Variable-Temperature High-Resolution Proton NMR Study of

866

Energy & Fuels 1997, 11, 866-878

Variable-Temperature High-Resolution Proton NMR Study of Laboratory-Frame and Rotating-Frame Spin-Lattice Relaxation in Coals Jincheng Xiong and Gary E. Maciel* Department of Chemistry, Colorado State University, Fort Collins, Colorado 80526 Received December 13, 1996. Revised Manuscript Received April 1, 1997X

We have carried out the first systematic in situ variable-temperature (25-180 °C) highresolution proton NMR study of laboratory-frame and rotating-frame proton spin-lattice relaxation of coal samples, based on the CRAMPS technique. For coal samples that have been exposed to air, we confirmed the fact that paramagnetic oxygen is the main source of laboratoryframe proton spin-lattice relaxation (T1). We demonstrate that paramagnetic oxygen trapped in coal can be used as a sensitive probe for monitoring structural and dynamical changes in coal as the temperature is varied. High-temperature spin-lattice relaxation experiments help to reveal the structural heterogeneity of coal because of reduced proton and electron spin-diffusion rates at high temperature. Large domains, on the order of 200-800 Å, with distinctively different paramagnetic oxygen concentrations, were found in all three coal samples studied, consisting of one low-volatile and two high-volatile bituminous coals from the Argonne Premium Coal bank. In particular, we found that aliphatic-rich domains with a length-scale larger than 500 Å exist in Premium Coal 601. The observed dependences of the rotating-frame 1H spin-lattice relaxation time T1F on the strength of the spin-lock field and temperature support the view that the main relaxation mechanism is time-dependent 1H-1H dipolar interactions in coals. From these dependences, we estimate that the correlation time of molecular motion responsible for rotatingframe proton spin-lattice relaxation in coals is on the order of 5 µs, which is in agreement with conclusions drawn from previous proton dipolar-dephasing studies. Two T1F values were identified for each of the three coal samples studied, indicating the existence of structural heterogeneity in coal on a spatial scale of at least 50 Å. The sizes of heterogeneous domains in coal are estimated on the basis of measured spin-lattice relaxation times and the analysis of proton spin-diffusion processes.

Introduction One of the important advances in coal science in the past decade has been the realization that noncovalent associative forces make major contributions to stabilizing the structure of coal, although a fundamental understanding at a molecular level of temperature effects on noncovalent associative interactions in coal has still been very limited.1-4 A detailed knowledge of such effects would open the possibility for future coal conversion technology under mild conditions, rather than thermolysis. As covalent bonds in coal are largely unchanged under mild thermal treatment (below 250 °C), the NMR study of coal structure and dynamics between 25 and 250 °C should be of interest primarily for revealing the nature and behavior of noncovalent associative interactions. An understanding of coal over this temperature range is also important if one hopes to refine or modify current structural models of coal, such as the molecular/macromolecular model.5-7 There* To whom correspondence concerning this paper should be addressed. Telephone: (970) 491-6480. FAX: (970) 491-1801. E-mail: [email protected]. X Abstract published in Advance ACS Abstracts, May 15, 1997. (1) Gorbaty, M. L. Fuel 1994, 73, 1819. (2) Iino, M.; Takanoshashi, T.; Ohsuga, H.; Toda, K. Fuel 1988, 67, 1639. (3) Nishioka, M. Fuel 1992, 71, 941. (4) Aida, T. In Proceedings, 45th Conference of Hokkaido Coal Research Group, 1989; p 11.

S0887-0624(96)00223-X CCC: $14.00

fore, we have carried out the first systematic in situ variable-temperature high-resolution 1H NMR study of coal samples between 25 and 230 °C, based on the CRAMPS (combined rotation and multiple pulse spectroscopy) technique.8,9 In a previous study,8,9 we found unexpectedly that there are no dramatic changes of 1H CRAMPS resolution over this temperature range. To examine explicitly the dependence of molecular motion on temperature,8 we carried out proton CRAMPS dipolardephasing experiments based on the BR-24 sequence and a “time-suspension” experiment using the CMG48 pulse sequence. From these experiments, we estimated the correlation time of the thermally promoted molecular motion to be on the order of 10 µs, which is several orders of magnitude slower than the molecular motion induced with pyridine saturation of coal at room temperature. This result suggests that thermal treatment alone up to 230 °C is not enough to break either the covalent bonds or the noncovalent associative interactions that contribute to the structure of the macromolecular network of coal. (5) Berkowitz, N. In An Introduction to Coal Technology, 2nd ed.; Academic Press: San Diego, CA, 1994. (6) Given, P. H; Marzec, A; Barton, W. A.; Lynch, L. J; Gerstein, B. C. Fuel 1986, 65, 155. (7) Derbyshire, F.; Marzec, A.; Schulten, H.-R.; Wilson, M. A.; Davis, A.; Tekely, P.; Delpuech, J.-J.; Jurkiewicz, A.; Bronnimann, C. E.; Wind, R. A.; Maciel, G. E.; Narayan, R.; Bartle, K.; Snape, C. Fuel 1989, 68, 1091. (8) Xiong, J. Ph.D. Dissertation, Colorado State University, 1996. (9) Xiong, J.; Maciel, G. E. Energy Fuel, in press.

