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J. Phys. Chem. B 2007, 111, 7972-7977
Electron Spin Relaxation in x-Lithium Phthalocyanine Hideo Sato, Lauraine A. Dalton, Duc Ha, Richard W. Quine, Sandra S. Eaton,* and Gareth R. Eaton Department of Chemistry and Biochemistry and Department of Engineering, UniVersity of DenVer, DenVer, Colorado 80208 ReceiVed: January 31, 2007; In Final Form: May 14, 2007
Continuous-wave linewidths and spin susceptibilities, spin-spin relaxation rates (1/T2), and spin-lattice relaxation rates (1/T1) for two sources of x-LiPc were measured at 9.5 GHz between 15 and 298 K. Relaxation rates at 34 GHz were measured between 80 and 298 K. Room-temperature relaxation rates also were measured at 250 MHz, 1.9 GHz, and 2.76 GHz. The temperature dependences of linewidths and spin susceptibilities are characteristic of 1-D organic conductors. The ratio of populations of localized and delocalized electrons varies with sample preparation. For a single needle between 15 and about 200 K, 1/T2 is higher for the parallel orientation, but 1/T1 is higher for the perpendicular orientation, consistent with predictions based on dipolar interactions. Between about 60 and 150 K, which is the temperature regime in which spin susceptibility is changing rapidly with temperature, 1/T1 exhibits a non-monotonic dependence on temperature and is lower at 34 GHz than at 9.5 GHz. In other organic conductors, this dependence has been attributed to a bottleneck mechanism of relaxation. At higher temperatures, 1/T1 becomes less orientation-dependent. At room temperature, T1 increases rapidly between 250 MHz (3.0 µs) and 2.76 GHz (6.3 µs) and then shows less frequency dependence up to 34 GHz (9.8 µs). The relaxation rate near room temperature might have a substantial contribution from spin hopping perpendicular to the stacking axis of the molecules.
1. Introduction Lithium phthalocyanine (LiPc) has been prepared in x, R, and β forms.1 The linewidth of the electron paramagnetic resonance (EPR) signal from the x-form is highly sensitive to oxygen concentration, so this material has been extensively studied as an oximetric indicator.2,3 The temperature dependences of EPR linewidths and magnetic susceptibilities for x-LiPc in crystals and thin films show that this material behaves as a one-dimensional conductor.4 The molecules stack with 3.2 Å spacings between the planes, and the conductivity is highest along the stacking axis.1 Although considerable data have been reported for the linewidths as a function of temperature, little information is available concerning electron spin relaxation rates. We report spin-lattice and spin-spin relaxation rates as a function of temperature at both the X-band and Q-band to provide greater insight into the relaxation mechanisms and properties of this material. 2. Methods 2.1. Sample. Electrochemically prepared samples of x-LiPc were graciously provided by Prof. Harold M. Swartz (Dartmouth Medical School)5 and Prof. Periannan Kuppusamy (The Ohio State University).2 The oxygen sensitivity of the linewidths at room temperature for both preparations is consistent with assignment as x-LiPc. The needles from Dartmouth were about 1 × 0.3 × 0.3 mm. The sample from Ohio State contained a range of needle lengths up to about 1 mm with much smaller widths than the Dartmouth sample. Four sample tubes, containing differing amounts of LiPc, were prepared. In each case, the * Corresponding author. Phone: 303-871-3102. Fax: 303-871-2254. E-mail:
[email protected].
