ANALYTICAL CHEMISTRY, VOL. 51, NO. 8,JULY 1979 (25) E. L. Crow, F. A. Davis, and M. W. Maxfield, "Statistics Manual", Dover Publications, New York, 1960. (26) D. C. Bankston, in preparation. (27) A. N. Zaidel, V. K.Prokoviev, S. M. Raisky, and E. Y. Shreider, "Tablitsi Spektralnikh Linii" (Russian), Fiziko-Matematicheskoi Literaturi, Moscow, 1962. (28) M. S. Cresser, P. N. Keliher, and C. C. Wohlers, Anal. Chem., 45, 111 (1973). (29) P. W. J. M. Bournans, "Spectrochemical Excitation". Plenum Press. New York, 1966. (30) F. J. Flanagan, T. L. Wright, S. R. Taylor, C. S . Annell, R. C. Christian, and J. I . Dinnin, in "Descriptions and Analyses of Eight New U.S.G.S. Rock Standards", F. J. Flanagan, Ed., Geological Survey Professional Paper 840,U. S.Government Printing Office, Washington, D.C., 1976, p 33.
1225
(31) S. S. Shapiro and M. B. Wilk, Biometrika, 52, 591 (1965). (32) A. L. Wilson, Talanta, 17, 31 (1970). (33) F. J. Flanagan, Geochim. Cosrnochim. Acta. 37, 1189 (1973)
RECEI~ZD for review December 22,1978. Accepted March 30, 1979. This research was funded by Grant No. DES 75-22971 from the National Science Foundation. This is Contribution Number 4269 from the Woods Hole Oceanographic Instituion. Presented, in part, at the Fifth Annual Meeting of the Federation of Analytical Chemistry and Spectroscopy Societies on October 30, 1978, in Boston, Mass.
Electron Spin Resonance Study of Coal by Line Width and Line Shape Analysis C. L. Kwan and T. F. Yen* Department of Chemical Engineering, University of Southern California, Los Angeles, California 90007
ESR spectra were obtained for coal samples of various ranks. New parameters for line width which are directly obtainable from first derivative curve of ESR spectrum and invariant with line shape are investigated. Plots of those parameters against carbon content show a positive correlation. The line width phenomena can be explained by the formation of larger polynuclear, condensed aromatic ring systems in high-ranking coals using the theory developed by Weiss and Anderson of exchange narrowing in paramagnetic resonance. The positive correlation of line width and spins-per-gram with ranks is consistent with the hypotheses of Austin and of Ingram. Line shape parameters may be used to characterize coals and their derivatives.
ESR has been proved a valuable tool in the study of the free radicals in coal (1-5). T h e origin of the free radicals in coal and subsequent change in the quantity and nature of the radicals with coal rank is an important part of coal metamorphosis. For ESR experiments, the following information is usually obtained: Ng (spins per gram), g-value, line width. and line shape. Correlations have been made for Hg and g-value with respect to a number of parameters related to coal rank (1-5). However, the utilization of line shape and line width data has been scarce and no definite conclusions have been drawn ( 3 , 4 ) . Retcofsky et al. ( 3 , 4 )obtained a reasonable correlation of ESR line width with hydrogen content of the vitrains. They proposed that the variation of the line width with coal rank is a direct result of spin-spin interactions between the free radicals, electrons, and protons in the coal. This analysis appears not to be very rigorous; exchange effect was not accounted for, and the spinspin interaction between electrons and protons in the coal generally had opposite correlation with hydrogen content. However, in more recent work ( I d ) , they reported that the removal of hydrogen via catalytic dehydrogenation decreased the observed ESR line width. If we consider coal to be modeled by extensive aromatic rings, the larger the number of rings, the larger would be the number of peripheral hydrogen atoms per molecules (cluster),meaning a greater spinspin interaction between electrons and protons, 0003-2700/79/0351-1225$01 .OO/O
even though the hydrogen content is lower. (From benzene to naphthalene, the number of peripheral hydrogen atoms increases from 6 to 10, while hydrogen content drops from 7.7% to 6.25%). Also, the line shape has been ignored when line width information is taken from the spectra. Austin (6) et al. suggested three possibilities as to the genesis of the free radicals in coal and the changes in quantity, as well as the nature of free radicals during subsequent coalification: (1)stable free radicals were formed during diagenesis of the organic sediment and these have persisted; (2) radicals were formed in pyrolytic reactions during metamorphosis as a result of homolytic splitting of certain functional groups; and (3) radicals were produced by radiolysis. The second hypothesis is consistent with the increase of Ng with coal rank and also accounts for the variation of g-values. It is generally believed that unpaired spins produced this way are stabilized in the aromatic skeletons, which were formed by homolytic bond scission, as T electrons, Figure 1 shows an average structure for coal proposed by Wiser ( 7 ) . The extensive aromatic clusters are separated from each other by u bonds. Free electrons are stabilized by delocalization in the aromatic clusters. Since these aromatic clusters are close to each other, free-electron transfer from one aromatic site to another is possible and would result in exchange effects. It is known that when the exchange frequency is small, compared with the hyperfine splitting constants of the protons, the envelope formed by unresolved hyperfine lines adopts a Gaussian line shape. On the other hand, if the exchange frequency is much larger than the hyperfine splitting constants and exchange narrowing occurs, the line shape is Lorentzian (8). By studying the line shape, it is possible to obtain information about the exchange effect, and, thus, the size and compactness of the aromatic clusters.