© 1997 American Chemical Society

Spin-Lattice Relaxation in Coals

To further examine molecular dynamical and structural changes of coals over this temperature range, we have carried out measurements of proton spin-lattice relaxation times in both the laboratory frame and the rotating frame, based on CRAMPS techniques. These experiments provide a means for probing molecular dynamics in coal on time scales that are different from that of dipolar-dephasing experiments.10,11 Proton spinlattice relaxation in the laboratory frame can be used to probe molecular motion with a correlation time on the order of 10-8-10-9 s, while spin-lattice relaxation in the rotating frame is sensitive to molecular motion on the order of 10-4-10-5 s. Thus, knowledge of the spin-lattice relaxation of coal should compliment the molcular dynamics information we obtained from previously reported dipolar-dephasing experiments.8,9 Since spin-diffusion in proton-rich solids such as coals is typically much faster than spin-lattice relaxation, spin diffusion may average out T1F and/or T1 differences of protons in different structural/dynamical environments.12-14 Information on this kind of behavior can be useful for elucidating heterogeneity in coals on a submicroscopic scale (50-800 Å). As spin-lattice relaxation processes in untreated coal are much slower than proton dipolar-dephasing, spin-lattice relaxation measurements also provide a means for probing structural heterogeneity in coal on different length scales from those relevant to dipolar-dephasing experiments. 1. Laboratory-Frame 1H Spin-Lattice Relaxation in Coal. Laboratory-frame proton spin-lattice relaxation (T1) in coal has been investigated quite extensively via wide-line 1H NMR techniques.15-22 A wide variety of relaxation behaviors have been found for various coals. Both exponential and nonexponential relaxation behaviors have been observed. The presence of moisture and paramagnetic oxygen were found to decrease the relaxation time significantly.15-22 Although nonexponential relaxation behavior was attributed to the existence of different domains in coals in previous studies,16,19,21,22 those experiments were not able to relate the heterogeneity of coals directly to their chemical structures, due to limitations in wide-line 1H techniques. The combination of a spin-lattice relaxation technique with 1H CRAMPS detection should be able to provide much deeper insight into the chemical origin of the heterogeneity of coals. In this paper, we (10) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: 1961. (11) Mehring, M. Principles of High-Resolution NMR in Solids; Springer-Verlag: Berlin, 1983. (12) Veeman, W. S.; Maas, W. E. J. R. NMR 1994, 32, 127. (13) Schmidt-Rohr K.; Spiess H. W. Multidimensional Solid-State NMR and Polymers; Academic Press: London, 1994. (14) Deng, F.; Hu, J.; Xiong, J.; Du, Y. Solid State Nucl. Magn. Reson. 1993, 2, 97. (15) Gerstein, B. C.; Chow, C.; Pembleton, R. G.; Wilson, R. C. J. Phys. Chem. 1977, 81, 565. (16) Sullivan, M. J.; Szeverenyi, N. M.; Maciel, G. E.; Petrakis, L.; Grandy, D. W. In Magnetic Resonance. Introduction, Advanced Topics and Applications to Fossil Energy; Petrakis, L., Fraissard, J. P., Eds.; D. Reidel: Dordrecht, The Netherlands, 1984; p 607. (17) Wind, R. A.; Dujivestijn, M. J.; van der Lugt, C.; Smidt, J.; Vriend, J. In Magnetic Resonance. Introduction, Advanced Topics and Applications to Fossil Energy; Petrakis, L., Fraissard, J. P., Eds.; D. Reidel: Dordrecht, The Netherlands, 1984; p 461. (18) Wind, R. A.; Dujivestijn, M. J.; van der Lugt, C.; Smidt, J.; Vriend, J. Fuel 1987, 66, 876. (19) Webster, D. S.; Lynch, L. L. Fuel 1961, 60, 549. (20) Ripmeester, J. A.; Coutour, C.; MacPhee, J. A.; Nandi, B. N. Fuel 1984, 63, 522. (21) Jurkiewicz, A.; Idziak, S.; Pislewski, N. Fuel 1987, 66, 1066. (22) Wind, R. A.; Jurkiewicz, A.; Maciel, G. E. Fuel 1989, 68, 1189.

Energy & Fuels, Vol. 11, No. 4, 1997 867

present the first variable-temperature 1H spin-relaxation study on coals with 1H CRAMPS detection. Laboratory-frame 1H NMR spin-lattice relaxation mechanisms in coals were analyzed quantitatively by Wind et al.22 It was found that this relaxation in coals is mainly due to two relaxation mechanisms: timedependent 1H-1H dipolar interactions and time-dependent dipolar interactions between protons and unpaired electrons. It was well established experimentally that paramagnetic oxygen is an effective source of relaxation; it is the dominant relaxation source even for some coal samples that are never exposed to air. Most previous studies on this subject tried to avoid oxygen in the sample. However, this is unavoidable, especially for lower rank coals, since the paramagnetic oxygen is apparently incorporated into the coal structure during the coalification process. It is also difficult to eliminate paramagnetic oxygen in coal nondestructively, e.g., with evacuation of coal samples at mild temperatures.22 Instead of trying to avoid paramagnetic oxygen, we have tried to use it to our advantage in this work. On the basis of the previous work by Wind et al., the electron spin-lattice relaxation time (T1e) is known to be explicitly independent of the rank of coal.22 It is the concentration of paramagnetic oxygen that makes the laboratory-frame 1H spin-lattice relaxation time rank dependent. In the presence of ambient oxygen, the oxygen concentration and distribution in coal changes with temperature. Such changes should be detectable through the 1H spin-relaxation time. As the distribution of oxygen depends on the density and the pore distribution in coal, the distribution of 1H relaxation times could in principle be used to map the pore structures in coals, using paramagnetic oxygen as probe molecules. In the following sections, we will demonstrate that structural heterogeneity in coals can be probed by this strategy. 2. Rotating-Frame Proton Spin-Lattice Relaxation. Most reported 1H T1F data on coals were measured indirectly from 13C CP/MAS experiments, as T1F(1H) is a very important parameter for setting up and interpreting CP/MAS experiments.23 The indirect measurement from 13C CP/MAS also provides resolution of protons in aliphatic and aromatic regions in coal (referred to as “aliphatic and aromatic protons”), information that is not available in wide-line 1H NMR experiments. There are also limitations for such indirect (13C CP/MAS) measurements of T1F(1H). Only protons that are strongly dipolar coupled to carbon are detectable via indirect (13C) detection, and the quantitation of proton signals is complicated by the cross-polarization spin dynamics. And, of course, the sensitivity of such indirect measurements is limited by 13C detection. The rotating-frame 1H spin-lattice measurement based on CRAMPS detection used in this work overcomes these limitation. It provides good quantitation of 1H signals, with both “high resolution” (differentiating aromatic and aliphatic protons via chemical shifts) and high sensitivity. Experimental Section 1. Sample Preparation. 1H CRAMPS experiments were performed on the following three coal samples obtained from the Premium Coal Bank of the Argonne National Laboratory: Illinois No. 6 (Premium Coal 301, a high volatile bituminous (23) Sullivan, M. J.; Maciel, G. E. Anal. Chem. 1982, 54, 1615.

868 Energy & Fuels, Vol. 11, No. 4, 1997

Figure 1. Diagrams of pulse sequences of time-domain experiments based on CRAMPS detection. (a) Rotating-frame spin-lattice relaxation time (T1F) measurement. (b) Inversionrecovery experiment for measuring laboratory-frame spinlattice relaxation time (T1). R ) 35.3°; β ) 45°. (HVB) coal), Utah Blind Canyon (Premium Coal 601, a high volatile bituminous coal), and Pocahontas No. 3 coal (Premium Coal 501, a low volatile bituminous (LVB) coal). To reduce the effect of residual water on the 1H CRAMPS spectra of coals, the coal samples were evacuated at about 10-3 Torr for approximately 24 h at room temperature and stored in a glovebox under a dry N2 atmosphere. Prior to rotatingframe proton spin-lattice relaxation measurements, each coal sample was packed and sealed in a homemade Pyrex glass rotor designed for the Chemagnetics 5-mm pencil-type magicangle spinning (MAS) module in the glovebox.8,9 The sample preparation procedure for the laboratory-frame proton spin-lattice relaxation (T1) measurements were a little different, as we wanted for those experiments to introduce paramagnetic oxygen intentionally into the coal structure in order to render the O2-based T1 mechanism dominant. The coal samples used for T1 measurements were exposed to air for about 4 months, subsequently packed into homemade glass MAS rotors (vide supra), and then evacuated very briefly at 10-2 Torr at 25 °C to minimize possible oxidation of samples from excess O2 at high temperature. The MAS rotors containing the samples were then sealed in a glovebox with epoxy resin, which is far enough from the active volume of the transmitter/receiver coil in the NMR probe to preclude generating significant background signals. 2. NMR Experiments. All 1H NMR experiments were performed on a severely modified NT-200 NMR spectrometer operating at a proton resonance frequency of 187 MHz.24 Details of new hardware and software that were designed, developed, and implemented to improve the reliability, performance, and efficiency of 1H CRAMPS techniques during this work are described elsewhere.8 A Chemagnetics variabletemperature (VT) CRAMPS probe was used. The sample temperature was calibrated on the basis of 1H chemical shifts of ethylene glycol and the melting points of known crystalline compounds.8,25,26 We estimate the errors of the sample temperatures measured in this work to be within (2 °C. The pulse programs used for measuring spin-lattice relaxation times in the laboratary frame and the rotating frame are shown in Figure 1. The BR-24 multiple-pulse decoupling sequence was used in the detection period to separate contributions from aliphatic and aromatic protons.27 A significant improvement of the pulse sequences made in this work is the (24) Maciel, G. E.; Bronnimann, C. E.; Hawkins, B. L. In Advances in Magnetic Resonance: The Waugh Symposium; Warren, W. S., Ed.; Academic: San Diego, CA, 1990; Vol. 14, p 125. (25) Van Geet, A. L. Anal. Chem. 1970, 42, 679. (26) Ammann, C.; Meier, P.; Merbach, A. E. J. Magn. Reson. 1982, 46, 319.

