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!ONCLUSI 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:ERATURECITED (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
.
.
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
26
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982
1 can be expressed f(x) =
DATA 6201i computer
c2c3
(x
- c1)2 + c32
The purpose is to estimate parameters cl, c2, and c3 of expression 2 by the method of least squares. As the model used is nonlinear, it is reduced to a linear one by approximation so that the method of least squares can be used. The following expression is obtained from a Taylor expansion which is terminated at a linear term. f(x;
~1
+ Ac1, ~2 + Ac,,
~3
+ AcJ
E d i t i n g
=
A
Supposing that the left side of expression 3 is the observed value, n equations are obtained for n observed values.
c-af I
I
xi
Main
Program
Plot
Program
I
SAC, = Aflxi
i = 1, ..., n
(4)
Least
of
Lorentzian
Squares
Block diagram of quantitative analysis program: (-) represents the program control and (=) represents the data flow. Flgure 1.
where
Applying the method of least squares, the problem is reduced to estimating Acj 0' = 1, 2, 3) which minimize the following sum of squares:
The following equation is obtained by dSS/d(Aci) = 0 (i = 1, 2, 3).
From this
This is expressed
A-c = b where A = (aij),b = (bl, bz, b3)t, c = (Ac1, Acz, AcJt
Method
(8)
(t means transposed). Parameters cj are replaced by cj + Acj by solving eq 8, and this process is repeated until the residual converges. EXPERIMENTAL SECTION This method of quantitative analysis was applied to several kinds of spectra. In this paper, the analysis of abundance of in CHC13is discussed in detail as an example of the determination of a trace component. The method was applied also t o the determination of the saponification degrees of PVA t o show the separating process for overlappingcomponents in multicomponent NMR spectra. NMR spectral data were collected with a Varian HA-100 controlled by a DATA 620/i computer, and output to paper tape. 1. Constitution of Programs. The block diagram of the procedure is shown in Figure 1. NMR spectral data stored by the DATA 620/i computer are dumped in the form of binary values to paper tape by the program BINARY DUMP, and edited by the program EDITING. EDPIWG performs the following data processing: (1)Smoothing data. Raw data are smoothed by the weighted moving average
method to reduce random error. The number of points for calculating the moving average is selected from the set of (5, 7, 9, ..., 25). The abscissa is partitioned into several sections according to the kind of spectral curve, and the most suitable number is selected. (2) Phase compensation. To compensate for phase distortion, each peak is inverted at the center of the peak ( x = cl), and the inverted peak is added to the original one. That i s to say, cf(x) + f(cl - x ) ) / 2 is used as spectral data instead of the original spectral data f ( x ) . This procedure is applied to bisymmetric spectral patterns. (3) Base line compensation. A new base line is set up so that the average of 50 points at the bottom of the spectral curve is to be zero. Systematic errors are reduced by this treatment. (4) Accumulation of trace components. Trace components are extracted from the original data and accumulated under the condition that the peak center should be adjusted. After the editing process described above, the reduced data are output to magnetic tape. The Plot program is used to plot spectra and the Lorentzian curve. The program for the method of least squares performs the calculation for the algorithm described in the previous section, and the main program controls all of these programs and generates the report. 2. Selection of Initial Values. The selection of the initial values of parameters cl, c2, and c3 (expressed here as colt co2, and co3)is important in the application of the method of least squares. col, which corresponds to the position of the peak center, is set at the position of the maximal value of spectral data; co2,which correspondsto the intensity, is set at the maximal value of spectral , corresponds to the half-width, is set at the data; and ~ 0 3 which mean of the actual values obtained from several spectra. The convergence is significantly influenced mainly by the distortion of col and is stable for co2 and ~ 0 3 . It is sufficient to select initial values as described above because col is determined accurately. 3. Selection of Sampling Points for the Method of Least Squares. Selection of sampling points also significantly influences convergence. It was determined with pseudodata that good values result from arbitrarily selected points given that the points are sampled approximately symmetrically about the peak center. There is almost no change as the number of sampling points is varied within the range from 5 t o 30 points (cf. Figure 4). Consequently the sampling points for the actual spectra are selected from the frequency area near the peak center where the random error seems relatively small. RESULTS AND DISCUSSION 1. Determination of a Trace Component. General. The
suitability of this method for determining trace components in multicomponent NMR spectra is most clearly shown when the trace component is hidden in the shoulder of a main spectral component. The process of detecting such a trace component is shown in Figure 2. It is the result of computer
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982 27 baseline range/half width 10
6
I
I
1
14
18
22
26
30
34
38
X103
",
'I i l
T
f: -
5
0
L
f
f
- 2 0.-
? L
m a,
-
.->
-3.0-
f
m
-5 0
The effect of the ratio "base line rangelhalf-width" on the accuracy of measurement of the area.
Figure 3.
the estimation described below, so they are not treated directly. Systematic errors are reduced by using ( f ( x ) + f ( c l x ) ) / 2 instead of f ( x ) as spectral data, which means the correction of phase distortion, and by setting up the new base line. Random error is reduced by the smoothing process. The relative error 6 is estimated by
I
'
!
