Inversion-recovery of nitroxide spin labels in solution and microheterogeneous environments

Article abstract of DOI:10.1021/ja952152d

Two modifications of a conventional inversion-recovery experiment which exclude the effect of spectral diffusion on the measured spin-lattice relaxation times of rapidly tumbling nitroxide spin labels are described. In the first approach an almost uniform inversion is achieved by means of specially designed pulse trains with excitation patterns which match the three-line nitroxide ESR spectrum. In the second approach we essentially combine an inversion-recovery for the M₁ = 0 line with an analog of a pulsed ELDOR technique for M₁ = ±1 lines in a single experiment. This allows us to reconstruct the recovery of the total magnetization of ensemble of radicals which is not affected by spectral diffusion. The spin-lattice relaxation times of several nitroxide spin labels in different homogeneous and microheterogeneous environments are measured and compared. The temperature dependence of T₁ times is compared for two solvents, methylcyclohexane and carbon disulfide, which differ in nuclear spin concentration by almost a factor of 1000. The reported experimental evidence suggests that interactions with the nuclear spins of a solvent do not significantly contribute to the spin-lattice relaxation of nitroxide spin labels.

Full text of DOI:10.1021/ja952152d

J. Am. Chem. Soc. 1996, 118, 1435-1445
1435
Inversion-Recovery of Nitroxide Spin Labels in Solution and
Microheterogeneous Environments
Igor V. Koptyug,† Stefan H. Bossmann,‡ and Nicholas J. Turro*
Contribution from the Department of Chemistry, Columbia UniVersity,
New York, New York 10027
ReceiVed June 30, 1995X
Abstract: Two modifications of a conventional inversion-recovery experiment which exclude the effect of spectral
diffusion on the measured spin-lattice relaxation times of rapidly tumbling nitroxide spin labels are described. In
the first approach an almost uniform inversion is achieved by means of specially designed pulse trains with excitation
patterns which match the three-line nitroxide ESR spectrum. In the second approach we essentially combine an
inversion-recovery for the MI ) 0 line with an analog of a pulsed ELDOR technique for MI ) (1 lines in a single
experiment. This allows us to reconstruct the recovery of the total magnetization of the ensemble of radicals which
is not affected by spectral diffusion. The spin-lattice relaxation times of several nitroxide spin labels in different
homogeneous and microheterogeneous environments are measured and compared. The temperature dependence of
T1 times is compared for two solvents, methylcyclohexane and carbon disulfide, which differ in nuclear spin
concentration by almost a factor of 1000. The reported experimental evidence suggests that interactions with the
nuclear spins of a solvent do not significantly contribute to the spin-lattice relaxation of nitroxide spin labels.
1. Introduction
applications of inversion-recovery technique to measure electron
spin-lattice relaxation times of nitroxide radicals are relatively
scarce.15
In the last 30 years electron spin resonance (ESR) spectros-
copy has been widely and successfully used in the studies of
the structure, the internal mobility, and rotational and transla-
tional diffusion in various microheterogeneous systems of
chemical and biological nature.1-3 One very instructive example
of these endeavors is the evaluation of the correlation times of
rotational reorientation of stable nitroxide radicals by studying
the line shapes in their continuous wave (cw) ESR spectra. Many
application examples4-8 have proven this approach to be highly
reliable in the case of slow anisotropic tumbling of nitroxides.
However, for fast isotropic tumbling conditions spin-lattice
relaxation time measurements have a higher information content.
Due to the recent developments in the field of pulsed ESR this
latter approach is currently gaining popularity. As an extension
of our studies of various microheterogeneous environments9 we
have attempted to implement pulsed ESRsnamely the inversion-
recovery techniquesfor spin-lattice relaxation measurements
of nitroxide spin labels. As a first step in this direction it is
necessary to develop a reliable experimental protocol, since
It is widely appreciated that spectral diffusion10 can lead to
significant complications in spin-lattice relaxation measure-
ments, if only a portion of an ESR spectrum is perturbed during
the preparation period.11-15 For modern pulsed ESR instruments
the typical microwave (mw) field magnitudes are insufficient
to saturate or invert the entire motionally narrowed ESR
spectrum of a nitroxide spin label. For example, for the Bruker
ESP-380 instrument equipped with the dielectric ring cavity the
effective mw field amplitude can be estimated as B1 ≈ 5.6 G
in the rotating frame from the nominal 32-ns duration of the
180° pulse. The value of B1 gives a rough estimate of the
inversion bandwidth of a single 180° pulse, which is obviously
much smaller than the spread of a nitroxide ESR spectrum. As
a result, the evolution of a perturbed ESR line toward equilib-
rium is driven by both true spin-lattice relaxation and the
redistribution of initial perturbation across the non-uniformly
perturbed spectrum. Furthermore, the rates of both processes
are environment-dependent, and thus a change in an apparent
obs
relaxation time T1 does not necessarily imply a change in a
† Permanent address: Institute of Chemical Kinetics and Combustion,
Novosibirsk 630090, Russia.
true spin-lattice relaxation time T1. Such complications render
the interpretation of the results in such experiments extremely
difficult or impossible.
‡ Present address: Lehrstuhl fu¨r Umweltmesstechnik, University of
Karlsruhe, D-76128 Karlsruhe, Germany.
X Abstract published in AdVance ACS Abstracts, January 1, 1996.
(1) Berliner, L. J., Ed. Spin Labeling: Theory and Applications; Academic
Press: New York, 1979; Vol. 2.
(10) We use the term “spectral diffusion” to refer to any process which
transfers magnetization within the ensemble of spins, from one part of an
ESR spectrum to another. Intra- and intermolecular mechanisms of spectral
diffusion essential for nitroxide radicals in solution studied in this work
are nuclear spin relaxation, Heisenberg spin exchange, and electron dipole-
dipole interaction.
(11) Hyde, J. S. In Time Domain Electron Spin Resonance; Kevan, L.,
Schwartz, R. N., Eds.; Wiley-Interscience: New York, 1979; pp 1-30.
(12) Brown, I. M. In Time Domain Electron Spin Resonance; Kevan,
L., Schwartz, R. N., Eds.; Wiley-Interscience: New York, 1979; pp 195-
229.
(2) Berliner, L. J.; Reuben, J., Eds. Biological Magnetic Resonance;
Plenum Press: New York/London, 1989; Vol. 8.
(3) Martini, G. Colloids Surf. 1990, 45, 83.
(4) Ottaviani, M. F.; Ghatlia, N. D.; Bossmann, S. H.; Barton, J. K.;
Du¨rr, H.; Turro, N. J. J. Am. Chem. Soc. 1992, 114, 8946.
(5) Ottaviani, M. F.; Ghatlia, N. D.; Turro, N. J. J. Phys. Chem. 1992,
96, 6075.
(6) Winnik, F. M.; Ottaviani, M. F.; Bossmann, S. H.; Garcia-Garibay,
M.; Turro, N. J. Macromolecules 1992, 25, 6007.
(7) Winnik, F. M.; Ottaviani, M. F.; Bossmann, S. H.; Pan, W.; Garcia-
Garibay, M.; Turro, N. J. Macromolecules 1993, 26, 4577.
(8) Winnik, F. M; Ottaviani, M. F.; Bossmann, S. H.; Pan, W.; Garcia-
Garibay, M.; Turro, N. J. J. Phys. Chem. 1993, 97, 12998.
(9) Wu, C.-S.; Jenks, W. S.; Koptyug, I. V.; Ghatlia, N. D.; Lipson, M.;
Tarasov, V. F.; Turro, N. J. J. Am. Chem. Soc. 1993, 115, 9583 and
references therein.
(13) Thomann, H.; Dalton, L. R.; Dalton, L. A. In Biological Magnetic
Resonance; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York/
London, 1984; Vol. 6; pp 143-186.
(14) Gorcester, J.; Millhauser, G. L.; Freed, J. H. In Modern Pulsed and
Continuous-WaVe Electron Spin Resonance; Kevan, L., Bowman, M. K.,
Eds.; Wiley-Interscience: New York, 1990; pp 119-194.
(15) Schweiger, A. Angew. Chem., Int. Ed. Engl. 1991, 30, 265.
0002-7863/96/1518-1435$12.00/0 © 1996 American Chemical Society

1436 J. Am. Chem. Soc., Vol. 118, No. 6, 1996
Koptyug et al.
Several experiments described in the literature are designed
to exclude the interference of spectral diffusion to a certain
extent. The most reliable results are probably obtained with a
long-pulse saturation-recovery technique,12,13,15-17 in which a
long saturating mw pulse allows the spin system to reach a
steady state during the preparation period. This leads to a more
uniform initial perturbation of a spectrum, which results in a
substantial quenching of spectral diffusion. Alternatively, a
sequence of short intense pulses and delays can be used for the
same purpose.15,18 Also, only the latter portions of the recovery
traces are often measured16,19 and low concentrations of radicals
are used to further reduce the influence of spectral diffusion.