sample was evacuated overnight and flame-sealed under vacuum. A single needle (∼0.8 mm long), prepared at Dartmouth, was placed in a 1.6-mm-o.d. quartz tube with the long axis of the needle oriented perpendicular to the axis of the tube. This sample (1a) was used for the variable-temperature studies of linewidths, signal intensities, spin echo measurements of T2, and inversion recovery measurements of T1, including orientation dependence. For X-band g value measurements at room temperature, a small amount of diphenylpicrylhydrazyl (DPPH) was dissolved in acetone and evaporated onto the surface of a 4-mm-o.d. quartz tube into which the 1.6-mm-o.d. quartz capillary containing the needle of LiPc was placed. Four partially aligned needles of LiPc prepared at Dartmouth were placed in a small quartz capillary supported in a 4-mm-o.d. tube. This sample (1b) was used for T2 measurements and for free induction decay (FID) and inversion recovery measurements of T1 between 80 and 298 K. Multiple needles of LiPc, prepared at Dartmouth, were placed in a 4-mm-o.d. tube. This sample (1c) was used for variable-temperature measurements of T1 by saturation recovery at X-band and for room-temperature measurements of T1 and T2 at 0.25, 1.9, and 2.76 GHz. Multiple needles of LiPc prepared at Ohio State were placed in a 1.6-mm-o.d. quartz capillary, supported in a 4-mm-o.d. quartz tube. This sample (2) was used to measure T1 by saturation recovery at 9.2 GHz as a function of temperature and T1 and T2 at room temperature at 0.25, 1.9, and 2.76 GHz. 2.2. EPR Spectroscopy. Continuous-wave (CW) spectra were recorded on a locally constructed X-band CW and pulse spectrometer6 with a Bruker split-ring resonator, an Oxford ESR935 cryostat, and a wide-gap Harvey Wells magnet. Although the field homogeneity for this magnet is not as good as for the Bruker magnets, the inhomogeneity is small over the small dimensions of the needles. To avoid sideband broadening
10.1021/jp070810y CCC: $37.00 © 2007 American Chemical Society Published on Web 06/21/2007
Electron Spin Relaxation in x-Lithium Phthalocyanine for these narrow spectra, 10-kHz magnetic field modulation was used. The signals above about 110 K are so narrow and intense that the response of the automatic frequency control (AFC) circuit on passing through resonance can distort the signal lineshape. To avoid this problem, the AFC circuit was turned off during data acquisition.7 To properly phase the signal recorded with AFC off, the reference arm phase and detector current were carefully adjusted before the AFC circuit was turned off. The Q factor of the split-ring resonator, which varied from ∼1100 near room temperature to ∼ 2800 at 25 K, was calculated from the ring-down time after a single microwave pulse. Spectra were simulated as Lorentzian curves by minimizing the sums of the squares of the residuals. Integrated intensities were calculated from the simulated curves. Relative signal amplitudes (Figures 1 and 3, below) were calculated by correcting for differences in resonator Q factor and spectrometer gain and modulation amplitude. Variable-temperature spin echo measurements of T2 (90-τ-180-τ-echo) and inversion recovery (180-Tvar-90-τ-180-τ-echo) measurements of T1 were performed with 180° pulse lengths of 40 or 80 ns. The impact of the FID on the echo decays was minimized by using phase cycling and by putting a magnetic object near the sample to introduce magnetic field inhomogeneity. The single-needle sample 1a was visually aligned parallel to the magnetic field. Values of T2 were measured, and small adjustments in sample position were made to find the minimum T2 value, which corresponds to the parallel orientation of the needle. The perpendicular orientation was then defined by a 90° rotation of the sample. Long-pulse X-band saturation recovery (SR) experiments were performed on a locally constructed spectrometer.8 The length of the saturating pulses were long relative to T1. The Q factor of the resonator was about 3000, and the deadtime following a pulse for SR was about 1.5 µs. Temperatures above 100 K were obtained with a Varian flowthrough dewar and temperature controller and nitrogen gas cooled with liquid nitrogen. Temperatures between 10 and 90 K were obtained with liquid helium and an Oxford ESR900 flow cryostat and an ITC601 temperature controller. X-band room-temperature inversion recovery experiments and two-pulse echo experiments were performed on a Bruker E580 instrument with a split-ring resonator and Oxford ESR935 cryostat. Variable-temperature measurements of T1 and T2 for the single needle (1a) also were obtained at Q-band (34 GHz) on a Bruker E580 instrument with a SuperQFT bridge and an ER5107D2 probehead. A 16-pulse phase cycling sequence was used to minimize the impact of the FID on the spin echo decays. Room-temperature values of T1 and T2 also were measured on locally constructed spectrometers operating at 2.76,9 1.9,10 and 0.25 GHz.11 Phase cycling and a magnetic object in the magnetic field (or a field gradient) were used to minimize the impact of the FID. Relaxation time constants were calculated from the recovery curves by fitting with a single exponential. To test for possible distributions in relaxation rates, data also were fitted with a stretched exponential. 3. Results 3.1. Temperature Dependence of CW Linewidths and Signal Intensity. The EPR linewidths for LiPc are strongly temperature-dependent.1,4 Examples of X-band spectra for a needle of LiPc (1a) oriented with the long axis along the magnetic field are shown in Figure 1. Within experimental uncertainty, the g value is independent of temperature. The
J. Phys. Chem. B, Vol. 111, No. 28, 2007 7973
Figure 1. X-band (9.7058 GHz) CW spectra at three temperatures of LiPc (needle 1a) oriented with the stacking axis (long axis of the needle) parallel to the external field. The spectra were scaled to the same y-axis amplification with the scaling factors shown beside each trace.