EXPERIMENTAL Coal samples were obtained from the sample collection of Pennsylvania State University (9)and ground to sizes smaller than 100 mesh. Their properties are listed in Table I. ESR spectra were recorded on a Varian E-12 X-band spectrometer equipped with V-4532 dual sample cavity operated in the TE-104 mode with a resonance frequency near 9.5 GHz and a modulation frequency of 100 KHz. About 20 mg of the sample was put into standard '/8-in. i.d. quartz sample tubes. The small amount of sample was C 1979 American Chemical Society
1226
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979 n I
0
Figure 1. An average structure of coal _-
Table I. Chemical Analysis for Coal Samples” rank
PSO=
C%
H%
0%
N%
S%
An Semi-An LVB MVB HVB HVB HVB HVB HVB SB SB SB SBC lignite lignite
081 084 129 133 002
92.77 92.90 90.75 91.31 85.61 84.97 82.10 81.97 76.30 77.64 75.62 16.63 73.62 72.36 70.96
2.66 3.93 5.06 4.41 5.62 5.63 5.79 5.07 5.98 5.42 5.18 5.07 5.81 4.94 5.21
3.78 1.76 3.17 3.20 7.32 7.90 10.63 11.59 16.37 16.87 17.46 16.57 19.11 21.87 23.24
0.79 1.40 1.02 1.07 1.46 1.51 1.48 1.37 1.35 0.08 1.74 1.73 1.45 0.84 0.58
0.54 1.62 0.78 0.62 0.63 0.45
011
068 107 152 156 248 231 415 090
092
0.90
0.53 0.72 1.44 0.66 0.41 0.89 0.50 1.02
a An = anthracite, LVB = low volatile bituminous. MVB = medium volatile bituminous. HVB = high volatile bituminous. SB = sub-bituminous. SBC = sub-bituminous C.
deliberately chosen to ensure that sample size would not interfere with the accuracy of the intensity measurement. The g-factor measurements were made relative to standard 0.1% DPPH diluted with KBr in the second channel of the dual cavity. For the intensity measurement, another DPPH sample diluted to intensity comparable to the sample intensity and having the same geometric factor was used in the first channel of the cavity. The purpose of the first DPPH samples (in the second channel) was to make certain that differences in microwave power, crystal biasing current and Q-factors were compensated. The use of the second DPPH sample was to make certain that geometric factors, such as sample size, would not affect the accuracy of the intensity measurement. For DPPH samples, double integration by the Gaussian quadrature method was used to calculate total spin intensity. For coal samples, a modified formula described in the following section was used.
