ8This must result from increasing probability of electron reaction with cations and radicals as the concentration increases to a value where the spurs overlap Thus studies of the mechanisms of trap formation can best be made at lower doses. Characteristics of t h e Trapping Process Deduced from Optical Spectra Electrons trapped in organic and alkaline ice glasses all give broad (>3 eV) absorption spectra in the visible or near infrared.lg These spectra have bandwidths at half-height ranging from -0.5 eV for hydrocarbons to >1 eV for some alcohols, long tails on the high energy side of A,, and shorter tails on the low energy side, and extinction coefficients at A,, of lo3 to lo4. They have been the single most fruitful source of evidence on the properties of the traps and the dynamics of trapping. Effects of Polarity and Phase. A plot of the photon energy at A,, at 77 K vs. the static dielectric constant (D,) of the matrix compound for D , values for 12 compounds, from 2 for the hydrocarbons to 42 for glycerol, gives a smooth curve.2o This suggests that trap depths increase with increasing polarity of the matrix molecules, as do similar data on blue shifts with increasing polarity in a series of glassy alcohols,21in liquid alcohols,22and in liquid ethers as comThe Journal of Physical Chemistry, Vol. 79, No. 26, 1975
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John E. Willard
0.3
o.21 0.1
O L 60’
t
OD
I
OL
1200
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-..--J-.:m-
-L. .LI600 2000 WAVELENGTH, nm
1
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Figure 2. (A) Spectra of et- produced in MTHF glass by photoionization of TMPD at different temperatures. At 97 K, the 3-min photoionization was followed by 10 min in the dark prior to cooling to 50 K for measurement. The other spectra, produced by 3-min illuminations, were measured at the temperature of production after 10-min stabilization. (B) Spectra of trapped electrons in 3MP-dl4 at 23 K: (A) electrons produced by photoionization of TMPD at 72 K and cooled to 23 K; (B) after partial photobleaching of A at 23 K with 7001000-nm light.
pared to alcohols.23The spectra of et- in glassy alcohols are similar to those in liquid alcohols but are blue shifted and narrowedz0 in a manner suggesting that the trapping configuration in the glass a t 77 K is of the same type responsible for solvation in the liquid but is contracted and stabilized. The optical spectra of electrons in liquid hydrocarb o n ~ measured ,~~ on the nanosecond time scale, appear to be shifted relative to the et- spectra in glasses in a manner similar to the shifts in liquid alcohols relative to the glasses. While recognizing the correlations of A,, with polarity, it is important to note that molecular structure may play an equally important role in determining the solvation energies and spectra of electrons. This is indicated by data on longer chain and branched chain liquid alcohols,23band is also illustrated by noting that A,, for the absorption by solvated electrons in liquid dimethyl sulfoxide (D,= 48) is >1500 nmZ5which is more similar to A,, values observed in hydrocarbons (D,N 2) than in the more polar compounds such as glycerol (0,= 42) for which A,, of esolv- is -510 nm at 300 K. When electrons are produced in glasses made from mixtures of similar types of molecules such as isopropyl alcohol and ethylene glycol, there is a single absorption peak and A,, shifts from its value in the less polar compound toward that in the more polar as the concentration of the latter is increased,20,26suggesting that each et- is interactThe Journal of Physical Chemistry, Vol. 79, No. 26, 1975
ing with the two types of molecules to an extent dependent on their concentration. By contrast, when a glassy matrix is prepared from such dissimilar molecules as 3MP and n C,3H70H,20,26two well-separated et- absorption peaks characteristic of the two components are found, indicating aggregation of each type of molecule with others of the same kind. The fraction of the trapped electrons which are in the alcohol is greater than the alcohol mole fraction, and the et- concentration in the alcohol increases as thermal decay of the et- in the 3MP occurs, indicating that the eborn in the 3MP can move to the alcohol regions. Preferential solvation by the alcohol environment has also been observed in methanol and ethanol solutions in several liquid hydrocarbons.27 Evidence for Self-Induced Traps with a Continuum of Trapping Energies. Three types of evidence, (1) the time dependence of spectral shapes, (2) the temperature dependence of spectral shapes, and (3) preferential bleaching of narrow regions of the spectra by monochromatic light, indicate that electrons which become trapped in organic glasses are first localized in weak traps and then deepen their traps by orientation of molecules through polarization forces and interaction with bond or molecular dipoles.28The same evidence indicates that the observed broad spectra are envelopes of the spectra of electrons in a continuum of trap depths. Some examples will be cited. The spectra of et- produced in alcohols at 77 K by a 1900 nm and a decrease at lower wavelength^.