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The Journal of Physical Chemistry, Vol. 83, No. 26, 7979
(16) M. Zerner and M. Gouterman, Theor. Chim. Acta, 4 , 44 (1966). (17) W. A. Eaton, L. K. Hanson, P. J. Stephens, J. C. Sutherland, and J. B. R. Dunn, J . Am. Chem. Soc., 100, 4991 (1978). (18) J. Fajer and M. S. Davis in "The Porphyrins", Vol. IV, D. Dolphin, Ed., Academic Press, New York, 1979, p 197. (19) J. Fajer, M. S. Davis, D. C. Brune, L. D. Spaulding, D. C. Borg, and A. Forman, Brookhaven Symp. Bid., 28, 74 (1976). (20) The unpaired spin density profile of ZnTPiBC' is similar to that found'' for the isomeric tetraphenylbacteriochlorin, ZnTPBC'. (21) J. Subramanian in "Porphyrins and Metalloporphyrins", K, M. Smith, Ed., Elsevier, New York, 1975, p 555. (22) R. H. Felton in "The Porphyrins", Vol. V, D. Dolphin, Ed., Academic Press, New York, 1979, p 53. (23) A simihr oxidation of a porphyrin has been reported for the analogous Ru(1I)TPP complex
Schlick and Kevan
4-
Ru(II)TPP(py)(CO) [Ru(II)TPP(py)(C0)lt. and not [Ru(III)TPP(py)(CO)]
'
G. M. Brown, F. R. Hopf, J. A. Ferguson, T. J. Meyer, and D. G. Whitten, J . Am. Chem. Soc., 95, 5939 (1973). See also A. Antipas, J. W. Buchler, M. Gouterman, and P. D. Smith, ibid., 100,3015 (1978), for a MO description of the ruthenium complexes. (24) I. Morishima and S. Ogawa, Biochemistry, 17, 4384 (1978). (25) D. Dolphin, A. Forman, D. C. Borg, J. Fajer, and R. H. Felton, Proc. Natl. Acad. Sci. U . S . A . , 68, 614 (1971); J. Fajer, D. C. Borg, A. Forman, A. D. Adler, and V. Varadi, J . Am. Chem. Soc., 96, 1238 (1974); C. E. Schulz, P. W. Devaney, H. Winkier, P. G. Debrunner, N. Doan, R. Chiang, R. Rutter, and L. P. Hager, F€BS Lett., 103, 102 (1979).
Study of g Anisotropy Associated with Molecular Motion in the Triphenylmethylperoxy Radical. An Enviromental Probe Shulamlth Schllck" and Larry Kevan Department of Chemistry, Wayne State University,Detroit, Michigan 48202 (Received July 9, 1979) Publication costs assisted by the Army Research Office
ESR spectra of triphenylmethylperoxy radical, Ph,COO., in y-irradiated polycrystalline triphenylacetic acid, Ph,CCOOH, were measured at 35 GHz as a function of temperature from 80 to 290 K. Multiple lines observed are due entirely to g anisotropy. Principal values of the g tensor at 80 K are 2.0320, 2.0092, and 2.0035. At 290 K an axial g tensor is observed with gll = 2.0175 and g, = 2.0128. A t intermediate temperatures new lines appear in the spectrum. All spectral changes with temperature are reversible. The spectra are interpreted with the modified Bloch equations for motional processes. All salient features over the entire temperature range are well reproduced by a motional model involving 120' jumps of the peroxy group about the C-0 bond. The jump rates fit an Arrhenius plot and give an activation energy of 9.2 kJ/mol. The possibility of using the peroxy group as an environmental probe of its motional freedom is discussed and several systems where this may be applicable are given.
