Quantitative determination of different carbon types in fusinite and

Jian Zhi Hu , M. S. Solum , R. J. Pugmire , Chaohui Ye , and D. M. Grant ... Thomas H. Fletcher , Mark S. Solum , David M. Grant , and Ronald J. Pugmi...
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Anal. Chem. 1@88,60, 1574-1579

Quantitative Determination of Different Carbon Types in Fusinite and Anthracite Coals from Carbon4 3 Nuclear Magnetic Resonance Chemical Shielding Line-Shape Analysis Naresh K. Sethi, Ronald J. Pugmire, J u l i o C. Facelli, and David M . Grant*

Departments of Chemistry and Fuels Engineering, University of Utah, Salt Lake City, Utah 84112

‘‘C NMR shielding tensors have been determined for two anthracite coals and a fuslnite macerai by uslng powder pattern line shapes whkh have been analyzed as a superposition of three different bands due to benzenellke, condensed (bridgehead and inner) and substituted carbons. Theoretical calculations on circumcoronene ( I ) as a model compound support the interpretations of the experimental data. Determination of the ratio of nonprotonated to protonated aromatic carbons obtained on the anthracites by the spectroscopic analysls Is In excellent agreement with the elemental analysls and previous studies by c#polar dephasing NMR techniques. The method therefore COneHtutes a valuable way to analyze the structure of high rank coals and should be useful in char characterization. The mole fraction of condensed carbons obtained by this technique Is used to estimate the average cluster size in these poiycondensed aromatic hydrocarbon materials.

13C magnetic resonance spectroscopy has found several applications for identifying structural parameters in coals and related materials in the past decade. NMR is a unique nondestructive analytical tool for probing the microscopic electronic environqenc surrounding nuclear spins. The analytically determined !ine intensities obtained in an NMR experiment are in direct proportion to the relative population of the spins being observed. Recently developed NMR methods, using cross-polarization and macroscopic sample spinning (1-3),are very useful for the study of solids which are amorphous and do not readily dissolve in any solvent. Some questions have been raised about the quantitative nature of the solid-state NMR techniques applied to the study of coals (4-9).A diversity of opinions exist among researchers regarding this issue. Factors such as (1)the effects of different relaxation times (TIH,TlpH,T C H ) on the line intensities (4, (2)coupling of small amplitude molecular motion with external sample spinning (9),and (3)the presence and population of paramagnetic impurities in coal samples (5,6)have all contributed to the controversy surrounding the quantitative usefulness of the cross polarization magic angle spinning (CP/MAS) method applied to coal research. In spin counting experiments,for instance, reported detection limits range from 30% to 100% of the spins present. The various arguments surroundingthis controversy have been treated by Wilson (IO), who concluded that frequently conditions are encountered which provide a quantitative representation of all the carbon types present in geochemical samples. The 13C CP/MAS technique has become an established and widely used tool for measuring the fraction of carbon that is aromatic (fa) in coals and kerogen samples (12,12).Furthermore, extensive use has been made of dipolar dephasing magic angle spinning (DD/MAS) techniques to estimate the fraction of observable carbon that is strongly dipolar coupled to protons. Several accounts of DD/IMAS techniques applied to the study of fossil fuels have appeared in the literature (13-16). 0003-2700/88/0360-1574$01.50/0