^^ When the light is turned off, the OD at lO-5 mole fraction) in M C H Xand ~ ~ 3MP16a and g-l mole fraction) in ethanol18bcan be produced by y irradiation of the glasses at 77 K. If cations were evenly spaced in the glass and the et- randomly distributed, the nearest neighbor cationcation distance for 3MP sould be -200 8, and the average electron-cation distance -60 A. The corresponding distances for C2HsOH would be -40 and 12 A. For isolated ion pairs with these intrapair separations (i.e., with no influence from the other charges present), and assuming dielectric constants of 2 and 25, respectively, the Coulombic energy of separation between the et- and cation would be 0.12 and 0.05 eV. In actual y-irradiated organic glasses the upper limit of et- concentration achievable is determined as much or more by the growth in concentration of radicals,’6 with which the electrons can react to form carbanions, as by the cations. The above considerations of charge separation were related to glasses which have received sufficiently high radiation doses so that the spurs in which the radiation energy is deposited overlap. Studies of the spin-spin relaxation times (T2)of et- and trapped radicals as a function of dose give indication of the minimum doses a t which spur overlap is significant and allow estimates of the spur sizes. The upper limits of the “spur radii” for et- in MTHF, triethylamine, and 3MP so obtained are 60, 100, and 130 A, respectively.’Ra,4* Earlier ESR saturation studies in MTHF give -45 A. The intraspur separations of the radicals are less,49 consistent with the expectation that the latter are trapped at the site of formation whereas the electrons migrate while being thermalized before trapping. The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Electron Decay Processes Spontaneous removal of et- by combination with cations, radicals, or additives in y-irradiated organic glasses and alkaline ice occurs with half-lives of the order of tens of minutes near the glass transition temperature. The rates increase rapidly with increase in temperature and decrease rapidly with decrease in temperature. Possible mechanisms of the electron migration include: (1) thermal detrapping and movement to a reaction partner by a hopping mechanism (This appears improbable since the photodetrapping thresholds are -0.5 eV in hydrocarbons and much higher in more polar matrices, while KT at 77 K is 0.006 eV); (2) diffusion of the et- coupled with its “solvation shell’’ of surrounding molecules; (3) diffusion of et- without molecular movement, the polarization passing to new molecules as the et- moves; (4) quantum mechanical tunneling to a cation, a radical, or added scavenger of greater electron affinity than the trap. Electron Tunneling. Present evidence50 suggests that diffusion is the rate-controlling step in et- decay observed on the time scale of tens of minutes in 3MP near the glass transition temperature but that tunneling predominates as the mode of removal of e- which are trapped relatively close to a cation, radical, or scavenger molecule and disappear on the time scale of to lo2 sec, and also of electrons trapped at greater distances at temperatures far below Tg. Convincing evidence for tunneling includes (1) temperature independent decay over wide temperature ranges from 4 K up; (2) transfer of et- to scavengers a t rates which decrease linearly with increase in the log of the time over many decades in the range of to 1 sec; (3) enhancement of the yield of the anion of a strong scavenger by the added presence of a weaker scavenger; (4) linear dependence of the log of trapped electron yields 0x1 the concentration of scavengers as contrasted to the linear dependence of the reciprocal yields on the scavenger concentration expected for competitive diffusive encounters. The results seem to indicate that scavenging in glasses occurs to a great extent by tunneling after trapping rather than by competition between traps and scavengers for mobile electrons. Electron Decay in 3MP and MTHF at 77 K at Longer Times. Electron decay in pure 3MP and MTHF a t 77 K observed on the time scale of minutes and longer appears to involve diffusion and the kinetics are revealing as to the distribution of the et- relative to cations and radicals. Several types of e ~ i d e n c eindicate ~ ~ , ~ that a substantial fraction (perhaps 50%) of the et- present after y irradiation of organic glasses combine with a positive ion or radical within the parent spur when they are detrapped by absorption of light or diffuse. Likewise, there is evidence that many et- produced by photoionization of TMPD in 3MP combine with the geminate TMPD+ ~ a t i o n . ~The g evidonce includes the following. (1)The fractional rates of electron decay after short irradiations are independent of the radiation dose, and hence of the concentration of electrons, cations, and radical^.^",^^ (2) The decrease in the quantum yields for photobleaching of et- with increasing fraction bleached is independent of the initial electron (and hence cation and radical) c o n c e n t r a t i ~ n ? ~ > ~When ~ (3) et- produced in 3MP glass by photoionization of TMPD by vertically polarized light are photobleached in the presence of a large population of cations produced by horizontally polar-