Xiong and Maciel introduction of a composite pulse, (35.3°)-x(45°)-y , right before the BR-24 detection. As 1H CRAMPS spectra of coals are still quite broad, even with MAS and multiple-pulse narrowing, the accuracy of quantitation depends very critically on the quality of 1H CRAMPS spectra, especially the flatness of the baseline and the absence of interfering rotor lines.28 To avoid baseline distortions, well-calibrated composite preparation pulses (vide supra) before the multiple-pulse cycles were designed and used in this work so that proton magnetization that is spin-locked along the effective field of the average Hamiltonian is minimized. Without the composite pulse, the quantitation of CRAMPS spectra of coals is very difficult. The receiver phase was also optimized to minimize baseline distortions due to the “spin-locked” signal. Details on this issue are discussed elsewhere.8 A 108 µs cycle time and a 90° pulse width of 1.2-1.3 µs were used in the BR-24 pulse sequence for high-resolution 1H NMR detection. The number of BR-24 cycles used in the experiments was between 128 and 512, depending on the required resolution of the CRAMPS spectra. The recycle delays were 3-10 s. The sample spinning speeds were between 1.4 and 2.0 kHz. For measuring rotating-frame spin-lattice relaxation based on CRAMPS detection, a home-built eight-level transmitter RF (radio frequency) amplitude control unit was used to switch the RF amplitudes between the spin-lock period and the CRAMPS detection period within 100 ns during the experiment.8 The field strength of the spin-lock field was measured from the 90° pulse width in a multiple-pulse tuneup experiment.11 Two spin-lock field strength of 93 and 46 kHz were used in this work.

Results 1. Laboratory-Frame Spin-Lattice Relaxation Measurements. Figures 2, 3, and 4 show stack plots of 1H CRAMPS spectra obtained at 25, 120, and 180 °C from inversion-recovery experiments on Argonne Premium Coals 301, 501, and 601, respectively. One general characteristic of these spectra is that they each consists of two broad contributions. The band that is centered at about 1-3 ppm is associated with protons attached to aliphatic carbons, and the band centered around 6-8 ppm is due to protons attached to aromatic carbons. The peak areas of these “aliphatic and aromatic protons” were obtained from computer peak deconvolution, using a home-written peak deconvolution program described elsewhere.8,9 The peak area-vs-time data were then fit with a sum of individual inversionrecovery expressions as follows:

M(t) )

∑i Mi(∞)(1 - 2e-t/T ) 1i

(1)

where T1i is the spin-lattice relaxation time of the ith individual component, t is the inversion-recovery time used in the experiment, and M(t) is the peak area measured at the inversion-recovery time t. Examples of such data analyses are shown in Figure 5, in which experimental data and simulated inversion-recovery curves based on eq 1 are compared for Premium Coal 301. It can be seen from Figure 5 that the simulated curve matches well with the experimental data. Tables 1-3 present the relaxation parameters obtained from a home-written nonlinear least-squares fitting program8 based on eq 1. (27) Haeberlen, U. High-Resolution NMR in Solids, Selective Averaging; Academic Press: New York, 1976. (28) Burum, D. P.; Rhim, W.-K. J. Chem. Phys. 1979, 71, 944.



Figure 2. Stack plots of 1H CRAMPS spectra of Premium Coal 301 obtained from inversion-recovery T1 measurements performed at (a) 25, (b) 120, and (c) 180 °C. A 90° pulse width of 1.25 µs and a cycle time of 108 µs were used to obtain the BR-24 spectra, with 256 data points. The number of scans was 300. The recycle delay was 3 s. The MAS speed was 1.6 kHz.

Figure 3. Stack plot of 1H CRAMPS spectra of Premium Coal 501 obtained from inversion-recovery T1 measurements performed at (a) 25, (b) 120, and (c) 180 °C. A 90° pulse width of 1.25 µs and a cycle time of 108 µs were used to obtain the BR-24 spectra, with 256 data points. The number of scans was 400. The recycle delay was 3 s. The MAS speed was 1.6 kHz.

Several interesting features of the results will now be pointed out for later discussion. In general, the relaxation data fitted with eq 1 consist of two exponential decays, i.e., with a slow-relaxing component and a fast-relaxing component. At room temperature, a very small fraction (0.8 s), except for aliphatic protons in Premium Coal 601. This small fraction of very slow relaxation component (T1 > 0.8 s) apparently disappears at the higher temperatures. At 120 and 180 °C, we also observed a slow relaxation component, but with smaller T1 values (0.34-0.45 s) and much larger fractions (23%-60%). Most of these slowly relaxing protons must come from the fast relaxation components at room temperature. In other words, the fast relaxation component observed at 25 °C is split into two components at 120 and 180 °C. As shown in Tables 1-3, the T1 values of these two components at high temperatures are not smaller than the T1 value of the fast component at 25 °C. This means that the average T1 values of more than 90% of the protons in coals are increased when the temperature is increased.

2. Rotating-Frame Spin-Lattice Relaxation Measurements. Two spin-lock RF field strengths of 93 and 46 kHz, and three temperatures (25, 120, and 180 °C), were used for all three coals in these variable-temperature (VT) T1F experiments. As an example, stack plots of VT 1H CRAMPS spectra from T1F measurements on Argonne Premium Coal 601 at spin-lock fields of 93 and 46 kHz are presented in Figures 6 and 7, respectively. Each spectrum in the stack plot was deconvoluted into two peaks, corresponding to aliphatic and aromatic protons. The dependences of peak areas on spin-lock time were fitted with a sum of individual exponential decays as follows:

M(t) )

∑i Mi(∞)e-t/T

1Fi

(2)

where T1Fi is the rotating-frame spin-lattice relaxation time of an individual relaxation component, t is the spinlock time, and M(t) is the peak area measured at spinlock time t. The relaxation parameters obtained from nonlinear least-squares fits of the experimental data to eq 2 are