However, even if a spin system is allowed to achieve a steady
state under saturating mw field, a factor of 1.5-2 difference in
the true and apparent relaxation times is still possible,11 since
under selective mw pumping the steady state does not neces-
sarily correspond to a uniform perturbation. The largest errors
are expected when the rates of the spin-lattice relaxation and
spectral diffusion are comparable.11,20,21
An alternative approach to measuring spin-lattice relaxation
times is a short-pulse saturation-recovery with (in general) a
multiexponential fitting of the experimental recovery traces.22-25
However, it is usually preferable to deal with single exponential
traces, since in many cases the result of a multiexponential fitting
of data with the limited signal-to-noise ratio is much less
reliable.26 A different but related experimental technique
employed in T1 measurements is a pulsed electron-electron
double resonance (ELDOR) experiment,13,20,23,24,27 in which an
evolution of a given ESR line is monitored after a pulsed
perturbation (e.g., inversion) of a second ESR line takes place
at a different mw frequency. The resulting traces are described
by a sum of at least two exponentials, and a least-squares fitting
yields the rates of both the true and competing pseudo-secular
relaxation processes. Under conditions when the rate of spectral
diffusion is smaller than the spin-lattice relaxation rate,
however, the ELDOR signal is weak, and a successful imple-
mentation of this technique is not possible.14 Spin-lattice
relaxation time measurements by other experimental techniques,
such as cw28,29 or pulsed30 longitudinally detected ESR
(LODESR), and stimulated (3-pulse) spin echo,15,31 are affected
by spectral diffusion and thus do not yield the true T1 time in
the case of a non-uniform spectral coverage of the mw pulses.
Thus each of the available techniques requires a certain
relation of the rates of spectral diffusion and spin-lattice
relaxation (faster, slower, or comparable) for its successful
Scheme 1. Chemical Structures of the Nitroxide Radicals
application. In this work we aimed at developing an experi-
mental procedure free from the interference of spectral diffusion
in a wide range of experimental conditions, irrespective of the
relative rates of spectral diffusion and spin-lattice relaxation.
It is also desirable that a single experiment provides all the
necessary data, and that the true T1 time is evaluated while fitting
single-exponential recovery traces, with the latter obtained with
minimum or no data manipulation. Since a development of such
an experiment for a general case would be unrealistic, we limit
ourselves to the case of motionally narrowed ESR spectra of
stable nitroxide radicals exhibiting a well-resolved three-line
pattern.
We implement and compare two different approaches to
exclude the influence of spectral diffusion on the observed
recovery traces. Both are based on modifications of a conven-
tional pulsed inversion-recovery scheme. In the first approach
it is the preparation period of an experiment which is modified.
In this case the goal is to achieve a more uniform initial
perturbation of an ESR spectrum under study. We will
demonstrate that for the case of motionally narrowed ESR
spectra of nitroxide spin lables a uniform inversion of all three
ESR lines can be achieved with specially designed pulse trains.
We refer to this experiment as RUP (recovery after uniform
perturbation). Another possible approach, however, is to modify
the detection part of the relaxation-measurement pulse experi-
ment so that it becomes insensitive to pseudo-secular processes
even in the case of a non-uniform perturbation. Here we take
advantage of the fact that these latter processes only redistribute
magnetization among different ESR transitions but do not
change the total magnetization of the ensemble of radicals. Thus
reconstructed recovery of the total magnetization (RRTM) is
free from pseudo-secular contributions.
(16) Percival, P. W.; Hyde, J. S. J. Magn. Reson. 1976, 23, 249.
(17) Nakagawa, K.; Candelaria, M. B.; Chik, W. W. C.; Eaton, S. S.;
Eaton, G. R. J. Magn. Reson. 1992, 98, 81.
(18) Cheng, C.; Lin, T.-S.; Sloop, D. J. J. Magn. Reson. 1979, 33, 71.
(19) Kusumi, A.; Subczynski, W. K.; Hyde, J. S. Proc. Natl. Acad. Sci.
U.S.A. 1982, 79, 1854.
We employ the two modified inversion-recovery experiments
to obtain a concentration dependence of the T1 time for benzene
solution of TEMPONE. The RRTM approach is also used to
study the temperature dependence of T1 time of TEMPONE
and PYTEMPO in both methylcyclohexane (nuclear spin
concentrated solvent) and carbon disulfide (nuclear spin dilute
solvent) to check the possible involvement of the solvent nuclear
spins in the electron spin-lattice relaxation of nitroxide spin
labels. Finally, we show preliminary results of the inversion-
recovery studies of host-guest interactions for three nitroxide
spin labels with CT-DNA and SDS micelles.
(20) Freed, J. H. J. Phys. Chem. 1974, 78, 1155.
(21) Freed, J. H. In Time Domain Electron Spin Resonance; Kevan, L.,
Schwartz, R. N., Eds.; Wiley-Interscience: New York, 1979; pp 31-66.
(22) Yin, J.-J.; Hyde, J. S. Z. Phys. Chem. N.F. 1987, 153, 57.
(23) Yin, J.-J.; Pasenkiewicz-Gierula, M.; Hyde, J. S. Proc. Natl. Acad.
Sci. U.S.A. 1987, 84, 964.
(24) Hyde, J. S.; Feix, J. B. In Biological Magnetic Resonance; Berliner,
L. J., Reuben, J., Eds.; Plenum Press: New York/London, 1989; Vol. 8,
pp 305-337.
(25) Hyde, J. S.; Yin, J.-J.; Feix, J. B.; Hubbell, W. L. Pure Appl. Chem.
1990, 62, 255.
(26) Clayden, N. J.; Hesler, B. D. J. Magn. Reson. 1992, 98, 271.
(27) Gorcester, J.; Freed, J. H. J. Chem. Phys. 1988, 88, 4678.
(28) Giordano, M.; Martinelli, M.; Pardi, L.; Santucci, S. Mol. Phys.
1981, 42, 523.
(29) Giordano, M.; Martinelli, M.; Pardi, L.; Santucci, S.; Umeton, C.
J. Magn. Reson. 1985, 64, 47.
(30) Schweiger, A.; Ernst, R. R. J. Magn. Reson. 1988, 77, 512.
(31) Salikhov, K. M.; Semenov, A. G.; Tsvetkov, Y. D. Electron Spin
Echoes and Their Applications; Nauka: Novosibirsk, 1976.
2. Experimental Section
Chemicals and Sample Preparation. The structures of nitroxide
radicals employed in this study are shown in Scheme 1. TEMPO
(2,2,6,6-tetramethyl-1-piperidinyloxy), TEMPONE (4-oxo-2,2,6,6-tet-
ramethyl-1-piperidinyloxy), 4-amino-TEMPO (4-amino-2,2,6,6-tetra-
methyl-1-piperidinyloxy), PROXYL (3-carboxy-2,2,5,5-tetramethyl-1-
pyrrolidinyloxy), benzene, cyclohexane (spectroscopic grade), carbon
disulfide (HPLC grade), Sephadex G25, Trizma, and NaCl were

InVersion-RecoVery of Nitroxide Spin Labels
J. Am. Chem. Soc., Vol. 118, No. 6, 1996 1437
purchased from Aldrich and used as received. Sodium dodecyl sulfate
(SDS, Aldrich) was recrystallized from the mixture of diethyl ether
and methanol (5:1, v:v). Calf Thymus DNA (CT-DNA) was purchased
from Sigma (best quality available) and carefully dialyzed against
Trizma buffer, pH 7.2. Other solvents and concentrated hydrochloric
acid were purchased from Fisher and were of ACS “certified” quality.
TMATEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy-4-trimethyl-
ammonium iodide) was synthesized according to a standard procedure
from 4-amino-TEMPO and methyl iodide in DMF32 and further purified
by dissolution in water (Millipore) followed by three consequent
extractions with methylene chloride. The aqueous phase was evapo-
rated in vacuum at room temperature, and the product was passed
through a small chromatography column employing Sephadex G25 as
the stationary phase and ethanol as the eluent. PYTEMPO (pyrene-
1-(4-oxy-2,2′,6,6′-tetramethyl-1-piperidinoxy)carboxylic acid ester) was
synthesized33 and characterized by elemental analysis (Calcd: C, 77.97;
H, 6.544; N, 3.947. Found: C, 77.91; H, 6.52; N, 3.98) and mass
spectroscopy (FAB-MS: calcd 400.49; found 401 (0.2%), 58 (100%)).
