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Lineshapes and polarization ratios in the continuous-wave ESR spectra of spin-polarized transient radicals
JOURNAL
OF MAGNETIC
RESONANCE
67, 35
l-355 (1986)
Lineshapes and Polarization Ratios in the Contkmus-Wave Spectra of Spin-Polarized Transient Radicals K. A. MCLAUCHLAN
ESR
AND A. J. D. RITCHIE
Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, England Received August 15, 1985
Methods for obtaining the ESR spectra of transient free radicals involve the repetitive production of the observed species, typically by flash photolysis, as the magnetic field is advanced. The magnetization is produced in the field direction and is then rotated under the influence of a resonant microwave field into the perpendicular direction for observation. The radicals are almost invariably produced in an electron spin-polarized state via a CIDEP process (I) and in a continuous wave experiment the magnetization of hyperfine line k is given by (Z), M;(t) = [pk(Z)g;(t)
+ Z-‘,T;‘G,k(t)]n(t).
111
Here pk(Z), and Peq represent the initial and equilibrium polarizations of line k, respectively, T, is the electron spin-lattice relaxation time, and n(t) is the radical concentration at time t. The quantity g;(t) is a complex, and often oscillatory, function of T,, T2, the off-set from resonance and the microwave field strength; G;(t) is its time integral at time t. An important feature of Eq. [l] is that the magnetization has separate components from the spin-polarized and equilibrium terms. In the most straightforward experiment the ESR spectrum is reconstructed at a particular time after radical creation by taking point samples from the magnetization decay curves obtained at each field value. However, since M;(t) may oscillate in time, oscillations can occur in the field domain also (3) and be observed as sidebands on spectral lines (4). These can be suppressed by sampling each curve over a period of time and summing the result, in the time-integration spectroscopy (TIS) technique (5, 6). This employs digital sampling but analog (boxcar) experiments would also be expected to display the effects discussed here. There are, however, some situations in which TIS may not remove lineshape anomalies. First, if high microwave fields are used to accentuate weak or broad signals, violent oscillations in M:(t), and in the derived spectra, may occur which cannot be removed using even quite long integration periods. For an initially emissively polarized radical, the center of the line at certain times after radical creation may appear to be in absorption, in contrast to the wings. The general appearance of the line is similar to that discussed in detail below, and single lines may appear as doublets in observed spectra (7). The behavior can be recognized simply by reducing the microwave field strength and observing the change either in the lineshape or in the time-evolution of the signal. 351
0022-2364J86
$3.00
Copyright 0 1986 by Academic Press. Inc. All rights of reproduction in any form reerved
NOTES
352
A more interesting case occurs even at low microwave field strength when the signal is sampled over a period of time during which it relaxes through zero intensity to absorption. In TIS the signal observed at a given field value is the sum of samples made over a chosen time interval and, if the sampling interval is short enough, it is given by the integral of Eq. [l] between the start and finish times of the sampling. It consequently also has separate contributions from the polarized and equilibrium terms but they are different functions of time: one term, the equilibrium one, changes in phase before the other. As pointed out previously (6), in the spectrum obtained by stepping the magnetic field through the resonance, these two contributions to the signal also yield different lineshapes. The equilibrium one is comparatively broad, while the polarized one is unusually sharp and indeed the resolution obtained in continuous-wave spectra which display CIDEP may be high as compared with conventional spectra. Near the time at which the magnetization changes phase from emission to absorption therefore, the TIS line comprises the sum of two terms of different widths and different phases. This cannot be changed, however wide the integration period is made. The effect on observed spectra can be diminished by making the sampling period asymmetric about the time of zero signal. This behavior, and its onset, is demonstrated in Fig. 1 which shows the lineshapes calculated for a single line using the parameters given in the caption. The traces are normalized to the same
fiJ_ d.
e.
f.