Xiong and Maciel

Figure 4. Stack plots of 1H CRAMPS spectra of Premium Coal 601 obtained from inversion-recovery T1 measurements performed at (a) 25, (b) 120, and (c) 180 °C. A 90° pulse width of 1.25 µs and a cycle time of 108 µs were used to obtain the BR-24 spectra, with 256 data points. The number of scans was 300. The recycle delay was 3 s. The MAS speed was 1.6 kHz.

presented in Tables 4-9. Figure 8 shows an example of the data analyses graphically. As shown in Figure 8, the simulated curves, which were calculated from the best fits between experimental data and eq 2, match well the experimental data. Except for Premium Coal 301 at 25 °C, the relaxation data fit with eq 2 consist of two exponential decays. The fact that two relaxation components can be detected reflects the structural heterogeneity in coal that cannot be averaged out by spin diffusion on the experimental time scale (1-10 ms). Discussion 1. Laboratory-Frame Spin-Lattice Relaxation Mechanisms. It has been found that the proton spinlattice relaxation in coals is mainly due to two relaxation mechanisms:22 time-dependent 1H-1H dipolar interactions and time-dependent dipolar interactions between protons and unpaired electrons. Random molecular motion in coals renders the 1H-1H dipolar interactions time-dependent. The 1H-1H contribution to the laboratory frame spin-lattice relaxation time (T1) of a specific component in coal due to isotropic motion is given by10

(

)

τc 4τc 1 ) AH + 2 2 T1 1 + ωH τc 1 + 4ωH2τc2

(3)

where AH is a parameter that depends on the strength of the proton-proton dipolar interactions and on the specific type motion, τc is the correlation time characterizing the molecular motion, and ωH is the proton Larmor frequency. In this case, the Zeeman spin-lattice relaxation time T1 is related to the spectral density of random motion around the 1H Larmor frequency ωH (187 MHz in this work) and 2ωH (374 MHz). Thus, T1 is useful for detecting fast motion (i.e., with short correlation times), if time-dependent 1H-1H dipolar interactions contribute significantly to T1. On the basis of our previous dipolar-dephasing study of coal, the correlation time of thermally promoted molecular motion is on the order of 10-5 s, which is also in agreement with the correlation time estimated from the rotatingframe spin-lattice relaxation study discussed in a latter

Figure 5. Experimental data (open circles) from the inversion-recovery T1 measurements of Premium Coal 301 obtained at 120 °C. The data are fitted with eq 1. Dashed curves represent fast and slow relaxation components; solid curves represent the sum of the two relaxation components. (a) Aliphatic protons. (b) Aromatic protons.

section of this paper. Thus, the molecular motion is in the slow motion regime in which ωHτC . 1. In this regime, the T1 due to time-dependent 1H-1H dipolar interactions is proportional to τC and thus will decrease with an increase of temperature. This is certainly not in agreement with the observed T1 dependence on temperature for more than 90% of the protons in these coals (see Tables 1-3). Therefore, we conclude that time-dependent 1H-1H dipolar interactions cannot be the dominant relaxation mechanism of T1 in the three coal samples studied. There are at least three sources of unpaired electrons in coals: paramagnetic metal ions in the mineral matter of coal, organic radicals, and paramagnetic oxygen. A



Figure 6. Stack plots of 1H CRAMPS spectra of Premium Coal 601 obtained from 1H T1F measurements performed at (a) 25, (b) 120, and (c) 180 °C. The spin-lock field was 46 kHz. A 90° pulse width of 1.25 µs and a cycle time of 108 µs were used to obtain the BR-24 spectra, with 256 data points. The number of scans was 200. The recycle delay was 3 s. The MAS speed was 1.6 kHz.

Figure 7. Stack plots of 1H CRAMPS spectra of Premium Coal 601 obtained from 1H T1F measurements performed at (a) 25, (b) 120, and (c) 180 °C. The spin-lock field was 93 kHz. A 90° pulse width of 1.25 µs and a cycle time of 108 µs were used to obtain the BR-24 spectra, with 256 data points. The number of scans was 200. The recycle delay was 3 s. The MAS speed was 1.6 kHz.

simplified model to describe the spin-lattice relaxation of coal due to time-dependent interactions between the protons and unpaired electrons is given by22

1/T1 ) Aer-6

(4)

where r is the distance between a proton and an unpaired electron and Ae depends on the nature of the time dependence of the proton-electron interaction. Such a time-dependent interaction can result from molecular motion, electron spin-lattice relaxation, and electron-electron flip-flops. It has been reported22 that electron spin-lattice relaxation (characterized by the time constant, T1e) of paramagnetic oxygen is the dominant contributor to proton relaxation based on time-dependent proton-electron interactions in coals, and all protons in the vicinity of the paramagnetic centers relax exponentially with a uniform average relaxation rate, since the fluctuating local fields from unpaired electrons are much stronger than other interactions. In other words, all protons are inside a socalled “diffusion barrier” around the unpaired electrons; thus, electron-proton interactions completely dominate

other interactions. In this case, the relaxation rate can be expressed as22

T1e 1 4 h 2 Ne ) γeγH T1 10 2π b3 1 + ω 2T

(

)

H

2

(5)

1e

where Ne is the concentration of paramagnetic oxygen and b is the radius of the diffusion barrier. A quantitative assessment of the relaxation mechanism due to paramagnetic oxygen in coal requires the measurement of its electron spin properties, including the electron spin-lattice relaxation time (T1e), electronelectron spin flip-flop rate, and concentrations. However, direct measurements of these parameters are very difficult, since the ESR line of paramagnetic oxygen is extremely broad. Nevertheless, it was well established experimentally that paramagnetic oxygen is an effective source of relaxation.17,18,22 This is the basis on which we have employed trapped oxygen in coal as a probe to study the structural heterogeneity of coal from 1H spinlattice relaxation measurements. Since electron spinlattice relaxation times for solids are not very temper-


Xiong and Maciel

Figure 8. Experimental data (open circles) from 1H T1F measurements on Premium Coal 601 with a spin-lock field of 46 kHz (a, b) and 93 kHz (c, d) at 120 °C. The data were fitted with eq 2. Dashed curves represent fast and slow relaxation components; solid curves represent the sum of the two relaxation components. (a, c) Aliphatic protons. (b, d) Aromatic protons.