For T1 concentration dependence measurements various concentra-
Figure 1. A schematic representation of the general inversion-recovery
pulse sequence used in this work. A single point of an FID not affected
by a detector deadtime (Tdead), as exemplified by the arrow, is used to
measure the signal intensity.
(Oxford Instruments) were used in variable-temperature experiments.
The ESR cavity with the sample was immersed into the cryostat and
cooled by a permanent flow of evaporating helium. The sample was
allowed to equilibrate at a desired temperature for at least 1 h, and
several T1 time measurements were performed and discarded until no
further change in T1 time was observed. The accuracy of the
temperature readings was 1-2 K.
Data Handling and Calculations. Rotational correlation times of
nitroxide spin labels were obtained from the 2-pulse spin-echo decays.
The decay times were obtained by single-exponential fitting of the
decays for all three nitroxide lines and analyzed in terms of eq 137,38
where (A:A) is the square of the anisotropic part of the hyperfine tensor,
tions of TEMPONE in benzene in the range 2.5 × 10-5 M to 10-2
M
were prepared by dilution of a common stock solution. In variable-
temperature experiments the concentration of TEMPONE and PYTEM-
PO in methylcyclohexane and carbon disulfide was 1.0 × 10-3 M. To
compare the spin-lattice relaxation times of nitroxides in various
environments the following solutions were prepared. (i) Aqueous
solutions: 5 mM Trizma-HCl buffer, pH 7.0, 50 mM NaCl, 2.0 ×
10-4 M nitroxides. (ii) CT-DNA solutions: 5 mM Trizma-HCl buffer,
pH 7.0, 50 mM NaCl, 1 mM CT-DNA in phosphate units, 2.0 × 10-4
M nitroxides. (iii) SDS: pH 9.0, 100 mM SDS in surfactant molecules,
2.0 × 10-4 M nitroxides. The actual concentration of nitroxides in
these samples has been verified by comparing the integrals of their cw
ESR spectra with that of a stock solution.
1/T2 ) a + bMI + cMI2
c ) (A:A)[5τR - τR/(1 + ω2τR2)]/60
(1)
MI is the nitrogen nuclear spin quantum number, and τR is the nitroxide
rotational correlation time. We note that, strictly speaking, the
characteristic decay time of the primary echo should be referred to as
“phase memory time Tm”. In many cases in solution the Tm and T2
times are equal, while we realize that this might be questionable for
the lowest temperatures used in the work. However, this has no effect
on the evaluation of the rotational correlation times, since only the
M1-dependent contribution to the T2 (Tm) time is used (coefficients c
or b in eq 1). We use only coefficient c, and the expression shown is
valid for arbitrary ωτR, while in the literature its reduced form for ωτR
, 1 is usually cited.
The calculations of the excitation patterns for pulse trains were
performed in the following way. Each soft pulse in a pulse train was
approximated by an alternating sequence of N hard pulses and delays,
(φ - τ)N, with the cumulative nominal flip angle Nφ and the duration
Nτ equal to those of the soft pulse (N ) 5-20). The cumulative effect
of the sequence of hard pulses and free precession delays was then
calculated using the quaternion formalism.39 A 16-ns nominal length
of a 90° pulse was used in the calculations. All the pulses were assumed
to be rectangular, and relaxation of the spins during the pulse trains
was neglected.
All samples were degassed by at least 4 freeze-pump-thaw cycles
and flame-sealed in 5 (quartz or pyrex, nonpolar solvents) or 2 mm
o.d. tubes (quartz, aqueous solutions). In order to ensure that the DNA
retained its double-stranded structure (B-DNA) in all experiments
reported here, the luminescence of the [Ru(phen)3]2+ complex (phen
) 1,10-phenanthroline) was monitored for equivalent samples and under
equivalent experimental conditions, except that no nitroxides were
added. In all cases a double exponential luminescence decay of the
ruthenium complex in the presence of DNA has been found, with the
typical values of 950 ( 50 ns (30 ( 3% of the recorded luminescence
decay) for τ1 and 1900 ( 75 ns (70 ( 3%) for τ2. This control
experiment clearly demonstrates that the double-stranded structure of
the DNA is retained since the complex does not bind significantly to
single-stranded DNA.4
Instrumentation. Pulsed ESR experiments were carried out with
a Bruker ESP-300/380 pulsed FT ESR spectrometer equipped with a
dielectric ring cavity (ESP380-1052 DLQ-H) and a 1 kW TWT
amplifier (90° pulse length is 16 ns). A LeCroy 9450A oscilloscope
(400 megasamples/s) was used to accumulate complete FIDs, while
the dual channel sampling digitizer (SDI) of the ESP-380 instrument
was employed in the inversion-recovery and spin-echo experiments.
An appropriate phase cycling was performed in all pulsed ESR
measurements. To facilitate the decay of an FID in the spin-echo
measurements the magnetic field homogeneity was spoiled14,34-36 by
inserting two rods made of a high-µ material into the holes along the
axes of the magnet poles. High pass BHP-25 (3 dB loss at 25 MHz)
and low-pass BLP-21.4 (3 dB loss at 24.5 MHz) analog radio frequency
filters (Mini-Circuits) were used to separate FIDs corresponding to
different ESR lines (Vide infra).
The Levenberg-Marquardt least-squares algorithm was employed
in single- and double-exponential fitting of the data. Standard
deviations are given as the uncertainties of the extracted parameters,
where appropriate.
3. Results and Discussion
1. The General Experimental Procedure. The general
pulse sequence of our inversion-recovery experiments is shown
in Figure 1. It is convenient to distinguish the three periods,
preparation, evolution, and detection, as is often done in pulsed
nuclear magnetic resonance experiments.40 The preparation
period starts with a relaxation delay to assure that the mag-
A CF series helium flow cryostat and a ITC4 temperature controller
(32) Berliner, L. J., Ed. Spin Labelling: Theory and Applications;
Academic Press: New York/London, 1976; pp 287-291.
(33) Jenks, W. S. Time-Resolved EPR and Photophysical Studies of the
Interactions of Doublet and Triplet States with Stable Nitroxides. Ph.D.
Thesis, Columbia University, New York, 1991.
(34) Schwartz, R. N.; Jones, L. L.; Bowman, M. K. J. Phys. Chem. 1979,
83, 3429.
(35) Gorcester, J.; Freed, J. H. J. Chem. Phys. 1986, 85, 5375.
(36) Bowman, N. K. In Magnetic Resonance of Carbonaceous Solids;
Botto, R. E., Sanada, Y., Eds.; American Chemical Society: Washington,
DC, 1993; Vol. 229, pp 91-105.
(37) Carrington, A.; McLachlan, A. D. Introduction to Magnetic
Resonance; Harper & Row: New York, 1967.
(38) Banci, L.; Bertini, I.; Luchinat, C. Nuclear and Electron Relaxation;
VCH: Weinheim/New York/Basel/Cambridge, 1991.
(39) Bluemich, B.; Spiess, H. W. J. Magn. Reson. 1985, 61, 356.
(40) Bax, A. Two-Dimensional Nuclear Magnetic Resonance in Liquids;
Delft University Press: Delft, 1984.

1438 J. Am. Chem. Soc., Vol. 118, No. 6, 1996
Koptyug et al.
netization of a spin system achieves an equilibrium after a
perturbation in a previous cycle. Then at the end of the
preparation period the equilibrium magnetization is inverted.
In a conventional experiment inversion is achieved by means
of a single 180° pulse. However, as discussed below, a single
pulse is not always adequate, since an exact inversion occurs
only in a limited frequency range, and is sometimes replaced
with inverting pulse trains. The evolution period in our case is
a variable delay τ which is incremented stepwise in subsequent
repetitions of the sequence. During this period the perturbed
magnetization recovers to its equilibrium value. The detection
period begins with a 90° pulse which tips the partially relaxed
magnetization into the transverse plane and thus creates an
observable free induction decay (FID) signal. The FID can be
detected and Fourier transformed to give an ESR spectrum, and
the intensity of an ESR line can be plotted vs τ, which yields
a recovery trace. However, in certain cases another strategy
can be implemented, namely one can acquire a single point of
an FID, keeping the delay between the 90° pulse and acquired
point invariable, and use it as a measure of intensity of an ESR
line.12,41 This is analogous to the electron spin echo (ESE) time-
domain experiments in which the echo intensity is monitored
at its maximum,15,36 considering an echo as a zero-deadtime
FID.13,42 This way of detecting a recovery trace is justified if
either all the ESR lines in the spectrum show the same recovery
behavior or if only one ESR line contributes to the observed
FID. The latter condition can be readily met for a motionally
narrowed ESR spectrum of a nitroxide radical if one of the lines
is placed in resonance with the mw field and the bandwidth of
the videoamplifier is set to a sufficiently low value (e.g. 25
MHz) to exclude the contributions of the other lines. The
detection of a single FID (echo) point reduces dramatically the
duration of the experiment, amount of data processing, and
memory size for data storage as compared to a conventional
experiment with the detection of the whole FID and Fourier
transformation. All this allows us to detect a recovery trace
with a dwell time of 2 ns or larger and with up to several
thousand points in a trace.
