1726
Anal. Chem. 1987, 59, 1726-1731
Temperature Dependence of the Electron Spin Resonance Spectra of a Coal-Derived Vacuum Distillation Residue and Components Salvatore M. Castellano,’ William P. Chisholm? Richard F. Sprecher,* and Herbert L. Retcofsky Division of Coal Science, Pittsburgh Energy Technology Center, Pittsburgh, Pennsylvania 15236
-
Measurements of the lntensltles of the electron spln reso2 reglon of the specnance (ESR) absorptions, In the g trum, of the title materials were performed over a wMe range of temperatures. Linear correlatlons of the measured lntensitles vs. the reclprocal of the absolute temperature were obtained. The regresslon lines have Intercepts which are larger than the standard devlatlons of the measurements. This study shows that the Intercepts arise from systematic errors In the measurements that Introduce curvature Into the plots. Two converglng llnes of research were followed: (a) a theoretical study of the effect of systematlc errors on the outcome of ESR intensity measurements; and (b) repeated sets of measurements on two major fractions of the title materials. A complete analysis of all data shows condusively that the materials of both fractions obey the Curie law exactly and that any observed devlatlon from thls behavior lles within the range of systematic errors predicted by the theoretical study.
the great majority of experimental data pass the first test but fail the second, Retcofsky et al. (2) referred to them as data exhibiting “Curie law-type behavior”. A mistaken interpretation of the significance of the intercepts can lead to erroneous conclusions ( 4 ) . The hypothesis that the paramagnetic centers of coal and coal-derived products may be located in electron donor-acceptor complexes was put forward in an early paper of Elofson and Schultz ( 5 ) . The same hypothesis was later reproposed by Schwanger and Yen (6). In both cases, experimental evidence in support of the proposed hypothesis was insufficient. The idea that such charge-transfer complexes may make a major contribution to the ESR signal of coal products can be dismissed a t once, since in that case the temperature dependence of the absorption intensities should show a trend considerably different from that observed experimentally (7). The case in which only minor contributions are expected must be dealt with in more detail. Experimental data may be fit to a regression line of the form
Y=A+BX Interest in the nature of the paramagnetic centers that give rise to electron spin resonance (ESR) absorptions near g = 2 in coal and coal-derived products continues to be strong. Because of the location of the ESR signal, it is generally thought that the unpaired spins reside on organic moieties whose precise structures are still completely unknown. Although this hypothesis remains the most plausible, one cannot exclude that some contribution to the total intensity of the rather broad and unstructured signal observed in this region of the spectrum may also arise from inorganic paramagnetic species. In their work in this area, Retcofsky et al. (1,Z) showed that there is an inverse relationship between the intensity of the ESR signal and the temperature. From this they inferred that the system of spins responsible for the ESR absorption was in a doublet ground state. This inference led to the conclusion that organic free radicals were the main source of the observed ESR absorption. Recent electron spin echo measurements provide supporting evidence that the coal radical spin multiplicity is doublet, S = 1 / 2 ( 3 ) . Retcofsky et al. (1, 2) found excellent linear correlations between the intensities of the ESR signals and the reciprocal of the absolute temperature. This is the prerequisite condition for the validity of the Curie law. The same law requires that the correlation lines pass through the origin. This is a much more stringent requirement because, in effect, one needs to extrapolate the experimental data from a finite range of temperature to T = m (or alternatively to 1 / T = 0). Since
Present address: Instituto di Chimica Fisica, Universits di Parma, Via Massimo D’Azerrlio 85, 53100 Parma. Italv. 2Present address: US DOE-METC 503, Collins Ferry Rd., Morgantown, WV 26507-0880.