ature dependent,21 changes in unpaired electron contributions to the proton T1 with temperature variation should be caused mainly by changes in the concentration of paramagnetic centers, as reflected in eq 5. According to this relaxation mechanism, the fast relaxation component should correspond to protons in domains with relatively high concentration of trapped oxygen. Such domains should have relatively open and/ or loose structures, with large voids. The oxygen concentration in these domains is expected to decrease with increasing temperature. Therefore, the average T1 of the fast relaxation component observed at room temperature should increase as the temperature is increased. This predicted behavior is in excellent agreement with the experimental results presented here. Therefore, the temperature dependence of 1H T1 observed in this study also supports the view that paramagnetic oxygen is the main source of laboratory-frame spin-lattice relaxation in coals. At room temperature, a very small fraction (0.8 s), except for aliphatic protons in Premium Coal 601. Such slow relaxation components should represent protons in very densely packed and/ or highly cross-linked (closed) domains with relatively low concentrations of trapped oxygen, as the spinlattice relaxation rate is smaller with a low concentration of paramagnetic oxygen in coal. Paramagnetic oxygen cannot easily diffuse into such dense and closed domains. Protons in such domains should also be well isolated from other protons in coal, as 1H spin diffusion from fast relaxing protons cannot reach these isolated protons. At higher temperatures (120 and 180 °C), we also observe a slow relaxation component, but with smaller T1 values (0.34-0.45 s) and much larger fractions (23%-60%). Most of these slowly relaxing protons must come from the fast relaxation components at room temperature. This result suggests that the distribution of trapped oxygen in coal has changed dramatically with

increasing temperature. The apparent disappearance of the small fraction of the very slow relaxation component (T1 > 0.8 s) at the higher temperatures may be due to two reasons. First, paramagnetic oxygen may penetrate into the dense and rigid structures in coals at higher temperature; high-temperature imparts some flexibility to the rigid structures and thus lowers the energy barrier for oxygen to diffuse into them, while the oxygen molecules themselves have increased their thermal energy at higher temperature. The relaxation time of protons in the dense structure can thus be reduced at high temperature as a result of increased concentration of paramagnetic oxygen. Second, a very small fraction of the protons with T1 > 0.8 s may still exist in the very dense structure at higher temperatures, but they are difficult to observe convincingly in the experimental data because the fraction is too small to ensure a meaningful fit of the data to a three-component model. Nevertheless, the disappearance of this slow relaxation component above 120 °C suggests that the densely packed and/or highly cross-linked structural domains in coal can be mobilized to allow oxygen diffusion into such domains under relatively mild thermal treatment above 120 °C. As shown in Tables 1-3, for each coal, the fast relaxation component at room temperature is split into two components at higher temperatures, except for aromatic protons in Premium Coal 601. This can be explained as a result of a redistribution of trapped oxygen in coal and reduced spin-diffusion rates at higher temperatures. There are actually two relevant spindiffusion processes in this case, proton-proton spin diffusion and electron-electron spin diffusion. Both processes are capable of averaging out the differences between spin-lattice relaxation times of protons that exist in a relatively uniform domain, which is defined as a domain with a relatively uniform spatial distribution of protons and paramagnetic oxygen centers. In such a domain, there are no big spatial gaps between protons and paramagnetic oxygen centers, so that spin-


diffusion processes can effectively spread over all protons in the domain on the relevant experimental time scale (on the order of T1 in this case). Due to motions promoted at higher temperatures, the effective dipolar interactions among protons and among unpaired electrons are reduced; thus both proton and electron spin-diffusion rates are reduced as the temperature is increased. In addition, the desorption of paramagnetic oxygen in coal at high temperature will decrease the concentration of paramagnetic oxygen centers. This will also create spatial gaps among the paramagnetic oxygen centers and slow electron-electron spin diffusion. The net result is that domains with two distinctly different average concentrations of paramagnetic oxygen centers can be detected and distinguished at higher temperatures. The fast relaxation components correspond to domains with relatively high concentrations of paramagnetic oxygen; the slow relaxation components correspond to domains with relatively low concentrations of paramagnetic oxygen. The void space is very limited in densely packed, rigid structures in coals, and it is relatively difficult for paramagnetic oxygen to diffuse into them. Thus, we propose that the slow relaxation component is due to protons in such densely packed structures. The expected redistribution and desorption of paramagnetic oxygen in coals at high temperature is also consistent with the observed changes of relaxation time constant (T1) at higher temperature. At room temperature, the relaxation time of the fast relaxing component is an average of the relaxation times of all protons in that domain. As we have discussed above, the fast relaxation component at room temperature is spilt into two components at high temperature. If we assume that the relaxation time constant of each individual proton is invariant as the temperature is increased, then the only change to be considered is the decrease in 1H1H spin-diffusion rate, so that two relaxation time constants can be distinguished at higher temperature. In this case, the relaxation time constants of a fast relaxation component at higher temperature will be smaller than at room temperature, which is supposed to be the average of the two relaxation time constants at high temperature. However, we can see from Tables 1-3 that T1 for the fast relaxation components at 180 °C is clearly not shorter than the T1 of the fast component at room temperature. This result suggests that the spin-lattice relaxation time of protons in coal domains with relative large voids and open structures increases with an increase of temperature. The longer proton spin-lattice relaxation time at higher temperature can be explained by the reduced concentration of paramagnetic oxygen. Almost all of the spin-lattice relaxation data in Tables 1-3 can be well interpreted via a dominant relaxation mechanism from time-dependent dipolar interactions between protons and electrons in paramagnetic oxygen. However, as the temperature increases, the concentration of paramagnetic oxygen in coal is expected to decrease, and the electron-proton relaxation mechanism may no longer be predominant. The 1H-1H dipolar relaxation mechanism is then expected to show its significance at a high enough temperature and/or in domains with low enough concentration of paramagnetic oxygen. For example, the relaxation time

Energy & Fuels, Vol. 11, No. 4, 1997 873 Table 1. Laboratory-Frame Spin-Lattice Relaxation Times of Illinois No. 6 Coal (301) slow component 25 °C 120 °C 180 °C

aliphatic aromatic aliphatic aromatic aliphatic aromatic

fast component

percenta

T1 (s)b

percenta

T1 (s)c

8 4 23 24 27 36

1.4 0.91 0.41 0.34 0.43 0.24

92 96 77 76 73 64

0.055 0.056 0.093 0.090 0.092 0.088

a Estimated standard error for percentage: (3%. b Estimated standard error for slow T1: (0.03 s. c Estimated standard error for fast T1: (0.005 s.

Table 2. Laboratory-Frame Spin-Lattice Relaxation Times of Blind Canyon Coal (601) slow component 25 °C 120 °C 180 °C


fast component

percenta

T1 (s)b

percenta

T1 (s)c

41 12 32

0.35 1.4 0.45

31

0.38

59 88 68 100 69 100

0.059 0.069 0.059 0.065 0.081 0.098


Table 3. Laboratory-Frame Spin-Lattice Relaxation Times of Pocahontas No. 3 Coal (501) slow component 25 °C 120 °C 180 °C


fast component

percenta

T1 (s)b

percenta

T1 (s)c

9 5 62 48 65 64

0.79 0.95 0.31 0.31 0.34 0.31

91 95 38 52 35 36

0.10 0.099 0.078 0.11 0.12 0.11


constant of the slowly relaxing aromatic protons in Premium Coal 301 decreases from 0.34 to 0.24 s when the temperature is increased from 120 to 180 °C, as shown in Table 2. The decrease of relaxation time at high temperature is probably due to time-dependent 1H-1H dipolar interactions. The aliphatic protons in coal 601 show some unique relaxation behaviors, as shown in Table 2. Even at 25 °C, there is a large fraction (41%) of the slow relaxation component, with a relaxation time of 0.35 s. Similar behaviors are observed only at 120 and 180 °C for Premium Coals 301 and 501. This suggests that the aliphatic domains in Premium Coal 601 have a more open, or looser, structure than those in Premium Coals 301 and 501. The phase separation of two aliphatic components in Premium Coal 601 can be very clearly seen from the 1H CRAMPS spectra near the null point of a inversion-recovery experiment, as shown in Figure 9. The aliphatic portion of the 1H CRAMPS spectra can be well simulated by a superposition of two peaks with the same chemical shift but different line widths. The slow relaxation component corresponds to a much narrower peak. This is consistent with a relatively uniform and well-packed structure. Although a very large fraction (41%) of aliphatic protons in Premium Coal 601 undergo spin-lattice