Figure 2. (a) Comparison of the excitation patterns of a single 180°
pulse (s) and a composite 180° pulse (- - -) shown as the relative
magnitudes of the MZ magnetization component after the pulse versus
the offset from resonance. M0 is equilibrium magnetization. A 180°-
pulse length is taken as 32 ns. Overbar indicates a 180° phase shift of
a pulse. Arrows point to the side bands of the excitation patterns. (b)
FT ESR spectrum of TEMPONE in benzene at room temperature
obtained with a single 90° pulse. The relative line intensities are
different from the expected 1:1:1 pattern due to a limited microwave
power and a finite Q of the cavity.
into account in the calculations, e.g. non-rectangular pulses, spin
relaxation, etc.
However, the excitation bandwidth of a pulse train cannot
be increased infinitely for a given power level in the transmitter
channel. The attainable limit depends very much on the
flexibility of the particular instrument. The pulse trains (or
rather, shaped pulses) with the best performance can be designed
for instruments where widths, phases, and magnitudes of the
pulses can be changed continuously or by small increments.49
In pulsed ESR experiments, however, the amplitude of the mw
field is usually fixed, because a TWT amplifier is usually
operated near the saturation level.14,48 Moreover, with the
Bruker ESP-380 spectrometer the pulse widths can only be set
in multiples of 8 ns and the number of pulse channels (8) limits
phase shifts to 45° steps (usually quadrature phase settings 0°,
90°, 180°, 270° are used). This allows us to implement easily
the composite 180° (or π) pulses well known in pulsed NMR
spectroscopy.43,47 Figure 2a compares the performance of a
single 180° pulse with that of a 270°x-180°-x-90°x sequence,
showing the much broader frequency range of an almost uniform
excitation for the latter. However, to invert uniformly the
spectrum of a nitroxide radical (Figure 2b) it would be necessary
to design a pulse train with even broader excitation band
extending to offsets ∆ ≈ 3ω1, where ω1 is the magnitude of
the mw field in frequency units (ω1 ) gâB1/p) and ∆ is the
offset from resonance. While the pulse trains with a uniform
inversion extending to the offsets as large as ∆ ) 4.7ω1 have
been reported,48 their implementation requires the flexibility not
available with the instrument employed.
2. A Uniform Inversion of the Three-Line ESR Spectrum.
It is a commonly encountered situation in both pulsed NMR
and ESR that the spectral range of interest exceeds the “region
of hardness” of a single 90° or 180° pulse. The very least
outcome of this is the loss of sensitivity at the edges of the
detected spectrum, but usually more significant complications
can be expected. Numerous attempts are documented in the
literature to improve the spectral coverage of pulses for different
applications in magnetic resonance.43-49 Usually a single pulse
is replaced with a pulse sequence (a pulse train) which contains
several pulses of different width, phase, and sometimes different
magnitude. These parameters and interpulse delays, if any, are
computer optimized to achieve the best performancesa broader
and more uniform excitation of a spin system and acceptable
phase of the induced signal. A fine adjustment of a pulse train
can be performed empirically to correct for the effects not taken
(41) Brown, I. M. J. Chem. Phys. 1974, 60, 4930.
(42) Keijzers, C. P.; Reijerse, E. J.; Schmidt, J.; Eds. Pulsed EPR: A
New Field of Applications; North Holland: Amsterdam, 1989.
(43) Freeman, R. R.; Kempsell, S. P.; Levitt, M. H. J. Magn. Reson.
1980, 38, 453.
(44) Waugh, J. S. J. Magn. Reson. 1982, 50, 30.
(45) Levitt, M. H.; Suter, D.; Ernst, R. R. J. Chem. Phys. 1984, 80, 3064.
(46) Tycko, R.; Schneider, E.; Pines, A. J. Chem. Phys. 1984, 81, 680.
(47) Levitt, M. H. Progr. NMR Spectrosc. 1986, 18, 61.
(48) Crepeau, R. H.; Dulcic, A.; Gorcester, J.; Saarinen, T. R.; Freed, J.
H. J. Magn. Reson. 1989, 84, 184.
(49) Kessler, H.; Mronga, S.; Gemmecker, G. Magn. Reson. Chem. 1991,
29, 527.
Figure 2a also reveals another feature of the pulse trainssthe
presence of the excitation side bands, or side lobes; they are
marked with arrows in the figure. In fact, even a single pulse
has these side bands. In designing pulse trains one often ignores
them. In certain cases it is necessary to eliminate excitation

InVersion-RecoVery of Nitroxide Spin Labels
J. Am. Chem. Soc., Vol. 118, No. 6, 1996 1439
side bands,50,51 as e.g. in selective excitation sequences or water
1
suppression experiments in H NMR, since they can lead to
undesirable peturbations of a spin system. However, for the
ESR spectrum of a nitroxide radical in a relatively nonviscous
solution with its simple 3-line pattern almost symmetric with
respect to its center these side bands can in principle be utilized
to invert the MI ) (1 components while the main excitation
band would invert the MI ) 0 component of the spectrum.
The calculated excitation patterns (the relative magnitudes
of the Mz magnetization component after applying the pulse train
vs the offset from resonance) are shown in Figure 3 for the two
pulse trains (eqs 2 and 3) which we used as a starting point
45°-16 ns-45°-8 ns-45°-16 ns-45°-16 ns-45° (2)
135°-45°-45°-8 ns-45°-45°
(3)
(overbar indicates a 180° phase shift of a pulse). Both calculated
patterns show excitation maxima at 0 and around (45 MHz
offsets, matching well the positions of the three ESR lines of
TEMPONE radical in nonviscous solution. However, as
mentioned in the Experimental Section, the calculations were
done for the idealized pulse trains (rectangular pulses, precise
timing and phase settings) and did not take into account the
relaxation of spins during the pulse train. Thus to achieve
acceptable performance a pulse train was further tuned empiri-
cally by varying the delays and pulse lengths (only 8-ns
increments are possible) and usually repeating several times the
whole train or part of it. Finally, to evaluate the performance
of a pulse train we compared the ESR spectra of a nitroxide
radical detected after a single 90° pulse with that detected after
applying the pulse train followed immediately by a 90° pulse.
If the train does indeed invert the three lines uniformly, the
second spectrum will appear as inversion of the first one. The
result of such a comparison for the modification (4) of the pulse
train (3) is presented in Figure 4 which shows that the
performance is quite satisfactory.
Figure 3. The two pulse trains designed for uniform perturbation of
a nitroxide triplet and their excitation patterns. Delays are shown in
nanoseconds; 45° pulse is 8 ns long.
135°-[45°-45°-8 ns]4
(4)
The successful performance of such trains obviously depends
on how close the excitation pattern matches the nitroxide triplet.
Since the HFI constant of a nitroxide depends on its chemical
structure as well as the solvent used, each nitroxide/solvent
combination requires its own pulse train for uniform inversion.
By varying empirically the interpulse delays (0, 8, or 16 ns,
trains (2) and (4)) and the number of pulses (5 or 6 45° pulses,
train (2)) we were able to match seven different HFI constants
in the range 40.0-47.7 MHz. The approach to achieving
uniform inversion described in this section is time-consuming
since the performance of such pulse trains is very sensitive to
experimental conditions and tuning/matching of the pulsed
cavity. Nevertheless, the spin-lattice relaxation time measure-
ments performed employing several pulse trains show that this
approach works and gives the true T1 relaxation times of
nitroxides in solution. Some of the results obtained are
discussed in sections 3.4 and 3.6. We believe that the design
of such pulse trains deserves further development.
Figure 4. Evaluation of the performance of the inverting pulse train
of eq 4. (a) FT ESR spectrum of TEMPONE in solution obtained after
Fourier transform of an FID acquired following a single 90° pulse. (b)
FT ESR spectrum of the same sample detected with the inverting pulse
train of eq 4 immediately preceding the detection 90° pulse.
of magnetization to and from each transition. In this section
the detection part of the inversion-recovery experiment is
modified instead so that it becomes insensitive to spectral
diffusion caused by pseudo-secular processes. The approach
is based on the fact that spectral diffusion does not lead to the
true spin-lattice relaxation in the sense that it only redistributes
magnetization between the three transitions of a nitroxide. On
the contrary, spin-lattice relaxation changes the total magnet-
ization of the electron spins involved. Thus if one could monitor
the recovery of the total magnetization of all three nitroxide
ESR lines the experiment would yield the true T1 time,36,52 eVen
for a non-uniform initial perturbation. Unfortunately, this
3. Reconstructed Recovery of the Total Magnetization.
In the previous section we addressed the preparation period of
an inversion recovery experiment. The goal was to achieve a
more uniform initial perturbation of an ESR spectrum under
study. In such a case the pseudo-secular processes have no
apparent effect on a recovery trace, since there is an equal “flux”
(50) Freeman, R. Chem. ReV. 1991, 91, 1397.