(1)
where
Y=I X = 1/ T
...relative ESR intensity
(2)
...reciprocal absolute temperature A and B
...constants
If a good fit can be found, then the data satisfy the inverse linear relationship between I and T demanded by the Curie law I = C/T (3) At low enough temperature ( h w >> hT), this approximation is expected to break down. However, the lowest temperature used in this study is still far above that necessary to satisfy the requirement that tzw be much less than hT (8). In practice, all regression lines will have intercepts ( A ) at t,he origin. In some cases, the values of A will lie outside the range of stochastic errors. Attempts to interpret the values of those intercepts in physical terms are speculative and dangerous. A more reasonable approach is to try to find an explanation in terms of systematic errors that may affect the measurements. A large number of possible sources of systematic errors can be readily listed. This treatment assumes that only three types of systematic errors occur during the measurements. Clearly several sources may contribute to the same type of error.
EXPERIMENTAL SECTION A Varian Associates Model E112 spectrometer equipped with a field frequency lock, a Model E102 microwave bridge, and a Model E232 dual sample cavity was used in this study. The magnetic field strength and the field scan were calibrated with peroxylaminedisulfonate (PADS) in aqueous sodium carbonate solution before every run. A g value of 2.005 50 for the PADS
0003-2700/87/0359-1726$01.50/0 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 13, JULY 1, 1987
1727
Table I. Temperature Dependence of the ESR Signal Intensity for the Distillation Residue and Four Components T/K 325.5 300.2 275.2 248.7 225.2 202.2 179.7 164.7
run 1
run 2
3.075 3.332 3.634 4.022 4.441 4.947 5.566 6.073
1387 (18) 1508 (20) 1660 (26) 1857 (14) 2091 (31) 2431 (28) 2710 (29)
4422 (33) 4817 (56) 5198 (79) 5561 (31) 6131 (49) 6844 (34) 7689 (95)
92 (6) 37 (4) 26(4) 27 (4) 34 (4) 33(6)
-260.3 483.1 0.9960
583.8 1142.4 0.9918
42
A/1015 B/1018 K r2 a
5.
ESR intensit~J10'~" run 3 run 4
( 1 / ~ ) / 1 0 - 3K-1
3114 (48) 3380 (34) 3762 (25) 4268 (34) 4775 (50) 5411 (63) 6212 (64)
run 5 923 (14) 1009 (23) 1117 (16) 1231 (14) 1373 (19) 1540 (19) 1770 (32)
average 1683 1869 2084 2310 2601 2969
b -767.3 1250.8 0.9997
-114.0 336.4 0.9992
-208.4 571.2 C
Parentheses indicate standard deviation of a group of five consecutive measurements. Calculated as weight-average of Runs 2, 3,4, and Calculated as weight-average of the Darameters of Runs 2, 3, 4, and 5.
Table 11. Temperature Dependence of the ESR Signal Intensity for the Acid Fraction, the Base Fraction, and Mixtures of the Two Fractions ( 1 / ~ ) / 1 0 - 3K-'
run 6
run 7
3.218 3.542 3.943 4.435 5.072 5.558 5.935 6.697 7.301
4297 (34) 4771 (82) 5270 (87) 5902 (54) 6623 (86) 7300 (67) 7711 (82) 8479 (97) 9331 (109)
1244 (16) 1346 (20) 1501 (25) 1674 (26) 1893 (15) 2176 (40) 2424 (55) 2704 (61)
d
15324 (304)
4507 (57)
~/1015
476.6 1211.6 0.9988
114.0 350.0 0.9985
T/K 310.7 282.4 253.6 225.5 197.2 179.9 168.5 149.3 137.0
B/10'* K r2
ESR inten~ity/lO'~" run 8
run 9
averageb
2362 (26) 2601 (55) 2924 (27) 3359 (67) 3720 (59) 4025 (81) 4341 (54) 4797 (48) 5188 (48)
1068 (23) 1112 (12) 1202 (11) 1326 (14) 1495 (23) 1634 (14) 1738 (20) 1947 (18) 2108 (31)
2632.9 2904.6 3216.0 3597.9 4045.1
200.4 689.5 0.9973
188.0 261.2 0.9974
4694.8 5179.0 5718.0
279.3c 742.OC
Parentheses indicate standard deviation of group of five consecutive measurements. Calculated as weight-average of runs 6 and 7. Calculated as weight-average of the parameters of runs 6 and 7. Probe with liquid N, Dewar. Data are not included in the correlations. was assumed for the field calibration, and the hyperfine splitting was taken to be 1.3 mT for the scan calibration. The microwave frequency was measured with an EiP Model 350D high-frequency counter. The signal from a sample of diphenylpicrylhydrazyl (DPPH) was used as an intensity reference and to check the field stability during experiments. No significant drift of the field was noted during any of the measurements. Before every series of measurements, the integrated intensity of the reference signal was calibrated against the integrated intensity of the signal from a standard sample