Xiong and Maciel

which the aromatics are in relatively small aromatic systems with aliphatic substituents.30 2. Rotating-Frame Spin-Lattice Relaxation. Under the spin-lock condition, with continuous irradiation of the B1 field along one axis of the rotating frame, a homonuclear dipolar interaction is scaled by -1/2 from its value in the absence of the spin-lock condition.11 Spin diffusion still occurs under the spin-lock condition. However, the magnetization spin-locked along the direction of the RF field will not dephase under dipolar interactions. The decay of the spin-locked magnetization is caused by rotating-frame spin-lattice relaxation, originating from fluctuations of local fields, e.g. due to random molecular motion. Since paramagnetic oxygen has not been introduced intentionally into the samples used for these T1F measurements, the main relaxation mechanism for 1H T1F is time-dependent 1H-1H dipolar interactions. If we assume that the random motion is a Gaussian-Markov process with the correlation time τc, then the T1F due to such “random isotropic modulation” of the dipolar Hamiltonian is given by11

(

τc τc 5 1 ) M2 + + 2 2 T1F 3 1 + 4ω 2τ 2 1 + 4ω1 τc 0 c Figure 9. 1H CRAMPS spectra (a, c) of Premium Coal 601 obtained in inversion-recovery 1H T1 measurements at 25 °C. The recovery time for a and c were 100 and 64 ms, respectively. The number of scans was 300. The recycle delay was 3 s. The MAS speed was 1.6 kHz. The spectra show clearly two components of aliphatic protons. The corresponding simulated spectra from peak deconvolutions are shown in b and d.

relaxation slowly at 25 °C, most of the aromatic protons (93%) relax very fast, with a T1 of 0.068 s. This implies that the slow relaxation domain consists mainly of aliphatic structures. The experimental results clearly prove the existence of large aliphatic-rich and aromaticrich domains in coals. This finding is consistent with the coalification process proposed by Hatcher et al.29 They concluded that most of the aliphatic structures in coal are due to algae or microbial residues, while the aromatics are derived mainly from lignin. Our results clearly demonstrate that 1H CRAMPS detection is able to provide much deeper insight into chemical structural details, such as the chemical origin of the heterogeneity of coals, than could wide-line 1H detection. The aromatic protons in Premium Coal 601 also show an interesting relaxation behavior. As seen in Table 2, almost all of the aromatic protons (96%) relax fast, with a T1 value that is the same as that of the fast relaxation component of aliphatic protons at 25 °C. At 120 and 180 °C, only one relaxation component can be observed for the aromatic protons, and the relaxation time of the aromatics is the same as that of the fast relaxation component of the aliphatic protons within experimental error. This result suggests that the aromatic protons in Premium Coal 601 are in the same domain as the aliphatic protons with fast relaxation. It also implies that the aromatic protons are inside a relatively open structural domain in which the concentration of paramagnetic oxygen centers is high. This is consistent with the aromatic structures one expects in HVB coals, in (29) Hatcher, P. G.; Breger, I. A.; Szeverenyi, N.; Maciel, G. E. Org. Geochem. 1982, 4, 9.

)

τc 2 (6) 3 1 + 4ω 2τ 2 0 c

where ω1 ) γB1, ω0 ) γB0, and M2 ) 3/5(γ14p2/r6)I(I + 1). M2 is the second moment due to the dipolar interaction between two spins with the gyromagnetic ratio γI, separated by the distance r. The maximum relaxation rate under isotropic rotation is reached for ω1τc ) 1/2. According to eq 6, T1F will increase as ω1 increases when τc is close to or larger than 1/(2ω1). For fast random motion with τc , 1/(2ω1), no effect of ω1 on T1F can be observed. A T1F increase with increasing ω1 can be seen in the fast relaxation components of both aliphatic and aromatic protons in Premium Coal 501 at 25, 120, and 180 °C, as shown in Tables 8 and 9. A similar T1F increase can also be seen for both aliphatic and aromatic protons of Premium Coal 301 at 25 °C. In fact, we can obtain a semiquantitative estimate of the correlation time τc on the basis of the T1F dependence on ω1. From eq 6, we obtain a very simple relationship between T1F and τc:

1 + 4ω1′τc2 T1F′ ) , ω0 . 1/τc and ω0 . ω1 (7) T1F′′ 1 + 4ω ′′τ 2 1

c

where the single and double primes corespond to experiments carried out at two different spin-lock fields, ω1′ and ω2′′. Thus, τc can be directly estimated from the ratio of T1F measured at two different spin-lock fields. For example, the correlation time of the fast relaxation aliphatic protons in coal 501 at 120 °C is estimated as 5 µs, which is in agreement with the correlation time estimated from our previous dipolar-dephasing studies.8,9 An increase in T1F is not always observed when ω1 is increased from 46 to 93 kHz, if we examine T1F values (neglecting changes in fractions) of a relaxation com(30) Schobert, H. H. The Chemistry of Hydrocarbon Fuels; Butterworths: London, 1990.



Table 4. Rotating Frame Spin-Lattice Relaxation Times of Illinois No. 6 Coal (301), Measured with a Spin-Lock Field of 46 kHz slow component 25 °C 120 °C 180 °C


fast component

percentagea

T1F (ms)b

100 100 29 44 36 38

7.6 6.3 13 9.0 14 12

percentagea

average

T1F (ms)c

T1Fav (ms)d

4.0 2.6 4.4 3.6

7.6 6.3 5.0 3.8 5.8 4.9

71 56 64 62

a Estimated standard error for percentage: (3%. b Estimated standard error for slow T : (0.8 ms. c Estimated standard error for 1F fast T1F: (0.2 ms. d T1Fav is calculated as (∑Pi/T1Fi)-1, where Pi is the fraction of the ith component and T1Fi is the rotating-frame spinlattice relaxation time of the ith component.

