Electron Spin-Lattice Relaxation Mechanisms of Radiation Produced Trapped Electrons and Hydrogen Atoms in Aqueous and Organic Glassy Matrices : Modulation of Electron Nuclear Dipolar Interaction by Tunnelling Modes in a Glassy Matrix B Y MICHAEL K. BOWMAN* AND LARRY KEVAN Department of Chemistry, Wayne State University, Detroit, Michigan 48202, U.S.A. Received 6th December, 1976 The spin lattice relaxation of trapped electrons in aqueous and organic glasses and trapped hydrogen atoms in phosphoric acid glass has been directly studied as a function of temperature by the saturation recovery method. Below 50 to 100 K, the major spin lattice relaxation mechanism involves modulation of the electron nuclear dipolar(END) interaction with nuclei in the radical's environment by tunnelling of those nuclei between two or more positions.This relaxation mechanism occurs with high efficiency and has a characteristic linear temperature dependence. The tunnelling nuclei around trapped electrons do not seem to involve the nearest neighbour nuclei which are oriented by the electron in the process of solvation. Instead the tunnelling nuclei typically appear to be next nearest neighbours to the trapped electron. The identities of the tunnelling nuclei have been deduced by isotopic substitution and are attributed to: Na in 10 mol dm-3 NaOH aqueous glass, ethyl protons in ethanol glass, methyl protons in methanol glass and methyl protons in MTHF glass. For trapped hydrogen atoms in phosphoric acid, the phosphorus nuclei appear to be the effective tuiinelling nuclei.Below -10 K the spin lattice relaxation is dominated by a temperature independent cross relaxation term for H atoms in phosphoric acid glass and for electrons in 10 mol dn1-3 NaOH aqueous glass, but not for electrons in organic glasses. This is compared with recent electron-electron double resonance studies of cross relaxation in these glasses. The spin lattice relaxation of 0- formed in 10 mol dmP3 NaOH aqueous glass was also studied and found to be mainly dominated by a Raman process with an effective Debye temperature of about 100 K. Electron paramagnetic resonance (e.p.r.1 spectroscopy has proved to be a most powerful tool in the study of trapped radicals in y-irradiated solids. E.p.r. techniques have been very successful in the identification and quantitative studies of radical kinetics and mechanisms in radiation chemistry.Two of the most studied radicals have been trapped electrons and trapped hydrogen atoms in frozen glasses. E.p.r. studies of the static properties of trapped electrons in a series of matrices of differing polarity have given a rather detailed picture of the trapped electron in aqueous glasses like 10 mol dm-3 NaOH glassy ice,' ethanol,2 methyltetrahydrofuran and 3-methyl- pentane4 glasses. One rather neglected area of e.p.r. research in radiation chemistry has been the study of the dynamic properties of radicals and their environment. This can be done most incisively by the study of spin lattice relaxation of the radicals as a function of temperature. Electron spin lattice relaxation is the process by which a collection of radical spins attain thermal equilibrium.In solids, the thermal motions of both the lattice * Present address : Argonne National Laboratory, Chemistry Division, Argonne, Illinois.8 ELECTRON SPIN-LATTICE RELAXATION MECHANISMS OF RADIATION itself and the radical in the lattice are capable of causing a time dependent perturbation of the electron spin of the radical. Possible spin lattice interactions are the Kronig- Van Vleck mechanism involving the spin-orbit orbit-lattice interaction or the electron nuclear dipolar (END) intera~tion.