20
Anal. Chem. 1982, 5 4 , 20-25
Estimation of Oxygen Group Concentrations in Coal Extracts by Nuclear Magnetic Resonance Spectrometry C. E. Snape" and C. A. Smith Natlonal Coal Board, Coal Research Establishment, Stoke Orchard, Cheltenham, Gloucester GL52 4RZ, England
K. D. Bartie Department of Physical Chemlstty, University of Leeds, Leeds LS2 9JT, England
R. S. Matthews School of Chemistty, Unlverslty of Durham, Durham DH 1 3HP, England
NMR methods for estlmatlng the concentratlons of hydroxyl and nonhydroxyl oxygen groups In coal extracts are described. Hydroxyl groups are converted to sllyloxyl, acetyl, and methoxyl groups or adducted wHh hexafiuoroacetone and their concentratlons are estlmated from the speclflc bands In the NMR spectra of the derivatives. These methods have been assessed for a selection of coal extract fractlons by comparing the estlmated hydroxyl group concentratlons with those obtalned by enthalplmetry, which Is an established tltratlon procedure. Concentratlons of nonhydroxyl oxygen groups are estlmated directly by 13C NMR.
Information on the distribution of the oxygen groups in coal extracts is important when attempting to understand the reactions that occur during the catalytic hydrocracking of these complex materials. By far the most extensively measured oxygen type is hydroxyl, which is found in phenols in bituminous coals and in both phenols and carboxylic acids in lignites (I). Some procedures for the structural analysis of bituminous coal extracts incorporate the concentration of phenolic hydroxyl groups (2-5). The most successful early attempts at measuring the concentrations of phenolic hydroxyl groups in bituminous coals and their extracts involved titration after acetylation ( I ) and silylation, followed by determining the percentage of silicon in the silylated coals (6). More recently, enthalpimetric titration (7), which measures the concentration of acidic hydrogen, i.e., that in phenols and carboxylic acids, has been used. There are, however, no established procedures for the overall measurement of nonhydroxyl groups, although some attempts have been made at estimating the concentration of carbonyl groups and ether groups by chemical means (I, 8). In principle, 170NMR offers the ideal technique for estimating the concentrations of oxygen groups in coal extracts, since the chemical shift ranges of carbonyl (350-600 ppm) and ether plus hydroxyl (0-100 ppm) groups are well separated (9). Unfortunately, 170NMR has not yet been utilized in coal research, primarily because of the low sensitivity of the 170 nucleus (receptivity relative to IH is 1.1X The 'H, 19F,and I3C NMR methods used in this investigation are summarized in Table I. Even though phenolic hydroxyl resonances can be observed in 'H NMR spectra of coal extracts ( 4 ) , these are broad and severely overlap with aromatic hydrogen resonances. Therefore, derivatization techniques which introduce magnetic labels into coal extract molecules have been used for the estimation of hydroxyl oxygen. These techniques have the added advantage that they significantly increase the solubility of benzene-insoluble fractions ( 1 0 , l l )so that hydrogen and carbon distributions
of these normally insoluble fractions can be readily measured by NMR. The derivatization procedures have been assessed by comparison of the results with those obtained by enthalpimetric titration. 13C NMR spectrometry has also been employed to estimate concentrations of nonhydroxyl oxygen groups. EXPERIMENTAL SECTION Extract Fractions. The following fractions of extracts prepared by supercritical gas (SCG) extraction were used: (i) the benzene insolubles from a bituminous coal extract; (ii) the asphaltenes from the same bituminous coal extract; (iii) the asphaltenes from a perhydrous coal extract; (iv) the asphaltenes from a lignite extract. The elemental analyses, the aromaticities (obtained from 13C NMR), and the number average molecular weights of the extract fractions are given in Table 11. The SCG extracts were prepared at 420 "C using toluene (3,5). Structural analyses of these extract fractions are described elsewhere ( 2 , 4 ) . For comparison, hydroxyl contents of the fractions were estimated by enthalpimetry (7). Derivatizations. The procedures used are given in Table I. Silylation was carried out with a combination of reagents which derivatize hindered phenols, such as 2,6-xylenol, but do not react with amines (12). Methylation was carried out following essentially the procedure described by Liotta (13). Acetylation was performed following the method described by Blom et al. (1);this method has also been used by Baltisberger et al. (14) for products from the solvent refined coal (SRC) process. Indole and carbazole were also acetylated in order to investigate the extent of reaction for aromatic secondary amines. Adduction with hexafluoroacetone (HFA) was carried out by a procedure described by Bartle et al. (15) for coal tar phenols and is similar to that used earlier by Leader (16) for alcohols and amines. NMR Spectrometry. Continuous-wave 'H NMR spectra were obtained at 60 and 220 MHz by using Perkin-Elmer R24B and R34 instruments, respectively, and chloroform-d as solvent. Pulsed FT 13CNMR spectra were obtained at 20 MHz using a Bruker WP80-WG instrument. To obtain reliable quantitative measurements, we added chromium acetylacetonate (-0.02 M concentration) to chloroform-d solutions of the extract