J . Phys. Chem. 1987, 91, 6467-6469
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Spectral-Spatial Electron Paramagnetic Resonance Imaging and Transport of Radicals in Nonuniform Media Eric D. A. Stemp, Gareth R. Eaton,* Department of Chemistry, University of Denver, Denver, Colorado 80208
Sandra S . Eaton,+and Martin M. Maltempot Departments of Chemistry and Physics, University of Colorado-Denver, Denver, Colorado 80202 (Received: September 21, 1987)
Spectralspatial EPR imaging is extended to a demonstration of the transport of nitroxyl radicals in solution under conditions in which the line width of the nitroxyl changes as a function of time and position in space. The changing spatial distribution and the time-dependentvariation in line shape through the sample are faithfully displayed in the two-dimensional spectralspatial images.
Introduction Many of the initial applications of EPR imaging have been to problems of diffusion and transport of nitroxyl In some cases the imaging was done in such a way that only one line of the nitroxyl three-line pattern was o b ~ e r v e d . ~Galtseva ,~ et al. obtained diffusion coefficients under conditions that the natural line width was small relative to the width of the spectrum in the presence of the magnetic field gradier~t.~Demsar et al. simulated the CW EPR spectrum obtained with a constant gradient to obtain diffusion rates of nitroxyl radicals in fat tissue.6 Freed and co-workers obtained diffusion coefficients for nitroxyl radicals by performing a one-dimensional experiment in which the conditions were chosen such as to keep the nitroxyl line shape invariant during the diffusion. The concentration profile in space was obtained by deconvolution with this constant line shape.’ All of these experiments were limited to samples in which the nitroxyl line width was spatially invariant. In this paper we demonstrate that spectralspatial EPR imaging can be used to obtain the full, varying, EPR line shape as a function of location in a sample in which the nitroxyl radical is undergoing transport in inhomogeneous media. This result greatly expands the class of problems for which EPR imaging can yield diffusion and other transport information.
Spectral-Spatial EPR Imaging To obtain a spectral-spatial EPR image, spectra are collected at a series of static magnetic field gradient^.^^^ Each gradient corresponds to an angle cy in the spectral-spatial plane. The magnetic field sweep at each orientation equals v‘/ZAH/COS a, where AHis the length of the magnetic field axis in the resulting image. The length of the spatial axis in the resulting image, L, is equal to AH tan (a,,,)/maximum gradient. For the images shown in this paper the maximum magnetic field gradient was 400 G/cm (1.0 G = 0.1 mT). For each image, 60 spectra with 128 data points per spectrum were obtained at gradients corresponding to equally spaced angles between f82.97” in the spectralspatial plane. Data collection for each image required about 9 min, which was short compared with the rate of transport in this sample. Since data were not obtained for a full f90”, the image was reconstructed with an iterative algorithm in which the four “missing” projections (angles between f9Oo and f82.97”) were estimated from an image constructed from the experimental data.I0 Five iterations were used. Di-o-xylylethane (viscosity about 30 cS) was placed in a Ushaped tube made from 0.40-cm-0.d. Pyrex tubing. The cenof Chemistry. Department of Physics.
t Department f
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Figure 1. Spectral-spatial image of the nitroxyl radical tempamine in toluene solution in one side of a U-shaped tube. The remainder of the U-tube was filled with di-o-xylylethane. The image was obtained 10 min after addition of the radical. Spectra to construct the image were obtained with 8-mW microwave power, 0.32-G modulation amplitude, 100-kHz modulation frequency, and 8-s scan times. The location of the slice through the image shown in Figure 2A is indicated.
ter-to-center spacing of the upright portions of the tube was about 0.6 cm. Toluene was layered on top of the di-o-xylylethane on (1) Ohno, K. Appl. Spectrosc. Rev. 1986, 22, 1; Magn. Reson. Rev. 1987, 11, 275. (2) Eaton, S . S.; Eaton, G. R.Spectroscopy 1986, I , 32. (3) Berliner, L. J.; Fujii, H. Science 1985, 227, 517. (4) Berliner, L. J.; Fujii, H. J . Magn. Reson. 1986, 69, 68. (5) Galtseva, E. V.;Yakimchenko, 0. Ye.; Lebedev, Ya. S. Chem. Phys. Lett. 1983, 99, 301. (6) Demsar, F.; Cevc, P.; Schara, M. J . Magn. Reson. 1986, 69, 258.