RESULTS AND DISCUSSION A typical ESR spectrum of coal sample is a single symmetric curve without hyperfine structures. Generally, line shapes
are classified either a5 Lorentzian or Gaussian. They are distinguishable by the ratio of half-width of the absorption curve to the peak-to-peak distance of derivative curve (H,,). The use of the ratio is most unfortunate, since an integration of the experimentally obtained, first derivative curve is always necessary. This is tedious and difficult. In order to get a reasonably accurate (5 % error) integration of Lorentzian line, the curve cannot be truncated a t less than 20 H,, (IO). It is more convenient to use parameters obtained directly from the first derivative curve. Hpphas been used to calculate directly the spin intensity, as well as a representative of line width. However, it is not invariant with line shape, e.g. in terms of l / T 2(where T 2is the effective spin-spin relaxation time), H,, for Gaussian line shape is 70% higher than that of Lorentzian line shape. Therefore, using line width without referring t o line shape can be very misleading. The use of a simplified formula for spin-intensity, S = Zpp-Hp~, gives as much as 250% error if line shape is ignored. So, it is desirable t o use some line width parameters that are independect of line shape, as well as parameters directly obtainable from the experimental curve. For this purpose, the parameters H, and R, are investigated. H, is the width a t the position ( l / n )of the peak-to-peak height of the first derivative curve, and R, is the ratio of H , to Hpp. Figure 2 shows the definition of these parameters. T h e conventional, as well as the new, parameters for Gaussian and Lorentzian line shapes are listed in Table 11. T h e last column shows the ratio of the parameters for these two line shapes. When the ratio is equal to 1, the parameter is invariant with line shape. We can see that H5,HI,, and Slo can be classified in this category. ESR parameters for samples of different ranks of coal are listed in Table 111. Figure 3 shows the plot of Ng vs. C % . Ng was calculated using the modified formula S = 0.285 I,,.Hlo2. This formula is exact if the line shape is either Gaussian or Lorentzian. T o check the validity of this formula, an ESR spectrum of one coal sample was digitized and doubly integrated using the Gaussian quadrature method, and excellent agreement was obtained. For the coal samples studied, a plot of H,, vs. C% (Figure 4) gives no correlation. However,
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
1227
7-
?
Y 24;
c
231
5-
92 psc ,a,
c
*-----
zoo2
8c
'0
90
82
m
s,
"~ D
,
Figure 4. Variation of ESR peak to peak line width of first derivative curve with carbon content
Figure 2. Definition of H,'s and R,'s. Spectra shown is the first derivative curve
1 i
1
/
i
6J 7C
~
ec *A
90 %
'M5.
C
Figure 5. Plot of H, as a function of carbon content. Straight line is the least square fit
I
70
80
c Y.
100
Figure 3. Variation of spin concentration with carbon content. Straight line is the least square fit the plot of H 5 (Figure 5) and Hlo(Figure 6) vs. C % shows a positive linear correlation. In the case of the H5, the correlation coefficient appears good (0.84), with only three points discarded ($81'~ unusual line shape may be due to the conducive eiectrons for anthracite). The fact that H , and H I , give a linear correlation, whereas H,, does not, can be explained by the near invariance of H5 and Hl0 with respect to line shape
(Gaussian and Lorentzian). Although the ESR line shape of coal samples is intermediate between Gaussian and Lorentzian, it is assumed that H5 and Hlocan still be used as a representation of 1/T2. The narrow line width (4-8 gauss) of ESR signals in coal samples suggests that exchange narrowing in paramagnetic resonance, Anderson and Weiss (8) pointed out that when exchange frequency (We)is larger than the amplitude in frequency of the perturbation ( Wp),which is represented by the spectrum content (SC) of the radical, the lineshape is Lorentzian with linewidth ( l / T 2 )equal to Wpz/We. Spins in higher-ranking coals are generally believed to be more delocalized than in lower-ranking coals; therefore, exchange is faster in higher-ranking coals. In order to obtain the positive correlation indicated in Figures 5 and 6, it is necessary that W , and We be comparable. They tend to compensate for each other. Consequently, the line width would be proportional to W,, ergo, proportional to carbon content. As the size of the paramagnetic aromatic centers increases, the spectrum content, defined as the span of the stick diagram, also increases because of the larger number of peripheral hydrogen atoms. McConnell (11) suggested the
1228
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
Table 11. Parameters of Gaussian and Lorentzian Lineshape absorption curve max height half-height line widtha integrated intensity derivative curve
Lorentzian L(H) = ( T , / r )x (1 + T z 2 H 2 ) - ’
1
G ’ ( H ) =-(T,HI&) exp(- I I , T2’ H 2 ) 0.484T2‘ 2 1.60 2.33 2.71 0.8 1.17 1.36
I,, HQP H,O
HSa H,oa
R, R5 R,, S, = HPP2.1PP SI, = H,,?.I,, a
Gaussian G(H) = ( T 2 / & ) x e~p(-T,~H~/2) T, l d - 5 2.36
R = G/L
T iIn
1.25
2
1.18
1
1
L ’ ( H )= - ( 2 ~ , 3 ~ /x ~ (1 + T,?H,2)-2 0.414T2
X
)
1.32 1.09 0.95 0.76 0.63 0.54 3.51 1.03
2.13 2.86 1.05 1.85 2.50
1.94
0.55
3.55
3.46
1.17
1.73
21J3 1.21
In unit of ( l / T 2 ) .