(51) Emsley, L.; Bodenhausen, G. J. Magn. Reson. 1992, 97, 135.

1440 J. Am. Chem. Soc., Vol. 118, No. 6, 1996
Koptyug et al.
Figure 5. A schematic diagram of the detection scheme modified for
the separate detection of the on-resonance MI ) 0 line and MI ) (1
lines of a nitroxide spin label. LPF ) low-pass filter, HPF ) high-
pass filter; Ref 1 and Ref 2 are the reference input signals of the two
mixers (X). One point of each of the two filtered FIDs is detected, as
shown by the arrows. For further details see the text.
cannot be done directly. Due to the limited excitation bandwidth
of pulses already discussed above and also a limited bandwidth
of a cavity with a finite Q value, the sensitivity of a pulsed
ESR experiment toward the MI ) 0 line placed in resonance
and toward the off-resonance MI ) (1 lines is different. Thus
their relative contributions to an FID are unequal. Besides,
different evolution patterns of the three signals in time (simple
exponential decay of the on-resonance signal and damped
sinusoidals for the off-resonance ones, as well as different
damping factors due to different line widths) lead to the variation
of their relative contributions across the FID. Thus detecting
the inversion-recovery trace by monitoring an intensity of any
point of the original FID (cf. Figure 1) would give yet another
apparent relaxation time T1obs rather than the true T1 time. Since
we do not want to discard the basic scheme of the experiment
outlined above in section 3.1, it definitely has to be modified.
Figure 6. (a) The recovery of the on-resonance MI ) 0 line (A) and
the off-resonance MI ) (1 lines (B) of TEMPONE in methylcyclo-
hexane at 163 K after a perturbation with a single 180° pulse. Relative
intensities of traces A and B are shown as detected. The inset shows
the difference of trace B and its double-exponential fit. (b) Recon-
structed recovery of the total magnetization. The inset demonstrates
the quality of its single-exponential fit. A slight discontinuity at 560
ns (the longest interpulse delay for which the two pulses are amplified
within a single TWT duty cycle) is caused by phase properties of the
TWT amplifier73 and is present on all traces to a certain extent.
An example of the application of the procedure outlined above
is shown in Figure 6a. The two recovery traces A and B have
been detected for 1 mM TEMPONE in methylcyclohexane at
163 K with a single 180° pulse used for inversion. For both
traces a considerable deviation from a simple exponential
behavior is obvious, which in this case is caused by fast nuclear
relaxation often observed for nitroxides in viscous media20,23-25,53
(see, however, the paper by Zhong and Pilbrow54). Trace A is
identical to that obtained in a conventional two-pulse inversion-
recovery experiment. Trace B is similar to those obtained in
pulsed electron-electron double resonance (ELDOR) experi-
ments.14,53,55,56 The signal intensity of trace B at t ) 0 is lower
than the equilibrium value since the inversion 180° pulse affects
the off-resonance lines to a certain extent. Fast nuclear spin
relaxation transfers perturbation from the on-resonance line to
the less perturbed off-resonance lines. This results in the initial
decrease of trace B and the fast initial rise of trace A. After a
common spin temperature is established throughout the spin
system, both traces evolve toward thermal equilibrium at a
slower rate.
The strategy employed was to separate the contributions of
the MI ) 0 line and MI ) (1 lines first, detect independent
recovery traces for the two separated signals, and then combine
them with appropriate weights. The separation can be achieved
quite easily. In the detection system of the FT ESR spectrometer
the mw signal is split and fed into two mixers for detection42
(Figure 5). Usually the reference inputs of the two mixers differ
in phase by 90° for the quadrature detection of an FID.
Fortunately, the design of the spectrometer allows one to adjust
the phases of the two channels independently. In our experiment
the two channels have the same reference phase, i.e. the same
FID appears in both detection channels. To separate the
contributions we install two analog RF filters between the mixers
and the digitizer. One channel contains a low-pass filter (LPF)
rejecting frequencies higher than the cut-off frequency (ca. 25
MHz), and thus only the contribution from the MI ) 0 line
placed in resonance reaches the digitizer (Figure 5). Another
contains a high-pass (band-pass) filter (HPF) rejecting low-
frequency signals (below ca. 25 MHz) and thus selecting the
contributions of MI ) (1 lines. With this configuration after
applying a 180° inversion pulse at zero frequency (in resonance
with the MI ) 0 line) the two recovery traces for the MI ) 0
and MI ) (1 lines can be detected separately in a single
experiment monitoring the intensity of the two separated FIDs
at the same point in time (cf. Figure 5).
We now proceed with the reconstruction of the recovery of
the total magnetization. The two traces A and B are added
together in such a proportion that their relative contributions at
t ) ∞ (t . T1) are 1:2, equal to the relative statistic weights of
MI ) 0 and MI ) (1 radical ensembles. The reconstructed
recovery trace (A + (2x/y)B) is shown in Figure 6b, and it
(53) Hyde, J. S.; Froncisz, W.; Mottley, C. Chem. Phys. Lett. 1984, 110,
621.
(54) Zhong, Y. C.; Pilbrow, J. R. J. Magn. Reson. A 1995, 112, 109.
(55) Mailer, C.; Robinson, B. H.; Haas, D. A. Bull. Magn. Reson. 1992,
14, 30.
(52) Kababya, S.; Luz, Z.; Goldfarb, D. J. Am. Chem. Soc. 1994, 116,
5805.
(56) Robinson, B. H.; Haas, D. A.; Mailer, C. Science 1994, 263, 490.

InVersion-RecoVery of Nitroxide Spin Labels
J. Am. Chem. Soc., Vol. 118, No. 6, 1996 1441
represents the recovery of the entire ensemble of spins and is
quite close to a single exponential behavior with T1 ) 2409 (
2 ns.
The separate detection of the on-resonance and off-resonance
recovery traces at low temperatures (cf. Figure 6a) provides an
independent test for our RRTM method. The two traces A and
B are expected53 to exhibit double exponential behavior with
the same characteristic times τ1 ) T1 and τ2 ) (1/T1 + 3Wn)-1
.
Here T1 is the true electron spin-lattice relaxation time and
Wn is the probability of a nuclear spin transition, which for a I
) 1 nuclear spin system is related37 to the nuclear spin relaxation
n
time T1n as Wn ) 1/T1 . Double-exponential fitting of traces A
and B is expected to be quite accurate, for electron and nuclear
relaxation under these conditions have comparable contributions
to these traces, while the individual rates of the two processes
are substantially different. The values T1 ) 2450 ( 6 ns, (τ1
n
) T1) and T1 ) 718 ( 5 ns (τ2 ) 218 ( 1 ns) for the on-
Figure 7. Concentration dependence of the spin-lattice relaxation time
measured for TEMPONE (labeled NO in the figure) in benzene at room
temperature. The results of the RRTM (9), RUP (×) and saturation-
recovery (4) experiments are shown. The solid line shows the best fit
to RRTM data assuming a linear dependence of relaxation rate on
nitroxide concentration (see text).
n
resonance (MI ) 0) line and T1 ) 2412 ( 5 ns and T1 ) 697
( 8 ns (τ2 ) 212 ( 2 ns) for the off-resonance (MI ) (1)
lines were obtained from the double exponential fittings of traces
A and B (Figure 6a), respectively, which is in very good
agreement with the value obtained above from the single-
exponential fit of the reconstructed recovery trace and with the
literature data (Vide infra). It was found, however, that the
reconstruction method works equally well under a variety of
experimental conditions, including those where a double-
exponential fit does not provide reliable results. For instance,
at ambient temperatures Heisenberg spin exchange leads to a
noticeable spectral diffusion even at relatively low nitroxide
concentrations (Vide infra). Reconstruction of the recovery of
the total magnetization eliminates the effect of spectral diffusion
and yields single-exponential recovery traces in all experiments
performed in this work.