~ The temperature dependence of the spin lattice relaxation rate gives information about the dynamics of the modulating interaction, while the magnitude of the relaxation rate is determined by the magnitude of the perturbation.We report here on the results of a spin lattice relaxation study of trapped electrons and trapped hydrogen atoms in a number of y-irradiated frozen glasses. In the analysis of the temperature dependence of the electron spin lattice relaxation rates we shall make use of a new relaxation mechanism which we have recently described and which seems particularly important in glassy matrices. This relaxation mechanism is based on the modulation of the END interaction by tunnelling of nuclei or molecular groups in the environment of the radical. The general form of the temperature dependence of the relaxation rate (Tl-I) in the glassy systems studied is given by eqn (1) Ti-' = C2 + D2T + O2 exp(-AE/kT). (1) The C2 term is due to cross relaxation between the radical under study and another much faster relaxing radical in the sample.The second term, D2T, is the temperature dependence expected for the relaxation process involving the tunnelling modes. D2 is a measure both of the strength of the time dependent modulation of the END interaction and of the characteristic correlation time of that modulation. The final term, O2 exp(-AE/kT) where k is Boltzmann's constant, is merely a functional form which we have found useful in describing the spin lattice relaxation rate at high temperatures. At temperatures above -loOK, other spin lattice relaxation mechan- isms can become much more eEective than the relaxation due to the tunnelling modes. In addition, the temperature dependence of the tunnelling mode relaxation mechanism itself may also deviate from T1-' cc Tat these temperatures.6 As a result, the last term in eqn (1) is included for its utility in describing the data and not from any understanding of the high temperature relaxation mechanisms.We shall, therefore, confine our interpretation to the first two terms in eqn (1). The effect of deuteration of the glass on the relaxation rate due to tunnelling modes (D2T) has been calculatedS6 Three limiting cases were treated. For conditions typical of the frozen glasses used in this study: TiH/TiD = 1.17 when deuteration does not affect the mass of the tunnelling particle or the END interaction between the trapped radical and the tunnelling particle ; when the END interaction does involve a proton but deuteration does not change the mass of the tunnelling particle; and TiH/TiD = 0.030 when the tunnelling particle is a hydrogen nucleus.Thus the effect of isotopic substitution on the magnitude of the spin lattice relaxation rate due to tunnelling particles (D2) can be used to identify the nuclei involved in the END interaction being modulated by tunnelling and also to identify the tunnelling particle.MICHAEL K. BOWMAN A N D LARRY KEVAN 9 EXPERIMENTAL All H20 used was triply distilled in Pyrex. The NaOH was obtained from B & A Speciality Chemical Division of Allied Chemical. Stohler Isotope Chemicals was the source of D20, 40 weight % NaOD/D20, 85 weight % D3P04/D20, CH30D, CD30H, CD30D and C2D50H. The 85% H3P04 and CH30H were obtained from Mallinckrodt.The C2H50H was Rossville Gold Shield Alcohol and Matheson, Coleman and Bell was the source of 2-methyltetrahydrofuran (MTHF). The MTHF was purified by passing it over activated silica gel, dried by repeated vacuum distillations into flasks containing Na + K alloy and stored under vacuum over a potassium mirror until vacuum distilled into a sample tube and sealed. All of the methanol samples had 5 % water added to assure formation of a good glass. H20 was added to the -OH samples and D20 to the -OD samples. The deuterated or partially deuterated samples were placed in 3 mm 0.d. Spectrosil quartz tubes, evacuated and sealed. Nondeuterated samples were placed in similar tubes but were unsealed. Sample tubes were 4-5 cm in length and contained 2.0-2.5 cm of sample solution.Samples were frozen in as nearly a reproducible manner as possible by slowly lowering them into liquid nitrogen at a rate which minimized bubbling of liquid nitrogen around the sample. All samples were clear glasses with a minimum of cracks. Samples were irradiated in liquid nitrogen in a U.S. Nuclear Corp. GR-9 Co-60 y-irradiator at a dose rate of approximately 0.16 Mrad h-l. After irradiation, samples were stored in liquid nitrogen in darkness until measurements were made. The time domain spectrometer used to measure spin lattice relaxation rates is similar to the saturation recovery spectrometer described by Brown and Sloop7 and has been described in detail.