of DPPH in silica, which contained 6.31 X lo4 mol of DPPH/g of silica. The reference sample was shielded by a Dewar insert and maintained at 20 "C by a steady flow of nitrogen gas. Microwave power incident on the sample was never greater than 0.5 mW. All samples were contained in 4 mm diameter quartz tubes and were evacuated and sealed. The ESR spectra were measured and the data were reduced with a Nicolet Model 1180 data system and programs developed in this laboratory. Intensities are reported for 1 g of sample relative to a hypothetical standard that would contain one unpaired electron per gram of standard and would be maintained at 20 OC. Altogether 11 sets of ESR measurements (runs 1 through 11) were made in the course of this study. They are reported in Tables I, 11, and 111. The sample was produced from an Illinois No. 6 coal at the Catlettsburg, KY, H-coal Pilot Plant while operating in the synfuel mode (9). A blend of "light" and "heavy" oil products (1:1.5)was distilled by Chevron into narrow-boiling range samples. The start-400 "F distillate and the 850 O F + vacuum still bottoms were also obtained. The bottoms fraction was separated into an acid fraction (29.2% yield), a base fraction (30.6% yield), an aromatic fraction (32.3% yield), and an insoluble fraction (7.9% yield) by a published
procedure (IO). All ESR samples were prepared from stock materials generated by one separation. Runs 1 and 5 were made with ESR samples left over from a previous exploratory study. Unfortunately, an attempt to extend the upper end of the range of temperatures under study caused the melting of the materials in the ESR tubes, thus preventing their use for further intensity measurements. When an analysis of the early results suggested the need for new measurements (runs 6 through 11)to further probe some interpretative hypothesis, new samples had to be prepared from the original stock materials. Since the available amounts of the latter were rather limited, the material of several samples had to be used, after a given run was over, for the preparation of other samples. The following list establishes the relationship between the entries of Tables I, 11, and 111, and the materials to which they refer: run 1, H-coal bottoms (first sample from stock); run 2, insolubles (first sample from stock); run 3, aromatics (first sample from stock);run 4, bases (first sample from stock); run 5, acids (first sample from stock); run 6, bases (second sample from stock); run 7, acids (second sample from stock); run 8, mechanical mixture of bases (45.9%) and acids (54.1%)(prepared from samples 6 and 7); run 9, reprecipitated mixtures of bases (45.9%) and acids (54.1%) (prepared from sample 8); run 10, bases (third sample from stock); run 11, reprecipitated bases (prepared from sample 10). The mechanical mixture of the bases and acids fractions was prepared by mixing the two fractions in a mortar and using the pestle to establish intimate contact between the two materials. For the reprecipitated samples, CHzClzsolutions were allowed to stand under nitrogen atmosphere for several hours. Afterward, the evaporation of the solvent, and the drying of the materials were carried out in a vacuum line. All operations were executed with weight losses amounting to only a few percent of the ma-
1728
ANALYTICAL CHEMISTRY, VOL. 59, NO. 13, JULY 1, 1987
where T* is the true temperature of the sample and I* is the ESR intensity demanded by the Curie law. We define now
Table 111. Effect of Reprecipitation of the Base Fraction on the Temperature Dependence of the ESR Signal Intensity -
T/K 310.7 282.4 253.6 225.5 197.2 179.9 168.5 149.3 137.0 A/lO'j B/1018 K r2
AT=T-T*
(5)
6 1 = I, - I*
(6)
ESR intensity/lO'j
(i/n/io-3 K-L
run 10
run 11
3.218 3.542 3.943 4.435 5.072 5.558 5.935 6.697 7.301
4412 (73) 4859 (51) 5451 (92) 6129 (88) 7071 (116) 7743 (138) 8321 (120) 9391 (99) 10019 (120)
2068 (43) 2205 (41) 2446 (12) 2759 (35) 3112 (32) 3373 (46) 3663 (66) 4085 (62) 4488 (69)
-71.8 1401.3 0.9989
111.5 595.0 0.9989
In eq 5 , T is the temperature a t which one assumes the experiment is being performed; Io is the ESR intensity that is expected from measurements affected solely by the errors AT and AC. By differentiation of eq 4, one obtains
61* = I * ( - FA T
?)