Table 5. Rotating Frame Spin-Lattice Relaxation Times of Illinois No. 6 Coal (301), Measured with a Spin-Lock Field of 93 kHz slow component 25 °C 120 °C 180 °C


fast component

percentagea

T1F (ms)b

100 100 36 46 53 53

11 9.7 16 13 15 12

percentagea

average

T1F (ms)c

T1Fav (ms)d

5.7 4.3 4.5 3.0

11 9.7 7.4 6.2 7.2 5.0

64 54 47 47


Table 6. Rotating Frame Spin-Lattice Relaxation Times of Blind Canyon Coal (601), Measured with a Spin-Lock Field of 46 kHz slow component 25 °C 120 °C 180 °C


fast component

average

percentagea

T1F (ms)b

percentagea

T1F (ms)c

T1Fav (ms)d

60 48 45 57 53 49

8.9 8.2 12 6.9 9.5 7.8

40 52 55 43 47 57

2.7 2.3 3.2 1.4 1.8 1.8

4.6 3.5 4.8 2.6 3.2 2.6


Table 7. Rotating Frame Spin-Lattice Relaxation Times of Blind Canyon Coal (601), Measured with a Spin-Lock Field of 93 kHz. slow component 25 °C 120 °C 180 °C


fast component

average

percentagea

T1F (ms)b

percentagea

T1F (ms)c

T1Fav (ms)d

66 81 74 69 65 84

12 9.6 13 9.3 12 9.2

34 19 26 31 35 16

3.0 2.2 2.4 1.6 1.8 2.3

5.9 5.9 6.2 3.7 4.0 6.2


ponent obtained at two different spin-lock fields. For example, T1F values of the fast-relaxing aliphatic protons in Premium Coal 601 are lowered from 3.2 to 2.4 ms at 120 °C when the strength of the spin-lock field is increased from 46 to 93 kHz (Tables 6 and 7). A quick explanation based on the discussion above would be that the random motion is so fast (τc , 1/(2ω1)) that the increase in T1F is not detectable from the experimental data. However, that explanation is not very convincing when we examine the T1F data of aromatic protons in Premium Coal 601 at 25 °C, shown in Tables 6 and 7. No significant change of T1F with ω1 can be seen for the aromatic protons in this coal at 25 °C. According to the

above (τc , 1/(2ω1)) explanation, all of the aromatic protons would have a correlation time τc , 5 µs, which seems to be too small on the basis of dipolar-dephasing results.8,9 The T1F dependence on ω1 is actually complicated by the spin-diffusion process, which averages out, on a time scale of T1F (1-10 ms), any T1F differences between protons that are strongly dipolar coupled to each other. If spin diffusion is fast and effective, the increase of T1F with ω1 may give more time for spin diffusion to spread over a larger distance and result in a redistribution of domains observed in terms of the T1F behavior. This may lead to a result that a large number of fast-relaxing protons are effectively exchanging mag-


Xiong and Maciel

Table 8. Rotating Frame Spin-Lattice Relaxation Times of Pocahontas No. 3 Coal (501), Measured with a Spin-Lock Field of 46 kHz slow component 25 °C 120 °C 180 °C


fast component

average

percentagea

T1F (ms)b

percentagea

T1F (ms)c

T1Fav (ms)d

20 17 18 15 19 11

12 6.5 16 7.5 13 7.6

80 83 82 85 81 89

1.6 1.4 1.2 1.1 1.0 1.0

1.9 1.6 1.4 1.3 1.2 1.1


Table 9. Rotating Frame Spin-Lattice Relaxation Times of Pocahontas No. 3 Coal (501), Measured with a Spin-Lock Field of 93 kHz slow component 25 °C 120 °C 180 °C


fast component

average

percentagea

T1F (ms)b

percentagea

T1F (ms)c

T1Fav (ms)d

31 17 17 15 18 20

13 9.1 16 10 15 7.8

69 83 83 85 82 80

2.5 1.4 1.9 1.7 1.6 1.3

3.3 2.2 2.2 1.9 1.9 1.6


netization with slowly relaxing protons via spin diffusion in a larger domain. The average T1F of the large domain with slow relaxation protons may not increase with ω1 because a larger number of fast relaxation protons are involved in the averaging process. Instead, an increase of T1F with ω1 may actually reflect an increase in the fraction of the slowly relaxing component. If spin diffusion is slow, the increase of T1F with ω1 will not be effectively averaged by spin-diffusion processes; thus, this increase is still observable in the experimental data. In summary, when the strength of the spin-lock field is increased, one would observe either an increase in T1F, an increase in the fraction of the slow relaxation component, or both. By reexamining all the T1F data in Tables 4-9 in these terms, one can see that the above discussion explains well the T1F dependence on ω1. Thus, the weighted-average of T1F due to the two components should be a better measure for comparing the spin-lock field dependence of T1F. Indeed, the average T1F, as listed in Tables 4-9, increases with ω1 in each case. The temperature dependence of 1H T1F in coals is not very simple, since the correlation time of random motion is close to the minimum of the T1F-vs-τc curve.11 In such an intermediate motion regime, T1F changes with modest changes in temperature (or τc) may not be significant due to the relatively shallow well of the T1F-vs-τc curve (eq 6) around the T1F minimum. For fast-relaxation protons in Premium Coal 501, the T1F value measured with a spin-lock field of 93 kHz decreases consistently with increasing temperature. This indicates that random motion is in the slow motion regime, or τc > 1/(2ω1) ) 5.4 µs. For a spin-lock field of 46 kHz, we can see that T1F levels off when the temperature is increased from 120 to 180 °C. This implies that the correlation time at 120 and 180 °C is very close to the T1F minimum at τc ≈ 1/(2ω1), or 5.4 µs. This is also in good agreement with the τc value estimated from the T1F dependence on ω1.

One thing worth mentioning here is that we observed initial transient oscillations in the 1H NMR signals in the T1F(1H) experiments on all three coal samples at all three temperatures employed in this study. The transient oscillations in the initial spin-lock period can last as long as 200 µs. The theoretical origin of such transient oscillations was discussed by VanderHart and Garroway.31 They are due to an exchange of energy between the spin-locked rotating-frame Zeeman and rotating-frame dipolar reservoirs. For on-resonance irradiation, the oscillations occur at a frequency near 2ω1 and damp out with a time constant on the order of the dipolar-dephasing time Tdd. Our experimental observation is qualitatively in agreement with that theoretical analysis. Such transient oscillations will complicate the cross-polarization dynamics in 13C CP/ MAS experiments. 3. Estimating Domain Sizes in Coal. Coal is known to be an extremely heterogeneous material because of the lack of physical mixing of coal components during the coalification process. For virtually any coal (except the anthracites), it is possible with a microscope to see “grains” of individual components, called macerals, that are clearly related to the original sources. We demonstrate in this work that such heterogeneous domains can be directly identified from timedomain NMR experiments based on 1H CRAMPS detection. Time-domain NMR experiments measuring dynamical processes on different time scales correspond to probing spatial structural heterogeneity on different length scales, when effective spin-diffusion processes exist. These NMR experiments provide a nondestructive way of probing structural heterogeneity in coal on length scales ranging from 5 to 800 Å. The existence of two or more time constants for a relaxation process (such as T1) in a system means that spin-diffusion processes cannot effectively average the (31) VanderHart, D. L.; Garroway A. N. J. Chem. Phys. 1979, 71, 7.



different dynamical behaviors of protons in different spatial domains on the relevant time scale of the specific relaxation process. The minimal domain size can thus be estimated from the time constant of the relaxation process Ti and the spin-diffusion coefficient, D, as follows:10,12

LD ) x6DTi

(8)

As seen in eq 8, to obtain information on domain size and morphology of a heterogeneous system, spin-diffusion coefficients must first be evaluated, or at least estimated. If the morphology of a heterogeneous system is well defined, the spin-diffusion coefficient can be directly determined experimentally from spin-diffusion experiments on the system.12,32 So far, there have been no direct experimental determinations of spin-diffusion coefficients on any coal samples due to the lack of a welldefined morphology in coal. Fortunately, spin-diffusion coefficients can be estimated indirectly from other experimental parameters. From previous studies on coal, we know that a proton dipolar-dephasing curve can be fitted with one or two Gaussian decays. For Gaussian-type dipolar-dephasing behavior with a dephasing time constant Tdd, we have derived the following equation for estimating the diffusion coefficients:8,33

