Microheterogeneity of Solvent-Swollen Coal Probed by Proton Spin

Oct 27, 1999 - It is shown that coal swells in a nonuniform fashion on a fine scale and that phase separation occurs on a scale ranging up to 20 nm ev...
0 downloads 0 Views 136KB Size
Download PDF
Energy & Fuels 1999, 13, 1239-1245

1239

Microheterogeneity of Solvent-Swollen Coal Probed by Proton Spin Diffusion Koyo Norinaga* Institute for Chemical Reaction Science, Tohoku University Katahira, Aoba-ku, Sendai, 980-8577, Japan

Jun-ichiro Hayashi and Tadatoshi Chiba Center for Advanced Research of Energy Technology (CARET), Hokkaido University N13, W8, Kita-ku, Sapporo 060-8628, Japan

George D. Cody Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road, Washington, DC 20015 Received June 21, 1999. Revised Manuscript Received August 30, 1999

The phase-separated structure of solvent-swollen coal was characterized using its proton flipflop spin diffusion property. Five coals of different ranks were swollen by saturation with deuterated pyridine and were subjected to 1H NMR relaxation measurements. At least two distinct structural regions exist in the swollen coals based on the transverse relaxation characteristics as reported in the literature. The observed longitudinal relaxation was characterized by a single component, since spin diffusion, i.e., the transfer of 1H magnetization from the mobile to the rigid phase is active in the swollen coals. The process of this transfer was monitored using a partially modified Goldman-Shen pulse sequence and analyzed with a simple model. It is shown that coal swells in a nonuniform fashion on a fine scale and that phase separation occurs on a scale ranging up to 20 nm even in good solvents such as pyridine.

Introduction The most convincing model of coal structure is that of a cross-linked macromolecular network.1-5 The swelling of coal in various solvents has been studied to evaluate the molecular weight between cross-link points.2,4-8 The Flory-Rehner theory 9 has been frequently employed to relate the macromolecular network parameters to the degree of swelling in a good solvent. The theory assumes that the deformation is affine, i.e., the primitive chain is deformed in the same way as the macroscopic deformation (swelling) of the sample. Accordingly, the coal must swell uniformly in the segmental scale when we relate the macroscopic swelling to molecular characteristics such as the cross-link density. Based on the 1H NMR transverse relaxation characteristics, however, it was found that the coal hydrogen in * Author to whom all correspondence should be addressed. Fax: +81-22-217-5655. E-mail: [email protected]. (1) van Krevelen, D. W. Fuel 1966, 45, 229. (2) Green, T.; Kovac, J.; Brenner, D.; Larsen, J. W. In Coal Structures; Mayers, R. A., Ed.; Academic Press: New York, 1982. (3) Brenner, D. Fuel 1985, 64, 167. (4) Larsen, J. W.; Green, T. K.; Kovac, J. J. Org. Chem. 1985, 50, 4729. (5) Lucht, L. M.; Peppas, N. A. Fuel 1987, 66, 803. (6) Sanada, Y.; Honda, H. Fuel 1966, 45, 295. (7) Kirov, N. Y.; O’Shea, J. M.; Sergeant, G. D. Fuel 1968, 47, 415. (8) Nelson, J. R. Fuel 1983, 62, 112. (9) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY; 1953.