Trapped Electrons in Organic Glasses ized light, the fluorescence is predominately vertically pol a r i ~ e d . ~ g(4) , ~ l Application of an electric field to a photoionized sample of TMPD in 3MP causes a burst of luminescence, which is repeated with a second application of the field with reversed p ~ l a r i t y , ~ gindicating Jj~ that some or all the electrons are trapped within the coulomb field of the geminate cation and overcome the potential barrier for recombination with the aid of the external field. Despite the pattern of predestined combination indicated by the above evidence, all of the electrons that can be physically trapped in the pure matrices are captured to form biphenylide ion when as little as mole fraction of biphenyl solute is p r e ~ e n t . Furthermore, ~~,~~ many of the et- in pure matrices can be detrapped by photon absorption and retrapped many times without capture by a cation or r a d i ~ a l . l ~ From ~ a ~the combined data it may be concluded that about 50% of the et- react within the parent spur, the fractional rate of thermal decay decreasing as the spur population is depleted, and that the remaining et- escape intraspur combination. If the molecules of the mole fraction biphenyl which remove all trapped electrons were uniformly distributed, they would be -10 molecular diameters apart, the maximum distance of a trapped electron from a scavenger molecule would be -7 molecular diameters and the average distance -3 molecular diameters (-15 A). These are distances over which tunneling may be expected to occur5obefore observations of y-irradiated samples are started. In both 3MP53 and MTHF48 at 77 K, the fractional decay rates of et- produced by y irradiation show composite first-order kinetics, i.e., they decrease as the fraction decayed increases, but are independent of y dose (i.e., of initial concentration). After 40-50% decay the rates are discontinuously slower than for the earlier decay. This pattern is similar to that of the decay of 3-methylpentyl radicalG4 in 3MP at 77 K, for which intraspur radical-radical reaction accounts for the composite first-order fast portion of the decay (57%) and random radical-radical reaction after diffusion accounts for a second-order slow portion. The second-order rate constant for the slow portion is independent of dose. The electron decay kinetics differ from the radical decay kinetics in that the rate of the slow portion is not proportional to the square of the dose.55 Several factors may cause the slow electron decay kinetics to be different than those for radicals: (1)coulomb interactions may result in a larger fraction decaying by intraspur reaction; (2) electrons may decay by reaction with radicals to form carbanions as well as by reaction with cations, so the concentration of potential reaction partners is much greater than the concentration of et-, leading, in the limiting case, to pseudo-first-order kinetics; (3) tunneling may contribute to the decay. Since the decreases in quantum yields of photobleaching of et- in 3MP4' and MTHF43with fraction bleached are independent of dose, they indicate that the initial bleaching involves intraspur reactions of the e- with cations and radicals rather than reactions dependent on the average acceptor concentration in the matrix. Presumably geminate recombination with the sibling cation occurs for some et- produced by y irradiation as it appears to for some formed by photoionization of TMPD.51*52One feature of y-irradiated hydrocarbons which reduces the probability of the geminate process is the ability of positive charge to migrate,5cwhereas this cannot occur when the charge is initially on TMPD, which has
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a lower ionization potential than the hydrocarbon. The migration of positive charge to a localizing center is indicated by increases in G(et-) and by slow decay rates of et- when positive charge scavengers such as alkenes, ethers, or alcohols are present as solutes in the hydrocarbon.2e Trapped electrons produced by photoionization of TMPD in 3MP at 77 K have characteristics strikingly similar to et- formed by y i r r a d i a t i ~ n(infrared ~ ~ . ~ ~ absorption, decay rates, saturation of their ESR signal, and photobleaching). However, prolonged illumination of TMPD produces a relatively randomized steady state populawith a lower fraction of geminate pairs and slower decay rate.57 The characteristics of the ESR singlet and decay of etformed by photoionization of Na in 3MP are similar to those of et- produced by y irradiation," again indicating that the nature of the cation is not a dominant factor in determining the properties of the traps. Effect of Annealing on Decay Rates. Differential thermal analysis measurements on 3MP glass held at 77 K (i.e., near the glass transition temperature) for different lengths of time following quenching of the liquid to 77 K show that free volume and enthalpy are progressively lost over a period of several hours.8 Parallel experjments on the rate of decay of et- produced in such glass following different times of annealing show initial half-lives ranging from 6 min for minimal annealing of 3MP to a limit of 60 min for completely relaxed samples, but no change in C(et-) or the shape of the optical spectrum of the et-.9 This implies that in 3MP a t 77 K annealing does not change the probability of trapping or the characteristics of the traps formed but decreases the rate of diffusion of the e