fractions and gated decoupling was employed as previously reported for a mixture of model compounds and coal extract fractions (17). Following a data acquisition period of 0.5 s, a 3-s delay was used in the gated decoupling sequence. A 90' pulse angle was employed with a sweep width of 8 kHz and between 20000 and 50000 scans were accumulated. Pulsed FT l9F NMR spectra were obtained at 84.7 MHz using a Bruker WH90 instrument ( 1 5 ) . Trifluorotoluene was used for calibration of the 19F chemical shifts (measured from the signal of the HFA-H20adduct) and as an internal standard for the determination of hydroxyl contents from the intensity of the resonances from the HFA adducts. RESULTS AND DISCUSSION Hydroxyl Oxygen. Silylation. Silylation, in conjunction with 'H NMR, has been used previously to estimate the hydroxyl contents of products from the Synthoil(18) and SRC
0003-2700/82/0354-0020$01.25/0Published 1981 by the American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982
AROMATIC
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ALIPHATIC BAND
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30
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Flgure 2. I3C NMR spectrum of acetylated asphaltenes, bitmuminous
coal extract. of hexamethyldisilazane (silylating reagent) and hexamethyldisilozane (hydrolysis product). As for the 'H NMR spectra, no fine structure has been observed in the silyl bands of the 13C NMR spectra of coal extracts (10). The hydroxyl contents of the extract fractions have been estimated by use of the following expression: % hydroxyl = [(intensity of silyl band) X ( % H in extract fraction) X 17]/[9(intensity of aromatic band aliphatic band + f/g silyl band)]
+
6
7
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5 CHEMICAL
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Figure 1. 'H NMR spectra of silylated extract fractions: (a) benzene insolubles, bituminous coal extract: (b) asphaltenes, bituminous coal extract; (c) asphaltenes, perhydrous coal extract; (d) asphaltenes, lignite extract.
(19) processes. We have already shown that silylation renders the benzene insolubles from the bituminous coal extract used in the present study completely soluble in benzene (10) thus enabling NMR spectra to be obtained using chloroform-d as solvent. Silylation has an advantage over methylation and acetylation in that derivatives can be prepared more quickly (Table I). However, it is recommended that NMR spectra are recorded soon after preparation of the derivatives since silyl ethers hydrolyze readily (12). It is also a useful practice to check qualitatively that complete silylation of hydroxyl functions has been achieved by the disappearance of the -OH stretching vibration at 3200-3500 cm-l in the infrared spectra of coal extracts. The IH NMR spectra of the silylated extract fractions (Figure 1)show that the silyl bands, which have maxima a t about 0.3 ppm and broad shoulders extending to -1 ppm indicative of the presence of both unhindered (meta and para substituted) and hindered (ortho substituted) phenolic groups, are reasonably well separated from the other aliphatic resonances. In the lignite extract fraction, carboxylic acid groups are also likely to give rise to silyl resonances close to 0.3 ppm (18). Unlike the spectra of Synthoil products (18),no splitting of the silyl band was observed, even a t 220 MHz. The two sharp peaks between 0 and 0.2 ppm are due to small amounts
The method is relatively sensitive since each derivatized hydroxyl group gives rise to nine hydrogens. Table I1 shows that there is reasonable agreement between hydroxyl contents determined by silylation and by enthalpimetry, although a slightly higher value was obtained by silylation for the benzene-insoluble bituminous coal extract fraction (Table I1 and ref 10). For the lignite extract fraction, the enthalpimetrically determined hydroxyl content is slightly higher than that from silylation, probably because some hydrolysis of siloxyl groups has occurred; it is known that silyl esters of carboxylic acids hydrolyze more readily than silyl ethers of phenols (12). Acetylation. In both the lH and 13C NMR spectra of acetylated coal extract fractions, the methyl resonances from the acetyl groups severely overlap other aliphatic resonances. Thus, estimation of hydoxyl contents from these methyl resonances is prevented. However, the carbonyl resonances from the acetyl groups a t 169 ppm in the I3C NMR spectra are well-separated from aromatic carbon resonances (Figure 2) and this enables hydroxyl contents to be estimated using the following expression as long as precautions are taken to ensure rapid relaxation of carbonyl groups: % hydroxyl = ((intensity of carbonyl band) /[ (intensity of aromatic + aliphatic bands) (carbonyl band)]] X (%C in extract fraction) X lYl2 The hydroxyl contents determined in this way (Table 11) demonstrate that good agreement is obtained with values from silylation and enthalpimetry for bituminous coal extract fractions. For the benzene insolubles, however, better agreement is obtained with silylation than with enthalpimetry. A lower value was obtained for the perhydrous coal extract
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982 023
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Expansions of aliphatic bands from I3C NMR spectra of methylated asphattenes: ((a) bRuminous coal extract; (b) lignite extract. Flgure 3.