(7) Hornak, J. P.; Moscicki, J. K.; Schneider, D. J.; Freed, J. H. J . Chem. Phys. 1986, 84, 3381. (8) Maltempo, M. M. J . Magn. Reson. 1986, 69, 156. (9) Maltempo, M. M.; Eaton, S. S.;Eaton, G. R. J . Magn. Reson. 1987, 72, 449.
0022-3654/87/2091-6467.$01.50/0 0 1987 American Chemical Society
6468 The Journal of Physical Chemistry, Vol. 91, No. 26, 1987
Letters
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Figure 3. Spectralspatial image of the same sample as in Figure 1, after
160 min. The experimental conditions used to obtain the spectra were the same as for Figure 1. The locations of the slices through the image that are shown in Figure 2B,C are indicated. Figure 2. Spectral slices through the images in Figures 1, 3, and 4. (A) Slice through the image in Figure 1 that shows the initial spectrum of the concentrated tempamine solution in toluene. (B) Slice through the image in Figure 3 that shows the spectrum of tempamine at low concentration in solvent that is predominantly di-o-xylylethane. (C) Slice through the image in Figure 3 at the position where the radical was added, which shows that the line width of the signal has decreased due to movement of di-o-xylylethaneinto the initially toluene solution. (D) Slice through the image in Figure 4 at the position where the radical was
added that shows the line shape when the solution is close to equilibrium. The full widths at half-height of the nitroxyl signals are 4.5 (A), 3.3 (B), 3.9 (C), and 3.6 G (D). one side of the tube. The volume of toluene was about l / g of the volume of the di-o-xylylethane, A toluene solution of tempamine (4-amino-2,2,6,6-tetramethylpiperidine1-0xyl) was added to the toluene layer. The resulting average concentration of tempamine in the toluene layer was about 2.5 mM. The tube was positioned in the cavity of a Varian X-band spectrometer with the horizontal section of the tube parallel to the axis of the magnetic field gradient. The spectralspatial image of the assembly 10 min after addition of the radical is shown in Figure 1. Horizontal slices through the image show the EPR spectrum at a point along the spatial axis. Vertical slices show the spatial distribution of the EPR signal intensity at a particular value of magnetic field. The characteristic three-line nitroxyl signal was localized in one portion of the U-tube. A horizontal slice through the image is shown in Figure 2A. The slice accurately represents the broadening of the signal due to nitroxyl-nitroxyl collisions and nitroxyhxygen collisions. The spectralspatial image after 160 min (Figure 3) shows that the nitroxyl signal had started to redistribute through the U-tube. Two slices through the image in Figure 3 are shown in Figure 2B,C. The nitroxyl that had moved furthest through the tube (Figure 2B) had a narrower line width (3.3 G) than the nitroxyl that remained in the region where the nitroxyl was added (3.9-G line width, Figure 2C). Two factors contribute to the sharper lines in part B of Figure 2 than in parts A or C. (1) The nitroxyl (10) Maltempo, M. M.; Eaton, S . S.; Eaton, G. R. J . Mugn. Reson., accepted for publication.
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Figure 4. Spectralspatial image of the same sample as in Figure 1, after 1060 min. The experimental conditions used to obtain the spectra were the same as for Figure 1. The location of the slice through the image that is shown in Figure 2D is indicated.
concentration in that region of the sample is lower than the starting concentration. (2) The solvent in that region is primarily di-oxylylethane so the higher viscosity of the solvent than in the starting solution causes less nitroxyl-nitroxyl and less nitroxyloxygen collisions. The line width (3.9 G) of the spectrum in Figure 2C is also narrower than for the starting solution (4.5-G line width) due to diffusion of the viscous di-o-xylylethane into the toluene solution. The image after 1060 min is shown in Figure 4. The con-
J. Phys. Chem. 1987, 91, 6469-6478 centrations of nitroxyl in the two arms of the tube are nearly equal (about 0.3 mM), and a uniform line width of 3.6 G is observed throughout the sample. A slice through the image is shown in Figure 2D. The line width of the signal in Figure 2D is intermediate between those observed in Figure 2B,C. These results demonstrate that spectral-spatial EPR imaging provides both the line width of the EPR spectrum as a function
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of time and position in the sample and the spatial distribution of the signal. Thus, EPR imaging studies of transport process can be extended to cases in which the line width of the radical signal varies spatially.
Acknowledgment. This work was supported in part by N S F Grant CHE8421281.