* Great care was taken to ensure that the saturating pulses were several times longer than the observed recovery time and that the magnitude of the microwave power used to observe the recovery of the e.p.r.signal after saturation was far below a level which would perturb the populations of the spin levels. The control and measurement of the sample temperature has been described.6 Estimations of the coefficients in eqn (1) were made by an iterative least-squares fit’ to the data. The F test (variance ratio test statistic) the R test (deviation ratio test statistic) or the t-test (Student’s t ) were used to test hypotheses about the various coefficients in eqn (1)’ with the significance criterion beingp = 0.05 or better. RESULTS TRAPPED ELECTRONS IN 10 mol dmV3 SODIUM HYDROXIDE GLASSY ICE The spin lattice relaxation rate as a function of temperature was studied most completely for trapped electrons in 10 mol dm-3 sodium hydroxide glassy ice.Fig. 1 shows representative saturation recovery curves for trapped electrons. It was noticed quickly that the spin lattice relaxation rate was strongly dependent on the freezing conditions for the sample. As a consequence, great care was taken in this study to ensure that the samples were frozen as reproducibly as possible. Some of the different samples of 10 mol dm-3 NaOH glassy ice measured were; three samples of 10 rnol dm-3 NaOH irradiated to 0.42 Mrad, one sample each of 10 mol dm-3 NaOH irradiated to 4.0 Mrad, 10 mol dm-3 NaOD irradiated to 0.42 Mrad and 9 mol dm-3 NaOH doped with 20 atom % 1 7 0 irradiated to 1.0 Mrad. Radio- lysis produces trapped electrons and 0- ions in this matrix.Least squares fits were made to eqn (1) by varying all parameters, with C2 set equal to zero and with AE/k set equal to 400 K. Statistical analyses (R-test) of the results of these fits showed that C2 was non-zero for every sample, indicating a significant amount of cross relaxation between the trapped electrons and another fast relaxing radical in the matrix. The10 ELECTRON SPIN-LATTICE RELAXATION MECHANISMS OF RADIATION tl s FIG. 1 .-Representative saturation recovery signals plotted as the difference between the signal at infinite time after a pulse and the signal at time t after a saturating pulse. The lower left signal is the signal on a linear scale, the sample is trapped electrons in 10 mol dm-3 NaOH at 62.4 K. The observing power is 40 nW and the pump pulses are 20 mW.The spin-lattice relaxation time TI is 8.2 ms and the zero point is not indicated on the graph. The upper right corner shows the logarithm of the recovery of a sample of trapped electrons in 10 mol dm-3 NaOH at 10.1 K. The observing power is 1 nW and the pump power is 1 mW. TI is 175 ms. radical 0- is the other major radical in this matrix and, since it saturates less easily than the trapped electrons, it is a prime candidate for a cross relaxation partner. The statistically best fits (R-test) for these samples are given in table 1. Experi- mental rates as a function of temperature are plotted in fig. 2 for trapped electrons in 9 mol dm-3 Na170H with the best least-squares fit. TABLE l.-cOEFFICIENTS OF EQN (1) FOR TRAPPED ELECTRONS IN 10 MOL DM-3 SODIUM HYDROXIDE GLASSY ICE matrix dose/Mrad C2/s - D2/s - lK - 021s-1 AEk - l/KU NaOHb 0.42 2.25 1.81 1.40 x 104 (400) NaOHb 0.42 7.92 1.08 1.80 x 104 (400) NaOHb 0.42 3.86 1.62 5.25 x 103 (400) NaOHb 4.0 27.4 2.25 6.90 x 103 (400) NaODb 0.42 11.6 2.22 6.65 x 103 3 14 Na”0H“ 1 .o 19.7 2.27 9.09 x 104 577 ~ ~~~~ ~~ ~ ~~~~~~ Values in parentheses were coiistrained to the values shown.