fraction than by silylation and enathalpimetry. This is because carboxylic acids do not react with acetic anhydride and, therefore, acetylation offers a method for the selective determination of phenolic hydroxyl groups in extracts (Table I), such as those from perhydrous coals and lignites, which contain both phenolic and carboxylic acid functions. Unlike reagents used for the other derivatizations, reaction of acetic anhydride with indole and carbazole has shown that aromatic secondary aimines, as well as phenols, can be derivatized. However, only 60% conversions were obtained jfor indole and carbazole, even after long reaction times (24 h), in comparison with 100% conversions for phenols. Since aromatic secondary amine groups are only minor components of most coal extract jfractions (for example, there are approximately 7 times more phenolic groups in the bituminous coal extract fractions) and their acetylation is only partially complete, their effect on measured phlenolic hydroxyl concentrations is likely to be small. An alternative acetylation procedure to that described here is trifluoroacetylation, which has been applied to coal-derived materials by Dorn and co-workers (20,21). This technique may give reliable estimates of phenolic hydroxyl concentirations but the range of 19Fchemical shifts for trifluoroacetylated phenols is much smaller than that for HFA adducts of phenols (22)* Methylation. As with silylation, methylation of hydroxyl groups gives rise to marked increases in solubility of coal extract fractions (11). Methylation has the added advantage that, unlike silyl ethers, methyl ethers do not readily hydrolyze and thus methylated coal extract fractions can be further separated. In the lH NMR spectra of methylated extract fractions, the bands due to methoxyl resonances between 3.3 and 4.0 ppm overlap with resonances attributed to ring-joining methylene groups (Ha,2)in extract fractions, and, therefore, as for acetyl derivatives, it has not been possible to eBtimate the hydroxyl content from 'I3 NMR. Figure 3 shows expansions of the d i p hatic bands from the NMR spectra of the bituminous coal and lignite extract asphaltenes, respectively, and shows that the methoxyl peaks (50-60 ppm) are well separated from the other aliphatic carbon resonances. The major peak at 55 ppm is attributable to
phenolic groups with either one or no adjacent alkyl or ring substituents, e.g., cresols and naphthols, while the minor peak at 60 ppm is attributed to groups with two adjacent alkyl or ring substituents (e.g., 2-methyl, 1-naphthol,and 2,6-xylenol). The methoxyl peak at 51 ppm, which is evident in Figure 3b only, is attributed to methyl esters (23). From the relative intensities of the methoxyl peaks, it is estimated that carboxylic acids account for approximately 40% of the total hydroxyl functions in the lignite extract fraction compared to less than 3% in the bituminous coal extract fraction. Moreover, the ratio of the peak at 60 ppm to that at 55 ppm is greater for the lignite extract fraction which indicates that a greater proportion of the phenolic functions are in more hindered environments. This finding is consistent with the previously reported structural analysis of the extract fractions (2, 4)which showed that the aromatic nuclei in the lignite extract were, on average, more substituted than bituminous coal extracts. From the overall intensity of the methoxyl peaks, the hydroxyl contents of the extract fractions can be estimated by the following expression: % hydroxyl = [(intensity of -OCH, bands)/(intensity of aromatic t- aliphatic bands)] X % C in extract X *y12 The results in Table I1 indicate that methylation gives lower values than the other methods and are in agreement with those of Vaughan arid Swithenbank (7) who obtained higher hydroxyl contents for coal-tar pitch fractions by enthalpimetry than by nonaqueous potentiometric titration with a base (nbutyltrimethylammonium hydroxide) similar to that used in the methylation procedure. Indeed, we have been able to determine residual hydroxyl contents in methylated extract fractions by silylation and enthalpimetry, indicating that methyl ether formation is incomplete. These results strongly suggest that only the stronger phenols in coal extracts are methylated, agreeing with the results of early methylation work on coal using diazomethane ( I , 24). Hexafluoroacetone Adduction. Like acetylation, HFA adduction carried out a t ambient temperatures offers a selective technique for investigating phenolic groups in coal extracts since carboxylic acids are only adducted to a significant extent at temperatures typically less than -40 "C (25). It has been shown by Ho (22)and Bartle et al. (15) that the 19Fchemical shifts of phenol HFA adducts occur over a range of 2 ppm and can be classified into unhindered (meta and para substituted) and