966
Ding-ping Lin and Larry Kevan
Mechanism of Spin Diffusion in Electron Spin Resonance Spectra of Trapped Electrons in Aqueous Glasses. Electron-Electron Double Resonance Studies Ding-ping Lln' and Larry Kevan. Deparfment of Chemistty, Wayne State University, Detrolt, Michigan 48202 (Received December 28, 1976)
Electron-electron double resonance (ELDOR) has been used to test the validity of the noninteracting spin packet model for inhomogeneouslybroadened ESR lines. For trapped electrons in 10 M NaOD/D20 glassy ice the saturation of field-swept ELDOR spectra fits the above mentioned model in contrast to earlier work on trapped electrons in protiated matrices. In the protiated matrix spin diffusion produces significant interaction between the spin packets. The differencebetween the protiated and deuterated matrices suggests that nuclear relaxation is the mechanism for spin diffusion. The deuterated matrices show no structure in frequency-swept ELDOR spectra due to deuteron spin-flip transitions whereas structure due to proton spin-flips is seen in protiated matrices.
Introduction Electron spin resonance (ESR) spectra of trapped radicals in disordered solids are typically inhomogeneously broadened due to unresolved hyperfine interaction with matrix nuclei. Inhomogeneous broadening arises because the average static magnetic field varies for different spins and this variation can be associated with different nuclear configurations around the unpaired spins. To describe the microwave power saturation behavior of inhomogeneously broadened ESR lines Portis originally introduced a "noninteracting spin packet" model in which he assumed that each set of electron spins that interacted with the same nuclear configuration formed a homogeneously broadened spin packet.2 The various spin packets superimpose to produce the observed inhomogeneously broadened line. This noninteracting spin packet model has been widely used to interpret power saturation behavior of ESR lines in terms of radical spatial distributions and to deduce the magnetic relaxation parameters T I ,spin-lattice relaxation time, and T,, spin-spin relaxation time.3 Portis originally assumed that the spin packet width was much less than the observed inhomogeneous line widthe2 Castner4 generalized the model so that this assumption was not necessary. Recently, Bowman et al.5 have further extended the model to include ESR detection by magnetic field modulation which is the common experimental method now used. We now explore the interaction between spin packets. Communication or interaction between spin packets can be described as spin diffusion within an ESR line. Portis' apparently first introduced the concept of spin diffusion and considered the specific mechanism of electron spinelectron spin dipolar interaction. In later treatments other^^-^ have considered a variety of mechanisms of spin diffusion, including electron spin-lattice relaxation, exchange interactions, nuclear relaxation, instantaneous diffusion by microwave pulses, and even macroscopic diffusion of individual radicals. Thus spin diffusion now broadly means transfer of saturation between spin packets without implying any specific mechanism. Electron-electron double resonance (ELDOR)" has been used to incisively study the spin packet model for trapped electrons in KC1 crystals (F centers)" and for trapped electrons in y irradiated 10 M NaOH aqueous glass.I2 In both cases the noninteracting spin packet model fails quantitatively, although not qualitatively, and indicates the existence of significant spin diffusion. ELDOR is ideal The Journal of Physical Chemistry, Vol. 81,
No.