High speed magic angle spinning eliminates the broadening effects of chemical shielding anisotropy (CSA) of different carbon spins thus producing narrow lines and simplifying spectral analysis. However, valuable CSA information is lost in the process. The chemical shift of a nuclear spin depends upon the relative spatial orientation of the external magnetic field and the molecule to which the spin belongs. Due to this orientational dependence, chemical shielding is characterized by a second rank tensor (nine elements) but only the symmetric part of the shielding tensor (six elements) is measureeble in an NMR experiment as the antisymmetric portion (three elements) produces only second-order effects in the external magnetic field and, for the purposes of this study, can be neglected (17). The six elements required to fully determine the CSA tensor are, for instance, the three principal values of the tensor and the three Euler angles which specify the orientation of the principal axis of the tensor in some arbitrary molecular frame (18). The orientational information, however, is not readily obtainable in amorphous samples for which single crystals cannot be grown and the shielding in such cases can only be characterized by the three unique shielding parameters ull, uzZ,and u33known as tensor principal values (17-20). These shielding parameters can be obtained from the 13CNMR spectral pattern of the powdered sample. This broad but highly characteristic band has break points which can then be analyzed to extract the tensor principal values of each chemically unique spin. Spectral analysis can provide not only the tensor principal values but also quantitative population factors for different spins as well. Wemmer et al., (20)analyzed such line-shapesto quantify contributions from simple aromatic, condensed aromatic, alkoxy, and aliphatic carbons for several coals and model organic compounds. Another noteworthy method for obtaining shielding principal values is the analysis of the spinning side bands from samples spinning slowly at the magic angle (21).Sethi et al. (22-24)have demonstrated the value of variable angle sample spinning (VASS) as an adjunct method to powder pattern analysis in order to unscramble overlapping tensors. The VASS method is especially useful when one is interested in studying the aromatic constituents of the sample. This paper reports the quantitative tensor analysis of the aromatic components from static powder patterns of two anthracite coals (PSOC-867 and PSOC-628). The VASS method has been used to extract the same information for a coal fusinite maceral. Powder patterns have been simulated and compared with the experimental spectra to obtain the relative population of the different aromatic carbon types. From these data it is possible to differentiate between the condensed (bridgehead/inner) and peripheral (protonated and substituted) carbons in the aromatic cluster. The ratio of peripheral to inner carbons is then used to estimate the total number of carbons in the aromatic cluster. The tensor components of the inner and peripheral carbons obtained from the spectral analysis are compared with the “in-plane’’ shielding componentspredicted from semiemperical (MNDO) (25-27)calculations of the shielding tensors in circumcoronene 0 1988 American Chemical Soclety

ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988

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Table I. Data on Samples Studied" sample

seam/location

ASTM rank

PSOC-628b PSOC-867* fusiniteC

Penna No. 2, PA Primrose, PA silkstone, Aldwarke

an an

*

maceral composition, % vitrinite inertinite exinite 92

8

78 14

22 86

0 0 0

% dmmf

C

H

N

S

O(diff)

94.9 96.9

3.4

0.6

92.1

3.7

1.0 0.8 0.7

0.1 0.7 3.1

1.0

0.6 0.4

a Reference 15. Data supplied by the Penn State Coal Sample Bank. Sample and data supplied by A. H. Smith of the (British)National Coal Board.

n

n

n

sum of squares deviation between the simulated and experimental spectra. For the VASS method, all spectra taken at different spinning angles are fit simultaneously with the same set of parameters. The minimization of the total sum of squares of the deviation from all spectra is used as the criteria for fitting success. This method of analysis of multiple angle data has been demonstrated for model compounds (24) and provides refinements in fitting parameters which may exhibit ill-conditionedbehavior for a single spectrum. In the case of the fusinite maceral, the two spectra obtained at angles of 43.6' and 72' with respect to the external magnetic field were analyzed simultaneously (see Figure 5).

C. Samples Studied. Two anthracites obtained from the Perm State Coal Sample Bank and an inertinite (fusinite)maceral were studied. The detailed description regarding these samples is given in Table I. Circumcoronmo ( I

)

Flgure 1. Idealized structure of circumcononene showing the numbering system. Bond orders obtained from MNDO calculations are shown for unique bonds.