FIG. 1. Lineshapes calculated for an emissive radical using a short integration period of 0.5 PS centered at (a) 0.5 ps, (b) 4.0 w, (c) 11.O @, (d) I 1.2 ps, (e) 11.6 ps, and (f) 20 ps atIer radical creation. The broader equilibrium contribution changes phase to absorption before the narrower polarized one does, yielding distinctive lineshapes during the period of time when the signal tends to zero intensity as it changes phase. The lines am displayed with normalized intensities in all the figures and are calculated here assuming values of T, = 5 ps, Tz = 1 @, microwave field strength, o, = 0.01 tad. MHz, and P(Z) = -15P,. A denotes absorption, and E emission.
NOTES
353
intensity but the magnetization changes phase, as a result of relaxation and microwave pumping, between 11 and 12 PS after radical creation. Shortly after the radical is formed the line is a little broad, as expected (3), but it sharpens up in time before. between 11 .O and 11.6 ~LSin the diagram, it appears to split into a doublet of characteristic form. The two separate components to the line are apparent, in opposite phases and with different linewidths, and the admixture of the two varies as time evolves. It is notable that the behavior is the exact opposite of that for the strong microwave field case discussed above in that it is now the outer parts of the line which change phase first. Spectra which demonstrate this type of lineshape have been reported in systems undergoing exchange when the lines approach the phase change-over time (7-9) but it should be realized that the phenomenon is general to all emissively polarized radicals. The distinctive lineshape is observed when the equilibrium and polarized contributions to the signal are of similar magnitude, and this provides an unusual opportunity
I C.
d
4-
FIG. 2. Variations in lineshapes calculated with a basic set of parameters ( r, = 18 ps, T, = 2 p,s,w, = 0.01 rad. MHz and Z’(Z) = -18P,) as their values are varied. The basic pattern (a) taken is that which conva@ouds to 40 @ after radical creation. Traces (b) and (b’) show the appearance of the line at 1 ps in time either side of this. The efkct of 5% changes in TI is shown in traces (c) (T, = 18.9 cs) and (c’) (7’, = 17.1 go); similar effixts are obtained by much larger percentage changes in T2 (in (d) T, = 3 ps, and in (d’) Tt = I g+). Alteration of Z’(Z) by 10% yields the lineshapes shown in (e) (P(Z) = -19.8P,) and (e’)(P(Z) = -17.2P,).
354
NOTES
for determining the absolute polarization ratio (P(I)/P,) of the line. At low microwave power levels (~0.05 rad MHz) this behavior, and the time at which it occurs, depends strongly on the ratio and on T, , but only weakly on T2. This is demonstrated in Fig. 2 using a set of parameters relevant to an experimental situation. Figures 2a, b, and b’ demonstrate the rapid change in appearance of the line as it is sampled at 40 + 1 PS after radical creation; fitting to all three taken together is rather sensitive to the polarization and T, values. The other traces investigate the effects of varying the T, , T2, and polarization ratio values on the 40 I.LSlineshape. It is seen to be very sensitive to 5% variations in T, and 10% variations in the polarization ratio; however, 50-100% variations in T, are needed to cause similar effects. Values of Tl and T2 may be obtained independently by analysis of the tails of decay curves and of lineshapes at earlier times, respectively. It appears that values of the polarization ratio accurate to about 15% of the true value should be attainable. The method appears applicable where other continuous-wave methods are not but is less accurate than the MIST1 method, which requires additional instrumentation (8). An experimental demonstration is provided in Fig. 3 which shows calculated and observed spectra from the emissively polarized radical u-i-anion from benzene- 1,2,4,5tetracarboxylic acid at various times after it is created. The chemical system is complex, with the possible occurrence of exchange reactions and the possible presence of other radicals (7), and some of the lines are so sharp as to make them difficult to record without distortion. Nevertheless the experimental behavior is reproduced satisfactorily
T T- wyr A
t E
a.
-B b.
-T!
FIG. 3. Spectra from the radical trianion of benzene-1,2,4,5-tetracarboxylic acid observed in the upper traces at (a) 48 ps, (b) 52 @, and (c) 55 PSafter radical formation; the basic pattern (a) results from coupling to two equivalent ring protons and two equivalent protons which bridge the carboxyl groups on each side of the molecule. The lower traces show the theoretical spectra calculated witb T, = 18.6 @ and P(1) = -16P,; the fit in (c) is imperfect largely for the reasons indicated in the text but the major features are visible in the experimental spectrum. The integration pe.riod was 1.0 ps.