* Concentration 10 mol dm-3. Concentration 9 rnol dm-3. The cross relaxation rate (C2) is larger for trapped electrons in 10 mol dm-3 NaOH irradiated to 4.0 Mrad than for samples irradiated to 0.42 Mrad (P = 0.01, t-test), which is to be expected since 0: radicals are closer on the average to trapped electrons in samples irradiated to a higher dose. D2 is not significantly different for samples of 10 mol dm-3 NaOH irradiated to different doses, nor is it significantly different for the 10 mol dm-3 NaOH, 10 mol dm-3 NaOD or 9 mol dm” Na170H samples.The relaxation rate was also found to be independent of which part of the e.p.r. line was being observed and is a property of the entire e.p.r. line.MICHAEL K. BOWMAN AND LARRY KEVAN 11 The trapped electrons in the sample of 10 mol dmW3 NaOH irradiated to 4.0 Mrad were progressively optically bleached by 50% and the spin lattice relaxation rate was remeasured as a function of temperature. Further bleaching was then done until only 12.5% of the original trapped electrons remained. Neither C2 nor D2 showed any statistically significant changes due to this bleaching.1 I 1 1 10 25 50 100 TI K FIG. 2.-The spin lattice relaxation rate of trapped electrons in 20 atom % oxygen-17 doped 9 mol dmP3 NaOH irradiated to a dose of 1 .O Mrad. The solid line is the least-squares fit described in the text. The spin lattice relaxation rate of the trapped QT radical was measured at the g1 feature of its e.p.r. spectrum. The results are plotted in fig. 3. The solid line is given by Ti1 = lS(T/8)’J8(0/T) s-l with 8 equal to 100 K; J8 is the eighth transport integral. This functional form is that of the well-known Raman process for the Kronig-Van Vleck relaxation mechanism in a matrix with a Debye temperature of 100 K5 Below 10 K the temperature dependence of the relaxation rate is much weaker, characteristic of a direct process. TRAPPED ELECTRONS I N ETHANOL GLASS Detailed experimental results for trapped electrons in glassy C2H50H, C2D50H The best fits and C,H,QD irradiated to 1 Mrad have been presented of eqn (1) to the ethanol data are given in table 2.TRAPPED ELECTRONS I N MTHF GLASS The best fit of eqn (1) to the experimental spin lattice relaxation rates for trapped electrons in MTHF glass is T-l = 38.8(s-IK-l)T + 2.69 x 104(s-l) exp[-128(K)/T]. The coefficient of the temperature independent term is not statistically different from zero, but note the large coefficient for the term linear in temperature.12 ELECTRON SPIN-LATTICE RELAXATION MECHANISMS OF RADIATION 5 10 25 50 T I K FIG. 3.-The spin lattice relaxation rate of oxygen radicaI anions, OT in 10 mol dm-3 NaOH as a function of temperature.The solid line is a plot of T1-l = 15 (T/lOO K)9 J8 (100 K/T). TABLE 2.-cOEFFICIENTS OF EQN (1) FOR TRAPPED ELECTRONS IN ETHANOL IRRADIATED TO 1 MRAD matrix C"S - la D2/s-lK- 0 " s - AEk - l/K C2H50H (0) 18.9 4.74 x 103 84 C2H50D (0) 7.30 4.71 x 103 92 C2D5OH (0) 3.22 1.69 x 104 148 Values in parentheses were constrained to the value shown. TRAPPED ELECTRONS I N METHANOL GLASS Samples of trapped electrons in CH30H, CH30D, CD30H and CD30D showed very peculiar behaviour. At low temperatures, the recovery of the e.p.r. signal from saturation depended strongly on experimental conditions, particularly on the micro- wave powers used for both observing and saturating the signal. These effects were strongest in CD30D and data for this sample are shown in fig. 4.Below 10 K there is a cluster of points with Ti1 E 50 S" which were measured using a very low saturating pulse power and low pulse repetition rate. Between 8 and 30 K there are two sets of data where Ti1 actually increases with decreasing temperature. These two sets of data were measured under similar conditions but with different microwave powers. Also, it was found that at 6 K, a 10 min, 100 mW microwave pulse reduced the magnitude of the e.p.r. signal by nearly 90%. The e.p.r. signal took several minutes to return to its original intensity. These very peculiar observations have been rather simply explained by Clough and Hill.lo If the methyl groups in the methanol are undergoing tunnelling rotation at a frequency equal to the e.p.r. frequency, the electron spins are strongly coupled toMICHAEL K .BOWMAN A N D LARRY KEVAN 13 100 c 50 1 + +++ + I- I I I t 10 25 50 100 T I K FIG. 4.