the pyridine-swollen state could be divided into two groups: those with relaxation characteristic of solids and those with relaxation characteristic of liquids.10-17 Barton et al.12 reported that up to 60% of coal’s macromolecular structure becomes mobile when immersed in deuteriopyridine, while the remaining 40% remains rigid as detected through 1H NMR transverse relaxation measurements. Base on this finding, they first established that the swollen coal has a phase-separated structure involving a solvent-rich phase and an apparently solvent-impervious phase. Phase separation has been recognized as an important aspect of coal swelling.18,19 Nevertheless, scale of heterogeneity in the (10) Jurkiewicz, A.; Marzec, A.; Idziak, S. Fuel 1981, 60, 1167. (11) Jurkiewicz, A.; Marzec, A.; Pislewski, N. Fuel 1982, 61, 647. (12) Barton, W. A.; Lynch, L. J.; Webster, D. S. Fuel 1984, 63, 1262. (13) Kamienski, B.; Pruski, M.; Gerstein, B. C.; Given, P. H. Energy Fuels 1987, 1, 45. (14) Jurkiewicz, A.; Bronnimann, C. E.; Maciel, G. E. Fuel 1990, 69, 804. (15) Jurkiewicz, A.; Bronnimann, C. E.; Maciel, G. E. High-Resolution 1H NMR Studies of Argonne Premium Coals. In Magnetic Resonance in Carbonaceous Solids; Botto, C. E., Sanada, Y., Eds.; Advances in Chemistry; American Chemical Society: Washington, DC, 1993; No. 229, 401. (16) Yang, X.; Larsen, J. W.; Silbernagel, B. G. Energy Fuels 1993, 7, 439. (17) Yang, X.; Silbernagel, B. G.; Larsen, J. W. Energy Fuels 1994, 8, 266. (18) Painter, P. C.; Park, Y.; Sobkowiak, M.; Coleman, M. M. Energy Fuels 1990, 4, 384.

10.1021/ef990131p CCC: $18.00 © 1999 American Chemical Society Published on Web 10/27/1999

1240

Energy & Fuels, Vol. 13, No. 6, 1999

Norinaga et al.

Table 1. Properties of Coal Samples swelling ratiod[-] coal

(symbol)

Ce

Yallourn Beulah Zap Illinois No. 6 Pittsburgh Upper Freeport

(YL) (BZ) (IL) (PT) (UF)

65.0 72.9 77.7 83.2 85.5

a

b

c

By difference. Dry-ash-free. Moisture-free.

d

He

Ne

Se

Oa,e

pyridine

4.6 4.8 5.0 5.3 4.7

0.6 1.2 1.4 1.6 1.6

0.2 0.7 2.4 0.9 0.7

29.6 20.3 13.5 8.8 7.5

2.7 2.2 2.8 2.4 1.0

Determined by the method proposed by Green et

swollen coals is presently not fully understood, and this forms a subject matter of this study. Despite its indirect character, measuring 1H spin diffusion by pulsed NMR has proven a useful technique for evaluating the compatibility of polymer blends20-23 and the microdomain structure of multiphase polymers.24-29 This technique has also been applied to dried and solvent-swollen bituminous coal.25,30 When a nuclear spin system is disturbed from equilibrium via resonant excitation during an NMR experiment, the nonequilibrium state may remain long after spin coherence is lost via transverse relaxation processes, i.e., T2 relaxation. This follows directly from the fact that in solids the longitudinal relaxation time, T1, is much larger than T2.31,32 While the spin system returns to equilibrium once again, the spin energy can disperse between neighboring nuclei by energy-conserving “flip-flop” spin transitions. This process is termed spin diffusion, and may provide observable energy transport over distances of several tens of nanometers. Recently, Xiong and Maciel33 studied proton longitudinal relaxation characteristics in dry coal, using a solid-state high-resolution NMR technique. On the basis of time domain data of the longitudinal relaxation process in both laboratory and rotating frames, it was found that coal is an extremely heterogeneous material, involving structural heterogeneity over broad spatial dimensions from 0.5 to 80 nm. For coal swollen by saturation with deuterated pyridine, at least two distinct morphological regions exist in the NMR sense. In such a case, mobile regions provide exceptionally efficient transfer of energy to the lattice, owing to a favorable phonon distribution of state near the larmor frequency of protons. The rigid components are weakly coupled to the lattice and transfer of polarization to the lattice is inhibited. It is possible, through the mechanism of spin diffusion, for a component that is tightly coupled to the lattice to relax other resonant nuclei in the spin system, either totally or partially. By analyzing the spin diffusion process under appropriate initial and boundary conditions, we can estimate the diffusion path length, and then obtain information about the size of each phase. In this study, the phase-separated structure of solventswollen coal is characterized by its proton spin diffusion property. Five coals of different rank, swollen by saturation with deuterated pyridine, were subjected to 1H NMR relaxation measurements. The NMR experiments provide the transverse relaxation time, T2, the longitudinal relaxation time, T1, and that in the rotating frame T1F. The time dependence of the spin diffusion was also monitored using the Goldman-Shen pulse sequence. The dimension of heterogeneity of the swollen coal was evaluated by analyzing the spin diffusion process.

al.35 e

wt % daf

pyridine/CS2 2.0 1.9 bcoal.