NOTES
355
by just one combination of T, and polarization ratio values, 18.6 PS and - 16, re.spectively. It is stressed that this behavior is observed in continuous-wave spectra only when the period over which the magnetization is sampled includes the time at which it changes phase, a time which may not be amenable to study by existing alternative transient ESR methods. It does not alSect the identification of radicals shortly after they are formed. Its onset is recognized simply from its very characteristic lineshape and, as shown here, it may be exploited to yield information difficult to obtain in other ways. It should be noted that all the lines in the spectrum of a nonexchanging radical demonstrate the effect simultaneously, in contrast to the slow electron exchange situation in which the lines invert from emission to absorption in the order of their degeneracies (7, 9). ACKNOWLEDGMENT A.J.D.R. thanks the SERC for a maintenance award. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9.
C. J. P. P. S. S. K. K. S.
D. BUCKLEY AND K. A. MCLAUCHLAN, Mol. Phys. 54, 1 (1985). B. PEDERSEN, .I. Chem. Phys. 59,2656 (1978). J. HORE AND K. A. MCLAUCHLAN, J. Mugn. Reson. 36, 129 ( 1979). J. HORE, K. A. MCLAUCHLAN, S. F~YDKJAER, AND L. T. Muus, Chem. Phys. Lett. 77, BASU, K. A. MCLAUCHLAN, AND G. R. SEALY, J. Phys. E 16,767 (1983). BASU, K. A. MCLAUCHLAN, AND G. R. SEALY, Mol. Phys. 5543 1 ( 1984). A. MCLAUCHLAN AND A. J. D. RITCHIE, Mol. Phys. 56, 141 (1985). A. MCLAUCHLAN AND G. R. SEALY, Mol. Phys. 52, 783 (1984). BASU, K. A. MCLAUCHLAN, AND A. J. D. RITCHIE, Chem. Phys. Lett. 105,447 (1984).
127 (198 1).
OF MAGNETIC
RESONANCE
67, 35
l-355 (1986)
Lineshapes and Polarization Ratios in the Contkmus-Wave Spectra of Spin-Polarized Transient Radicals K. A. MCLAUCHLAN
ESR
AND A. J. D. RITCHIE
Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, England Received August 15, 1985
Methods for obtaining the ESR spectra of transient free radicals involve the repetitive production of the observed species, typically by flash photolysis, as the magnetic field is advanced. The magnetization is produced in the field direction and is then rotated under the influence of a resonant microwave field into the perpendicular direction for observation. The radicals are almost invariably produced in an electron spin-polarized state via a CIDEP process (I) and in a continuous wave experiment the magnetization of hyperfine line k is given by (Z), M;(t) = [pk(Z)g;(t)
+ Z-‘,T;‘G,k(t)]n(t).