Figure 2. Temperature dependence of X-band linewidths obtained by simulations of spectra for LiPc needle 1a. Needle oriented parallel to the external field: narrow (b) and broad (2) components. Needle oriented at 90° to the external field: single component (O).
linewidth increases as temperature decreases (Figures 1 and 2), which is characteristic of x-LiPc.1 The large increase in linewidth and decrease in spin susceptibility at lower temperatures makes the amplitude of the signal much smaller than at higher temperatures. Above about 90 K, the lineshape could be simulated well as a single Lorentzian line, but below about 90 K, the sum of two Lorentzians was needed. For the perpendicular orientation, it was more difficult to separate the narrow and broad components, so a single component was used to simulate the signal. The narrowing in the wings that is characteristic of some exchange-narrowed signals12 was not observed. Over the full temperature range studied, linewidths (∆Bpp) for the needle oriented parallel to the external field were greater than for the perpendicular orientation (Figure 2). The room-temperature linewidths at X-band for this sample (45 and 19 mG for parallel and perpendicular orientations, respectively) are within the range of previously reported values for x-LiPc: minimum ∆Bpp ) 12 mG for a single crystal,13 20 mG for 1-mm-long microcrystals oriented perpendicular to the field,4 and 23-46 mG for a powder.1 The greater linewidth for the needle oriented with the stacking axis parallel to the external field than for the perpendicular orientation is characteristic of the 1-D conductor properties of the crystals.4,14 The lowtemperature linewidths of about 1 G also are consistent with literature reports for x-LiPc.1,4 The room-temperature g value (relative to DPPH ) 2.0036) is 2.00226 ( 0.00002, which is in good agreement with the literature value of 2.00214.4 Within experimental uncertainty, the orientation dependence of the g value was too small to measure at X-band. A very small g anisotropy of 4 × 10-5 was reported previously for x-LiPc.4 These comparisons demonstrate the similarity of the materials examined in this study to samples that have been studied
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Figure 3. Temperature dependence of the spin susceptibility (EPR signal intensity) for LiPc needle 1a, normalized to 1.0 at 295 K. For the parallel orientation of the needle, below 90 K, integrated intensities were calculated separately for the narrow (b) and broad (2) components. Spectra for the perpendicular orientation (O) were fit to a single Lorentzian. The temperature dependence predicted using the parameters (eq 1) discussed in the text (s) fit to experimental data between 25 and 175 K for LiPc needle 1a is compared with the literature fit for LiPc single crystal13 (- - -) and the literature fit for powdered LiPc1 (‚ ‚ ‚).
previously. At Q-band, ∆Bpp ) 50 and 96 mG for the perpendicular and parallel orientations, respectively. As discussed below, T2 is about the same at X-band and Q-band, so the differences in CW linewidths are due to distributions of g values. For samples 1c and 2, which contained many needles, the lineshapes were more complicated, and simulations required several Lorentzian components even at temperatures above 100 K. For these randomly oriented needles, the lineshape is the superposition of different linewidths for various orientations of needles relative to the external field. The spin susceptibility calculated from the integrated EPR signal intensity for sample 1a as a function of temperature is shown in Figure 3. There is good agreement between the values calculated for the parallel and perpendicular orientations of the needle. This temperature dependence is characteristic of 1-D organic conductors, including x-LiPc1,15-17 and can be modeled as13
χspin(T) )
C1 C2 exp(-Ea/kT) + T T - TCW
(1)
where the first term is for an Arrhenius activated process and the second term is the Curie-Weiss contribution. This model does not explain the observed leveling off of the susceptibility at higher temperatures, so the fitting parameters for the thermally activated process depend on the range of temperatures for which data were included. The fit line shown in Figure 3 was obtained by including data up to 175 K. The parameters for the Curie-Weiss contribution are relatively uncertain because of the small number of points at low temperatures, so TCW was fixed at 4 K, which is the value found for a single crystal of LiPc.13 The best-fit parameters are C1/C2 )1070, Ea ) 724 K. For comparison, the fit lines reported for single-crystal LiPc (C1/C2 ) 180, Ea ) 610 K, TCW ) 4 K)13 and powder LiPc (C1/C2 ) 40, Ea) 480 K, TCW ) -2 K)1 samples are also shown in Figure 3. Higher values of C1/C2 indicate higher ratios of conducting to localized electrons, which can arise from differences in defect concentrations in the preparations. In Figure 3, the literature fit lines are scaled to match the experimental susceptibility for 1a at low temperature and thereby emphasize the differences in ratios of conducting and localized electrons in the three samples.