Introduction Time-dependent processes strongly affect the line shapes of electron spin resonance (ESR) spectra. Fluctuating hyperfine splittings, electron transfer, electron spin exchange, and other events that alter the environment of the unpaired electron are widely reported and interpreted in ESR spectra of 1iquids.l In powders, single crystals, and solid solutions, anisotropy is commonly present. Dynamical processes affect these spectra if their time scale is of the order of the frequency width of the anisotropy. Fluctuations of the zero-field splitting,2 Jahn-Teller distortion^,^ internal rotations, and discrete jumps4 have been studied and interpreted in the solid state, thus providing valuable kinetic and structural information. g anisotropy is frequently found, and, in many cases, it serves as a method for identifying radical species. For example, triphenylmethyl radical, Ph,C., is formed by ultraviolet irradiation of triphenylacetic acid under vacuum and has g = 2.0024. Subsequent exposure of the irradiated sample to oxygen results in the appearance of an additional, slightly asymmetric line a t g = 2.014 which is attributed to the triphenylmethylperoxy radical, Ph3CO0..5 The g value is in agreement with the average value expected for peroxy radica1sGl3as seen in Table I. Absence of anisotropy was explained by assuming tumbling of the 0022-3654/79/2083-3424$0 1.OO/O
whole molecule at a rate sufficient to result in an averaged ~pectrum.~ The ESR spectrum of oxygen-17 enriched Ph3CO0. was studied a t ambient temperature and 123 K.14 Due to the complexity of the spectra, only the maximum hyperfine splittings from each oxygen were measured. The results were incompatible with a molecular tumbling model. Instead, partial averaging of the g and hyperfine tensors was assumed to be due to restricted rotation or discrete jumps of the 0-0 group within the molecule. The limited results precluded testing of a detailed motional model. In this study the g anisotropy of Ph3CO0. is measured a t 35 GHz in the temperature range 80-290 K and used to deduce a motional model. The spectrum can be interpreted in terms of a rhombic g tensor a t low temperature and in terms of an axial g tensor with little anisotropy a t high temperature. In the intermediate temperature range the spectra become very complex and many extra lines are observed so that it becomes impossible to interpret the spectra by picking g values a t inflection points. A motional model is assumed in which the 0-0 group executes discrete jumps about the C-0 rotation axis. Spectra were calculated with different rotation axes within the molecular axis system and with different jump angles, as a function of the jump rate, by using the formalism of the modified Bloch equations. The calculated spectra are 0 1979 American
Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
Molecular Motion in the Triphenylmethylperoxy Radical
TABLE I :
g
3425
Values of Peroxy Radicals g values
radical
H,O;CO(NH,),
ROO. ,OOCF,CONH,
ROO.
single crystal
liquid alkanes CF,CONH, single crystal
poly( tetrafluoroethylene) powder
PMMA-00.
77 K
matrix
2.049 2.008 2.001 2.038 2.007 2.002
H
00
a
2.021 2.018 2.008
2.038 2.007 2.002 2.034 2.017 2.009
PMMAa powder tetralin single crystal
ROO.
2.042 2.013 (at 123 K ) 2.005
m
urea-PEb complex solid
(CH ,)C 00.
(CH,),COOH glass
Ph,COO.
Ph,C.COOH powder
Poly( methyl methacrylate).
300 K
2.037 2.008 2.002
2.032 2.020 2.005
2.0320 2.0092 2.0035 (at 8 1 K )
gll = 2.0175 P I = 2.0128 (at 291 K )
ref
gav
2.019
6
2.01 48-2.01 55
7
2.016
8
2.016
9
2.016
10
2.020
11
2.016
12
2.0187
13
2.0149 ( 8 1 K )
this work
-I
2.0143 (291 K )
Polyethylene.
sensitive to the particular jump model assumed. A model in which the 0-0 group executes 120’ jumps around the C-0 bond reproduces well the experimental results in the entire temperature range studied. The activation energy for jumping between the three equally populated potential minima is calculated to be 9.2 kJ/mol.
