J. Phys. Chem. 1987, 91, 3592-3599
3592
due to shielding anisotropy plus an inhomogeneous distribution of the chemical shifts.
Conclusions 133Csis shown to be a useful nucleus for monitoring the local environments in mordenite by N M R . The N M R spectrum of 133Csin Cs-exchanged mordenite indicates that the efg tensor increases with decreasing water content. The quadrupole coupling constant increases from 2 10 kHz for the fully hydrated sample to 3.1 MHz for the anhydrous sample. The static spectra increase in line width from 1.2 kHz for the fully hydrated sample to 6 kHz for the anhydrous sample. Under MAS, the anhydrous sample shows two peaks, with relative intensities of roughly 1.3. Two different sites are clearly observed in the anhydrous sample with
center of mass of the peaks at -191.0 and -57 ppm. The assignment of the peaks to Cs locations is made on the basis of the structural difference of the six-ring coordination site VI from the eight-ring sites I1 and IV. After correction for the second-order quadrupolar shift, the downfield peak, -24 ppm, may be attributed to site VI while sites I1 and IV with similar structures yield similar chemical shifts at -157 and -186 ppm (see Table V). In the fully hydrated sample all three sites possess an identical isotropic value of -64 ppm. Acknowledgment. This research was supported by the Assistant Secretary for Energy Research, Office of Energy Sciences, WPAS-KC-03-02-01. Registry No. '-'-'Cs,7440-46-2; Mordenite, 121 73-98-7.
Spin-Polarized Electron Paramagnetic Resonance Spectra of Radical Pairs in Micelles. Observation of Electron Spin-Spin Interactions' Gerhard L. Gloss,*+* Malcolm D. E. Forbes,+ and James R. Norris, Jr.+* Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, and Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: January 9, 1987)
A model for polarized EPR spectra generated in radical pair reactions in micelles is being proposed. The model is based on electron spin-spin interactions which remain observablebecause of limited diffusion in micelles. The experimental observable is a doubling of hyperfine transitions, split by the magnitude of the interaction. The polarization is generated by the nonadiabatic generation of the radical pair with a triplet or singlet precursor. The time evolution of the wave function leads to a non-Boltzmann distribution of the populations among the four energy levels. The theory is tested by comparison with experiments, previously reported and repeated in this laboratory, obtained by laser flash photolysis of benzophenone in sodium dodecyl sulfate (SDS) micelles. Simulations of the shape of the spectra and their time dependence give excellent agreement with experiment. The model is further supported by experiments in micelles modified by different salt concentrations as well as different chain lengths of the micelle-forming molecules.
Introduction In several recent papers Hayashi and collaborators reported time-resolved EPR spectra, obtained on photolyses of ketones in micelles, which showed highly unusual chemically induced dynamic electron polarization (CIDEP).Z,3 The authors attributed the unusual features of the spectra to fast intramolecular hydrogen migration in the alkyl groups of the micelle-forming molecules. If correct, this explanation requires drastic departure from conventional thinking in free-radical chemistry in which fast 1,2-shifts of hydrogen in straight-chain alkyl radicals have no p r e ~ e d e n t . ~ In this paper we wish to present evidence against the proposed mechanism and to suggest a different explanation which has as its foundation well-accepted principles of magnetic resonance and does not require any unusual chemistry. We believe the spectra to result from correlated radical pair states, the observation of which is made possible by the rather special diffusion processes associated with micelles. In fact, we believe these spectra represent the first examples where highly resolved EPR spectra, obtained from mobile radical pairs in which the two interacting electron spin carriers are not chemically linked or frozen into a matrix, show clear evidence for electron spin-spin interaction. However, spin-echo experiments, reported by Thurnauer and Meise15have revealed good evidence for electron spin-spin interactions in micelles by exhibiting unusual phase shifts. The authors interpreted their results qualitatively with a model which is very similar to the one offered here. Other work can be interpreted to show such interactions, although the explanations offered were very qualitative and did not address the important features of the model to be discussed here.6 'The University of Chicago. Argonne National Laboratory.