hindered (ortho substituted) phenols with the latter being more deshielded by 0.4-1.2 ppm. This, together with the fact that the formation constants reported by Ho (22) for phenol HFA adducts are large for all but 2,6disubstituted phenols, prompted us to see if this method could be utilized to estimate phenolic hydroxyl contents in coal extracts as well as to give information on the distribution of phenolic hydroxyl environments. Figure 4 shows the I9FNMR spectra of the HFA adducts of the asphaltenes from the extracts of bituminous coal, perhydrous coal, and lignite, respectively. The spectra display maxima at 2.7 ppm and broad shoulders extending from these to 3.5 ppm. The reported chemical shift data (15,22)suggest that the peak centered at 2.7 ppm can be attributed to unhindered and dihidric phenols and the broad shoulder to hindered phenols. In Figure 4a, the areas under the 2.7 ppm peak and the broad shoulder are approximately equal, indicating that similar numbers of phenolic hydroxyl groups from both environments in the bituminous coal extract have been adducted. In Figure 4b,c the broad shoulders are more prominent and, therefore, the perhydrous coal and lignite extract fractions contain more hindered phenolic environments. As for the methylation results, this is consistent with the previously reported structural analysis ( 2 , 4 )which showed
24
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982 I
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Flgure 4. lgF NMR spectra of HFA adducts of asphaltenes: (a) bitumlnous coal extract; (b) perhydrous coal extract; (c) lignite extract. the aromatic nuclei in the perhydrous coal and lignite extracts were more substituted. Table I1 shows that the phenolic hydroxyl content of the bituminous coal extract estimated from Figure 4a is lower than the values obtained by silylation, acetylation, and enthalpimetry. This is probably due to incomplete HFA adduction. Leader (16)has shown that hydrogen bonding interactions occurring in solution can significantly reduce the formation constants for polyfunctional model compounds. However, good agreement is obtained between the various methods for the perhydrous coal extract fraction. As expected, the phenolic hydroxyl content of the lignite extract fraction (Table 11) derived from Figure 4c is much lower than the total hydroxyl content determined by enthalpimetry because of the presence of a significant concentration of carboxylic acids. Nonhydroxyl Oxygen. Nonhydroxyl oxygen is thought to occur in coal extracts as aromatic and aliphatic ethers and carbonyls. The chemical shifts of carbonyl groups (170-210 ppm) do not overlap with those of carbon in aromatic ethers (148-168 ppm), and signals from both these groups are well separated from those of aliphatic ethers (55-75 ppm). In addition, the carbonyl and aliphatic ether resonances do not overlap with the aromatic and aliphatic carbon bands in coal extracts (26). This good separation between the various kinds of carbon bonded to nonhydroxyl oxygen means that 13CNMR is suitable for investigating these environments in coal extracts. The asphaltenes from the bituminous coal, perhydrous coal, and lignite extracts have been used to demonstrate the application of 13CNMR to the estimation of nonhydroxyl oxygen groups. The asphaltenes are 100% soluble in chloroform-d (the most commonly used NMR solvent for coal-derived materials). For benzene insolubles, a methyl or silyl derivative must be prepared since they are normally only partially soluble in chloroform ( 1 0 , I I ) . However, for lignite and perhydrous coal extract asphaltenes preparation of a methoxyl derivative is extremely useful, because, as described earlier, the concentration of carbonyl oxygen present in carboxylic acid functions can be derived from the methoxyl peak at 51 ppm in the 13C NMR spectra. Moreover, the chemical shifts of carbonyls in methyl esters occur about 5 ppm upfield from those of the corresponding carboxylic acids (27),and therefore a better separation is achieved between C=O of carboxylic acids and other carbonyl groups, such as ketones. Figures 5-7 show expansions of the aromatic and carbonyl chemical shift ranges from the 13C NMR spectra of the asphaltenes of the bituminous coal extract and the methylated asphaltenes of the lignite and perhydrous coal extracts. The nonhydroxyl group concentrations measured by I3C NMR are summarized in Table 11. In Figure 5 , carbonyl resonances are not detected in the 170-210 ppm chemical shift range. This indicates that virtually all the nonhydroxyl oxygen must be
I I90
I80
170
160
150 140 130 CHEMICIL SHIFT p p m
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110
100
Flgure 5. Expansion of aromatic band from 13C NMR spectrum of asphaltenes, bituminous coal extract.
t
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.