Experimental Section Polycrystalline Ph,CCOOH from Aldrich Chemical Co. was irradiated for about 48 h in air a t room temperature in a 6oCoy ray source at a dose rate of 0.1 Mrd/h. The powder was pressed into pellets which were measured at 35 GHz by a Varian bridge with 100-kHz magnetic field modulation. Field calibration was done with samples of DPPH (g = 2.0035) and a 53Cr3+-doped(0.071%) MgO single crystal (g = 1.980015). The scan was calibrated by using a 65Mn2+-dopedMgO single crystal. The value of 86.7 G for the separation of the center two lines of the hyperfine sextet was used.16 Cold helium gas served as coolant. y irradiation of Ph3CCOOH in air produces both Ph3C. and Ph3CO0.. Ph3C. saturates easily at microwave power levels of a few milliwatts, while the signal from Ph3CO0. increases linearly with the square root of microwave power up to a t least 50 mW. A combination of several days exposure to atmospheric oxygen and ESR measurements at microwave power levels of 10-50 mW resulted in spectra in which the signal from the peroxy radical dominated. Results Figure 1 shows the 35-GHz spectra of Ph3COO. at 81-282 K. The rigid lattice g values at -80 K are g, = 2.0320, g2 = 2.0092, and g3 = 2.0035. In the molecular coordinate system gl is along the 0-0 bond ( x ) , g3 is along the direction of the unpaired electron 2p orbital ( z ) , and the intermediate value is along y which completes the right-handed axis system. These rigid lattice g values are very similar to typical results for peroxy radicals at 77 K81gJ1Jzand at room temperaturelo (see Table I), indicating
that the g tensor is a property of the 0-0 group and is quite insensitive to the rest of the molecule. At 282 K the g anisotropy is reduced considerably to give axially symmetric values of gll = 2.0175 and g, = 2.0128. The average g values at low and high temperature, 2.0149 and 2.0143, respectively, are equal within experimental error. The spectral changes with temperature are completely reversible.
Spectral Simulations It is assumed that spectral changes occur due to internal motion of the 0-0 group with respect to the rest of the molecule. We consider discrete jumps between N welldefined species or sites in the lattice, each characterized by a different g tensor in a common rectangular coordinate system. The line shape is calculated in the presence of interconversion (jumps) between sites. It is worthwhile to note that the site g tensors differ only in their relative orientations and, therefore, in the rigid lattice limit, at low temperature, all sites are expected to have identical spectra. The calculation of the spectrum is based on the formalism of the modified Bloch e q u a t i ~ n s l ~which - ~ ~ are obtained by adding kinetic terms that express the changes in magnetization due to interconversions among different species or sites. The equation for the complex transverse magnetization of species A, MA, is given by
with
T ~ isAthe spin-spin relaxation time of species A; OA is the resonance frequency for species A; y is the magnetogyric ratio; H1 is the microwave field; MOA is the magnetization of species A along the z axis and it is used in place of MzA,
3426
The Journal of Physical Chemistry, Vol. 83,No. 26, 1979
Schlick and Kevan
CUBIC JUMPS
DPPH
0.005
i
d;Y
-d5O-IbO -5b
in the absence of saturation and for relatively long spin-lattice relaxation times TI; and k A = 1 / 7 ~ here ; 7.4 is the mean lifetime of species A. The prime on the summation in (1)denotes a sum over all species, except that for which the equation is written. The total complex transverse magnetization is the sum over all species: N
M = EMx x=l
(3)
The imaginary part of M in (3) gives the absorption line shape. A general solution for M was obtained for a system with N sites when all interconversion rates between sites were equally probablenZ0The imaginary part of the transverse magnetization is N
cf x G= N N ( 1 - c fJ
(4)
+ ax7)-1
(5)
iYHIMO7
x=1
x=l
with = (N
Id0 250
H - H e , GAUSS
‘OS Flgure 1. ESR spectra (35 GHz) of the triphenylmethylperoxy radical in triphenylacetlc acid as a function of temperature.
fx
5b
Here 7 is the mean lifetime of any species in the system and ax is defined as in (2). This equation is easily applicable to the two-jump and three-jump situations assumed here.
Flgure 2. Simulated ESR powder spectra obtained by assuming “cubic” jumps as a function of 7 , the mean,lifetime between jumps. The magnetic field is in units of H - H, where H, is the field corresponding to gav. The line width in the absence of intramolecular motion Is 13 MHz.