Figure 4. Temperature dependence of X-band relaxation rates. 1/T1: (O) needle 1a, perpendicular orientation, inversion recovery; (b) needle 1a, parallel orientation, inversion recovery; (3) needles 1b, inversion recovery; (+) needles 1c, saturation recovery; and (*) needles 2, saturation recovery. 1/T2: (4) needle 1a, perpendicular orientation, twopulse spin echo; (2) needle 1a, parallel orientation, two-pulse spin echo; (0) needle 1a, perpendicular orientation, from linewidths; (9) needle 1a, parallel orientation, from linewidths; (]) needles 1b, two-pulse spin echo; and (×) needles 1b, T2* from FID.
3.2. Electron Spin Relaxation Rates. The temperature dependence of spin relaxation rates for x-LiPc at the X-band are shown in Figure 4. Consistent with the linewidths shown in Figure 2, the spin-spin relaxation rate is higher for the parallel orientation than for the perpendicular orientation of the needle with respect to the external field. Between about 40 and 90 K, 1/T2 exhibits little temperature dependence. 1/T2 changes dramatically between about 100 and 150 K, which is the temperature interval in which the magnetic susceptibility changes rapidly (Figure 3). Above about 150 K, where the susceptibility is changing more slowly, 1/T2 also changes more slowly. Above about 200 K, 1/T1 approaches 1/T2, especially for the more slowly relaxing perpendicular orientation, and spin-lattice relaxation contributes to increasing spin-spin relaxation rates. Near room temperature, the spin-spin relaxation rates measured directly by two-pulse spin echo decay were consistently lower than those calculated from the CW lineshapes. The CW linewidths that would correspond to the longest T2 values are about 11 mG. These linewidths are so narrow that it is difficult to obtain accurate values. Thus, the differences are attributed to experimental contributions to inhomogeneity and to contributions to the CW spectra from regions with different spin concentrations or g values. This interpretation is supported by the observation that T2* (FID) < T2. Similar values of T2 were obtained for the perpendicular orientation of single-needle 1a and several partially oriented needles 1b that were close to the perpendicular orientation. Often, long-pulse SR is the preferred method for measuring T1 because of the ability to mitigate effects of spectral diffusion when B1 is not large enough to excite all spins. However, for samples with narrow lines, contributions from the FID might interfere with the early time points of the SR curve because of imperfections in phase cycling.18 If interference from the FID is a concern, inversion recovery might be the preferred measurement method. At higher temperatures, T2 for x-LiPc is long enough that inversion recovery measurements can be made with a timing (τ) between the two pulses of the echo-detection sequence that is short relative to T2, which gives a good signalto-noise ratio and provides recovery curves that are representative of all spins in the sample. As T2 for x-LiPc becomes shorter at lower temperatures (Figure 4), a larger fraction of the signal decays during the time τ, and if there is a distribution of relaxation rates, there could be undersampling of faster-relaxing components. In the temperature regimes where T2 is shorter,
Electron Spin Relaxation in x-Lithium Phthalocyanine
J. Phys. Chem. B, Vol. 111, No. 28, 2007 7975 processes that dominate at higher temperatures are different from the ones that dominate at lower temperatures. The frequency dependence of the relaxation times at room temperature between 250 MHz and 34 GHz is reported in Table 1. Values of T1 are similar at 34 and 9.5 GHz and decrease at lower frequencies. The orientation dependence at 296 K is much smaller than at lower temperatures. The higher rates at lower frequencies are indicative of a process that is described by a spectral density function and a correlation time that is long relative to 1/ω at X-band. Values of T2 are more strongly orientation-dependent than T1, and the frequency dependence is smaller than for T1.