+ hC
(7)
Combining eq 6 and 7 yields
In=I*+61=-
" ( I - -; +: "'")
T*
Equation 8 is not convenient for current use, since in general terials. The lower scale of the temperature control unit was calibrated twice. The first time, a digital thermometer was used. The second calibration was made later on, between runs 5 and 6, when the control unit malfunctioned and had to be repaired. After repairs, both a digital thermometer and a thermocouple (copperconstantan) were used. A comparison of the earlier and later calibrations indicated that changes had occurred during repair. The older calibration was therefore used only for the readings of' runs 1 through 5. The comparison between the calibrations made with the digital thermometer and the thermocouple showed only minor differences. Since it was thought that the calibration obtained by the use of the thermocouple and a Fluke Model 893A differential voltmeter was the more reliable, the latter calibration was used for all other runs. Tabulating of the Data, Correlations, and Errors. Each entry of Table I represents the average of at least five consecutive measurements. Seven to ten measurements were used for the entries of Tables I1 and 111. The numbers in parentheses give the corresponding standard deviations. Considering that each computer output (measurement) represents, by itself, the average result over three scans of the resonance signal, it is safe to assume that the average value of the observed relative standard deviations (ua$~= 2-3%) gives a good measure of the stability of the instrument and of the reproducibility of the results, for given instrumental calibrations and settings. According to this criterion, the data of run 3 are the least precise. This and the fact that the recorded values are at the threshold of the sensitivity of the instrument make that set of data less reliable. The data of all other runs were fitted with regression lines of the form of eq 1. The coefficients A and B are given at the bottom of each column in Tables I, 11, and 111, as is the coefficient of determination (r2).
RESULTS The systematic error AT surely occurs in the measurements of the temperature. Its sources may be the erroneous Calibration of the dial of the temperature control unit, the shifts in the scale of the same unit, the failure to reach thermal equilibrium a t the sample, and the changes in the calibration of the temperature scale caused by variations in the gas flow and microwave power. For computing the ESR intensity, the computer utilizes experimental information provided by the operator of the spectrometer, including the weight and the length of the sample, and some instrumental parameters. If any piece of information is incorrect, the constant C appearing in the Curie law will be affected by a systematic error, AC. The effect of AT and AC on the measurement of I can be obtained immediately from the Curie law, assuming T and C to be independent variables. It is convenient to rewrite eq 3 in a new notation
I* = C / T *
(4)
'Pis unknown. However, by the use of eq 5, followed by series expansion, one obtains
I,'T
[
...I+
1- ( 3 - 2 ( 3 - 3 ( $ ) -
c T [ 1 + (F) + (Fy+ (Ty + (Fy+ ...I
Keeping only terms up to the second order in the errors yields
The interesting feature of eq 10 is the presence of quadratic terms. The magnitudes of these terms are relatively small and so is the local curvature that they introduce in the plots of Z, vs. I / T . The local curvature is surely smoothed out by the stochastic errors that are always present in the measurements, and it generally goes undetected. This is evidenced by the excellence of the linear correlations that one obtains. The integral effect of the curvature, however, remains and manifests itself in correlation lines that do not pass through the origin. A third independent systematic error A I may also affect the measurement of the intensities. Its origin lies both in the heterogeneous nature of the samples studied and in the numerical algorithms and computational procedures needed to integrate the raw signal (derivative of the absorption peak) obtained from the spectrometer. Adding AI to I , in eq 10, we obtain