*
0022-3654/87/2091-3592$01.50/0
Experimental Section All spectra were recorded on a Varian E-9 X-band EPR spectrometer modified for direct detection in the following manner: the signal from the preamplifier of the microwave bridge was connected directly to both gates of a PAR Model 162 boxcar averager. The gate sizes were 250 ns for all experiments. The boxcar output, after amplification, was fed continuously to an IBM PC-AT computer equipped with a Data Translation DT2801 ADC board, where further data reduction was performed. All displayed spectra and simulations have a sweep width of 200 G. An optical transmission (V-line) microwave cavity was used with a Suprasil flat cell, 0.5 mm optical path length, through which the samples were pumped a t rates no slower than 1 L/h. The microwave power was 30 mW for all experiments. The laser, Lambda Physik Model 103-MSC, operating at 308 nm with a pulse of 15 ns fwhm, was fired at repetition rates of 80-120 Hz. The pulse energy exiting the laser was 120 mJ/pulse. Flowing (1) Work at the University of Chicago was supported by NSF Grant CHE-8520326 and work at Argonne by the Office of Basic Energy Sciences, US-DOE, under Contract No. W-31-109-ENG-38. (2) (a) Sakaguchi, Y.; Hayashi, H.; Murai, H.; I'Haya, Y. J. Chem. Phys. Lett. 1984, 110, 275. (b) Sakaguchi, Y.; Hayashi, H.; Murai, H.; I'Haya, Y. J.; Mochida, K. Chem. Phys. Lert. 1985, 1.20, 401. (c) Murai, H.; Sakagushi, Y.; Hayashi, H.; I'Haya, Y. J. J . Phys. Chem. 1986, 90, 113. (3) For general references on CIDEP see: (p) Spin Polarization and Magnetic Effects in Radical Reactions; Molin, Yu. N., Ed.; Elsevier: Amsterdam, 1984; Chapters 2, 4, 8. (b) Chemically Induced Magnetic Polarization; Muus, L. T., Atkins, P. W., McLauchlan, K. A,, Pedersen, J. B., Eds.; Reidel: Dordrecht, Holland, 1977; Chapters V-IX, XI, XIX. (4) Beckwith, A. L. J.; Ingold, K. U. In Rearrangements in Ground and Excited States: deMayo, P., Ed.; Academic: New York, 1980; p 252. (5) Thurnauer, M. C.; Meisel, D. J . A m . Chem. SOC.1983, 104, 3729. (6) (a) Turro, N. J.; Paczkowski, M. A,; Zimmt, M. B. Chem. Phys. Lett. 1985, 114, 561. (b) Trifunac, A . D.; Nelson, D.J . Chem. Phys. Left. 1977, 46, 346.
0 1987 American Chemical Society
Spectra of Radical Pairs in Micelles A
30 gauss
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3593
R
-
30 gauss
B
Figure 2. EPR spectrum taken 0.8 ps after excitation of benzophenone-dlo(0.1 M) in n-dodecane. See Figure l for assignments. Figure 1. EPR spectra taken (A) 0.8 ps and (B) 2.8 ps after excitation of benzophenone-dlo( 2 X M) in an aqueous solution of sodium M). The broad signal in the center is assigned n-dodecyl sulfate (8 X to the hydroxydiphenylmethyl-d,, radical. Lines attributed to the minor component, CH3CHCH2-, are marked by arrows. The major signals are due to radicals of the type -CH2CHCH2-. Note: In this and all subsequent figures, signals above the base line are in absorption and below in emission.
of the solution was made necessary to prevent heating and depletion of the sample. This kept the temperature of the measurements near 30 OC. All detergent solutions were prepared with distilled water. When necessary, the solubilization of the guest molecules was assisted by sonication at elevated temperatures. Nitrogen-saturated solutions gave results identical with those of air-saturated solutions. Sodium n-dodecyl sulfate (Sigma), n-dodecane (Aldrich), and the sodium n-octyl, n-decyl, n-undecyl, and n-tetradecyl sulfates (Lancaster) were all used as received. Benzophenone-dlo was prepared from benzene-d6 (Aldrich, 99.5%-d) according to literature methods’ and was purified by crystallization from hexane.