Figure 5. Comparison of relaxation rates at the X- and Q-bands for needle 1a. 1/T1: (O) perpendicular orientation, X-band; (b) parallel orientation, X-band; (]) perpendicular orientation, Q-band; ([) parallel orientation, Q-band. 1/T2: (4) perpendicular orientation, X-band; (2) parallel orientation, X-band; (0) perpendicular orientation, Q-band; (9) parallel orientation, Q-band.
the FID decays more quickly, so there is less likelihood of interference with the SR curve and SR might give more reliable results. In this study, the time constants obtained by long-pulse SR agreed well with those obtained by inversion recovery, which indicates negligible contributions from spectral diffusion. The temperature dependences of 1/T1 at X-band for several different samples of x-LiPc are included in Figure 4. For needle 1a, the spin-lattice relaxation rates are higher for the perpendicular orientation than for the parallel orientation over most of the temperature range studied, which is characteristic of dipolar relaxation in 1-D organic conductors.16 Between about 60 and 150 K, the relaxation rates 1/T1 go through a maximum. Above about 150 K, there is less anisotropy in the relaxation rates, and the slope of the plot of log(1/T1) vs log(T) is about 2.3 for the parallel orientation of needle 1a. Values of 1/T1 for partially aligned needles 1b between 80 and 298 K (Figure 4) are similar to those for the perpendicular orientation of 1a. For sample 1c, which contained many needles, values of 1/T1 below about 75 K were similar to those for the perpendicular orientation of needle 1a, which is consistent with the expectations for a powder distribution. Between 60 and 150 K, the deviation of 1/T1 from monotonic temperature dependence was smaller for 2 than for 1a, which suggests that the observation of non-monotonic temperature dependence varies with sample. For all of the samples near room temperature, recovery curves fit well to a single exponential, and fits to a stretched exponential gave an exponent of 1. At lower temperatures, either for the single-needle sample 1a or for samples containing multiple needles, single exponentials did not fit the data as well, and fitting with a stretched exponential gave exponents smaller than 1, which are indications of distributions of relaxation rates that can arise from the orientation dependence of dipolar interactions or multiple relaxation processes. To distinguish contributions from relaxation mechanisms that are frequency-dependent, relaxation rates at X-band and Q-band are compared in Figure 5. For 1/T2, the relaxation rates below about 120 K are frequency-independent. At higher temperatures, 1/T2 is slightly higher at Q-band than at X-band which suggests contributions from dynamic processes that are less completely averaged at Q-band than at X-band. For 1/T1 between 75 and 150 K, relaxation rates at Q-band are significantly lower than those at X-band, which implicates a process that is characterized by a spectral density function. At higher temperatures, 1/T1 is essentially the same at X-band and Q-band, and there is little orientation dependence, which indicates that the process or
4. Discussion 4.1. Linewidths. Between about 35 and 100 K, the spin susceptibility for LiPc is small (Figure 3), and the linewidth is weakly temperature-dependent (Figure 2). In this temperature range, lineshapes for needle 1a were fit by the sum of two Lorentzians. The linewidth and g value for the broader component are sufficiently different from those for β-LiPc1 that assignment to β-LiPc can be ruled out. By analogy with observations for other organic conductors, it is proposed that the broad signal is from localized spins and the sharp signal is from conduction electrons.1,19 The possibility that the broad component arises from a small amount of R-LiPc cannot be ruled out. The signal from R-LiPc is attributed to localized electrons,1 which would be expected to be similar to the localized component in x-LiPc, which might arise from defects in the low-temperature phase. Above about 100 K, the susceptibility increases dramatically, and the linewidth decreases (Figures 1-3), as has been observed for many conducting organic materials.17,19-21 The temperature dependence of the spin susceptibility (Figure 3) is typical of materials that undergo a spin-Peierls-type transition.4,22,23 Although the transition temperature for LiPc is not sharply defined, it is about 175195 K. The narrow EPR signals for conduction electrons in organic conductors is attributed to exchange narrowing and small spin-orbit coupling.24 The sharp decrease of the linewidth in the same temperature range in which the spin susceptibility increases might be due to increasingly effective exchange narrowing.25 An alternate model is that narrowing occurs because of increasing rates of interconversion between localized and delocalized spins, which averages the dipolar coupling.14 In 1-D organic conductors, EPR linewidths are orientationdependent because of the dipolar interactions between localized and conduction electrons.21 The contribution of the dipolar coupling to the linewidth is a maximum when the axis of maximum conductivity (the stacking axis for LiPc) is along the external field.16,19,21 For needle 1a, the ratio of the linewidths for the parallel and perpendicular orientations was about 2 in the temperature region studied (Figure 2). The isotropic contribution to the linewidth was around 80% and 50% for perpendicular and parallel orientations, respectively, and might be due to nuclear hyperfine interaction.4 The relative contributions to linewidths from isotropic and orientation-dependent terms depend on the conducting material.21,26 Analysis of the frequency dependence of the linewidths for exchange-narrowed systems predicts a minimum when the microwave frequency is approximately equal to the exchange interaction, which has been denoted as the “10/3 effect”.12,27,28 For LiPc, the minimum linewidth (maximum T2) is between 1.9 and 9 GHz (Table 1). If this minimum in linewidths is due to the 10/3 effect, it implies an exchange interaction on the order of several gigahertz.