Experimental Section Samples. Four Argonne Premium Coal Sample Program (PCSP) coals34 and a brown coal were used as coal samples. Their particle sizes were finer than 150 µm. They were dried under a pressure of less than 1 Pa at 333 K for 48 h, which was long enough to attain a constant weight. The elemental composition and swelling ratios35 of the coal samples in pyridine or a mixture of pyridine and CS2 are listed in Table 1. A coal sample (0.3 g) was weighed and transferred to an NMR tube with a 10 mm o.d. This tube was charged with 0.5 g of per-deutero pyridine (Aldrich, 99.99% atom D), py-d5, and sealed under a pressure of less than 2 Pa while frozen in liquid nitrogen. A mixture of py-d5 and CS2 (1:1 by volume) was also used as a solvent for UF coal. The coal-solvent mixtures were stored at 303 K for at least 4 months prior to the NMR measurement. Styrene/ divinylbenzene copolymers, purchased from Bio-Rad Laboratories, (St/DVB, cross-link density 2, 4, and 8%) swollen in benzene-d6 were also prepared. 1H NMR. NMR measurements were carried out at 303 K using a JEOL Mu-25 NMR spectrometer equipped with a spin locking unit operating at a proton resonance frequency of 25 MHz. The solid-echo pulse sequence,36 90°x-t-90°y (90° phase shift) provided an approximation to the complete free induction decay (FID). Typical values for the pulse width, pulse spacing, repetition time, and number of scans were 2.0 µs, 8.0 µs, 6 s, and 32, respectively. The saturation recovery pulse sequence, 90°x-t-90°x, was used to monitor the recovery of the magnetization with the pulse separation time, t, (19) Painter, P. C.; Graf, J.; Coleman, M. M. Energy Fuels 1990, 4, 393. (20) Kwei, T. K.; Nishi, T.; Roberts, R. F. Macromolecules 1974, 7, 667. (21) Nishi, T.; Wang, T. T.; Kwei, T. K. Macromolecules 1975, 8, 227. (22) Douglass, D. C.; McBrierty, V. J. Macromolecules 1978, 11, 766. (23) McBrierty, V. J.; Douglass, D. C.; Kwei, T. K. Macromolecules 1978, 11, 1265. (24) Assink, R. A. Macromolecules 1978, 11, 1233. (25) Cheung, T. T. P.; Gerstain, B. C. J. Appl. Phys. 1981, 52 (9), 5517. (26) Cheung, T. T. P. Phys. Rev. B 1981, 23, 1404. (27) Cheung, T. T. P. J. Chem. Phys. 1982, 76, 1248. (28) Tanaka, H.; Nishi, T. Phys. Rev. B 1986, 33, 32. (29) Schmidt-Rohr, K.; Spiess, H. W. Multidimensional Solid-State NMR and Polymers; Academic Press: London, 1994. (30) Barton, W. A.; Lynch, L. J.; Webster, D. S.; Simms, G. Diffusioncoupled relaxation and the submicroscopic structure of bituminous coals. In Magnetic Resonance in Carbonaceous Solids; Botto, C. E., Sanada, Y., Eds.; Advances in Chemistry; American Chemical Society: Washington, DC, 1993; no. 229, p 175. (31) Bloembergen, N. Nuclear Magnetic Relaxation; Benjamin: New York, 1961. (32) MacCall, D. W.; Douglass, D. C. Polymer 1963, 4, 433. (33) Xiong, J.; Maciel, G. E. Energy Fuels 1997, 11, 866. (34) Vorres, K. S. User’s Handbook for the Argonne Premium Coal Sample Program; Argonne National Laboratory: Argonne: IL, 1993. (35) Green, T. K.; Kovac, J.; Larsen, J. W. Fuel 1984, 63, 935. (36) Powles, J. G.; Mansfield, P. Phys. Lett. 1962, 2, 58.