111
Here pk(Z), and Peq represent the initial and equilibrium polarizations of line k, respectively, T, is the electron spin-lattice relaxation time, and n(t) is the radical concentration at time t. The quantity g;(t) is a complex, and often oscillatory, function of T,, T2, the off-set from resonance and the microwave field strength; G;(t) is its time integral at time t. An important feature of Eq. [l] is that the magnetization has separate components from the spin-polarized and equilibrium terms. In the most straightforward experiment the ESR spectrum is reconstructed at a particular time after radical creation by taking point samples from the magnetization decay curves obtained at each field value. However, since M;(t) may oscillate in time, oscillations can occur in the field domain also (3) and be observed as sidebands on spectral lines (4). These can be suppressed by sampling each curve over a period of time and summing the result, in the time-integration spectroscopy (TIS) technique (5, 6). This employs digital sampling but analog (boxcar) experiments would also be expected to display the effects discussed here. There are, however, some situations in which TIS may not remove lineshape anomalies. First, if high microwave fields are used to accentuate weak or broad signals, violent oscillations in M:(t), and in the derived spectra, may occur which cannot be removed using even quite long integration periods. For an initially emissively polarized radical, the center of the line at certain times after radical creation may appear to be in absorption, in contrast to the wings. The general appearance of the line is similar to that discussed in detail below, and single lines may appear as doublets in observed spectra (7). The behavior can be recognized simply by reducing the microwave field strength and observing the change either in the lineshape or in the time-evolution of the signal. 351
0022-2364J86
$3.00
Copyright 0 1986 by Academic Press. Inc. All rights of reproduction in any form reerved
NOTES
352
A more interesting case occurs even at low microwave field strength when the signal is sampled over a period of time during which it relaxes through zero intensity to absorption. In TIS the signal observed at a given field value is the sum of samples made over a chosen time interval and, if the sampling interval is short enough, it is given by the integral of Eq. [l] between the start and finish times of the sampling. It consequently also has separate contributions from the polarized and equilibrium terms but they are different functions of time: one term, the equilibrium one, changes in phase before the other. As pointed out previously (6), in the spectrum obtained by stepping the magnetic field through the resonance, these two contributions to the signal also yield different lineshapes. The equilibrium one is comparatively broad, while the polarized one is unusually sharp and indeed the resolution obtained in continuous-wave spectra which display CIDEP may be high as compared with conventional spectra. Near the time at which the magnetization changes phase from emission to absorption therefore, the TIS line comprises the sum of two terms of different widths and different phases. This cannot be changed, however wide the integration period is made. The effect on observed spectra can be diminished by making the sampling period asymmetric about the time of zero signal. This behavior, and its onset, is demonstrated in Fig. 1 which shows the lineshapes calculated for a single line using the parameters given in the caption. The traces are normalized to the same
fiJ_ d.
e.
f.
FIG. 1. Lineshapes calculated for an emissive radical using a short integration period of 0.5 PS centered at (a) 0.5 ps, (b) 4.0 w, (c) 11.O @, (d) I 1.2 ps, (e) 11.6 ps, and (f) 20 ps atIer radical creation. The broader equilibrium contribution changes phase to absorption before the narrower polarized one does, yielding distinctive lineshapes during the period of time when the signal tends to zero intensity as it changes phase. The lines am displayed with normalized intensities in all the figures and are calculated here assuming values of T, = 5 ps, Tz = 1 @, microwave field strength, o, = 0.01 tad. MHz, and P(Z) = -15P,. A denotes absorption, and E emission.
NOTES
353
intensity but the magnetization changes phase, as a result of relaxation and microwave pumping, between 11 and 12 PS after radical creation. Shortly after the radical is formed the line is a little broad, as expected (3), but it sharpens up in time before. between 11 .O and 11.6 ~LSin the diagram, it appears to split into a doublet of characteristic form. The two separate components to the line are apparent, in opposite phases and with different linewidths, and the admixture of the two varies as time evolves. It is notable that the behavior is the exact opposite of that for the strong microwave field case discussed above in that it is now the outer parts of the line which change phase first. Spectra which demonstrate this type of lineshape have been reported in systems undergoing exchange when the lines approach the phase change-over time (7-9) but it should be realized that the phenomenon is general to all emissively polarized radicals. The distinctive lineshape is observed when the equilibrium and polarized contributions to the signal are of similar magnitude, and this provides an unusual opportunity
I C.
d
4-
FIG. 2. Variations in lineshapes calculated with a basic set of parameters ( r, = 18 ps, T, = 2 p,s,w, = 0.01 rad. MHz and Z’(Z) = -18P,) as their values are varied. The basic pattern (a) taken is that which conva@ouds to 40 @ after radical creation. Traces (b) and (b’) show the appearance of the line at 1 ps in time either side of this. The efkct of 5% changes in TI is shown in traces (c) (T, = 18.9 cs) and (c’) (7’, = 17.1 go); similar effixts are obtained by much larger percentage changes in T2 (in (d) T, = 3 ps, and in (d’) Tt = I g+). Alteration of Z’(Z) by 10% yields the lineshapes shown in (e) (P(Z) = -19.8P,) and (e’)(P(Z) = -17.2P,).