-The saturation recovery rate as a function of temperature of trapped electrons in [2H4]methanol. The saturating pulses had a 50% duty cycle. The points denoted by circles were measured using 4 nW observing power and 40 mW, 50 ms pulses; the squares with 4 nW observing power and 1 mW, 50 ms pulses; the triangles with 1 nW observing power and 1 mW, 50 m pulses and the crosses with 1 nW observing power and 400 JAW, 860 ms pulses. the rotation. The assumptions used in deriving eqn (1) are then violated and eqn (1) cannot be expected to be applicable. At low temperatures, the rotation of the methyl groups is only weakly affected by the lattice.The methyl groups form a large thermal reservoir in good thermal contact with the electron spin system but isolated from the lattice. During the saturating pulses, the electron spin system is “ heated ” to a high temperature (the spin level population difference defines a Boltzmann spin temperature). Some of this “heat” flows from the spin system into rotational motion of the methyl groups to heat them up. After the pulse, the spin system “ cools ” (the population difference and hence the e.p.r. signal increases) until it reaches the temperature of the collection of methyl groups. The spin system then follows the temperature of the methyl groups as they “ cool ’’ down to the temperature of the lattice. It is expected that at higher methyl group temperatures, the approach of the spin temperature to the methyl group temperature is more rapid.Thus, the decrease plotted in fig. 4 shows the approach of the spin temperature to the methyl group temperature, the latter being determined by the average microwave power. The several minute recovery following the 10 min pulse is the cooling of the methyl group system. These observations are perhaps the clearest evidence for the existence of the tunnelling mode relaxation mechanism for an electron spin system in a glass. TRAPPED HYDROGEN ATOMS IN PHOSPHORIC ACID GLASS The spin lattice relaxation rate of both the high field hydrogen atom e.p.r. line and om of its spin flip satellites in 85 weight % M3P04 + H,O irradiated to a dose of 0.50 Mrad is described by T,-l = 22.6(s-l) + 0.206(~-~K-~)T + 7.41 x 102(s-l) exp[-195(K)/q.14 ELECTRON SPIN-LATTICE RELAXATION MECHANISMS OF RADIATION A I I I I 10 25 50 100 10 TI K FIG.5.-The spin lattice relaxation rate as a function of temperature of the low field (inverted, v), middle field (0) and high field (upright, A) deuterium atom e.p.r. lines in D3P04 + DzO glass. The solid lines are the minimum parameter least-squares fit for all three lines as described in the text. All three deuterium atom lines were studied in 8576 D3P04/D20. The data are shown in fig. 5; the solid curves are the best fits of eqn (1) to the data from each e.p.r. line using the smallest number of different coefficients. The coefficients are given in table 3. TABLE 3.-cOEFFICIENTS OF EQN (1) FOR EACH E.P.R. LINE OF TRAPPED DEUTERIUM ATOMS IN 85% D3P04 + D20.IRRADIATED TO 0.5 MRAD e.p.r. line C'/S - 1 D2/s-lK-l" 02/s - 1 AEk - I/Ka high field 1 5 . 2 0.243 0.429 x lo3 128 middle field 97.8 0.243 1.03 x 103 1 2 8 low field 42.3 0.243 1.05 x 103 1 2 8 ~~~ (I Coefficients in this column were constrained to be the same for all lines. DISCUSSION CROSS RELAXATION We have interpreted the temperature independent term in the relaxation rate as due to cross relaxation between the saturated spin system (electrons in our case) and another faster relaxing species in the matrix. If present, this relaxation mechanism dominates at sufficiently low temperature since all other mechanisms are temperature dependent. This can be seen most clearly in fig. 5 for trapped D atoms in D3P04 glass. The cross relaxation rate depends upon the matrix elements of the dipolar inter- action between the two spin systems and on the cross relaxation line-shape function.llMICHAEL K .BOWMAN A N D LARRY KEVAN 15 In concentrated spin systems the lineshape function depends on the overlap of the e.p.r. spectral lines of the cross relaxing species, but in magnetically dilute systems, such as we have, has shown that the second moment of the cross relaxation lineshape is much greater than the sum of the second moments of the individual lines. Thus cross relaxation can still be quite significant when the two spectral lines are separated by more than 20 times their linewidth. By saturation recovery methods cross relaxation is typically only observed when the relaxation times of the two species are quite different ; otherwise, the cross relaxation rate from the saturated spin system does not become dominant.The largest cross relaxation coefficients among the systems studied are found for D atoms in D3P04 glass (see table 3). In this system the other main radical produced by radiolysis is PO2, with a g-value of ~ 2 . 