Microheterogeneity of Solvent-Swollen Coal

Energy & Fuels, Vol. 13, No. 6, 1999 1241

and provided T1. T1F was measured using a spin-locking pulse sequence,37 that includes a 90°x pulse followed by a reduced-amplitude pulse, phase-shifted 90°, and sustained for a variable time, t. The magnetization remaining at time t is monitored by observation of the free induction decay signal. The rotating frame measurements were made in a 6 G radio frequency field. The spin diffusion was monitored with the Goldman-Shen pulse sequence.38 To avoid the dead-time effect after the pulse, the original pulse sequence was modified as 90°xt0-90°-x-t-90°x-t1-90°y, according to Tanaka and Nishi.28 Results and Discussion Transverse Relaxation Characteristics. The natural logarithm of the FID curves for the dried and swollen YL coal are drawn as a function of decay time in Figure 1(a). Although the solvent swelling enhances the fraction of slowly decaying components, a portion of the coal hydrogen remains rigid. For a dipole coupled rigid system such as dry coal, the time decay of the nuclear magnetization can be characterized by a Gaussian function. On the other hand, in a liquid or a liquidlike environment, the magnetization decay is approximately an exponential function. Therefore the observed FID was assumed to be expressed by the following equation and was analyzed numerically by the nonlinear leastsquares method.

I(t) ) IG(0) exp[-t2/2T2G2] + IL1(0) exp [-t/T2L1] + IL2(0) exp [-t/T2L2] (1) where I(t) and Ii(t) are the observed intensity at time t, and that attributed to component i, respectively, and T2i is the transverse relaxation time of the ith component. The fractions of hydrogen producing exponential decays, Hm, are listed in Table 2. Hm for the swollen coal samples ranges from 0.2 to 0.6, and the value of T2G is similar to that for the corresponding dry coal. In contrast, when exposed to benzene-d6, the hydrogens in the St/DVB cross-linked copolymer are entirely converted to mobile hydrogens producing exponential decays, regardless of the cross-link densities, as illustrated in Figure 1b. This indicates that the solvent penetrates thoroughly into St/DVB, which is likely to be deformed in a more-or-less uniform fashion. On the other hand, for the swollen coal samples, it is clear that there are domains that are not penetated by solvent and hence not swollen. This was first established by Lynch et al.12 based on 1H NMR transverse relaxation characteristics of the solvent swollen coal. The schematic representation of the phase structure of the swollen coal is shown in Figure 2. The phase structures of the swollen coal are separated into at least two phases: the solvent rich (SR) and solvent impervious (SI) phases. Brenner39 studied the changes in the optical anisotropy of dry and solvent-swollen thin-section samples of a bituminous coal. He found that the natural optical anisotropy was completely relaxed by immersion of the coal in pyridine. Different experimental techniques, i.e., 1H NMR and (37) Hartmann, S. R.; Hahn, E. L. Phys. Rev. 1962, 128, 2042. (38) Goldman, M.; Shen, L. Phys. Rev. 1966, 144, 321. (39) Brenner, D. Nature 1983, 306, 772.

Figure 1. 1H NMR transverse relaxation signals; (a) dried and swollen YL (pyridine-d5, S/C ) 1.75), (b) dried and swollen St/DVB (benzene-d6, S/C ) 2.31 for 4% and 8% cross-link densities, S/C ) 4.75 for 2%). Table 2. Fractions of Mobile Hydrogen of the Samples sample

solvent

S/Ca

Hm[-]b

YL YL BZ BZ IL PT UF UF St/2%DVB St/4%DVB St/8%DVB

py-d5 py-d5 py-d5 py-d5 + CS2 py-d5 py-d5 py-d5 py-d5 + CS2 benzene-d6 benzene-d6 benzene-d6