20
152 123
I
141
p0m
i
5i,;.../IZi
p a
0 8 t 06
“I”
70
,/
V’” 93%
lW%
C
H,, a s
90
80
c
DO90
Figure 6. Plot of
-
04
$02
80%
a function of carbon content
following relationship for hyperfine splitting constants of hydrogen atoms for aromatic systems:
Ai
G2
A
, , , , ’ 2 ~ ~ ,
70
_--__-_____-
= QlPiI
where A i= hyperfine splitting constant of atom i, pi = unpaired spin density a t atom i, Q is a McConnell constant. Because of the possibility of negative spin density and larger Q for larger rings, spectrum content increases with ring size (e.g., the McConnell constant for pyrene anion is -35 gauss, while Q for benzene and naphthalene anion is -23 and -25 gauss, respectively). Thus, positive correlation of line width can be explained by the size increases of the paramagnetic aromatic center as the coal becomes more mature (highranking coal). Ingram (12) proposed the following mechanism for the origin and the nature of the paramagnetic species for low temperature carbonaceous materials. During carbonization, hydrogen or edge-groups are removed by homolytic
I00
%
Figure 7. ESR line shape parameters as a function of carbon content. (A) Values for R,; (B) values for R,. Symbols are defined as in Table
I1
bond scission and the unpaired spins are stabilized in the aromatic skeletons as K electrons. As coalification progresses, large polynuclear aromatic ring systems are formed. The positive correlation of linewidth and spins per gram with coal ranks is consistent with the above hypothesis. The plots of RZ,R5 vs. C% are presented in Figure 7 . The line shapes of coal samples are closer to Lorentzian than Gaussian. This is consistent with the narrow line widths which come from exchange narrowing. Without exchange narrowing, the peak-to-peak line width of the envelope formed by unresolved hyperfine lines of naphthalene anion is around 9 gauss. With exchange narrowing, it is around 3 gauss (13). A larger aromatic anion should have a larger envelope than the naphthalene anion. If the free radical in coal is due to the paramagnetic aromatic center, it is difficult to understand the narrow line width (5 gauss) without the effect of exchange narrowing. Figure 8 shows the plot of R2 vs. Rs. Region I is for lowranking coals. Our limited data suggest t h a t line shape parameters can be used to characterize coals. I t is found that
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
1229
Table 111. ESR Parameter for Coal Samples PSO-
Ng
81
84 129 133 022 011
068 107 152 156 248 231 415 090 092 a
X J.0-lh
26.2 26.2 23.94 16.0 19.3 14.0 11.5 13.5 8.5 6.5 4.7 8.6 5.3 4.5 2.8
(G - 2) X 104 30 28.5 29 29 30 30.5 32 31 32 32 34.5 33 35 33.5 32
HPPa 7.1 5.7 6.3 5.9 4.8 5.2 5.4 4.7 5.8 5.3 5.7 5.6 6.9 4.9 4.9
HZa 8.7 6.0 6.5 6.2 5.6 6.1 6.1 5.8 6.3 5.5 5.8 5.9 8.0 5.0 5.0
HSa 15.9 10.1
10.5 9.8 9.0 9.6 9.3 9.2 10.3 8.7 9.2 9.63 13.1 8.0 8.0
H, o a 22.0 12.8 13.2 12.4 11.2 11.7 11.9 11.3 14.5 10.6 11.3 14.4 17.1 10.1 10.6
R2
R