The modified Bloch equations method is a secular method, implying that changes in the electron or nuclear spin during the process are not considered. However, the method has been successfully applied to systems where an entire range of exchange rates occur to give complete anisotropy or complete averaging.l9 The rate of interconversion between sites, T - ~ is , of the order of the frequency spread of the spectrum which is -190 G or -530 MHz. Spectral changes are expected therefore to occur for 7 2 X s. The other parameter that is needed for calculation is the line width in the absence of site interconversion. Values were used, based on a comparison of 11-15 MHz for TZv1 of calculated and experimental spectra in the limit of high and low temperature. In the inteimediate temperature range the line shape was not very sensitive to variation of the line width within the limits defined above. Cubic Jump Model. We first consider a “cubic” jump model in which the axes of three sites are interchanged by rotation about a body diagonal of a cube. The axes of the g tensor are interchanged as follows: site 1 gib), gZW, g&) site 2 g&), g&), gl(z) site 3 g&), gib), gdz) This situation is similar to that calculated previously by Hudson3 for an axial g tensor. Comparison of cubic jump simulations shown in Figure 2 with the experimental results in Figure 1 shows that the experimental results are
-
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
9 x y 20221
gxx=2.0320
r(ps)
giiv';2.0175
9yy '2.0092
0.0001
li
li
Y
,
-250 -150
-50
50
150
250
H-Ho, GAUSS
Figure 4. Simulated ESR powder spectra obtained by assuming a Jump angle of 180' about the CO bond. The COO angle Is 127' and the line width in the absence of intramolecular motion is 13 MHz.
N = 3 and N = 2, respectively. In all cases the diagonal g tensor of site 1, denoted by g(1) in the coordinate axis system x , y, z defined in Figure 3, is used to calculate the g tensor for all other sites. The calculation is dependent
upon the rotation model assumed. The g tensor for site 2, g(2), is given by g(2) = L[g(W-ll where the matrix L relates the molecular coordinate axis system of site 1 and site 2: /X\
(7 1
The elements of L are expressed in terms of the angles p, which is the jump angle about the C-0 bond, and y, the angle between x and x'in Figure 3. In most of the simulations y is 37'. We obtain22 cos2 y cos p t
i
sin2 y
L=
as measured a t 280 K. In Figure 3, a = 90 y = 127', and this value can be compared with a = 130' calculated for (02C-02)-.21 It is important to note that a = 120' is an unacceptable value because it leads to 2.026 + 7.0035 = 2.0149 gll = 2,0148 g, = 2
+
so that an isotropic spectrum is expected at the high temperature limit; this contradicts the experimental axiality of the g tensor under these conditions. Spectra were calculated for a three-jump process with a jump angle of 120' and for a two-jump process with a jump angle of 180'. Equations 2,4, and 5 were used with
sin y cos p cos y - -sin p cos cos 7 sin y
cos y sin y cos p - sin2 y cos p t sin y cos y COS2 y
-sin p sin
cos 7 sin p
cos p
sin y sin p
oi
(8 1
For calculations of the powder spectrum, we calculate, for each site orientation with respect to the magnetic field, the resonance frequency and then apply the modified Bloch equations. Figure 4 shows spectral simulations as a function of T for a jump angle of 180' around the C-0 bond. This jump model reproduces neither the spectra obtained a t intermediate temperature range nor the axial g tensor observed at 290 K. It is worthwhile to discuss simulations obtained with 180' jump angle because of possible applications to
3420
The Journal of Physical Chemktry, Vol. 83, No. 26, 1979
Schlick and Kevan
G O BONO ROTATION 120’JUMPS
-250 -150
-50
50
150
ill
250
H-He, GAUSS
0.5
Flgure 5. Simulated ESR powder spectra obtained by assuming a jump angle of 180’ about the CO bond as a function of the COO angle. 7 = 0.0001 ys and the line width in the absence of intramolecular motion Is 13 mHz.