significantly affect magnetization evolution during the inverting
pulse train (4) with total duration of 120 ns, which can cause
the uniform inversion to fail. For this reason the RUP method
was not applied at higher concentrations. The first important
conclusion that can be made is that the T1 times measured with
two methods are essentially the same even in the concentration
region where the influence of spin exchange is strongest (Vide
infra). Given the different principles of the two experiments,
this finding strongly supports our expectation that a true T1 time
is obtained in these experiments. The variation of T1 with
nitroxide concentration is then rationalized in a straightforward
way. The only (intermolecular) processes which potentially
contribute to the T1 concentration dependence are the spin
exchange and dipole-dipole interaction of electron spins. Of
these only the non-secular part of the intermolecular dipole-
dipole interaction is expected to alter the true T1 time, since
other contributions have a pseudo-secular nature. Thus at low
nitroxide concentrations (<10-3 M) the T1 time is almost
concentration independent, for the rate of the intermolecular
dipolar relaxation is too slow to compete with the intramolecular
relaxation pathways. At higher concentrations the T1 time
decreases reflecting the faster intermolecular process, and this
allows us to estimate the rate constant of non-secular dipole-
dipole relaxation. Assuming that the intermolecular relaxation
rate is proportional to nitroxide concentration,16,28,31 the fitting
of experimental data (Figure 7) yields 1/Tdd ) [(4.4 ( 0.2) ×
107] C s-1, where C is the concentration of TEMPONE. A
value of the same order of magnitude can be deduced from
Figure 4 of the paper by Giordano et al.28
For comparative purposes Figure 7 also shows the results
obtained in a saturation-recovery experiment (triangles). In this
case a (90°-200 ns)N sequence with N ) 8-20 was employed
for a prolonged saturation, followed by a variable delay and a
probe 90° pulse. As before, a single point of an FID was
detected, and the T1 times were obtained from single-exponential
fitting of the whole recovery traces. As was mentioned in the
introduction, fitting of the tails of the recovery traces obtained
in the saturation-recovery experiment should give a somewhat
better quantitative agreement with our inversion-recovery data,
while the qualitative behavior would still be the same. For
concentrations of TEMPONE around 10-3 M the deviation of
the experimental traces from the single exponential behavior
was pronounced, but still less than that for a conventional
It is important to note that a successful application of the
experimental procedure outlined above requires that all the
hyperfine components of the ESR spectrum have similar T1
times, otherwise some weighted average will be measured. The
same, however, is true about the majority of the other spin-
lattice relaxation techniques,13 and even for the inversion-
recovery with uniform perturbation, RUP, described in section
3.2. Fortunately, it has been shown for several nitroxide spin
labels under various experimental conditions that T1 times of
different hyperfine lines are indeed very close,16,24,28 which is
also in agreement with the T1 values obtained above.
Thus a single and relatively simple experiment contains all
the necessary information to reconstruct the behavior of the total
electron spin magnetization of an ensemble of nitroxide radicals
in solution and thus exclude the interference of spectral
diffusion. Its implementation requires that the spectrum under
study is in the motionally narrowed regime, and that the on-
resonance and off-resonance ensembles can be distinguished
and detected separately. We have verified experimentally that
even under the most unfavorable conditions used in this work
(TEMPONE in methylcyclohexane at 153 K, τR ) 380 ps) the
three lines can be distinguished in the ESR spectrum of a
nitroxide radical, despite a substantial line broadening, especially
pronounced for the low-frequency (high-filed, MI ) -1) line.
4. The Concentration Dependence of T1. To experimen-
tally test the two proposed modifications of the inversion-
recovery experiment we have studied the concentration depend-
ence of TEMPONE spin-lattice relaxation time T1 in benzene
at room temperature and compared the results with the literature
data. The T1 times measured using the RRTM and RUP
methods are shown in Figure 7. At nitroxide concentrations
higher than 1 mM spectral diffusion becomes fast enough to

1442 J. Am. Chem. Soc., Vol. 118, No. 6, 1996
Koptyug et al.
variation amounts to ca. 10% of the T1 extrapolated to zero
concentration, probably reflecting a higher accuracy of our data.
In fact, if only one nitroxide line is inverted, as in the
experiments of Schwartz et al.,34 an even larger variation of
obs
T1 is to be expected. It is, however, impossible to make a
more detailed comparison, since their work is mainly devoted
to a careful study of T2 times, and does not give a detailed
description of T1 measurements.
Giordano et al.28 have studied the T1 concentration depend-
ence of TEMPONE in toluene for an unusually wide concentra-
tion range, 2.5 × 10-4 to 5 M, by a combination of cw ESR
and LODESR techniques. In the low-concentration range the
values of T1 obtained almost coincide with those measured in
a cw saturation experiment, and thus are not free from pseudo-
secular contributions. This was taken into account in the
quantitative analysis of the data,28 and a value of T1 ) 570 ns
was obtained from an extrapolation to zero concentration. This
value is somewhat higher than those reported in the other papers
and measured in this work, and is probably overestimated due
to a limited number of points in the low-concentration range,
since the largest value actually measured was ca. 300 ns (350
ns in cw saturation experiments).
We conclude that the two modifications of the inversion-
recovery experiment developed in this work give the results
consistent with the data obtained in the other, independent
measurements described in the literature. This finding is
encouraging enough to proceed with practical applications of
these techniques.
5. The Temperature Dependence of T1. We have em-
ployed our RRTM technique to study the temperature de-
pendence of the T1 time of TEMPONE in order to address the
question about the mechanism of spin-lattice relaxation in
nitroxides, which remains to be a controversial issue in the
literature.11,16,24,55,56 In particular, we aimed at experimentally
testing the recent statement55,56 that spin-lattice relaxation
measurements can be rationalized assuming isotropic Brownian
rotational and translational motion of a nitroxide spin label, if
along with spin-rotation and electron-nuclear dipolar interaction
another relaxation mechanism, termed “spin diffusion”, is taken
into account. The essence of this latter mechanism is the
existence of a pool of interacting nuclear spins (e.g., of hydrogen
atoms) of a solvent bulk and a coupling of the nuclear spins
with the electron spin of a nitroxide modulated by translational
motion. Since the nature of the latter coupling is not specified,
the variation of the contribution of this mechanism with the
isotope labeling of a solvent cannot be predicted. Thus the only
way to examine the validity of the proposed explanation is to
design an experiment where the effect of spin diffusion is
excluded altogether, i.e. a solvent is used which does not contain
any magnetic nuclei. To do that we have compared the
dependence of the nitroxide spin label T1 times in methyl-
cyclohexane and carbon disulfide (CS2). The latter is a good
approximation for a “spinless” solvent, since the natural
abundances of the magnetic isotopes of carbon (13C, 1.1%) and
sulfur (33S, 0.75%) are very low. Thus, switching from
methylcyclohexane to carbon disulfide corresponds to almost a
1000-fold reduction in the concentration of magnetic nuclei of
a solvent and is expected to eliminate any solvent-induced
relaxation.
Figure 8. Temperature dependence of the absolute c/b ratio, calculated
according to eq 1 from the T2 times measured in the two-pulse spin-
echo experiments: (a) TEMPONE in methylcyclohexane (0) and
carbon disulfide (2); (b) PYTEMPO in carbon disulfide.
inversion-recovery trace, since a long saturating pulse train
partially quenches the spectral diffusion. The variation of the
apparent time T1obs measured in the saturation-recovery experi-
ment with concentration is different from that discussed above,
but can be readily rationalized20 if we assume that the effect of
spin exchange is not completely quenched, as expected. When
the radical concentration is low, the different ESR lines are not
coupled by the exchange interaction, and the recovery of a
perturbed ESR line occurs only due to the true spin-lattice
relaxation. This means that in the limit of zero TEMPONE
concentration the saturation-recovery experiment should yield
the true T1 time. This is clearly what is observed in the
experiment, though even at the lowest concentration studied (2.5
× 10-5 M) the T1obs is still slightly lower than T1. At the same
time, at high radical concentrations the coupling of the ESR
lines due to spin exchange is so efficient that the uniform spin
temperature in the spin system is established very rapidly and
is maintained throughout the recovery process. Thus in the
limit of high concentrations of TEMPONE the apparent
relaxation time also tends to the true T1, again in agreement
with observation. It is clear that the deviation of T1obs from T1
is maximized at some intermediate concentrations, when the
spin-lattice relaxation and spectral diffusion have comparable
rates. According to Figure 7, this happens at concentrations
around 10-3 M. This allows us to estimate the rate of
intermolecular spin exchange as 2.2 × 10-9 C s-1. This is in
agreement with the conclusions found in the literature14,24,57-59
that the rate of spin exchange in solution is usually comparable
with the rate of bimolecular collisions of radicals.