1.75 3.50 1.75 1.81 1.75 1.75 1.75 1.81 4.75 2.31 2.31

0.56 0.60 0.44 0.34 0.55 0.51 0.20 0.45 1.00 1.00 1.00

a Mass ratio of solvent to coal or polymer. b H m ) [IL1(0) + IL2(0)]/[IG(0) + IL1(0) + IL2(0)].

optical microscopy, produced different conclusions on the phase structure of the solvent-swollen coal. This contradiction results from the difference in the spatial resolution of these experimental techniques. The optical

1242

Energy & Fuels, Vol. 13, No. 6, 1999

Norinaga et al.

Figure 2. Conceptual model for microdomain structure of solvent-swollen coal.

microscopy technique can barely detect heterogeneities whose spatial dimensions are less than the optical wavelength (400-700 nm). Therefore, the dimension of heterogeneities of the swollen coal must be smaller than ∼700 nm. Longitudinal Relaxation Characteristics and Spin Diffusion. While the transverse relaxation characteristics of the swollen coals yield quantitative information about relative abundance of mobile hydrogens and rigid hydrogens, they give no information about the scale of heterogeneity of the swollen coal. The domain sizes can be estimated by studying the spin diffusion properties. Therefore proton longitudinal relaxation was measured in both the laboratory and rotating frames to examine whether the spin diffusion process is active in the swollen coal samples. Figure 3a shows the result of T1 measurement for the swollen UF coal. T1 is essentially composed of one component, while T1F can be analyzed as the sum of two exponential functions as shown in Figure 3b. Table 3 lists the results for the T1 and T1F measurements. From this table, one can clearly understand the effect of spin diffusion. T2 signals are composed of three components without the effect of spin diffusion, while T1F and T1 measurements are strongly affected by spin diffusion and the number of components decreases from T1F to T1. The existence of at least two time constants for a rotating frame longitudinal relaxation process (i.e., T1F ) in a system means that spin diffusion processes cannot effectively average the different dynamic properties of protons in different spatial domains on the relevant time scale of the specific relaxation process. On the other hand, on the time scale of T1 measurements, spin diffusion sufficiently averaged the distinctly separated spin systems. The scale of the spatial heterogeneity in swollen coals can be estimated by evaluating the diffusive path length, L, i.e., the maximum linear scale over which diffusion is effective.

Figure 3. T1 and T1F plots for solvent-swollen UF. (a) T1, (b) T1F. Table 3. Results of Proton Longitudinal Relaxation Measurements (25 MHz)a T1F[ms] sample

solvent

S/Cb

YL BZ IL PT UF UF

py-d5 py-d5 py-d5 py-d5 py-d5 py-d5 + CS2

3.50 1.75 1.75 1.75 1.75 1.81

fc

T1F

2.2(0.66) 0.8(0.37) 1.4(0.57) 1.2(0.56) 1.9(0.57) 1.5(0.56)

T1Fs d

T1[ms]

24.2(0.34) 7.4(0.63) 9.9(0.43) 8.0(0.44) 17.5(0.43) 11.9(0.44)

25(1.00) 27(1.00) 100(1.00) 157(1.00) 321(1.00) 145(1.00)

a Values in parentheses; fraction of each component. b Mass ratio of solvent to coal or polymer. c Fast. d Slow.

The approximate expression40 is

L ) (2dDt)1/2

(2)

where d is the spatial dimension, i.e., the degree of freedom of diffusion, D is the diffusion coefficient, and t is the characteristic time for diffusion. Values of d of (40) McBrierty, V. J.; Douglass, D. C. J. Polym. Sci., Macromol. Rev. 1981, 16, 295.