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TABLE 1: Frequency Dependence of LiPc Relaxation Times at 296 Ka sample
34 GHz
1a 1b 1c 2
8.8 (|),b 9.8 (⊥)b
1a 1b 1c 2
1.2 (|), 3.4 (⊥)
9.2-9.7 GHz T1 (µs) 9.6 (|),b 9.0 (⊥)b 8.0,b 8.5c 9.4c 8.8c
2.8 GHz
1.9 GHz
250 MHz
6.3,b 5.9c
5.4b 5.6,b 5.8c 5.8,b 6.1c
3.0,b 3.6c,d 2.8b
3.7
3.6 3.6 3.4
2.6 2.2
T2 (µs) 1.8 (|), 3.7 (⊥) 4
a | and ⊥ indicate the orientation of the stacking axis relative to the external magnetic field. The uncertainties in T and T are about 5%. 1 2 Measurements were made at 293-295 K. b Inversion recovery measurement c SR measurement d Uncertainty of approximately (0.4 µs. The larger uncertainty is due to the lower sensitivity at 250 MHz.
4.2. Spin-Lattice Relaxation T1. Between about 15 and 60 K, the spin-lattice relaxation times T1 for LiPc samples 1a, 1c, and 2 are between about 500 and 50 µs [1/T1) (2 × 103)(2 × 104) s-1, Figure 4]. The relaxation times are much shorter than are typically observed for magnetically dilute organic radicals in this temperature range29 and are less temperaturedependent. The temperature dependence of the spin susceptibility in this temperature interval is characteristic of Curie-Weiss behavior (Figure 3). Most of the area under the EPR signal at the lowest temperatures comes from the broad signal that is attributed to localized electrons. Based on data for a homogeneous-chain oligomeric system, it has been proposed that weakly temperature-dependent electron spin lattice relaxation times on the order of a few hundred microseconds near 25 K can arise from cross-relaxation to fast-relaxing radical pairs.30 A weak temperature dependence of T1 has also been observed for transpolyacetylene31 at low temperatures. As the relative population of localized electrons decreases, the effectiveness of this process decreases, but it continues to make a significant contribution above 60 K. Between about 60 and 150 K, the temperature dependence of 1/T1 is not monotonic, and relaxation is faster at X-band than at Q-band (Figure 5). These temperatures are below the Peierls-type transition, and the spin susceptibility is changing rapidly with temperature. Below the Peierls-type transition, it has been proposed that dipolar interactions between the conduction and localized electrons make major contributions to both T1 and T2.16 This dipolar coupling bottleneck model is consistent with the observation that 1/T2 is higher for the parallel orientation than for the perpendicular orientation, whereas 1/T1 is higher for the perpendicular orientation than for the parallel orientation (Figures 4 and 5). Because 1/T2 is higher than 1/T1, the J(0) term16 must be significant for T2. Sachs and co-workers modeled the temperature dependence of 1/T1 for the 1-D conductor (fluoranthene)2PF6 based on the temperature dependence of susceptibility and observed nonmonotonic behavior with higher rates at 200 MHz than at X-band.14 The similarities in the temperature, orientation, and frequency dependences of relaxation rates for LiPc and for (fluoranthene)2PF6 suggest that a similar process is significant for LiPc. Above about 150 K, the values of 1/T1 at X-band and Q-band become increasingly similar (Figure 5), which indicates that the relaxation process that dominates at higher temperature is frequency-independent (Table 1). One possible assignment of this process is the Elliot model for semiconductors in which electron scattering causes a spin flip with a probability that is proportional to spin-orbit coupling squared.32,33 This contribution to the spin lattice relaxation rate is given by 1/T1 )