and remembering X = 1 / T
I = AI
+ ( C + AC)X + A C A T X 2
-
C(ATI2X3 (12)
This equation seems to be a formal extension of eq 1, suited for the polynomial fitting of the experimental data. This, however, is not the case. First, AI and A T are assumed to be functions of the temperature, and therefore of X,and cannot be treated as constants. Second, there is no need for new correlative expressions to fit the data; eq 1 does that exceedingly well. The reason for developing eq 12 is to find the physical meaning of the parameters A and B obtained from the experimental data through the use of eq 1. To achieve this goal, we first need to find the derivative of Z with respect to X . We introduce the simplified notation
dAT - AT d' - - AI and -
dT
dT
ANALYTICAL CHEMISTRY, VOL. 59, NO. 13, JULY 1, 1987
After tedious algebraic manipulations, we obtain
d. CATATX2 = 8.8 x 1015
_ a - [C + AC(1-
e. C(AT)'X3 = 4.4 x 1015
AT)]
AI + 2AT(AC + C A T ) X --
1729
X2
dX
3C(AT)'X2 (14) Assume now that a set of measurements are carried out at different temperatures (constituting a run) using the same sample, the same equipment, and of course the same initial instrumental calibration and computer input information. The relationship between the measured intensities (I)and the reciprocal absolute temperature ( X ) will be that given by eq 12. However, with the measurements of our run, we will cover only a limited portion of the curve described by eq 12. If T, and T, are called the highest and the lowest temperatures of the experiments, all experimental points will cover the interval X,, X 2 , (X,< X,). The middle point of this
and the corresponding intensity from eq 12 is
I = AI
+ (C + AC)X + ACATX' - C(AT)2X3 (16)
In eq 16, and in successive formulas, a boldface variable indicates a value calculated at X. If the least-squares algorithm is now used to fit the data with eq 1,the slope of the correlation line will be equal to the slope of the tangent line of eq 12 at X
B = (dI/dX) v [C + AC(1- AT)] - AI/Xz
+
2AT(AC + CAT)X - 3C(AT),X2 (17)
Since the correlation line with slope B passes through the point (X, I), or nearby, its intercept A at the origin will be
+
A = I - BX = AI AI/X + ACATXAT(AC + 2CAT)X2 + 2C(AT),X3 (18) Equations 17 and 18 give the sought-for relationships between the constants of eq 1 and the error parameters and their gradients. Error Estimates. It is worthwhile to analyze these equations and eq 12 and 16 with the aid of some rough estimates of the various terms. Of course, no estimates of AI and AI can be given, since the values of these terms may include contributions from materials that do not follow the Curie law. Computational errors, which are impossible to predict, also contribute to these terms. For these experiments, a reasonable choice of representative parameters for the calculation of all other terms appearing in eq 16, 17, and 18 is
x = 5 x 10-3 K-1 C = 1.4 AC = 2.0
X
(19)
f. ACAT = 1.0 x 1019 K g. CATATX = 1.8 X l0l8 K
i. C(AT)2X2= 9.0
X 1017 K
-2O.c
AC
> 0:
-f-
Ac = 0: AC
AT=5K AT = 5 x lo-' The first three values were chosen on the basis of a comparison between run 10 and runs 4 and 6; the last two values were chosen on the basis of an educated guess. Through eq 19, we obtain 10l8
b.
ACATX = 5.0
X
10l6
c.