10, 1977
for such studies because two microwave frequencies are used which can be applied to different spin packets in a single ESR line. In the present work we investigate the mechanism of spin diffusion for trapped electrons in aqueous glasses by changing the magnetic matrix nuclei from protons to deuterons. The results indicate that nuclear relaxation is involved and, interestingly, that the noninteracting spin packet model is satisfactory for deuterated matrices. Experimental Section Fresh solutions of 10 M NaOD/D20 were prepared from 40 w t % NaOD/D20 and D 2 0 from Stohler Isotope Chemicals. Samples were sealed in 4-mm 0.d. suprasil quartz tubes, frozen rapid1 in liquid nitrogen to the glassy state, and irradiated with JCo y rays at 77 K at a dose rate of 0.21 Mrad h-I. Trapped electrons (e;) and 0- are the paramagnetic species produced by irradiation, with 0downfield from e;. The ELDOR spectrometer and operating procedures have been described." Magnetic field modulation at 100 kHz with a peak-to-peak amplitude of 0.6 G was used to record the spectra. The maximum pumping microwave magnetic field at 0 dB was HI,= 0.68 G . Field-swept ELDOR spectra are obtained with both pumping and detecting microwave frequencies held constant. Frequency-swept ELDOR spectra are obtained by sweeping the pumping microwave frequency f while holding the detecting microwave frequency f d an8 the magnetic field constant; different frequency swept spectra may be obtained for different magnetic field positions. The detecting microwave power was kept below the saturation region, 2 pW, for the trapped electrons. Different sets of spectra at various temperatures were studied and analyzed to compare with the data on protiated systems'2 under similar conditions. Results The field-swept ELDOR spectra for e; at Af = fp - fd = 6 MHz at various pump powers are shown in Figure 1. As the spectrum is swept from low to high field the pump frequency lags the detecting frequency when Af is positive as it is here. In Figure 1 at -39 dB with effectively no pump power applied, the usual ESR spectrum is seen. As the pump power increases, the spectra become asymmetric as the high field part of the derivative curve diminishes. The low field peak of the derivative curve slowly decreases. These results are similar to those previously observed for
ESR Spectra of Trapped Electrons in Aqueous Glasses
-39 db - 3 5 db -30 db -25 db - 2 0 db
- 15 db
- IOdb - 5db
- 4 0 MHz
0 db
Figure 1. Field-swept ELDOR spectra of trapped electrons in 10 M NaOD/D,O glassy ice y Irradiated to 2.3 Mrad at 77 K and measured at 40 K. The pumping frequency is higher than the detecting frequency by 6 MHz and the pumping microwave powers are shown in dB below the maximum: -39 dB corresponds to the ESR spectrum unperturbed by pumping power.
- 30 db - 25 db - 20 db - 15db
-
IO db 5 db
0 db
Figure 2. Field-swept ELDOR spectra ot trapped electrons in 10 M NaOD/D,O glassy ice y irradiated to 5.3 Mrad and measured at 77 K. The pumping frequency is higher than the detecting frequency by 6 MHz and the pumping microwave powers are shown in dB below the maximum; -39 dB corresponds to the ESR spectrum unperturbed by pumping power.
e t in 10 M NaOH/H20 except that the high field peak of the derivative curve decreases more rapidly with pump power in the deuterated matrix. This will be seen to be consistent with less spin diffusion in the deuterated matrix. Figure 2 shows the same type of ELDOR spectra as in Figure 1at a higher dose of 5.3 Mrad. The same type of behavior is observed except that the ELDOR spectra appear to be more strongly saturated at high pump power. Figure 3 shows field-swept ELDOR data for 0 dB pumping power for various A f from 50 to 6 MHz. At Af = 40-50 MHz no difference is observed between the spectra with and without pumping power. At 4= 30 MI& the ESR line shape is distorted constituting an ELDOR response. This frequency difference corresponds to about
- 5 0 MHz
Figure 3. Field-swept ELDOR spectra of trapped electrons in 10 M NaOD/D20 glassy ice y irradiated to 2.3 Mrad and measured at 77 K. The pumping microwave frequency is higher than the detecting microwave frequency by the amounts indicated. The pump power is 0 dB.