Results Figure 1A shows the EPR spectrum obtained by direct detection of a laser flash photolyzed aqueous solution of sodium n-dodecyl M)containing benzophenone-dlo (2.0 sulfate (SDS) (8 X X M). The spectrum represents the electron spin polarization at 0.8 ps after the excimer laser flash, averaged with a boxcar averager with 250-11s gate aperture. The spectrum is for all practical purposes identical with the one reported by Hayashi and co-workers.2 The assignment of the coarse features is straightforward, with the major peaks afising from the hydroxydiphenylmethyl-dlo radical, (C,D,),CO& and the alkyl radical fragments, -CH2-CH-CH2-. Some minor peaks are due to CH,-CH-CH,and are so indicated in the figure. The photochemistry leading to these radicals has been well studied before and involves a simple hydrogen abstraction by the triplet state of benzophenone from the micelle-forming molecules. What is highly unusual about the spectrum is the fact that each hyperfine line of the alkyl radical is clearly split into two components, one in emission and one in absorption (note: Figure 1 shows an absorption emission spectrum, not the usual EPR derivative spectrum). As has been pointed out by the discoverers of this (7) Org. Synth. Collect. Vol. I, 89.
effect,2 current CIDEP theory3 does not allow for this polarization pattern. Instead, it predicts that all low-field lines are in emission with all high-field lines in absorption (or vice versa), or a totally emissive or absorptive spectrum. Indeed, as Figure 1B shows, and as has been reported before, if the polarization is sampled at later times, t > 3 ps, a conventional radical pair CIDEP spectrum is seen with the low-field emission, high-field absorption (EA) pattern, expected for a triplet-initiated reaction. This means the unusual effect vanishes within a time span of little more than 2 PS *
The exceptional behavior of the system may be either due to the primary reactants and their chemical behavior or to the micellar environment. The previous explanations focused on the former. To get additional experimental evidence on this question we designed a number of experiments. First, if hydrogen migration is indeed important, most likely it should be observable in homogeneous solution as well since it is hard to see how a micellar environment can catalyze this unimolecular reaction. Figure 2 shows the result obtained when benzophenone-dIowas photolyzed in dodecane as a solvent. A spectrum obtained at the same time window (0.8 ps) shows a clean, conventional CIDEP spectrum with no evidence for splitting of the major hyperfine lines. Similarly, if the reaction was run in light and heavy paraffin oil as a solvent, again, only conventional EA CIDEP spectra were observed. Next, modifications were made on the micelle structures. It is known that added electrolytes such as alkali halides will affect the micelle aggregation numbers and the dynamic behavior.* Figure 3 shows the results obtained on adding sodium chloride to the solutions. As can be seen by comparing spectra taken at identical time windows, the unusual phase effect does diminish with increasing salt concentration. The size of the micelles is also affected by the length of the hydrocarbon chain of the micelle-forming m o l e c ~ l e s . ~Figure 4 shows the results obtained for micelles with different chain lengths. There are definite changes in the spectra, the details of which will be discussed below. The results of these experiments point to the micellar environment as the cause of the unusual observed pattern. We have conducted some other experiments supporting this point of view and they will be discussed in the context of the proposed model. (8) (a) Chen, J. M.; Su,T. M. Mou, C. Y . J . Phys. Chem. 1986,90,2418. (b) Aniansson, E. A. G.; Wall, S.N.; Algren, M.; Hoffman, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J . Phys. Chem. 1976, 80, 905. (9) Tanford, C . The Hydrophobic Effecf; Wiley-Interscience: New York, 1973; Chapter 8.