Microheterogeneity of Solvent-Swollen Coal

Energy & Fuels, Vol. 13, No. 6, 1999 1243

Table 4. Estimated Values of a j , D, and b h sample

solvent

S/Ca

YL BZ IL PT UF

py-d5 py-d5 py-d5 py-d5 py-d5 + CS2

3.50 1.75 1.75 1.75 1.81

a j D[10-12 τ0 [nm]b cm2/s] [µs] 1-Dc 2-Dc 3-Dc 0.29 0.29 0.29 0.29 0.30

5.7 6.2 5.6 5.5 5.1

100 70 70 70 60

2 2 5 5 5

5 5 12 12 10

8 8 19 21 16

a Mass ratio of solvent to coal or polymer. b a j was estimated from N -1/3, where N is the number of hydrogens per unit volume. c b h [nm].

one, two, and three correspond to domains shaped like a sheet, a cylinder, and a sphere, respectively. It has been shown that in a regular lattice with a lattice constant a, the spin diffusion coefficient due to the dipolar spin-flip is given by26

D ) 0.13a2 xM2

(3)

where M2 is the second moment of the NMR line shape. For both Gaussian and Lorentzian line shapes, xM2 ) T2-1. For a regular lattice, D can be principally calculated from eq 3, but since the lattice constant is an illdefined quantity for disordered materials such as coal, a theoretical value can only be estimated using

D = 0.13a j 2/T2G

(4)

where a j is the average of the square of the distances between adjacent protons in the solvent impervious domain. Since there is a lack of information on the molecular structure of coal, it is impossible to accurately determine a j . However, a j of the coal samples can be estimated semiquantitatively from the true densities evaluated by helium pycnometory41,42 and the hydrogen contents of the corresponding dry coal34 by assuming a cubic lattice of hydrogen atoms. Table 4 lists the estimated values of a j and D. D ranges from 5.1 × 10-12 to 6.2 × 10-12 cm2/s, and it has the same order in many organic polymer systems. The observed longitudinal relaxation time corresponds to the characteristic time t. By assuming d is 3, we can estimate L as 40 nm from eq 2 for UF/py-d5. Therefore, the linear dimension of the structural heterogeneity in UF/py-d5 is certainly less than 40 nm based on the T1 data. Following the same procedure for the T1F data, the lower limits of the heterogeneity can be estimated to be 3 nm from the short T1F, denoted as T1Fs. For UF/(py-d5 + CS2), the limiting size in heterogeneity can be estimated as 2-20 nm. However, coal always contains free radicals in concentrations of approximately 1018-1019 spins per gram.43 Since such paramagnetic impurities act as an energy sink for spin energy flow, they enhance the longitudinal relaxation rates.44 The spin diffusion induced by the interaction between electron and proton spins can also contribute to averaging T1 differences among different domains. Therefore, the L estimated (41) Huang, H.; Wang, K.; Bodily, D. M.; Hucka, V. J. Energy Fuels 1995, 9, 20. (42) Woskoboenko, F.; Stacy, W. O.; Raisbeck, D. The Science of Victorian Brown Coal; Durie, R. A., Ed.; Butterworth-Heinemann Ltd.: Oxford, 1991; p 152. (43) Petrakis, L.; Grandy, D. W. Free Radicals in Coal and Synthetic Fuels; Elsevier: New York, 1983. (44) Yokono, T.; Miyazawa, K.; Sanada, Y.; Marsh, H. Fuel 1979, 58, 896.

from the T1 data should be larger than the value estimated under the assumption of the proton spin diffusion alone. While these estimates are crude, they nevertheless provide some information on the maximum diffusive path lengths probed by the NMR experiment when spin diffusion is operative. Therefore, the Goldman-Shen pulse sequence was employed to monitor the spin diffusion process. The advantage of the GoldmanShen experiment relative to the longitudinal relaxation experiments is that the time for spin diffusion can be arbitrarily varied, and if this time is much less than T1, the analysis is straightforward. Goldman-Shen Experiment. The Goldman-Shen experiment is a technique that puts the separate spin systems at different spin temperatures and then sample them as a function of time so that their approach to equilibrium can be followed. The modified GoldmanShen pulse sequence used in this experiment is shown in Figure 4. The preparation times, t0, were chosen so that the magnetization in the SI phase decayed to zero, while there was still sufficient magnetization in the SR phase. Therefore, t0 depends on the sample types, as listed in Table 4. During the pulse interval, t, spin diffusion through the magnetic dipolar coupling occurs from the SR phase to the SI phase. The third 90°x pulse rotates the magnetization into the transverse plane for observation and the final 90°y pulse creates the solid echo. Typical decay signals after the Goldman-Shen pulse sequence observed in IL/py-d5 for various values of the pulse interval t are shown in Figure 5. Recovery of the fast decaying component is observed. The recovery factor, R(t), of the magnetization of the SI phase can be defined as