If 10
Figure 4. Frequency-swept ELDOR spectra of trapped electrons in 10 M NaOD/D,O glassy ice y irradiated to 2.3 Mrad and measured at 77 K with the pumping frequency higher than the detecting frequency. The frequency difference is given on the abcissa. The pump power is 0 dB. The trapped electron ESR spectrum is also shown on the right. The ELDOR spectra were obtained when sitting on the high field and low field derivative maxima of the ESR spectrum.
twice the ESR derivative line width A",of 5.4 G = 15.1 MHz. Frequency-swept ELDOR spectra are shown in Figure 4 for the magnetic field set on each derivative peak of the ESR line. There is no evidence of structure in these spectra as is observed in the spectra in the protiated matrix.12
Spectral Analysis The field-swept ELDOR spectra show the saturation of the ESR spectrum under ELDOR conditions. We analyze the spectra with the noninteracting spin packet model for ELDOR developed for e; in protiated rnatrices.l2 For detecting microwave power below the saturation region our signal is proportional to the imaginary part of the magnetic susceptibility at the detecting angular frequency given by x"(Cdd)
= CJ: [(a{a'
- wO)/AoG]2))/(1
+ [ ( a d -Cd')/ACd,]'})-' + Sa2{a2+
eXp{-[(Cd'
[(up
- C~')/AC~G]'}-')] d ( o ' / A w ) (1) where C is a constant, a = AWL/AWG,S = r2Hlp2T1T2, y The Journal of Physical Chemistry, Vol. 81, No. IO, 1977
968
t
Ding-ping Lin and Larry Kevan
\
\
. w
c
w
-I
PUMPING POWER (ARB.)
0
02
04
INHOMOGENEITY
06
08
10
Figure 6. Dependence of T, and T2 for trapped electrons in 10 M NaOD/D,O based on the ELDOR saturation measurements in Figure 2 and the noninteracting spin packet model vs. relative pumping microwave power.
PARAMETER, a
Figure 5. Theoretical analysis plot for pump saturation of fieid-swept ELDOR spectra with Af = 6 MHz. The various parameters are defined in the text and n varies with pump microwave power.
= 1.76 X 10' G-' s?, and up = 27rfp. The spin packets are assumed to be Lorentzian with a half-width at half-height of AWL = T;', and the distribution of spin packets is taken as Gaussian, in agreement with the observed ESR line shape, with a half-width at half-height of PoG = yAH,,(ln 2 /2)"'. The frequencies W , and W' are the centers of the observed line and the spin packet, respectively. Equation 1is integrated numerically. Our experiments at 100-kHz magnetic field modulation correspond to fast modulation conditions'' so the theoretical field-swept ELDOR spectra are given by dx"/dwd. We will characterize the shape of simulated field-swept ELDOR spectra for fp > f d in terms of an asymmetry parameter A(n) dependent upon the pump power and use this to deduce values of Tl and TP1' The constancy of Tl and T2vs. pumping power will serve as a criterion for the adequacy of the noninteracting spin packet model. A ( n ) is defined as the value of the low field derivative peak height, measured from the baseline and normalized to 1.0 in the absence of pump power, when the high field derivative peak height has decreased to n% of its value in the absence of pump power. Thus A(n) characterizes the ELDOR saturation. One should note that A ( n ) can be greater than unity. The saturation of the ELDOR line shape in terms of A ( n ) depends on the inhomogeneity parameter a as shown in Figure 5 for n = 50 and 20. The dependence of the saturation parameter S(n) for a given pump power corresponding to n also depends on a and S for a given n from theoretical curves such as those shown in Figure 5. T2is then determined from a = 1.7/ TzyAHm and Tl is determined from S = y2Hlp2TlTz.Figure 6 shows the T1and T2values calculated from the results shown in Figure 2. The values are obtained for n = 90 to 20 and correspond to a 15-fold range in pumping power.