The value of T1 extrapolated to zero TEMPONE concentra-
tion is found to be 455 ( 2 ns, very close to T1 ) 470 ns
measured by Percival and Hyde for 5 × 10-5 M perdeuterio-
TEMPONE in sec-butylbenzene.16 This comparison is justified
by the fact that spin-lattice relaxation of nitroxides is rather
insensitive to isotope substitution and is almost the same for
all hyperfine lines,16,24 although some small differences could
arise due to a different solvent.11 A similar value (T1 < 500
ns) was obtained by Schwartz et al.34 in a saturation-recovery
experiment with an echo detection for perdeuterio-TEMPONE
in perdeuteriotoluene at room temperature, as can be deduced
from Figure 8 of their paper. The authors also report an absence
of any noticeable dependence of T1 on nitroxide concentration
in the range 10-4 to 3.5 × 10-3 M. In our experiments this
To directly compare the T1 times measured in two different
solvents the corresponding rotational correlation times have been
determined. The latter can in principle be estimated from the
Stokes-Einstein equation, since the viscosity of methylcyclo-
hexane60 and carbon disulfide61 at various temperatures has been
(57) Hyde, J. S.; Chien, J. C. W.; Freed, J. H. J. Chem. Phys. 1968, 48,
4211.
(58) Davis, M. S.; Mao, C.; Kreilick, R. W. Mol. Phys. 1975, 29, 665.
(59) Molin, Y. N.; Salikhov, K. M.; Zamaraev, K. I. Spin Exchange;
Springer-Verlag: Berlin, 1980.
(60) Ruth, A. A.; Nikel, B.; Lesche, H. Z. Phys. Chem. 1992, 175, 91.

InVersion-RecoVery of Nitroxide Spin Labels
J. Am. Chem. Soc., Vol. 118, No. 6, 1996 1443
in methylcyclohexane shows very similar behavior. It is obvious
that the increase in the T1 time of TEMPONE with an increase
in the rotational correlation time is almost the same in
methylcyclohexane and CS2. The range of TEMPONE τR
values for the latter solvent in the temperature interval studied
is much narrower than that for methylcyclohexane. The use of
PYTEMPO allowed us to further slow down the tumbling of
the spin label and to almost completely match the range of τR
studied in the two solvents. This range is much narrower than
that studied in refs 55 and 56, mainly because this work is
primarily concerned with developing and testing the techniques
described above, and the latter are no longer applicable directly
at higher viscosities. Nevertheless, this range is wide enough
for the purposes of the comparison.
It is clear from the results of Figure 9 that the T1 times in the
two solvents are very close. Some small variations can be
caused by numerous factors, including various experimental
uncertainties as well as differences related to the spin labels
and solvents. However, the observed variations are negligible
as compared to what one should expect, if spin diffusion was
operative in one solvent and not in the other. The combined
action of spin-rotation, electron-nuclear dipolar interaction, and
spin diffusion (the three mechanisms which according to Mailer
et al.55 and Robinson et al.56 can account for the observed
relaxation times) is described by the following equation:
Figure 9. The dependence of the spin-lattice relaxation time T1 on
the rotational correlation time. Experimental data for TEMPONE in
methylcyclohexane (×), carbon disulfide (]), and PYTEMPO in carbon
disulfide (O). The dashed line shows the best fit of the experimental
data (×) with eqs 5 and 6 with Rsd as the only variable parameter. The
solid line shows the contribution of the first two terms in eq 5. The
dot-dashed line shows the same, but with the dipolar contribution (T1dip*)
calculated according to Robinson et al.56
sd
1/T1 ) 1/T1sr + 1/T1dip + 1/T1
(5)
where38,56
sr
1/T1
)
(g - g )2/(9τ );
i ) x, y, z
∑
i
e
R
dip
reported. However, when the T1 times for different spin labels
are compared, we found that more accurate results are obtained,
if the rotational correlation times are determined from the
analysis of the hyperfine-dependent part of the spin-spin
relaxation time T2 according to eq 1.37 This has a further
advantage that the character of motion of the spin label can be
deduced from the analysis of the temperature dependence of
the |c/b| ratio.62 Figure 8a shows the results obtained for
TEMPONE in methylcyclohexane and CS2. The behavior is
very similar to that found by Hwang et al.62 for perdeuterio-
TEMPONE in toluene: for τR > 10-10 s |c/b| is close to 1.0,
but drops to ca. 0.6 for τR < 10-11 s, which was shown to be
consistent with the isotropic tumbling of the nitroxide. The two
data sets in Figure 8a appear to be shifted relative to each other,
reflecting the fact that the viscosity of CS2 is lower than that of
methylcyclohexane at the same temperature.61 The tumbling
of another nitroxide, PYTEMPO (Scheme 1), is quite different,
as expected. As can be concluded from Figure 8b, for this
nitroxide the |c/b| ratio is constant over the temperature range
studied, which according to Hwang et al.62 implies an aniso-
tropic tumbling of the spin label. This observation is clearly
in agreement with the structure of PYTEMPO, which favors
anisotropic rotation around the ester tether. Nevertheless, this
modified tumbling has only a small effect on the T1 time of the
nitroxide (Vide infra).
1/T1
)
(1/30)(7I(I + 1) - M 2) (A - A )2τ /(1 + ω2τ )
2
∑
I
i
0
R
R
1/T1sd ) Rsd[2ωτR/(1 + (ωτR)1.5)]0.25
(6)
The quantity T1eEND used in the work of Robinson et al.56 is the
same as our T1dip*, while the expression for T1 is a more
dip
general and corrected form for the electron spin-lattice
relaxation due to electron-nuclear dipolar interaction. As
defined earlier in the text, MI is the spin quantum number of a
nitroxide nitrogen atom with nuclear spin I. The best fit of our
experimental data with eqs 5 and 6 is shown with a dashed line
in Figure 9, with Rsd being the only variable parameter of the
fit. The solid curve shows the contribution of the first two terms
of eq 5 to the T1 time. The two curves show the scale of the
expected difference of the relaxation behavior in the two
solvents, if solvent nuclear spins were indeed involved in the
relaxation. Moreover, for the upper limit of the τR range studied
in this work, at least an order of magnitude increase in the T1
time in CS2 is predicted from Figure 3 of the paper by Mailer
et al.55 This is clearly not what is observed experimentally.
Thus, no experimental evidence was found of the involvement
of the nuclear spins of a solvent in the relaxation of nitroxide
spin labels in solution.
6. T1 Times of Nitroxide Spin Labels in Some Microhet-
erogeneous Environments. While the main goal of this work
was to establish and test the reliable experimental procedures
for measuring accurate values of nitroxide spin-lattice relax-
ation times by the modified inversion-recovery techniques, it
was tempting to check if these techniques would indeed be
useful in studying systems of current interest. In particular,
we are interested in probing supramolecular microheterogeneous
systems such as micelles and polyions. Below we report the
The T1 times of TEMPONE and PYTEMPO obtained from
the single-exponential fitting of the reconstructed recovery traces
are shown in Figure 9 as a function of rotational correlation
time τR. The results are very close to the results of Percival
and Hyde.16 Although not shown, the T1 time for PYTEMPO
(61) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of
Liquids; Hemisphere Publishing Corp.: New York, 1989.
(62) Hwang, J. S.; Mason, R. P.; Hwang, L.-P.; Freed, J. H. J. Phys.
Chem. 1975, 79, 489.

1444 J. Am. Chem. Soc., Vol. 118, No. 6, 1996
Koptyug et al.
Table 1. Spin-Lattice Relaxation Times of the Three Nitroxide
from the table, SDS binds TMATEMPO significantly leading
to more than a 2-fold increase in the T1 relaxation time. In
agreement with our working paradigm, the values for TEMPO
and PROXYL remain almost unchanged in comparison to those
of water. Interestingly, no significant interaction of all three
spin probes with B-DNA has been detected. Nevertheless, our
control experiment (see Experimental Section) clearly demon-
strated that the DNA was intact during our measurements.
Therefore we conclude that the binding of all three spin probes
to DNA is apparently weak and that the mobility of the water
in proximity to the DNA’s structure is high. This experiment
provides some insights into the structure of the electrical layer
around DNA. Higher charged compounds such as ruthenium(II)
and rhodium(III) complexes possessing planar organic ligands
are strongly bound by intercalation.68 Compounds with a single
positive charge possess a high mobility next to DNA comparable
to their mobilities in the water bulk. This finding strongly
supports the existence of a diffuse electrical layer around the
polyelectrolyte DNA.
Another observation concerns the mechanism of spin-lattice
relaxation of nitroxide radicals. Apparently the relaxation times
for both six-membered-ring nitroxides are very similar, whereas
the value found for the five-membered ring is significantly
larger. These different relaxation behaviors can be related to
the different motion characteristics of five- and six-membered-
ring systems: in five-membered rings an envelope conformation
is dominant, but in six-membered rings chair conformations and
subsequently occurring ring interconversions are found leading
to a faster motion.69 The possibility that the spin-lattice
relaxation in nitroxides is dominated by intramolecular motional
modes was recognized in the literature11,16,62 and cannot be
discarded altogether while the main relaxation mechanism
remains unknown.