354
NOTES
for determining the absolute polarization ratio (P(I)/P,) of the line. At low microwave power levels (~0.05 rad MHz) this behavior, and the time at which it occurs, depends strongly on the ratio and on T, , but only weakly on T2. This is demonstrated in Fig. 2 using a set of parameters relevant to an experimental situation. Figures 2a, b, and b’ demonstrate the rapid change in appearance of the line as it is sampled at 40 + 1 PS after radical creation; fitting to all three taken together is rather sensitive to the polarization and T, values. The other traces investigate the effects of varying the T, , T2, and polarization ratio values on the 40 I.LSlineshape. It is seen to be very sensitive to 5% variations in T, and 10% variations in the polarization ratio; however, 50-100% variations in T, are needed to cause similar effects. Values of Tl and T2 may be obtained independently by analysis of the tails of decay curves and of lineshapes at earlier times, respectively. It appears that values of the polarization ratio accurate to about 15% of the true value should be attainable. The method appears applicable where other continuous-wave methods are not but is less accurate than the MIST1 method, which requires additional instrumentation (8). An experimental demonstration is provided in Fig. 3 which shows calculated and observed spectra from the emissively polarized radical u-i-anion from benzene- 1,2,4,5tetracarboxylic acid at various times after it is created. The chemical system is complex, with the possible occurrence of exchange reactions and the possible presence of other radicals (7), and some of the lines are so sharp as to make them difficult to record without distortion. Nevertheless the experimental behavior is reproduced satisfactorily
T T- wyr A
t E
a.
-B b.
-T!
FIG. 3. Spectra from the radical trianion of benzene-1,2,4,5-tetracarboxylic acid observed in the upper traces at (a) 48 ps, (b) 52 @, and (c) 55 PSafter radical formation; the basic pattern (a) results from coupling to two equivalent ring protons and two equivalent protons which bridge the carboxyl groups on each side of the molecule. The lower traces show the theoretical spectra calculated witb T, = 18.6 @ and P(1) = -16P,; the fit in (c) is imperfect largely for the reasons indicated in the text but the major features are visible in the experimental spectrum. The integration pe.riod was 1.0 ps.
NOTES
355
by just one combination of T, and polarization ratio values, 18.6 PS and - 16, re.spectively. It is stressed that this behavior is observed in continuous-wave spectra only when the period over which the magnetization is sampled includes the time at which it changes phase, a time which may not be amenable to study by existing alternative transient ESR methods. It does not alSect the identification of radicals shortly after they are formed. Its onset is recognized simply from its very characteristic lineshape and, as shown here, it may be exploited to yield information difficult to obtain in other ways. It should be noted that all the lines in the spectrum of a nonexchanging radical demonstrate the effect simultaneously, in contrast to the slow electron exchange situation in which the lines invert from emission to absorption in the order of their degeneracies (7, 9). ACKNOWLEDGMENT A.J.D.R. thanks the SERC for a maintenance award. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9.
C. J. P. P. S. S. K. K. S.
D. BUCKLEY AND K. A. MCLAUCHLAN, Mol. Phys. 54, 1 (1985). B. PEDERSEN, .I. Chem. Phys. 59,2656 (1978). J. HORE AND K. A. MCLAUCHLAN, J. Mugn. Reson. 36, 129 ( 1979). J. HORE, K. A. MCLAUCHLAN, S. F~YDKJAER, AND L. T. Muus, Chem. Phys. Lett. 77, BASU, K. A. MCLAUCHLAN, AND G. R. SEALY, J. Phys. E 16,767 (1983). BASU, K. A. MCLAUCHLAN, AND G. R. SEALY, Mol. Phys. 5543 1 ( 1984). A. MCLAUCHLAN AND A. J. D. RITCHIE, Mol. Phys. 56, 141 (1985). A. MCLAUCHLAN AND G. R. SEALY, Mol. Phys. 52, 783 (1984). BASU, K. A. MCLAUCHLAN, AND A. J. D. RITCHIE, Chem. Phys. Lett. 105,447 (1984).
127 (198 1).