R(t) )

M(t) - M(t f 0) M(t f ∞) - M(t f 0)

(5)

In Figure 6, R(t) is plotted versus t1/2 for the solventswollen BZ and PT coal. The evolution of R(t) with time is analyzed using the diffusion equation solved by Cheung and Gerstain25 to get information on the domain size. The transfer of the magnetization in solids via the dipolar spin flip interaction may be described by Fick’s diffusion equation

∂ m(r,t) ) D∇2m(r,t) ∂t

(6)

where m(r,t) is the local magnetization density at site r and time t. The differential equation is then solved according to the appropriate boundary and initial conditions. The analytical solution of eq 6 according to Cheung and Gerstain is

R(t) = 1 - φx(t)φy(t)φz(t) h 2R) erfc(Dt/b h 2R)1/2 for R ) x, y, z (7) φx(t) ≡ exp(Dt/b where b h and erfc are the mean width of domains in SR phase and error function, respectively. For the onedimensional case, where b h)b hx , b h y, b h z, the solution is

R(t) ) 1 - φx(t)

(8)

The respective solutions for two and three dimensions can be written as,

1244

Energy & Fuels, Vol. 13, No. 6, 1999

Norinaga et al.

Figure 4. Schematic figure of the modified Goldman-Shen pulse sequence.

Figure 5. Solid-echo signals of swollen YL (pyridine-d5, S/C ) 1.75) after the modified Goldman-Shen pulse sequence for various values of t. t is equal to 1, 25, 64, and 225 ms from the bottom.

2-D R(t) ) 1 - [φ(t)]2 where b h)b hx ) b hy , b h z (9) h)b hx ) b hy ) b h z (10) 3-D R(t) ) 1 - [φ(t)]3 where b The quantity (Dt/b h 2R)1/2 was considered to be an adjustable parameter. The solid curves in Figure 6 represent the nonlinear least-squares fits to the data using eq 10. The results for the analytical fits are listed in Table 4. These calculations indicate that the SR phase domains in the swollen coals range in size from several up to 20 nm. The mean size appears to decrease with decreasing coal rank; however, information regarding the morphology of the domains is required to estimate these trends more precisely.

Figure 6. Recovery of proton magnetization in SI phase as a function of t1/2 for the solvent-swollen BZ and PT coal. Solid lines represent the best fit to the data using eq 10.

Conclusions The macromolecular dynamics of a rank series of five coals, swollen by immersion in deuterated pyridine, were analyzed using 1H NMR relaxation methods. Although there exist at least two distinct structural regions in the swollen coals based on the transverse relaxation characteristics, the measured longitudinal relaxation was best characterized by a single component as spin diffusion is rapid in the swollen coals. The dynamics of spin diffusion were revealed using a partially modified Goldman-Shen pulse sequence and analyzed by a simple mathematical model of a twophase system. The results clearly indicate that the dilation of the coal network with immersion in good solvents is nonuniform at a fine scale with structural domains existing in a size range of several to 20 nm.

Microheterogeneity of Solvent-Swollen Coal

These results highlight the current limits in our understanding of the macromolecular structure of coals and place into question the use of affine models of strain for the interpretation of macroscopic swelling measurements. Acknowledgment. The authors are grateful to Drs. Tadashi Yoshida and Masahide Sasaki of the Hokkaido

Energy & Fuels, Vol. 13, No. 6, 1999 1245

National Industrial Research Institute for their useful advice on the NMR measurements.This work was supported in part by a “Research for the Future Project” grant from the Japan Society for the Promotion of Science (JSPS), through the 148th Committee on Coal Utilization Technology. EF990131P