Discussion The objective of the present experiment is to test the noninteracting spin packet model for inhomogeneously broadened ESR lines in deuterated disordered matrices. For ELDOR experiments this model is represented by eq 1. One test of the model is given by Figure 6. The model predicts that T1and T2should be constants independent of pumping microwave power. Figure 6 suggests that the model is satisfactory for trapped electrons in deuterated aqueous matrices. This implies that spin diffusion does not occur at a faster rate than spin-lattice relaxation. In contrast to the deuterated matrix, similar experiments on e< in 10 M NaOH/H20 have shown that the noninThe Journal of Physical Chemistry, Vol. 81, No. 10, 1977
teracting spin packet model is not satisfactory." In the protiated matrix T1 decidedly decreases with increasing pumping microwave power and implies that the spin packets do interact. This interaction occurs phenomenologically by spin diffusion characterized by a time TD such that T,' < TD< Tl' where T( and T,' are the relaxation times in the absence of spin diffusion. In both protiated and deuterated matrices T2 increases slightly with increasing pump power; this small effect is not understood in detail. The different relative importance of spin diffusion in the protiated and deuterated matrices suggests that the spin diffusion mechanism involves nuclear relaxation via an electron-nuclear dipolar (END) interaction. In this case the spin diffusion time is about yH2/yD2 42 times longer in the deuterated matrix compared to the protiated matrix and is consequently much less important in deuterated matrices. The nuclear gyromagnetic ratios have been used to make this estimate. The other mechanisms of spin diffusion mentioned in the are not directly dependent on the gyromagnetic ratio of the matrix nuclei. A related indication of the different importance of spin diffusion in protiated and deuterated matrices is given by the pumping power range over which the high field peak of the derivative ESR line decreases to the baseline; see spectra in Figures 1and 2. In the deuterated matrices this range is about 20 dB in pump power. However in protiated matrices this range is about 30 &.I2 When significant spin diffusion occurs, some effective desaturation occurs for the detected spin packet which causes saturation to occur more slowly with pumping power. Finally we comment on the absence of structure in the frequency-swept ELDOR spectra in deuterated matrices (see Figure 4). This stands in contrast to the structure observed in protiated matrices." The structure in protiated matrices was originally assigned to isotropic hyperfine structure, but subsequent analysis has shown that the isotropic hyperfine constant is much ~ m a l l e r ' ~and "~ that the structure in the ELDOR spectra is due to forbidden transitions involving simultaneous proton and electron spin-flips.15 A t our magnetic field deuteron spin-flip lines should occur with a spacing of about 2.2 MHz. However, the intensity of the deuteron s in flip -2lines in ESR spectra will be reduced by about YH /YD 42 times relative to proton spin-flip lines. Although the spin-flip transition probabilities may be altered somewhat in ELDOR spectra they still appear too weak to be observed.
-
f
Acknowledgment. This research was supported by the
U.S.Energy Research and Development Administration under Contract No. E(11-1)-2086. Larry Kevan thanks
969
Photoracemization of 1,l'-Binaphthyl
Drs. T. Higashimura and H. Hase at the Research Reactor Institute of Kyoto University and the Japanese Society for the Promotion of Science for their cooperation and support while this work was completed.
References and Notes (1) Present address: Edward Waters College, Jacksonvllle, Fla. (2) A. M. Portis, Phys. Rev., 9 1 , 1071 (1953). (3) See,for example, D. P. Lin and L. Kevan, J . Chem. Phys., 55, 2629 (197 1). (4) T. 0. Castner, Phys. Rev., 115, 1506 (1959). ( 5 ) M. K. Bowman, H. Hase, and L. Kevan, J . M a p . Reson., 22, 23 (1976).
(6) A. M. Portis, Phys. Rev.,l04, 584 (1956). (7) W. B. Mims, K. Nassau, and J. D. McGee, PhYS. Rev., 123, 2059 (1961). (8) J. R. Klauder and P. W. Anderson, Phys. Rev., 125, 912 (1962). (9) E. L. Wolf, Phys. Rev., 142, 555 (1966). (10) L. Kevan and L. D. Klspert, "Electron Spin Double Resonance Spectroscopy", Wiley-Interscience, New York, N.Y., 1976. (11) P. R. Moran, Phys. Rev., 135, 247 (1964). (12) H. Yoshida, D. F. Feng, and L. Kevan, J . Chem. Phys., 58, 3411 (1973). (13) B. L. Bales, M. K. Bowman, L. Kevan, and R. N. Schwartz, J. Chem. Phys., 63, 3008 (1975). (14) P. A. Narayana, M. K. Bowman, L. Kevan, V. F. Yudanov, and Yu. D. Tsvetkov, J. Chem. Phys., 83, 3365 (1975). (15) D. F. Feng, F. Q. H. Ngo, and L. Kevan, unpublished work.