other cases. g3(g,,) remained unchanged because any 180” rotation in the x-y plane does not change the value along z. Two “extra” lines in the region between g, and g2 become more prominent as T is shorter. Even for T = 0,0001 ps the spectrum is still characterized by a rhombic g tensor, but some averaging of g, and g2 has occurred. This spectrum does not change even when 7 is shorter by two orders of magnitude. Simulated spectra for 180’ jumps are very sensitive to the value of the COO bond angle, a. The variation with a is shown in Figure 5 for a constant T = 0.001 ps. An axial tensor is obtained for y = 45 (a = 135’) and deviations from axiality are observed when a is smaller and larger than this value. Simulations with a 120’ jump angle in Figure 6 reproduce most of the salient features of the experimental results in the entire temperature range. “Extra lines” are conspicuous and occur at the appropriate magnetic fields, and the axiality of the g tensor at high temperature is well reproduced. For 120’ jumps it is possible to reproduce the experimental spectra over the entire temperature range with the various values of 7. For instance, measured spectra are simulated well a t 81 K with 7 = 0.5 ys, at 148 K with 7 = 0.05 ps, at 166 K with 7 = 0.02 ys, and at 277-283 K with 7 = 0.001 ys. Figure 7 shows an Arrhenius plot of 7-l vs. T I . The linear range corresponds to an activation energy of 9.2 kJ/mol and a frequency factor of 4.6 X 1O1O s-l.
Discussion An important result of this work is that extra lines appearing in the anisotropic spectrum are reproduced by a suitable model for the molecular motion. These lines come from molecules for which the jump process does not change their resonance frequency much. To our knowledge they have been studied in only one case by Baram et al.4 for g anisotropy of AsOd4-trapped in y-irradiated KHPAs04
r
-250-150 -50
50
I50 250
H - H o , GAUSS
Figure 6. Simulated ESR powder spectra obtained by assuming a jump angle of 120’ about the CO bond. The COO angle Is 127’ and the line width in the absence of motion is 13 MHz.
F log/
7
E,,,
=
9.2k J / m o l e
0
IO6 2
6
IO
0
14
I x lo3 T
Flgure 7. Arrhenius plot of the jump rate 7-I as a function of T-I.
crystals.23 In this case two-dimensional jumps were considered about a principal axis of the g tensor; g3 was a constant and extra peaks appear in the frequency region between g,pH and g,pH. In the case of the peroxy radical in this study extra lines appear over the entire spectral range as the temperature varies because rotation takes place about an,axis that is
ESE of
Nitroxide Free Radicals
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979 3429
not a principal axis of the g tensor. The position, shape, and intensity of these extra features are very sensitive to the motional model assumed and it is this sensitivity that helps to reveal important information about the type of motion, the rate of the motion, and the symmetry of the potential barrier. When g anisotropy is studied a t 9 GHz the spectra are often compressed and many details are not discerned. This might sometimes be misleading and lead to conclusions that the spectrum is composed of more than one radical species.12 Care must be taken in these cases to avoid relating a particular line to a principal g value in a powder spectrum. For a three-site motional model at intermediate modulation rates spectra can be understood only by analyzing a series of results with varying symmetries of g modulation. The g anisotropy of the peroxy radical is very sensitive to its environment as seen from Table I. It is our belief that in systems, in which the peroxy radical has been detected, the study of dynamical averaging processes might provide important information on the properties of the environment. A case in point concerns g anisotropy in various polymeric peroxy radicals. The g tensor a t room temperature is rigid-lattice-like for the peroxy radical formed in poly(methy1 methacrylate),1° and almost axial in polyethylene and urea-polyethylene complexes,12 reflecting a basic difference in the environment of the peroxy group in these different polymers. Peroxy radicals are formed in many polymers and their g anisotropy has been measured.24 We believe the method outlined here has general applicability for these systems. Further studies of this point are in progress.
Acknowledgment. We thank Professor Zeev Luz whose important correction in the original manuscript helped clarify the subject. This work was supported by the Army Research Office. References and Notes L. T. Muus and P. W. Atkins, Ed., "Electron Spin Relaxation in Liquids",
Plenum Press, New York, 1972. S. Maniv, A. Reuveni, and Z. Luz, J. Chem. Phys., 66, 2285 (1977). A. Hudson, Mol. Phys., 10, 575 (1966). A. Baram. Z. Luz. and S.Alexander. J. Chem. Phvs.. 64.4321 11976). E. G. Janzen, F. J. Johnston, and C. L. Ayers, i.Am. Cbem. Soc., ~I
88, 2610 (1966); 89, 1176 (1967). T. Ichikawa, M. Iwasaki, and K. Kuwata, J . Chem. Phys., 44, 2979 11966).
k. W. Fessenden and R. H. Schuler, J. Chem. Phys., 39, 2147 (1963). K. Toriyama and M.