550
I
603
Hz
(b) Flgure 2. Accumulation lof a detected trace component on a shoukler of a main peak. The lower peak extracted from the main peak (shown in (a))enlarges to (b) aflter accumulation 30 times.
simulation for accumulating the spiectral component of poly(p-xyleneazipoaide) in poly@-xylieneterephthalamide), Figure 2a shows the original spectral p,attern which contains a trace component on its shoulder. The separated trace component is also shown in Figure 2a, and Figure 2b shows the trace component atfter it has been accumulated 30 times; its pattern is refined and enlarged enough to approximate by the Lorentzian curve. In practice, this technique for determining a trace component was applied t o the analysis of the abundance of 13C in CHC1,. This examplle is the case that the technique is useful for the spectrum of a very wide dynamic range. The abundance of 13C is given by where s is the true area of the satellite peak and S is the true area of the main peak. The area obtained by this program contains various errors such as systematic (instrumental) errors and random errors, and so the abundance calculated can be expressed
R
= (s
.f
e)/@ +E
+ s + e)
(11)
where e and E are the errors associated with experiment as well as calculation. If p and q are relative errors of s and S in expression 11, then expression 10 is reduced to
T = R(l
ik
q)/(l
+ q +R(g -p))
(12)
The abundance of 13C is estimated by expression 12. Error factors include (1) systematic errors resulting from instruments, (2) random errors during observation, (3) rounding errors, and (4) computational errors. The rounding error and computational error above are always included in
where 6 is the mean value of relative errors of estimate and am2is the variance of 6. Determina.tionof Base Line. The base line is determined so that the intensities of both ends of the spectral curve become equal to zero after phase compensation. In practice, base line compensated data are obtained by subtracting a straight line which connects both ends of a spectrum from the value of phase compensated data. This processing has almost no influence on the precision of approximation if the base line range considered is large enough for the half-width of the peak. Figure 3 shows the effect of the ratio "base line range/halfwidth" on the accuracy of measurement of the area. Figure 3 is for calculated pseudospectral data. For actual data, the following values were obtained: 6M
= -0.0012
6 ~ 1= -0.0013
UM US
= 0.0002
= 0.0001
(13)
where 6 is tho mean of the relative error, a2 is its variance, and subscripts M and S represent main and satellite peaks, respectively. Random Error. As described above, raw data are smoothed by the weighted moving average method. The extent to which random error is reduced by this smoothing method has been examined for pseudodata. The distribution of relative error as a function of the number of points used for computing the moving average is shown in Figure 4. The case of the number of sampling points equal to zero is the case of random error without smoothing. Figure 4 also shows that the five-points smoothing gives the minimal relative error. The distribution of the relative error as a function of the relative intensity of irregular noise is shown in Figure 5 for data with five-points smoothing and in Figure 6 without smoothing. For the actual spectra, the ratios "noise intensity/maximal value of peak" in Figure 5 and Figure 6 are about 0.0003 (main ]peak) and 0.0020 (satellite). Consequently the smoothing process is not very effective for the main peak but fairly effective for the satellite peak. The following values are obtained: 6~ = 0.0006 UM = 0.0001 6s = 0.0003
US
= 0.0007
(14)
ANALYTICAL CHEMISTRY, VOL. 54, NO. 1, JANUARY 1982
28
0 12
X
t
0
[ noi
se
i n t e n s i t y / rnax
peak )
x
io3
Flgure 6. Distribution of relative errors of estimated areas for irregular
noise (without smoothing). number
of
sampling
points
Flgure 4. Distribution of random errors by the number of sampling points for moving averages.
T
I 800
900
Hz
Flgure 7. Separation of overlapping components. , 0 4
,
, 1 2
,
,
2 0
(noise intenslty/max
2 8
36
peak)xro3
Flgure 5. Distribution of relative errors of estimated areas for Irregular noise (with five-point smoothing). ~~
Table I. Saponification Degree (%) saponification sample a degree samplea 87.6 96.5 98.6 a
85.8 96.1 98.2
99.3 99.7 99.9
saponification degree 99.5 99.6 100.0
Values determined by chemical analysis.
Finally, the abundance of 13C estimated by expressions 12, 13, and 14 is 1.107, f O.0Ol2. 2. Separation of Overlapping Components. The saponification degree of PVA was determined by this method, as an example of separating overlapping components in multicomponent NMR spectra. The object spectral data are approximated by the sum of four Lorentzian curves, so 1 2 parameters are determined by the method described in the
previous section. The original spectrum of PVA and the result of separation are shown in Figure I . Table I compares the saponification degree computed by this method with the one determined by chemical analysis.
C0NCLUSIO N This program is very useful not only for determining trace components of NMR spectra but also for separating overlapping components in a multicomponent mixture and detecting a small shoulder component. Thus the program is suitable and has been used for precise analysis, such as measuring the abundance of 13C, the saponification degree of PVA, the concentration of 314 couplings in polyisoprene, and the ratio of the cis-trans form in PIP. LITERATURE CITED (1) Barnett, H. A,; Bartoii, A. Anal. Chem. 1960, 32, 1153-1156. (2) Biackburn, J. A. Anal. Chem. 1965, 3 7 , 1000-1003. (3) Roberts, S. M.; Wilkinson, D. H.;Walker, L. R. Anal. Chsm. 1970, 4 2 , 886-893. (4) Physical Society of Japan "Data Processing of Physical Experiment by Computer"; Saiensu-sha, Inc.: Tokyo, 1973.
RECENEDfor review March 9,1981. Accepted October 1,1981.