*
Flgure 6. Expansion of aromatic and carbonyl band from 13C NMR spectrum of methylated asphaltenes, perhydrous coal extract.
.I
Flgure 7. Expansion of aromatic and carbonyl band from 13C NMR spectrum of methylated asphaltenes, lignite extract. present in aromatic ethers in the bituminous coal extract asphaltenes; the 13C NMR spectrum of the methylated asphaltenes has already shown that carboxyl groups are not present in significant amounts (Figure 3). As previously mentioned, the aromatic ether resonances occur between 148 and 168 ppm and overlap those due to aromatic carbon joined to phenolic oxygen between 148 and 158 ppm (25). Figures 6 and 7 show that, in addition to aromatic ethers, carbonyl groups are present in the asphaltenes from the perhydrous coal and lignite extracts (Table 11). The results indicate that the lignite extract fraction contains a much larger concentration of carbonyl groups (approximately 7 % of the
Anal. Chem. i g m , 5 4 , 25-28
total carbon) than the perhydrous coal extract fraction (approximately 2% of the total carbon). Two distinct carbonyl bands are present in the spectra of the lignite and perhydrous coal extract fractions. These are attributable to carboxylic acids, which largely give rise to the methyl ester resonances between 165 and 180 ppm, and other carbonyl functions, such as ketones and quinones, which give rise to the band between 185 and 205 ppm. No resonance bands were discernible Ibetween 55 and 75 ppm in any of the spectra of the asphaltenes and therefore, even for the lignite extract fraction, aliphatic ethers are not present in significant amounts. C!ONCLUS I ONS This study has shown that NMR methods complement and extend existing titration methods for the estimation of hydroxyl oxygen groups in coal extracts. Both silylation and acetylation give phenolic hydroxyl contents in good agreement with values obtained by enthalpimetric titration for bituminous coal extract fractions, but silylation has advantages in that shorter preparation times are requhed and that lH NNIR, which is a quicker and less expensive technique than IL3C NMR, can be used. Methylation and HFA adduction generally give lower values than the other methods but have the advantage that they provide novel information on the distribution of environments of hydroxyl groups. I3C NMR is a convenient method :for the overall asriessment of the environments of nonhydroxyl oxygen grou:ps in coal extracts.
ACKNO WLEDGMElNT The authors thank M. P. Mendoza for carrying out the enthalpimetric titrations. Permission to publish this work is given by the National Coal Board, United Kingdom, and the views expressed are thLose of the authors and not necessarily those of the board.
L1T:ERATURE CITED (1) Blom, L.; Edelhausein, 135- 153.