3594 The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 A
n
Closs et al. A
v
B
B
n
U C C
D
II
D
V
Figure 3. EPR spectra taken 1.0 ps after the excitation of benzoM) in SDS (8 X lo-* M) with [NaCI] = (A) 0.25 phenone-dlo(2 X M, (B) 0.5 M, (C) 0.75 M, and (D) 1.0 M.
The Micellar Radical Pair Model An acceptable model for the observed EPR spectra must account for the peculiar splitting of the major hyperfine lines and the emission-absorption pattern, as well as the transformation with time of the early, abnormal spectra to the conventional CIDEP spectra. Since a single line cannot have observable absorptive and emissive characteristics at the same time, it is clear that each major hyperfine transition must be a composite of at least two lines at slightly different magnetic field positions. The previous authors pointed to the protons a t the y-position of the radical carbon as the source of additional hyperfine splitting.2c These y-splittings are usually not resolved if all components are either absorptive or emissive, as for example, in the spectrum of Figure 2. If, however, half of the y-lines are in absorption and half are in emission, a pattern resembling the observed spectrum can result. Different radicals with slightly different hyperfine coupling constants and changes of the sign of the exchange cou-
Figure 4. EPR spectra taken 0.8 ps after excitation of benzophenone-dlo (2 X M) in (A) sodium n-octyl sulfate (0.38 M), (B) sodium n-decyl sulfate (0.17 M), (C) sodium n-undecyl sulfate (0.14 M), and (D) sodium n-tetradecyl sulfate (2.5 X M).
pling constant have been invoked as other sources of the splitting." An alternative explanation, to be developed here, is based on the splitting of each line in the normal spectrum into two lines due to an interaction usually not observable but brought into play by the special environment provided by the micelles. We believe this to be a small fine structure splitting among the electrons of the radical pair. Before we develop a model for this case, it is important to realize that it differs from the conventional treatment of CIDEP by calculating different expectation values, corre(IO) (a) McLauchlan, K. A.; Stevens, D. G . Chem. Phys. Lett. 1985, 115, 108. (b) Hayashi, H.; Sakaguchi, Y.; Murai, H.; I'Haya, Y.J. Chem. Phys. Lett. 1985, 115, 111. (c) Grant, A. I.; Green, N. J. B.; Hore, P. J.; McLauchlan, K. A. Chem. Phys. Lett. 1984, 110, 280.
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3595
Spectra of Radical Pairs in Micelles sponding to the observables in the special situations of micellar reactions. The cause for the polarization to be described is actually different from and more fundamental and yields larger polarization that that responsible for the conventional CIDEP phenomenon. However, in homogeneous solutions the effect vanishes because of degeneracies of the transition energies. Those degeneracies are lifted in micelles and other environments with restricted diffusion. We shall develop the model now. After the laser pulse, the quickly formed triplet state of benzophenone decays mostly by hydrogen abstraction from the hydrocarbon chain of the micelle molecules, forming a spin-correlated radical pair as shown in eq 1 . From the concentrations of micelles 3(C6D5)2C=0
+ H-Mic
-
(C,D,),t-OH
+ Mic
(1)
and benzophenone and the photon flux during the laser pulse it can be shown that on the average only one such radical pair is generated in a single micelle." Recombination is initially prohibited because of the triplet spin function of the pair, and the components will separate by diffusion and are describable by the usual radical pair Hamiltonian (eq 2). Here, J is the electron