DG )

2 xπ 〈d 〉 6 Tdd

(9)

where 〈d2〉 is the mean square distance between the nearest spins. As the exact molecular structure of coal is unknown, it is impossible to accurately determine 〈d2〉. However, a semiquantitative estimation of 〈d2〉 can be made from the known proton density of coal. Taking a typical value of hydrogen content of 5 wt % (dmmf: dry mineral matter free) and a density of 1.2 g/cm3, a dmmf hydrogen volume percentage of about 6% (dmmf, cm-3) in coal is obtained.34 (〈d2〉)1/2 can then be estimated as about 3 Å, assuming a cubic lattice of protons. For the fast Gaussian dipolar-dephasing components in coal, a typical dephasing time constant is 10 µs. The spin-diffusion coefficient can then be estimated from eq 9 as 2.7 × 10-11 cm2/s. For the slow Gaussian dephasing component with a dephasing time constant of 50 µs, the spin-diffusion coefficient is estimated to be about 5.3 × 10-12 cm2/s according to eq 9. Therefore, the proton spin-diffusion coefficient of coal should be on the order of 10 × 10-12 cm2/s. In many organic polymer systems, D is on the order of 10-11-10-12 cm2/s.12,13,32 For example, D for a diblock copolymer of polystyrene and poly(methyl methacrylate) was determined to be 8 × 10-12 cm2/s.32 Thus, the estimated spin-diffusion coefficient for coal is at least of the right order of magnitude. The inter-proton distance of 3 Å estimated above may be overestimated to some extent for rigid, fast-dephasing Gaussian components in coal, which could lead to an overestimation of the spin-diffusion coefficient for these components. The 1H-1H dipolar dephasing time constant of coals is on the order of 10-70 µs.8,9 If we use a spin-diffusion (32) Clauss J.; Schmidt-Rohr K.; Spiess, H. W. Acta Polym. 1993, 44, 1. (33) Xiong, J.; Maciel, G. E. Manuscript in preparation. (34) Vorres, K. S. Energy Fuels, 1990, 4, 420.

constant of 10 × 10-12 and a Tdd of 50 µs, we can estimate LD as 5 Å. This means that dipolar-dephasing experiments can probe local structural heterogeneity of the system over only very short distances. Only domains that are intimately mixed on a molecular level will show a single dipolar-dephasing time constant. The rotating-frame 1H spin-lattice relaxation time in coals have been determined to be on the order of 1-15 ms. As the dipolar interaction strength is scaled by 1/2 under a spin-lock condition, the spin-diffusion coefficient should correspondingly be scaled by 1/2. Using D ) 5 × 10-12 cm2/s and T1F ) 10 ms, we obtain LD(T1F) ≈ 55 Å. In most cases, we have identified two T1F components in untreated coals. This suggests, according to eq 8, that structural heterogeneity in coal also exists on a length scale of 50 Å. The laboratory-frame spin-lattice relaxation time of an untreated coal is on the order of 60-1000 ms. The limiting domain size LD can be estimated from eq 8, using D ) 10 × 10-12 cm2/s, as on the order of 200-800 Å. As electron-spin diffusion of paramagnetic oxygen can also contribute to averaging T1 differences among different domains, the LD should be larger than what we estimate from proton spin-diffusion alone. We have also found that two relaxation components are needed to describe the proton spin-lattice relaxation of most coal samples. This implies that very large domains exist in coal. The time-domain experiments clearly show that coal is an extremely heterogeneous material with structural heterogeneity over a broad spatial dimension from 5 to 800 Å. In the literature, the fast spin-lattice relaxation component in coal has been tentatively assigned as a molecular phase,21,22 which is defined as the mobile (slow-decay) component identified in experiments of the dipolar-dephasing type.6,7 We do not think this assignment is entirely appropriate, since the dipolar-dephasing experiment and spin-lattice relaxation measurement deal with spin dynamics with totally different time and spatial scales. One thing that is in common in both experiments is spin diffusion within the proton spin system, which averages out distinctly individual behaviors of protons over time and space. The relationship between the dipolar-dephasing experiment and the spin-lattice relaxation experiment is analogous to the relationship between looking at a subject with a magnifier and looking at the subject from a distance. If the sample is homogeneous, a good correspondence between the two observations may be found. However, for a heterogeneous system such as coal, a correspondence between the two experiments cannot be established simply. Conclusions The in situ variable-temperature proton CRAMPS study of proton spin-lattice relaxation in the laboratory frame and rotating frame provides both molecular structural and dynamical information on coal under thermal treatment conditions. We have confirmed that paramagnetic oxygen is the main source of proton spinlattice relaxation in the laboratory frame (T1) for coal samples that have been intentionally exposed to air. We have demonstrated that paramagnetic oxygen trapped in coal can be used as a sensitive probe for monitoring structural and dynamical changes in coal with temper-


ature variation. The redistribution and desorption of trapped oxygen in coal under thermal treatment, as detected from T1 measurements, suggest that densely packed and/or highly cross-linked structural domains in coal can be mobilized to allow oxygen to diffuse into them at temperatures above 120 °C. We found that high-temperature spin-lattice relaxation experiments help to reveal the structural heterogeneity of coal because of reduced proton and electron spin-diffusion rates at high temperatures. Large domains with dimensions on the order of 200-800 Å, and with distinctively different paramagnetic oxygen concentrations, were found in all three coal samples studied. In particular, we found that aliphatic-rich domains with a length-scale larger than 500 Å exist in Premium Coal 601. Rotating-frame spin-lattice relaxation time (T1F) measurements provide dynamical and structural information on a proton spin system on time and spatial scales that are intermediate between those relevant to dipolar-dephasing experiments and laboratory-frame spin-lattice relaxation measurements. The T1F dependences on temperature and the strength of the spinlock field support the view that the main relaxation mechanism is time-dependent 1H-1H dipolar interactions in coals. From these dependences, we estimate

Xiong and Maciel

that the correlation time of molecular motion that is responsible for rotating-frame proton spin-lattice relaxation in coals is on the order of 5 µs, which is in agreement with conclusions drawn from previous proton dipolar-dephasing studies.8,9 Two T1F values were identified for each of the three coal samples studied, which indicates the existence of structural heterogeneity in coal on a spatial scale of 50 Å. Based on measurements of spin-lattice relaxation times and the analysis of proton spin-diffusion processes, we were able to estimate semiquantitatively the limiting sizes of heterogeneous domains in coals. Time-domain 1H NMR experiments based on CRAMPS detection clearly reveal the extremely heterogeneous nature of coal on spatial scales from 5 to 800 Å. The structural heterogeneity in coal has also been addressed directly by our one-dimensional and two-dimensional proton spin-exchange NMR studies, based on proton CRAMPS detection, which will be discussed in a separate paper.33 Acknowledgment. This work was supported by U.S. Department of Energy Grant No. DE-FG2293PC93206. EF9602234

Variable-Temperature High-Resolution Proton NMR Study of

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