0 1 , ~ ~ above the free electron value. Cross relaxation of the D atoms corresponding to the centre D atom e.p.r. line nearg = 2.002 with PO2: is expected to be more efficient than cross relaxation to the other D atom e.p.r. lines due to the spectral overlap. Similarly, the D atoms corresponding to the low field D atom e.p.r. line should interact with some- what less efficiency, while the D atoms corresponding to the high field D atom e.p.r.line should interact least efficiently. The saturation recovery studies over the temperature I ange investigated do not indicate significant cross relaxation from trapped electrons in organic glasses (MTHF, ethanols, methanols) to the organic radicals in these glasses. The organic radicals formed by radiolysis do have shorter relaxation times than the trapped electrons but the difference is not too large.14 Furthermore, the D2 coefficient for the tunnelling relaxation mechanism is much larger for trapped electrons in organic glasses (MTHF, C2H50H) than in aqueous glasses (table 1) or for D atoms in acid glasses (table 3). These two factors suppress any observable contribution of cross relaxation from electrons to radicals. However, electron-electron double resonance (ELDOR) studies do demonstrate cross relaxation from radicals to electrons in organic glas~es.'~ In ELDOR two microwave frequencies are used, termed pumpitzg and detecting frequencies.Cross relaxation is revealed by saturation transfer from the pumped radical spins to the detected electron spins. For this observation the pumped spins are partially saturated but must be less easily saturated than the detected spins. Thus, ELDOR studies do not show saturation transfer when the electron spins are pumped and the radical spins are detected. In contrast to organic glasses, the trapped electrons in 10 mol dm-3 NaOH aqueous glass do show detectable cross relaxation from the saturation recovery data (table 1). It is postulated that cross relaxation occurs to the other major radical in this glass which is 0- with g, = 2.07.Fig. 3 shows that 0- has a much larger spin-lattice relaxation rate than e,. Cross relaxation of e; to 0- is supported by the radiation dose effect on the cross relaxation coefficient, C2. At 4.0 Mrad the average e;, 0- distance is less than at 0.4 Mrad so that cross relaxation rate is larger as observed. Optical bleaching of e; also destroys 0- because most of the mobilized electrons react with 0- radicals.16 The lack of an effect on the cross relaxation by the bleaching can be explained if correlated pairs of e;- and 0- react by bleaching so that the average distance between remaining e;- and 0- pairs remains the same. ELDOR studies have also been done on e, in 10 mol dm-3 NaOH ice.17 Evidence for cross relaxation from 0- to e; could not be observed, apparently because the 0- relaxation rate is too fast to allow enough saturation.It appears that ELDOR and saturation recovery experiments give complementary information on cross relaxation. This is what is observed. These predictions are borne out by table 3.16 ELECTRON SPIN-LATTICE RELAXATION MECHANISMS OF RADIATION NATURE OF TUNNELLING NUCLEI For trapped electrons in glasses the spin lattice relaxation due to tunnelling modes, (Ti1 = D2T) is much more efficient than in single crystals (e.g., F-centres in KC1) where there are no tunnelling modes. The value of D2 in the glasses studied here ranged from 1 to 40 s-lK-l while for F-centres in single crystals 18*19 the coefficient of the low temperature relaxation process linear in temperature is 5 x s-lK-l! This shows that the relaxation of trapped electrons in glasses is quite different from that in crystalline solids.We now try to deduce the details of this tunnelling relaxation model by evaluating isotopic results to determine the nature of the tunnell- ing