Iwasaki, J .
Chem. Phys., 73, 2663 (1969).
M. Iwasaki and Y. Sakai, J . Polym Sci., A - 2 , 265 (1968). L. Kevan and S. Schlick, unpublished results. E. Melamud, S.Schlick, and B. L. Silver, J . Magn. Reson., 14, 104 (1974). Y. Hori, S. Shimada, and H.
Kashiwabara, Polymer, 18, 567 (1977). K. U. Ingold and J. P. Morton, J. Am. Chem. Soc., 86, 3400 (1964). E. Melamud and 8. L. Silver, J . Magn. Reson., 14, 112 (1974). J. E. Wertz and P. Auzins, Phys. Rev., 106, 484 (1957). W. Low, Phys. Rev., 101, 1827 (1956). H. S. Gutowsky, D. W. McCall, and C. P. Slichter, J . Chem. Phys., 21, 279 (1953).
H. S. Gutowsky and C. H. Holm, J. Chem. Phys., 25, 1288 (1956). P. D. Sullivan and J. R. Boiton, "Advancesin Magnetic Resonance", Vol. 4 J. S. Waugh, Ed., Academic Press, New York, 1970, pp 39-85. I. Miyagawa and K. Itoh, J . Cbem. Phys., 36, 2157 (1962). Y. Ben Taarit, J. C. Vedrine, C. Naccache, Ph. de Montgoifier, and P. Meriaudeau. J. Cbem. Phvs.. 67. 2880 119771. M. Tinkham, "Group Theory aid Quantum Mechanics",McGraw-Hill, New York, 1964, Chapter 5. N. S. Dalal, C. A. McDowell, and R. Srinivasan, Mol. Phy., 24, 417 (1972).
B.Ranby and J. F. Rabek, "ESR Spectroscopy in Polymer Research",
Springer-Verlag, Berlin,
1977, Chapter 7.
Electron Spin-Echo Studies of Nitroxide Free Radicals in Liquids' Robert N. Schwartz,+ Loretta L. Jones, Depattment of Chemistry, University of Illinois at Chicago Circle, Chicago, Illinois 60680
and Michael K. Bowman Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received August IO, 1979) Publication costs assisted by Argonne National Laboratory
Direct measurements of the electron transverse (T2)and longitudinal (TI) relaxation times of two nitroxide free radicals in liquid solution have been carried out over a range of concentrations and temperature by the method of electron spin-echoes (ESE). Reorientational correlation times and the Heisenberg exchange rate for these radicals in toluene were obtained from the ESE data and compared with results from continuous wave (CW) EPR experiments. The radicals studied were perdeuterated Tempone (PDT) which is roughly spherical in shape and deuterated (in the nitroxide moiety) N-(p-methoxyybenzylidene)-4-amino-2,2,6,6-tetramethylpiperidinyl-1-oxy (DMBATPO) which is rod shaped. The Heisenberg exchange rates are approximately equal for the two radicals in toluene whereas the correlation times as well as the anisotropy of rotational diffusion are quite different for the two spin probes. The inhomogeneous broadening of nitroxide line shapes from unresolved intramolecular proton or deutron hyperfine interactions must be considered when extractingrelaxation data from CW spectra whereas the ESE measurements are independent of any source of inhomogeneous broadening. The electron spin-lattice relaxation rates for these two radicals in toluene and the liquid crystal MBBA were measured and are far less sensitive to the motion of the radicals than is the electron spin-spin relaxation rate.
Introduction The use of nitroxide free radicals as probes of the static and dynamic properties of isotropic and anisotropic fluids ?Temporarily on leave at the Department of Chemistry, University of California, Los Angeles, Calif. 90024. 0022-3654/79/2083-3429$01 .OO/O
of chemical, physical, and biological importance is now a well-established technique.' From a careful line shape analysis of the radical's electron paramagnetic resonance (EPR) spectrum information about the translational and rotational correlation functions as well as features of the rotational reorientation process may be d i ~ c e r n e d . In ~ 0 1979 American Chemical Society