L.; van
Krevelen, D. W. Fuel 1957, 3 6 ,
25
(2) Ladner, W. R.; Martin, T. G.; Snape, C. E.;Bartle, K. D. Prepr. Pap.Am. Chem. Soc., Div. FuelChem. 1980, 25(4), 67-78. (3) Martin, T. G.;Williams, D. F. Philos. Trans. R. SOC.London, Ser. A . 1981, A300, 183-192. (4) Herod, A. A.; Ladner, W. R.; Snape, C. E. Philos. Trans. R . SOC. London, Sur. A 1981, A300, 3-14. (5) Bartle, K. D.; Ladner, W. R.; Martin, T. G.; Snape, C. E.; Williams, D. F. Fuel 197% 58, 413-422. (6) Friedman, 8 . ; Kaufman, M. L.; Steiner, W. A,; Wender, I. Fuel 1981, 40, 33-46. (7) Vaughan, G. A.; Swlthenbank, J. J. Analyst (London) 1985, 9 0 , 594-599. (8) Ruberto, R. G.; Cronauer, D. C. "Organic Chemistry of Coal"; Larson, J. W., Ed.; American Chemical Society: Washington, DC, 1978; ACS Symp. Ser. No. 71, Chapter 3. (9) Rodger, C.; Sheppard, N.; McFarlane, C.; McFarlane, W. "NMR of the Perlodlc Table"; Harris, R. K., Mann, B., Eds.; Academic Press: New York, 1980;Chapter 12. 10) Snape, C. E.; Bartle, K. D. Fuel 1979, 58, 898-900. 11) Martin, T. Ci.; Smlth, C. A.; Snape, C. E.; Starkle, H. Fuel 1981, 60, 365-366. 12) Pierce, A. E. "Silylatlon of Organic Compounds"; Pierce Chemical Go., 1979. 13) Llotta, R. Fuel 1979, 5 8 , 724-728. 14) Baltisberger, R. J.; Patel, K. M.; Stenberg, V. I.; Woolsey, N. F. Prepr. Pap.-Am Chem. SOC., Div. Fuel Chem. 1979, 24 (2), 310-316. (15) Bartle, K. D.; Matthews, R. S.;Stadelhofer, J. Appl. Spectrosc. 1980, 34 (6), 615-517. (16) Leader, G. IR. Anal. Chem. 1973, 4 5 , 1700-1706. (17) Ladner, W. R.; Snape, C. E. Fuel 1978, 57, 658-662. (18) Schweighardt, F. K.; Retcofsky, H. L.; Friedman, S.; Hough, M. Anal. Chem. 1978, 5 0 , 368-373. (19) Schwager, I.; Yen, T. F. Anal. Chem. 1979, 51, 569-571. (20) Dorn, H. C.; Szabo, P.; Koller, K.; Glass, T. G. Prepr. Pap.-Am. Chem. Soc., Div. Fuel Chem. 1979, 2 4 , 301-309. (21) Sleevi, P. S.; Glass, T. E.; Dorn, H. C. Anal. Chem. 1979, 51, 193 1- 1934. (22) Ho, F. L. Anal. Chem. 1974, 4 6 , 496-499. (23) "Sadtler '3C> NMR Reference Spectra"; Heyden; London, 1979. (24) Yohe, G. R.; Bladgett, E. 0. J . Am. Chem. SOC. 1947, 69, 2644-2648. (25) Pelilssler, N. Org Magn Reson. 1977, 9 , 563-587. (26) Snape, C. iE.; Ladner, W. R.; Bartle, K. D. Anal. Chem. 1979, 51, 2189-2198. (27) Brietmaier, E.; Voelter, W. '% NMR Spectroscopy"; Verlag Chemie, Weinheim/Bergstr. 1974. I
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RECEIVED for review April 7,1981. Accepted October 1,1981. Financial support from the European Coal and Steel Community is gratefully acknowledged.
Computer Compensation for Nuclear Magnetic Resonance Quantitative Analysis of Trace Components Takashl Nakayama and Yuzuru Fujllwara" Institute of Information Sciences and Electronics, University of Tsukuba, Sakura-mura, Niihari-gun, Ibaraki, 305, Japan
A computer program hlas been wrltten tlhat determines trace components and separates overlapplng components In multicomponent NMR spectra. Thls prograni uses the Lorentrlan curve as a theoretlcal curve of NMR spectra. The coefflclents of the Lorentrlan are determlned by the method of least squares. Systematlc errors such as base) Ilne/phase distortDon are compensated and lrandom errors are) smoothed by takEng moving averages, so that these processes contrlbute sitbstantlally to decreaslrig the accumulallon tlme of spectral data. It Is posslble to Improve the accuracy of quantltatlve analysls of trace Components by two maire slgnlflcant flgures, than the results obtalned at a standard measurlng condltlon. Thls program was applied to determlnhg the abundance of ''C, the composltlon of copolyester anid the saponlflcatlon degree of PVA.
component NMR spectra. For quantitative analysis of trace components, accumulation is the only available method for instruments which are not supported with hardware compensation, and sufficient accumulation is not always feasible because of saturation of the main peak. The method of least squares is useful for determining the composition of trace component spectra (1-3). In this program, the Lorentzian curve is used as a theoretical curve of NMR spectra, and the coefficients of the Lorentzian are determined by the method of least squares. As the Lorentzian is a nonlinear model, it is reduced to a linear one by approximation so that the method of least squares can be applied ( 4 ) . I t is assumed that the Lorentzian curve approximates an NMR spectrum adequately. The Lorentzian is defined
Programs have been developed to dletermine trace cormponents and to separate overlapping components in multi-
where k, x , and w correspond to the intensity, the position of a peak center, and the half-width, respectively. Equation
0003-2i'00/82/0354-0025$01.25/0
0 1981 American Chemical Society