ACATX2 = 2.5
X
10l6
- 20.e = -29
(21)
X 1015
is of the same order of magnitude as gaV.It follows that the curvature of the plots is contained in the noise background owing to random errors. Other larger contributions to the errors of intensity measurements arise from the AI term. However, barring unexpected large variations of AI with X, the contributions of the latter terms are, at most, linear in X , so that the use of eq 1 for correlative purposes remains fully justified. Examination of eq 14, 15, and 17 shows that the sources of error in the determination of B are AC, 20.f, 20.g, 20.h, and 20.i. Again, and by far, the largest contribution is that of AC. Taking into account the numerical coefficients accompanying each of the other terms in the above equations, one notices that the contributions of 20.f and 20.h and those of 20.g and 20.i are roughly equal in magnitude. The total contribution of the four terms will depend on the actual signs of AC, AT, and AT. Nothing can be said about the sign of AC; however, for experiments carried out below room temperature, it is most likely that AT is negative and AT is positive. Heat leakage and microwave heating of the sample tend to bring the sample to a temperature higher than that indicated by the control unit dial (AT C 0). The magnitude of this effect should grow larger at lower experimental temperatures (AT > 0). With this assumption, the total contribution of 20.f, 20.g, 20.h, and 20.i to the error in B becomes
X 1020 K
X
X 10ls K
Considering first eq 16, the proper corrective terms are 20.a, 20.c, and 20.e. By far the largest error in the intensity measurements is provided by 20.a; its contribution may have either sign. This term, however, does not introduce "apparent" deviation from the Curie law, since the proportionality between Z and 1 / T remains unaltered. The higher order terms 20.c and 20.e introduce curvature in the plots of I versus 1/ T. The contribution of 20.e is always negative. The contribution of 20.c may have either sign, depending on the relative signs of AC and AT. However, even in the case in which the two terms are additive, their total effect
1021K
a. ACX = 1.0
h. ACATX = 5.0
2g - 2h - 3i = 2.6 -2g - 3i = -6.3
X
X 1019 K
(22)
10l8 K
< 0: f - 2g + 2h - 3i = 1.5 X
1019 K
Note that always when AC # 0, the quadratic terms tend to reduce the error produced by the linear term. The correlation parameter E is not affected by AI directly, but only by its gradient AI, which in general cannot have large values. All the above considerations lead to the conclusion that the errors incurred in the experimental determination of C are, in general, smaller than those affecting the measurements of the intensities. Proceeding with the analysis of eq 18 while keeping the same assumptions about the signs of AT and AT in the above paragraph, one finds that the total contribution of the terms 20.b, 20.c, 20.d, and 20.e amounts to
1730
ANALYTICAL CHEMISTRY, VOL. 59, NO. 13, JULY 1, 1987
Table IV. Comparison of Replicate Determinations of Slopes and Intercepts for Acid and Base Fractions B/
K
run
~11015
5 7
-114.0 114.0
336.4 350.0
av
0.0
343.2
4 6 10
-767.3 476.6 -71.8
1250.8 1211.6 1401.3
av
-120.8
1287.9
+ c - 2 d + 2e = 6.6 X 10l6 AC = 0: -201 + 2e = -8.8 X 1015 AC < 0: -b - c - 2 d + 2e = -8.4 X 10l6 AC > 0: b
(23)
First notice that even in the unlikely instance that AI = AI = 0, an intercept will always occur at the origin, even when AC = 0. This is due to the higher order terms in eq 13, which introduce a curvature in the I vs. 1 / T plots. Even though locally undetectable, it is nevertheless the effect of this curvature that bars the correlation lines from passing through the origin. The signs of the intercepts (eq 3 ) are those expected on the basis of physical intuition. Next, observe that by far the largest contribution to A comes from the first-order term AI. All things considered, one soon realizes that the A coefficient plays the role of a sink for the cumulative effects of all systematic errors in the measurements. Although it is true that evidence for the possible presence of paramagnetic species that do not obey the Curie law may be hidden within the data, it is unreasonable to attempt the extraction of this kind of information from the value of A without independent experimental evidence.