Laser Photolysis Study of the Photoracemization of 1,I' -Binaphthyl Masahlro Irle, Klkuo Yoshlda, and Koichlro Hayashi The Institute of Scientific and Industrial Research, Osaka University, Osaka, Suita, Japan (Received April 8, 1976; Revised Manuscript Received February 24, 7977)
The photoracemization mechanism of 1,l'-binaphthyl has been studied from the effect of additives as well as by a laser photolysis method. The effect of additives revealed that photoracemization occurs in the triplet excited state. The rotation process along the intraannular C-C bond, which causes the racemization,was directly followed by measurement of time-resolved triplet-triplet (T-T) absorption spectra of 1,l'-binaphthyl at low temperature with the laser photolysis technique. The almost rectangular conformationchanged to a less twisted coplanar conformation with a rate constant of 1.0 X lo4 s-l at -150 "C. The potential energy surface along the photoracemization coordinate was also discussed.
Introduction photoreso~utionof a racemic mixture by means of circularly polarized light was first observed for the oxalate complex of chromium(II1) by Stevenson et al.' This is a unique example of photoresolution. They suggested that the illumination of circularly polarized light on a racemic mixture would induce optical activity, if the photochemical reaction undergone by an isomer is only in inversion to its enantiomer. Although several works have dealt with the hotoracemization of biphenyl derivatives and sulfoxides,2g these works are limited to systems in which the racemization is accompanied by irreversible side reactions and has a low quantum yield. Up to the present moment, the mechanism of photoracemization has not yet been established. The purpose of this study is to reveal fundamental processes involved in the photoracemization of l,l'-binaphthyl and to apply the information to the study of photores~lution.~ 1,l'-Binaphthyl is one of the simplest chiral hydrocarbon^.^^^ The racemization is expressed as follows:
i
1
R(-)-1,l'-binaphthyl
S(+)-1,l'-binaphthyl
Its dissymmetry is molecular in nature and enantiomer conversion is induced by rotation along the intraannular bond. Information about the fundamental processes of the racemization reaction is of importance not only for pho-
toresolution study but also for study of the electronic structure of the excited state of nonplanar corn pound^.^-^
Experimental Section 1,l'-Binaphthyl was resolved by the method of Pincock et a1.l' The optically active 1,l'-binaphthyl thus obtained had an [(rl2'D of 156'. Tetrahydrofuran and 2-methyltetrahydrofuran were distilled twice over calcium hydride. Triplet quenchers or sensitizers, dibenzalacetone, fluorenone, piperylene, benzophenone, and acetophenone, were of analytical grade and used as received. All samples were degassed by the freeze-thaw cycle in vacuo. Photoillumination was carried out with a super-highpressure lamp (1kW), the wavelength being selected by Toshiba glass filters. The reaction was followed by measuring [aI2'D with a Hitachi polarimeter (Type PO-B). Triplet-triplet (T-T) absorption measurement was carried out with a ruby laser photolysis apparatus (JEOL, JLS-R9). The fundamental wavelength of 694 nm was doubled to 347 nm by use of a second harmonic generator of RDP. The second harmonic thus obtained has the pulse width of 20 ns and a photon number of 1X 1017per pulse. The time constant of the monitoring system is less than 10 ns. Results (i) Photoracemization under Stationary Light. Figure 1shows the dependence of the rate of photoracemization of 1,l'-binaphthyl in tetrahydrofuran at 0 "C on the wavelength of illuminating light. Photoexcitation of the absorption band of 1,l'-binaphthyl (which has an absorption tail around 340 nm) results in racemization, while no racemization is observed by light passed through a UV-39 filter (A >365 nm) or in the dark at 0 "C. This The Journalof Physicalchemistry, Vol. 81, No. IO, 1977