FEATURE ARTICLE Semiclassical Methods in Muitlphoton Diatomic Spectroscopy: Beyond Perturbation Theory Andri D. Bandrauk* DZpartement de Chimie, Facult; des Sciences, UniversitZ de Sherbrooke, Sherbrooke, Quebec, Canada Jl K 2Rl
and Osman Atabek Laboratoire de Photophysique MolZculaire, UniversitZ de Paris-Sud, 91 405 Orsay, France (Received: May 8, 1987; In Final Form: July 8, 1987)
Perturbations between bound-bound and bound-continuum states have been previously treated successfully by semiclassical techniques, thus bridging weak and strong perturbation regimes. In the case of multiphoton transitions, use of the dressed molecule picture enables us to extend these semiclassical techniques to treat simultaneously radiative and nonradiative perturbations. Applications of the semiclassical method to diatomic multiphoton spectroscopy are shown to be particularly useful in identifying new molecular bound states induced by lasers of high intensities and in interpreting multiphoton transition amplitudes in the nonperturbative regime.
I. Introduction Electronic perturbations in diatomic molecules generally involve couplings between electronic states which are most important a t crossings or near crossings of the potential curves of these states. Such perturbations are usually termed nonradiative, with the crossing case called diabatic, as it involves the neglect of certain electronic couplings (interstate electronic, spin-orbit, etc.), or adiabatic, the case of avoided crossings.'S2 In the latter case, the interstate diabatic electronic couplings referred to above have been included, and the remaining couplings are of the nonadiabatic type, involving nuclear coordinate derivatives of adiabatic electronic wavefunctions. These nonadiabatic couplings are a consequence of the law of conservation of total momentum. This law is violated in the adiabatic approximation since the adiabatic electronic functions are calculated a t fixed nuclear positions, Le., a t zero nuclear Perturbations between bound states can be usually treated by diagonalizing finite-size Hamiltonian matrices in the diabatic or adiabatic representation.* The more difficult perturbations occur whenever continuum states intervene. For instance, bound-continuum perturbations arise always in problems of predissociation.'V2 For the latter type of problems, (1) Herzberg, G. Molecular Spectra and Molecular Structure-Spectra of Diatomic Molecules, 2nd ed.; Van Nostrand: New York, 1950; Vol. 1. (2) Lefebvre-Brion, H.; Field, R. W. Perturbations in the Spectra of Diatomic Molecules; Academic: Orlando, FL, 1986. (3) Smith, F. T. Phys. Rev. 1969, 179, 111. (4) Bandrauk, A. D.; Child, M. S . Mol. Phys. 1970, 29, 95. (5) Bandrauk, A. D.; Nguyen-Dang, T. T. J. Chem. Phys. 1985,83, 2840.
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a semiclassical scattering theory approach has proved to be very useful as a guide to the understanding and interpretation of the bound to continuum transitions and also has served as a practical computational too1496-8for any coupling strengths. With the advent of lasers of tunable frequencies and variable intensities, radiative perturbations in the presence of intense fields lead to situations where treatments going beyond perturbation theory are needed. Thus a t high intensities (strong radiative couplings), it is not possible to predict interesting features in the multiphoton cross sections from a knowledge of the field-free (unperturbed) molecular levels alone as is usually done in traditional (weak-field) spectroscopy. In discussing intense field multiphoton processes, it is the levels of the total system, molecule and photons, which have to be considered. Such a representation is called a dressed state representation and leads naturally to multistate curve crossings for resonant multiphoton processes and The interstate noncrossings for nonresonant (virtual) ( 6 ) Child, M. S. J. Mol. Spectrosc. 1974, 53, 280; Mol. Phys. 1976, 32,
1495.
(7) Child, M. S.; Lefebvre, R. Mol. Phys. 1977, 34, 979. (8) Sink, M. L.; Bandrauk, A. D. J . Chem. Phys. 1977, 66, 5313. (9) Bandrauk, A. D.; Turcotte, G.; Lefebvre, R. J. Chem. Phys. 1982,76, 225. (10) Kroll, N.; Watson, K. M. Phys. Rev. A 1976, 23, 1018. (11) Voronin, A. I.; Samokhin, A. A. Sou. Phys. JETP (Engl. Trans/.) 1976, 43, 4. (12) Lau, A. M.F. Phys. Rev. A 1976, 13, 139. (13) George, T. F.; Z m e r m a n , I. H.; Yuang, J. M.; Laing, J. R.; Devries, P. L. Acc. Chem. Res. 1977, 10, 449. (14) Yuan, J. M.; George, T. F. J . Chem. Phys. 1978, 68, 3040.
0 1987 American Chemical Society