DISCUSSION The general conclusions drawn from the above theoretical error analyses are confirmed by the data reported in Tables I, 11, and 111. Of course, one should not expect numerical agreement between the estimates in eq 21, 22, and 23 and those calculated from the experimental data, but simply the verification of predicted trends. Runs 5 and 7 and runs 4, 6, and 10 provide the results of the sets of replicate independent measurements on different samples of the same materials: the acids fraction in the case of the first set; the bases fraction in the case of the second set. To our knowledge, no such comparison of experimental data has ever been presented in reported ESR studies of coal and/or of coal-derived materials. Notice, in Table IV, runs 5 and 7 , that the value of A is negative in one case and positive in the other. This indicates very clearly that the AI term entering eq 18, whatever its actual values for the two runs may be, cannot contain contributions that are due to the presence of spurious paramagnetic species. Actually one can see that the values of AT must be small in either case. If, in fact, the true value of C is about the same as the average value of B , then AC must be negative for run 5 and positive for run 7 . Since the signs for A for the two cases agree with those predicted by eq 23 for the contributions of the second-order terms to eq 19, it follows that AI contributions cannot be much larger than the latter. We see that for runs 4, 6, and 10 (Table IV), the signs of A alternate, thus proving beyond reasonable doubt that no spurious paramagnetic substances are present in the base
fractions. The large values of A obtained for two of the runs in this set of measurements indicate that the AI contributions in these cases must be rather large. This is a t odds with the findings from the previous set. However, if one considers that the ESR intensities of the base fraction are 3 to 4 times larger than those of the acid fractions, it should not be surprising to discover that the additive contributions of integration and/or of computational systematic errors of the two sets are also of the same relative size. The average values of B in Table IV represent the best experimental estimates of the Curie constant C for the acid and base fractions. An independent check of these values can be made through the intensity measurements reported in Table 11, runs 6 and 7, which were obtained by using a special probe whereby the samples could be kept in a Dewar jacket filled with liquid nitrogen. The results of these measurements were never used in the correlations of other data. From eq 1 and the average E values in Table IV, the temperatures of the samples corresponding to the above intensities are 76.3 K for acids and 84.4 K for the bases. Because the boiling point of liquid nitrogen is 77.4 K, the results for the bases are more in line with expectation. In any case, this independent test of the results confirms that the materials of both fractions obey the Curie law as closely as it is possible to verify experimentally. The values of C given in Table IV are believed to be within f7% of the true values, The mechanical mixtures and reprecipitated samples were prepared in an attempt to unravel the sources of the ESR signal in a coal-derived fuel. As can be seen by comparison of run 9 with run 8 and the weight average of runs 6 and 7 (see Table 11),mechanical handling of the sample produced small systematic differences in the radical content of the sample. As shown by the data from run 9 (see Table 11), reprecipitation from methylene chloride produced gross changes in the sample. Table I11 shows further evidence for gross changes on reprecipitation of a single fraction. The conclusion that the free radicals in these samples were altered by handling and solvent exposure is inescapable. The extent to which the nature of the radicals in the sample was altered during the separation procedure is not known with certainty. The weight averages in Table I show that the changes are small relative to the changes produced by methylene chloride and documented in Table 111. Nonetheless, differences are detectable and suggest that further investigation may be worthwhile. The smaller value of the Curie law constant for the original sample as compared to the weight average of the separated fractions indicates that some free radicals were produced by the separation process, perhaps by dissociation of compounds present in the original sample or by oxidation of the sample during handling. This study shows that the intercepts in plots of I vs. 1/T arise from systematic errors in the measurements that introduce curvature into the plots. The effects of the curvature over the experimentally accessible range of temperatures are hidden by the stochastic errors in the measurements, so that excellent linear fits of the data are always possible. I t is the integral effects of the curvature that are responsible for the nonzero intercepts at the origins of the plots.