nuclei. For electrons in 10 mol dm-3 NaOH aqueous glass the coefficient of the tunnelling mode relaxation term, D2, is independent, (within the accuracy of this study) of deuteration, doping with "0, irradiation dose and optical bleaching. The dose independence implies that D2 reflects properties of isolated trapped electrons rather than of interacting clusters. The independence of 1 7 0 and D substitution indicates that the tunnelling particle does not contain oxygen or deuterium atoms and that the END interaction responsible for the tunnelling relaxation does not involve oxygen atoms or protons.This severely limits the possibilities and brings us to the con- clusion that the trapped electron in 10 mol dm-3 NaOH aqueous glass has an END interaction with nearby sodium ions which is modulated by tunnelling of the Na+ ions between two potential minima. Recent work has elucidated the structure of the first solvation shell around e; in this it contains only H20 molecules. The Na+ nearest to e; must be at least 5 A away. It thus appears that the tunnelling nuclei must not be too tightly coupled to the electric field of the trapped electron in order to undergo a tunnelling modulation. This appears to be supported by the trapped electrons in other matrices, which will now be discussed.In ethanol, deuteration studies show that the ethyl protons affect the tunnelling relaxation rate coefficient more than do the hydroxyl protons even though the strongest magnetic interaction is with the hydroxyl protons.21 This is consistent with the picture that the nearest neighbour nuclei to a trapped electron are immcbilized by the potential field of the electron and do not undergo tunnelling motions while the more distant nuclei like the ethyl protons are able to undergo tunnelling motion. Similarly, it is the motion of the methyl groups in methanol which dominates. The identity of the tunnelling group in MTHF cannot be conclusively determined from the data presented. However, if it is assumed that the MTHF ring is im- mobilized in the trapped electron's first solvation shell, than the most likely candidate is the tunnelling rotation of the 2-methyl group which points away from the trapped ele~tron.~ The contribution of the methyl groups in MTHF to the second moment of the trapped electron3 is 0.6 G2.If this 0.6 G2 is assumed to be the magnitude of the modulation of the END interaction, the characteristic correlation time for tunnelling of the methyl groups can be calculated from eqn (1) in ref. (6). The calculated correlation time is 2 ns K/T i.e., 200 ps at 10 K and 20 ps at 100 K. This is slower than the characteristic correlation time of the methyl groups in methanol, which is the order of the e.p.r. frequency, and is long enough such that the approxi- mations in ref.(6) are valid. For trapped H atoms in phosphoric acid glass the tunnelling mode relaxation rate is independent of deuteration within experimental error and also independent of the nuclear quantum number of the trapped deuterium atom. This suggests that the END interaction is modulated by tunnelling motion of the phosphorus nuclei in the matrix. The detailed structure of the matrix molecules around trappedMICHAEL K. BOWMAN AND LARRY KEVAN 17 H atoms is not yet known. But perhaps in the acid glasses hydrogen bonded net- works prevent tunnelling motions of the protons. The picture of the trapped electron that has evolved from this study is that the electron is trapped in a very stable arrangement in which the nearest nuclei out to several Angstroms are constrained from undergoing much motion.The -OH groups in alcohols, the first solvation shell water molecules in aqueous glasses and the MTHF ring protons, which are all oriented by the potential field of the trapped electron are all fairly well immobilized compared with the more distant methyl or ethyl groups in MTHF and alcohols and the sodium ion in the aqueous glass. There is evidence22 that during the process of electron solvation, the charge of the electron helps to orient the nearest nuclei around it into an almost crystal-like structure. 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