(I) (Figure 1). The theoretical predictions support the interpretation of the experimental values obtained in the coals. EXPERIMENTAL TECHNIQUE AND SPECTRAL SIMULATION A. NMR Spectroscopy. Cross polarization l8C spectra were acquired on a Bruker CXP-100 spectrometer operating at a carbon frequency of 25.152 MHz. All samples used in this study were ground to a fine powder before recording the spectra. The Hartman-Hahn match was established with a sample of hexamethylbenzene (HMB) to obtain maximum signal intensity (3-ms contact time and 3-s recycle time were employed). Cross polarization contact times (t,) of 1-3 1119 usually sufcice to fuUy cross polarize most organic compounds (28).For the anthracite PSO(2-628 and fusinite sample, t , of 3 ms and recycle delay of 1 s were found to be the optimum experimental conditions, but in the case of PSOC-867, tFpof 10 ms was required for achieving maximum spin polarization. Such long contact times have been used before to achieve complete polarization for coronene (29) which, like anthracite, is completely aromatic. The TCHand proton T1, values are 1 and 36 ms, respectively, for PSOC-861 as determined by a standard variable contact time sequence. B. Spectral Fitting. Chemical shift tensors were obtained by deconvoluting a properly phased experimental spectrum by matching it with the simulated spectrum. Powder pattern analyea were carried out by means of a recently developed spectral fitting method (30). It is assummed that spins are only experiencing orientation-dependent chemical shielding interactions, which is the case when employing high-power proton decoupling during data acquisition. Single spectral simulation requires an initial estimate of these parameters: (1) the principal values of the different shieldingtensors or a linear combination of the principal values in an irreducible form; (2) the relative intensities of the different bands, and (3) line broadening parameters. One or more of these parameters can be locked to some predetermined or known value, which is then held constant through the fitting process. For example, in model organic compounds,the relative intensities are usually locked to the atomic ratios given by the molecular structure. However, for coals, these population parameters are allowed to vary freely so as to provide quantitative data on individual carbon types. Simulated spectra are calculated by using the "POWDER"method (30)and the parameters are adjusted with a Simplex optimization routine to minimize the

RESULTS AND DISCUSSION Aromatic carbon spectral bands of static solids can be classified into four different subgroups according to the distinct chemical environments. These subgroups which have tensor components that vary by only ca. 10-20% within each group, are (1)benzenelike sp2hybridized protonated carbons on the periphery of the aromatic ring, (2) substituted peripheral carbons (e.g. alkylated), (3) condensed inner and bridgehead carbons, and (4)carbons bonded to heteroatoms (e.g., nitrogen, oxygen, etc.) (20,31). As a first approximation, the effects of the last group on the experimental spectra are not considered in the fitting process for the high rank coals and the fusinite maceral herein studied, since the nitrogen, oxygen, and sulfur contents of these samples are relatively low, e.g., the combined mole fractions of N, 0,and S are 0.008, 0.013, and 0.022 for PSOC-628, -867, and Aldwarke Silkstone fusinite, respectively (15). Therefore, only the first three types of tensors are germane to this study. Typical band shapes for these three types of tensors are shown in Figure 2 together with the superimposed isotropic peak (average of the three principal values) which would be observed in a MAS experiment. Differences in the band shapes are a consequence of changes in the electronic environment associated with the chemical nature of the unique nuclear site. Of particular importance for aromatic compounds are differences in the bond orders between the aromatic ring carbons, which are directly related to the variations in the two low field tensor components, ull and uZ2(26, 27). Inner carbons in a large polycondensed aromatic system exhibit near CSvlocal symmetry (surrounded by similar bond orders so that ull and u22 values are quite similar) and consequently give powder patterns which are nearly axially symmetric. On the other hand, protonated benzenelike carbons are characterized by a highly asymmetric powder pattern but, upon substitution by an aliphatic group, the two in-plane tensor components move closer reducing somewhat the asymmetrical features of the tensor. The aromatic band shapes of high rank coals and chars can be considered as a linear combination of these three characteristic bands and a quantitative estimation of three different types of carbons is possible by determining the fraction of each band type required to successfully fit the given spectrum. Burgar made the same assumption for these three types of aromatic band-shapes and proposed quantitative