LITERATURE CITED Retcofsky, H. L.; Thompson, G. P.; Hough, M.; Friedel, R. A. ACS SVmp. Ser. 1978, No. 71, 142. Retcofskv, H. L.: HOuQh. M. R.: MaQuire. - M. M.; Clarkson, R. 6 . A&. Chem. Ser. 1981, NO. 192. Doetschman. D. C.; Mustafi, D. Fuel 1986, 62,684. Duber, S.;Wieckowski, A. B. Fuel 1984, 63, 1474. Elofson. R. M.: Schulz. K. F. Preor. PaD.-Am. Chem. SOC.. Div. FuelChem. 1967, 1 1 , 513. Yen, T. F. Prepr. Pap.-Am. Chem. SOC.,Div. Fuel Schwanger, I.; Chem. 1976, 2 4 , 199. Bill, D.; Kaimer, H.: Rose-Innes, A. C. J. Chem. Phys. 1959, 30,765
Anal. Chem.
IgS7, 59, 1731-1733
( 8 ) Poole. C. P.. Jr. E k t m n Spin Resonance, a Comprehensive Treatise 0" EXpS,h7W"ttl TechnqueS: Wiiey-Interscience: New YNk. \1983; p
410.
(9) Sullivan, R. F. '"Refining and Upgrading of s y n f ~ & fmm coal and Oil Shales ot Advan& Catalytic Prmesses": Monthly REPOR lor Feb 1983: US. DOE Contract NO. DE-AC22-76ET10532.
(10) Schiller, J. E.: Mathiason. D. R. Anal. Chem. 1977, 49. 1225-1228.
RECEIVED for review August 25,1986. Accepted Novemeber
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3, 1986. Reference to brand names is to facilitate understanding and is notmeantto imply endorsementby the u,S, Department of Energy. S.M.C. acknowledges support from the faculty research program administered by Oak Ridge Associated Universities for the Department of Energy. W.P.C. acknowledges support from the USDOE postgraduate research training program administered by Oak Ridge Associated Universities for the U S . Department of Energy.
CORRESPONDENCE Enantioselective Binding of 2,2,2-Trifluoro- 1-(9-anthryl)ethanol on a Chiral Stationary Phase: A Theoretical Study S i c During the past 15 years a large variety of chiral stationary phases have appeared in the literature (I). To better understand how chiral stationary phases interact with optical analytes, we have initiated a computational approach aimed at enlightening our views of the mechanism by which chiral surfaces enantioselectively hind optical isomers. The objective of our work is to provide a computational protocol for analysis of optical analytes on chiral stationary phases used in chromatography. We employ molecular orbital theory, molecular mechanics, and computer graphics as our tools. In this communication we report our preliminary results concerning the mode of binding of 2,2,2-trifluoro-1-(9anthryl)ethanol, 2, to the commercially available CSP, 1. This is a particularly well-studied system for which there exists a chiral recognition model (2). MC
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We introduce here new methodology and software needed in separation science to understand, from first principles, bow analytes interact with organic stationary phases. We conclude with an alternative cbiral recognition model to one which currently exists.
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Flgure 2. Intermolecular energy (kcal mol-') for RR and RS diastereomeric complexes: top left, RR; top right, RS. Contour lines are spaced every 1.0 kcal mol-'. H = high point, L = low point. Global minima are artificially set = zero. The top contours were constructed from 190 grid points wfih 816 unique orientations at each grid point (155040 total samples). Bottom left shows expansion of the minimum energy region from the RR plot directly above r. Contours are spaced every 0.25 kcal mol-'. The surface was created from 81 grid points with 3465 unique orientations at each grid point (280 665 total orientations). Bottom right shows expansion of the minimum energy region from the RS plot directly above it. Contours are spaced every 0.25 kcal mot'. Definitions of spherical coordinates 0 and d are in the text.
EXPERIMENTAL SECTION
Figure 1. Positbn of analyle wim respect to the chiral statiwry phase represented by spherical coordinates ( r . 0. 4 ). 0003-2700/87/0359-1731$01.50/0
Our approach first involves a conformational analysis of the stationary phase. If the phase is to act as a template with which analyte is to hind, one must know what forms are energetically allowed and which are forbidden. This has already been accomplished by using empirical force field and semiempirical molecular orbital techniques (3-5). Next we select the most stable form of the phase and of the analyte to compute the structure and the 0 1987 American Chemlcal Satiety