H = j3h-'Bo(glSIZ + gpS2r) - J(Y2 + 2S162) + SI*T*S2+ CaSI.Ij + CajS2.Ij ( 2 ) spin exchange coupling constant, T is the electron-electron dipolar coupling tensor, and a, and aJare the hyperfine coupling constants on either component of the radical pair, with the remaining symbols having their conventional meanings. As the basis set for the electron spin functions we choose the symmetrized singlet and IF'); triplet functions suitable for high magnetic field, (IS); IF); IT)), whose products with the nuclear basis product functions, lx), form a complete set. As indicated above, the electron-electron interactions which are separated in the Hamiltonian into the isotropic exchange interaction and the anisotropic dipolar interaction are of critical importance in the model. It should be noted that both interactions involve the dot product of the electron spin operators and therefore transform in a parallel way. For simplicity, we drop at this point the dipolar interaction, although, as will be discussed below, it may play a role and can be easily reinserted. Although not written as such, the Hamiltonian operator is time dependent because the electron interactions depend on distance. However, this time dependence is of no consequence for a simple model as developed here and will be neglected. Following the usual assumptions made in the radical pair theory of chemically induced spin p~larization,~ we note that radical pair formation is nonadiabatic leading to an initial nonstationary state describable by the three triplet functions each containing one-third of the population. After the components of the pair have separated enough to reduce the electron spin interactions to levels comparable with the hyperfine interaction, mixing between IS) and IF) will occur via the hyperfine interaction and Zeeman energy differences between the pair components. Again as usual, mixing involving IF)and IT)will be neglected because of the large energy gap at large magnetic fields. The wave functions resulting from this mixing can be written as in (3), where 8 is dependent on J and $2
+ sin qs)]lx) q F ' ) + cos els)]lx)
= [cos elP)
(3a)
= [-sin
(3b)
the hyperfine interaction. Since in EPR spectra only states with the same nuclear wave functions, Ix),give rise to allowed transitions and mixing between IS) and 170) also occurs only between states of the same nuclear wave function, the problem can be factored into 1 independent 2 X 2 systems, where 1 = 2" for n (1 1) Assuming an aggregation number of 60, the concentration of micelles is 1.3 X IO-3 M,giving on the average 1.5 benzophenone molecules per micelle. An estimate of the number of photons per pulse reaching the cell, and of the absorbance of the solution, shows that approximately 10-20% of the benzophenone molecules get excited. From this no more than 30% of the micelles host an excited benzophenone molecule and less than 10% may have two
excitations.
T.
N:OJ
T.
N = 113
Figure 5. A schematic energy-level diagram of a radical pair in a magnetic field with one hyperfine interaction (A) and an exchange interaction, -J. The left side of the figure shows the zero-order levels and the right side the levels after mixing. The initial population, N , is assumed to be in the triplet levels only.
protons which carry hyperfine coupling. The stationary state solutions for (3) follow from (4)-(6). Here q is defined for each w COS 28 = J (4) w
sin 2 8 = q
w =
(P+ q
y 2
(5)
(6)
hyperfine state by (7). The eigenvalues for +2 and $3 are given = [PBo(gl - g2) + C('lmJ- aJm,)l/2 by eq 8 and those for
€1
F
and T by eq 9. The four transition €2
= -w
€3
=w
(8b)
+ ~ ( a , m+, aJmJ)/2
(9a)
-vo - J - C(a,m, + aJmJ)/2
(9b)
= vo - J
c4 =
(7)
vo = PBOkI + g2)/2
(9c)
energies are
Ezl = vo
+ ( 1 / 2 ) C ( a l m l+ aJmJ)- J + w
(loa)
+ ( 1 / 2 ) x ( a , m ,+ u,mJ) - J - w (lob) E42 = vo + ( 1 / 2 ) C ( a , m ,+ aJmJ)+ J - w (1Oc) E43 = uo + ( 1 / 2 ) C(a,m, + a,m,) + J + w (1 Od) For each resolvably different value of C(a,m,+ a,mJ),four lines E31 = uo
will be observable. If, in addition w is greater in magnitude than J , then the four lines are grouped into two doublets. Each doublet is split by 2J and the separation of the centers of the doublets is 2w. For J