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ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988

Table 11. Tensor Components and Population Factors for Aromatic Carbons" sample

carbon type

PSOC-628

protonated

PSOC-867

fusinite

Qll

622

condensed

210 192

145 185

9 1

aliphatic protonated condensed protonated condensed substituted

215 193 221 204 231

138 181 149 192 161

21 -8 17 -30 46

LW (in ppm)

C/O

Q33

*

34 3 62 f 3 4b 13 f 2 87 f 2 39 f 2 54 f 2 7f2

17 15 9 27 11.0 11 1.0

" All values are in ppm for TMS. Aliphatic carbon in anthracite.

ia

One Tensor

n

Two Tensor

Substituted (Alkylated)

A' I 3M)

1 300

1 200

I 100

I 200

I 100

I 0

ppm

Flgwe 3. Experimental and simulated (overlaid) static spectra of anthraclte PSOC-867. The lower trace shows two bands and relative intensities used to obtain the two-tensor fit. 1 0

PPm

Figure 2. Chemical shielding tensor band shapes for three types of aromatic carbons. The narrow line (artificial broadening of 2 ppm was added) superimposed on each band is the isotropic line which would be obtalned in a MAS experiment.

determination via analyzing spinning side bands in a slow spinning MAS experiment for an anthracite and a vitrinite coal (32, 33). Experimental and simulated spectra for the anthracite PSOC-867 are shown in Figure 3. An aromaticity value (fa) of 1.0 has been previously reported for this coal (15),indicating the absence of any aliphatic structure and therefore absence of substituted aromatic carbons. A single tensor fit of the data is also shown in Figure 3. The best fit parameters for this simulation were ull = 195 ppm, u22 = 178 ppm, and u33= -3 ppm with a linewidth (LW) of 30 ppm. The tensor principle values are reasonably close to those in graphite (ull = uZ2= 178, uD = 0) (29)structure indicating that most of the carbons in this coal are condensed. A casual inspection of the fit seems reasonable but, on careful inspection, discernible differences exist between the experimental and theoretical spectral intensities, especially near the mid-field break point. A twotensor fit of the data exhibits a near perfect point-by-point match between the simulated and experimental data. Tensor principal values and the relative intensities of the two bands are given in Table 11. The shielding tensors obtained for the protonated ring carbon are within the standard deviation of values summarized by Duncan (31) on 24 benzene derivatives

and by Carter et al. for pyrene (27). The shielding tensor values obtained for the inner carbons are similar to those reported by Carter et al. (27) and Sethi et al. (24) which are characterized by an axially symmetric tensor (ull= u22)with a u33value upfield from TMS. The two bands arise from protonated carbons (asymmetric band shape) and the inner/bridgehead carbons (near axially symmetric band shape). These two bands are shown as the lower traces in Figure 3. From the relative intensity ratio of the two bands, it was determined that 13 f 2% of the carbons in this anthracite are of the C-H type. This quantitative value is essentially identical with the 0.123 mol fraction obtained from the elemental analysis (atomic H/C value). In a previous study of this anthracite by dipolar dephasing techniques, the fraction of protonated carbon was estimated to be 15 d~ 2% (15). The second anthracite (PSOC-628) of lower carbon content (94.9% compared with 96.9% for PSOC-867) was analyzed in order to compare the average cluster size (vida infra) in two different anthracite coals. An aromaticity value (fa= 1.0) for this coal had been reported previously (1.9, implying that the experimental line shape must be similar to PSOC-867 (Le., a superposition of two different bands). However, the static powder pattern could not be successfully fit with two tensors as the experimental intensity of the high field break point (see Figure 4) could not be rationalized. By careful rerunning of the CP/MAS spectrum, a small but measurable (4%) aliphatic component centered near 30 ppm was observed and a value of fa = 0.96 obtained. Subtraction of the aliphatic contribution

ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988

n

1577

e

eAL Analysis

Analysis CPNAS

07 I

I

300 200 loo 0 PPm Figure 4. Experimental and simulated spectra of anthracite PSOC-628. The fa value obtained from CP/MAS (lower trace) is 0.96. The static spectrum is fit with two aromatic tensors after subtracting a 4 % contribution of the aliphatic resonance (best fit simulated spectra is overlaid). The analysis of the two-tensor fit shows two different band shapes used for simulation. Ai is the aliphatic resonance and the asterisk, the spinning side band. from the powder pattern permitted an adequate fit of the spectrum (Figure 4). The presence of small amounts of aliphatic structure implies that the line shape must be represented as a sum of three bands. However, no further improvement to the fit is detected beyond the two tensor simulations shown in Figure 4, presumably because of the low concentration of alkylated aromatic carbons. Since the only detectable aliphatic carbons are centered at 30 ppm, it is reasonable to assume that the aliphatic carbons exist either as (CH,), bridges between aromatic clusters or as hydroaromatic structures. In a hydroaromatic structure (e.g. tetralin) four aliphatic carbons are incorporated into a structure with only two alkylated aromatic carbons. In this case, the mole fraction of alkylated carbon would be only 0.02 and is probably beyond the detection limits of this technique. The tensor principal values and the population factors for the PSOC-628 anthracite coal are given in Table 11. The quantitative value for protonated carbons obtained from line-shape analysis is 0.34. The atomic H/C value is 0.42 for this coal and, from a mass balance, one can readily determine that the H/C value of the aliphatic carbons is approximately 2.0. The anthracite coals also provide a useful model for characterizing chars that have been produced by extensive pyrolysis or other relatively high temperature processes (12). Coals undergoing pyrolysis for relatively short periods of time or at moderate tempertures are not expected to be entirely composed of polycondensed aromatic rings and aromaticity values in the range 0.8-1.0 have been reported for chars (34). Thus, the inertinite macerals such as semifusiniteand fusinite found in coals provide P reasonable model for such chars, in which natural processec )f heat and pressure or fungal action have produced charlike material. A good example is the Aldwarke Silkstone inertinite (86% inertinite with an fa value of 0.88) consisting chiefly of charcoallikefusinite. The tensor principal values and the population factors obtained by analysis of VASS spectra (Figure 5) are shown in Table 11. These provide a distribution of the three major types of aromatic carbons present. The experimental value of aromatic H/C = 0.39 for this fusinite has been reported previously by means of dipolar

240

120

0 PPm

Figure 5. VASS spectra of Aidwarke Silkstone inertlnite maceral (fusinite). Simulated static (bottom trace) is shown to portray the population factors. The slmuhted VASS spectra at 43' and 72' are overlaid on the experimental data. AI is the aliphatic resonance and the asterisk is the spinning side band. dephasing data (13) and, hence, this value was used in the fitting process. The fit of the VASS data provided the other two tensors. The mole fraction of condensed carbons (0.54) and substituted carbons (0.07) established the remainder of the aromatic structural types. The substituted aromatic carbon population is of the order of 0.05-0.10 and the total aliphatic carbon population is 0.12. By use of the elemental analysis, i.e., the total H/C ratio (0.48), it is clear that the alkyl substituents, on average, consist of one to two carbon fragmenb per substituted aromatic carbons with a H/C value of approximately 1.2. Aromatic Cluster Size. NMR data can provide significant information on the molecular structures of polycondensed aromatic hydrocarbons (PAH) (35). Ring systems formed by ortho fusion (i.e. rings with only two atoms in common and thus n common faces with 2n common atoms) e.g. naphthalene, anthracene, phenanthrene, tetracene, etc., may be considered to be one-dimensional growth even though ortho-fused compounds such as phenanthrene and chrysene represent chain growth along a nonlinear path. Such chain growth can be represented by a general molecular formula as C4n+2H2n+4 where n is the number of benzenelike rings. It is readily observed that the molar ratio H/C = ( n + 2)/(2n + 1) approaches 0.5 in the limit of very large n. The relationship between the mole fraction, xg,of bridgehead carbons to the total number of carbons, C, in ortho-fused PAHs, is given by