Radicals Measured in Various Environmentsa
T1/ns
TEMPO
TMATEMPO
PROXYL
H2O
SDS
CT-DNA
695
630
630
685
1560
680
845
945
900
a The structures of the radicals are shown in Scheme 1. The values
shown are accurate to (5%.
preliminary measurements of the T1 relaxation times for three
differently charged nitroxide radicals and two microheteroge-
neous systems: sodium dodecyl sulfate micelles and B-DNA.
Micelles are of great interest because they are widely used
in basic research as well as in many technical applications.63
A
micelle consists of a hydrophobic core formed by the aliphatic
chains and a negatively charged boundary region which is
formed by the polar head groups. Depending on the chain
length of the aliphatic groups and the concentration of the
surfactant monomers in the system, different aggregation
numbers can be found. For SDS micelles the aggregation
number for the concentrations used in these experiments is
between 85 and 100.64,65
B-DNA represents the most abundant form of DNA. In
contrast to a globular dynamic structure of micelles, DNA is
relatively rigid and possesses a rod-like shape.66 Among the
significant features of the DNA structure are the major and the
minor grooves with different abilities to bind charged and
noncharged particles such as metal complexes and proteins, and
the negative charges along the helical backbone which make it
a polyelectrolyte. As required by its molecular structure, there
are two negatively charged phosphate groups per DNA base
pair. The determination of the binding properties of differently
charged compounds to B-DNA and the mobility of water
(solvent) molecules in proximity to the DNA structure are of
special interest for the design of drugs, especially of anti-cancer
nature.67
Both SDS micelles and B-DNA have an electrical double
layer, which is formed by the immobile negative charges
imbedded in their structures and the mobile electrically com-
pensating countercations (e.g., sodium). The structure of the
electrical double layer depends on the total concentration of
ions in the microheterogeneous systems. Whereas at higher
concentrations (>0.1 M) a compact double layer can be formed
(model of Helmholtz), at lower concentrations a combination
of a compact and a diffuse double layer describes the observed
behavior (model of Stern).67 According to this paradigm a
positively charged nitroxide (TMATEMPO) should bind more
strongly to both B-DNA and micelles than a neutral nitroxide.
Furthermore, a negatively charged nitroxide (PROXYL) should
be repelled by the microheterogeneous structure. Deviations
from this simple scheme should be found in the cases where
hydrophobic interactions play a dominant role.
4. Concluding Remarks
In this work we have demonstrated that the inversion-recovery
experiment can be successfully applied to the spin-lattice
relaxation time measurements of nitroxide spin labels, if it is
modified to prevent the interference of spectral diffusion. Our
first approach (RUP) is to use triply-selective pulse trains, which
possess and excitation pattern matching the motionally narrowed
three-line ESR spectrum of a nitroxide radical, and thus provide
an almost uniform initial perturbation of the spectrum. In the
second approach (RRTM) we combine the conventional inver-
sion-recovry technique for the central line with the pulsed
ELDOR technique for the two outer lines, in one experiment,
and eventually reconstruct the recovery of the total magnetiza-
tion of the ensemble of radicals which is not affected by spectral
diffusion.
Obviously, a much more straightforward way to measure the
T1 times of nitroxide spin labels would be the conventional
inversion-recovery experiment with mw pulses short and
powerful enough to invert the entire motionally narrowed ESR
spectrum. At present this is not possible with the commercial
instruments, for the required incident mw power grows as a
cube of the spectral coverage of a pulse.27,48 Progress in the
field of pulsed ESR will eventually lead to higher mw fields
available commercially. In the meantime, the techniques
proposed in this work might prove useful in carrying out reliable
spin-lattice relaxation measurements under constraints of
limited mw power.
Table 1 summarizes the T1 relaxation times measured for
TMATEMPO, TEMPO, and PROXYL in the presence of SDS
micelles and CT-DNA. Aqueous solutions of the nitroxides
served as a reference system. As becomes immediately clear
(63) Rosen, M. J. Surfactants and Interfacial Phenomena; John Wiley
& Sons: New York/Chichester/Brisbane/Toronto, 1989.
(64) Myers, D. Surfaces, Interfaces and Colloids: Principles and
Applications; Verlag Chemie: Weinheim, 1991.
(65) Do¨rfler, H.-D. Grenzfla¨chen und Kolloidchemie; Verlag Chemie:
Weinheim, 1994.
(66) Saenger, W. Principles of Nucleic Acid Structure; Springer-
Verlag: New York/Berlin/Heidelberg/London/Paris/Tokyo, 1988.
(67) Turro, N. J.; Barton, J. K.; Tomalia, D. A. Acc. Chem. Res. 1991,
24, 332.
(68) Murphy, C. J.; Arkin, M. R.; Ghatlia, N. D.; Turro, N. J.; Barton,
J. K. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 5315.
(69) Christen, R. In Principles of Organic Chemistry; Otto Salle-
Verlag: Frankfurt (Main), 1982; pp 89-101.

InVersion-RecoVery of Nitroxide Spin Labels
J. Am. Chem. Soc., Vol. 118, No. 6, 1996 1445
One can take advantage of the improved accuracy of T1
measurements to reveal subtle changes in relaxation behavior.
For instance, in this work it allowed us to conclude that nuclear
spins of a solvent do not contribute noticeably to the electron
spin-lattice relaxation in nitroxide radicals. While we are
unaware of any other nitroxide spin-lattice relaxation studies
in a “spinless” solvent, this conclusion is in accord with the
literature findings that there are only minor differences in T1
times measured in different solvents of comparable viscosity.24
However, a careful systematic study of spin-lattice relaxation
times for a wide range of solvents was, in fact, never attempted.
It could, in principle, reveal the importance of other aspects of
solute-solvent interaction, if minor variations of the T1 times
were reliably detected.
Both RUP and RRTM methods have substantial limitations
of their applicability discussed in the preceding sections of this
work. In principle, it should be possible to extend these methods
to other radicals exhibiting simple hyperfine patterns. However,
given the present hardware limitations of the design of composite
pulses, the feasibility of the uniform inversion in the RUP
experiment should be specifically studied for a particular radical
in question. The RRTM approach essentially relies on the
invariance of the spin-lattice relaxation time across the ESR
spectrum of a radical. Both approaches are applicable only in
the fast motional limit. In our variable-temperature study of
nitroxide T1 times we have almost reached the limit of
applicability for the RRTM approach. While some advance to
larger rotational correlation times is still possible, the reliability
of the results will suffer due to a substantial broadening of the
high-field nitroxide ESR line and the resulting loss of sensitivity
due to a significant signal decay within the spectrometer
deadtime.
introduction of loop-gap resonators it became clear that the two
mw frequencies necessary for ELDOR experiments can be
accommodated within the same cavity.25 It was also demon-
strated that in a pulsed ELDOR experiment one mw pulse
produces all combinations of pump and probe frequencies, and
a two-dimensional Fourier transform can easily separate them.14
In our RRTM experiment we use analog filters to separate the
responses from various ESR lines. While analog filters are
useful in many applications of magnetic resonance,70 an obvious
improvement would be to implement digital filtering of data,
which is now routinely used in NMR spectroscopy71,72 and easily
outperforms analog filtering in many respects. Much like in
modern NMR, the digital filtering of ESR data can be performed
on the fly despite much higher repetition rates usually employed,
if the filtering is done while a sampling oscilloscope performs
an extensive averaging of an FID for the next step of a phase
cycle. This improvement in data acquisition and manipulation
will provide a very simple way of detecting one-dimensional
pulsed ELDOR traces for measuring the rates of spectral
diffusion due to nuclear spin relaxation, spin exchange, etc.
Acknowledgment. This work was supported by grants from
NSF, KAST (Kanagawa Academy of Science and Technology,
Japan), DFG (Deutsche Forschungsgemeinschaft), and Hewlett
Packard. We thank Professor David C. Doetschman (SUNY,
Binghamton) for help in mastering the practical aspects of pulsed
ESR spectroscopy and for helpful discussions.
JA952152D
(70) Skinner, T. E.; Pruski, J.; Robitaille, P.-M. J. Magn. Reson. 1992,
98, 604.
(71) Rosen, M. E. J. Magn. Reson. A 1994, 107, 119.
(72) Craven, C. J.; Waltho, J. P. J. Magn. Reson. B 1995, 106, 40.
(73) Bowman, M. K. In Modern Pulsed and Continuous-WaVe Electron
Spin Resonance; Kevan, L., Bowman, M. K., Eds.; Wiley-Interscience: New
York, 1990; pp 1-42.
Our RRTM experiment is in fact a close relative of the
ELDOR technique, and can be used as such. Since the