R(∆g)2/τ where R depends on the properties of the material studied and 1/τ is the electron scattering rate perpendicular to the stacking axis. Another possible assignment for the frequencyindependent process is relaxation via a local vibrational mode,34 as is commonly observed for magnetically dilute samples.29 At room temperature, the 1/T1 rates at frequencies lower than X-band are significantly higher than those at X- or Q-band (Table 1). The higher room-temperature relaxation rates at lower frequencies indicate contributions from an additional process that is described by a spectral density function. Full characterization of these processes will require variable-temperature data at the lower frequencies. One possibility is modulation of the dipolar coupling between the conduction electron and localized spin as a result of the diffusion of conduction electrons perpendicular to the stacking axis. For (naphthalene)2PF6, the spectral density function of the one-dimensional motion of the conduction electron is described by
(
)
2 2 1 τ|τ⊥ 1 + x1 + ω τ⊥ J(ω) ) 2 2 1 + ω2τ 2 ⊥
1/2
where τ| is the scattering time along the stacking axis and τ⊥ is the perpendicular-to-stack hopping time of conduction electrons.35 In the slow-motion limit where ωτ . 1, this model predicts that 1/T1 varies as ω-1/2. The data from Table 1 are plotted in Figure 6 as a function of ω-1/2, which demonstrates an excellent correlation. The nonzero y intercept indicates a frequencyindependent contribution of 0.82 × 10-5 s-1. To be in the slowmotion limit at 250 MHz requires that the transverse hopping time for the conduction electron be significantly longer than 10-10 s at room temperature, which is consistent with the suggestion based on the 10/3 effect that the exchange interaction is on the order of several gigahertz. Conclusion The properties of x-LiPc, including spin susceptibilities and relaxation times, are characteristic of 1-D organic conductors. The relative populations of localized and conduction electrons vary with sample preparation. 1/T2 decreases as spin susceptibility increases and shows characteristic orientation dependence that arises from dipolar coupling. Values of T2 at room temperature are weakly frequency-dependent between 250 MHz and 34 GHz. T1 for LiPc is less strongly temperature-dependent than for magnetically dilute samples and is more strongly orientation-dependent at lower temperatures than near room temperature. At room temperature, T1 is more strongly frequencydependent between 250 MHz and 3 GHz than at higher frequencies.
Electron Spin Relaxation in x-Lithium Phthalocyanine
Figure 6. Frequency dependence of 1/T1 for LiPc: (b) 1a; (9) 1b, ([) 1c, (2) 2. Values measured by inversion recovery and saturation recovery are shown in red and green, respectively. The solid line, which has a slope of 1, highlights the correlation between 1/T1 and ω-1/2.
Acknowledgment. A preparation of x-LiPc graciously provided by Dr. Oleg Grinberg and Professor Harold M. Swartz (Dartmouth Medical School) was used to make samples 1a-c, and a sample graciously provided by Prof. Periannan Kuppusamy (The Ohio State University) was used to prepare sample 2. Financial support of this work by NIH NIBIB Grants EB002807 and EB002034 (Howard Halpern, PI) is gratefully acknowledged. References and Notes (1) Brinkmann, M.; Turek, P.; Andre, J. J. J. Mater. Chem. 1998, 8, 675-685. (2) Ilangovan, G.; Zweier, J. L.; Kuppusamy, P. J. Phys. Chem. B 2000, 104, 4047-4059. (3) Ilangovan, G.; Zweier, J. L.; Kuppusamy, P. J. Phys. Chem. B 2000, 104, 9404-9410. (4) Brinkmann, M.; Andre, J. J. J. Mater. Chem. 1999, 9, 1511-1520.
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