c=-

6

1- 2 X p

In PAH's with ortho- and peri-condensed ring fusion (rings containing two atoms in common with two or more rings of a contiguous series of rings having n common faces and less than 2n common atoms), the two-dimensionalgrowth around a central benzene ring gives rise to a family of compounds like benzene, coronene, circumcoronene (see Figure 4), etc. These can be represented by the general formula C6kzHskwhere k is now the number of circular shells around the benzene core. The molar ratio H/C = 1/k, in the limit approaches zero as k becomes very large (e.g. k = m for graphite). Conversely, the fraction of condensed carbons approaches unity as k grows without bound and is represented by x g = 1 - (6/C)'/'

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ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988

’ h O

Table 111. Calculated ‘*C %-Plane” Shielding Components in Circumcoronenea

Graph“e

carbon C1

c3

Cza

\@ 0.4

ClBb Clsd ClBt

\

4 1

I

I

I

0.1

0.2

0.3

022

210 214 204 198

140 145 185 190 188 188

200 199

“All values are referenced to ppm from TMS. The A and B scaling factors calculated from the experimental values of pyrene were used (see ref 27).

\

i

0.0 i 00

011

\ @\ 0.4

1

0.5

1

GiGi Figure 6. A plot of the mole fraction of condensed carbons, xg, vs l / d C , the total number of carbons, for aromatic ring systems that are formed by two-dimensional ortho- and peri-ring fusion.

Many PAH ring systems represent intermediate cases between linear and two-dimensional cluster growth. A plot of the mole fraction of total carbon that is found at the condensed position, xg, vs l / d C is a linear function for the two-dimensional growth (Figure 6) and a linear function in 1 / C for one-dimensional growth. For extended PAH structures such as found in chars and high rank coals, ortho- and peri-ring fusion is required if the H/C ratio is to reach low values observed in these systems. It is thus possible to estimate the average number of carbon atoms (cluster size) from the mole fraction of condensed carbons obtained from experimental NMR data if it is assumed that the ring fusion proceeds in a two-dimensional growth pattern (Figure 6). With the C6kzH6kmodel it is apparent that a cluster of size k = 10 is needed to provide a molar H/C ratio of 0.10. In the case of PSOC-867, the average cluster size consists of approximately 350 carbons for xo = 0.87. For PSOC-628, a much smaller average cluster size of approximately 45 carbons is obtained from a xg value of 0.62. The data (xg = 0.58) on the fusinite maceral suggests an average cluster size of approximately 30 aromatic carbons. Calculations. The calculation of the two 13C “in-plane” shielding componentsin polycyclic aromatic compounds based on the semiemperical MNDO method (25) have been previously reported (26,27,29). In this paper the previously developed MNDO method is applied to circumcoronene (I) which serves as a useful model for anthracite. The calculated results are give in Table III. Since the size of circumcoronene (CMHI8)is comparable to the estimated size of the PSOC-628 anthracite (number of carbons = 50), this model hydrocarbon can be explored as a representative structure of high rank coals for the sake of evaluating the validity of using various shielding tensors in a quantitative analysis. It is clear from the calculations in this model compound that the shielding tensors divide between two categories, the protonated (C-H) and nonprotonated aromatic carbons, with a dispersion in the tensorial values of less than 10 ppm within each of the individual categories of carbons. The nonprotonated carbons exhibit near axial symmetry. Similar results have been found in several other model aromatic hydrocarbons (26). The calculated “in-plane” shielding tensors in circumcoronene are in good agreement with the experimental parameters found in the anthracites. The calculations support the interpretation of the experimental spectrum of the anthracites as a superposition of two different types of aromatic

shielding patterns. The relatively high line broadening values required to fit the spectrum (see Table 11) are an indication that the experimentalspectrum includes inhomogenous as well as homogeneous line broadening. The inhomogeneous broadening, as is suggested by the calculations, can be attributed to the expected environmental dispersion (approximately 10 ppm) of different shielding components within each category. Sullivan et al. (36)have examined the reasons for high broadening values observed in CP/MAS spectra by means of hole burning and two-dimensional Fourier transform experiments and they concluded that the largest contribution to the line widths in POWHATAN #5 coal is inhomogeneous in nature and is attributable to a distribution of slightly different structure types for otherwise similar chemical moieties. The calculated bond orders (Figure 1)for circumcoronene exhibit a high degree of correlation with the calculated shielding tensors indicating that the inner carbons (ClSb,CIM and C18J are in a highly axially symmetric electronic environment (i.e. the bond orders have very similar values for all the adjacent atoms bonded to the condensed carbons) while the C-H carbons on the ring periphery exhibit much greater variations in the bond orders of the three adjacent bonded carbons.

CONCLUSIONS The nonprotonated to protonated aromatic carbon ratios measured by quantitative shielding tensor analysis on these three coals are found to be in excellent agreement with data from dipolar dephasing measurements and the quantitative elemental analysis data. While the question remains unanswered regarding the fraction of total carbon that is actually observed, these data demonstrate that one observes a quantitative representation of all carbon types present in the sample. The mole fraction of condensed carbons determined by the experiment allows us to estimate the number of fused rings in an average molecule of the anthracite PSOC-867 to be between 140 and 170 and that for the anthracite PSOC-628 to be between 20 and 25. From X-ray scattering studies on several anthracites, Hirsch (37) estimated a cluster size of 30 fused rings with an average diameter of 160 nm for an anthracite with 96% carbon. Murphy et al. (38),using Hirsch’s X-ray data and DD/MAS for a similar anthracite, estimated the number of fused rings to be between 33 and 45. With only a 2% change in carbon content (-95% for PSOC-628 and -97% for PSOC-867) the average size of the cluster shows dramatic changes. Thus average cluster size of the high rank coals can vary widely with only small changes in the carbon content. It is quite clear from the above discussion that determination of the average aromatic cluster size entails a relatively precise estimation of the fraction of condensed aromatic carbons. This is not always possible from dipolar dephasing studies because this technique cannot cleanly separate the contributions from condensed and alkyl substituted aromatic

ANALYTICAL CHEMISTRY, VOL. 80, NO. 15, AUGUST 1, 1988

carbons. This study demonstrates that such discrimination can be achieved by exploiting the differences between the total

shielding band shapes in these two kinds of nonprotonated carbons. The ability to fit the line shapes with precision is vital to the analysis and the VASS technique has proven to be useful in this respect. The availability of multiple angle data decreases the chances of encountering a given spectrum which is insensitive to one or more of the adjustable parameters and thus reduces the chance of ill-conditioned fits of the data. The present results also clearly show that a combination of the analytical tools of solid-state NMR and computational chemistry at the semiempirical MNDO level can be used to gain some quantitative understanding of the structure of coals. The shielding tensor data for protonated aromatic carbons are similar to those in solid benzene (39) and provide a method for measuring peripheral aromatic ring carbons. Discrimination between the 13C shielding tensors of peripheral and inner carbons in large fused aromatic hydrocarbons is clearly achieved because of the marked differences in the two “inplane” shielding components associated with the protonated and the nonprotonated carbons.

ACKNOWLEDGMENT The authors express their gratitude to the San Diego Supercomputer Center for the use of the CRAY X/MP-48.

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RECEIVED for review December 8, 1987. Accepted February 29, 1988. This work was supported by the Office of Basic Energy Sciences, Department of Energy under Grant No. DE-FG02-86ER13510 and the National Science Foundation Advanced Combustion Engineering Research Center (ACERC), Contract No. CDR-8522618.