excite the analyte. An estimated effect can be calculated by assuming excitation is by an imaginary monochromatic wavelength that is two-thirds the wavelength of the analyte ahsorption edge. The error in the calculated effect will be greater in this case than when the analyte is excited by the target line. The technique for calculating the effect of matrix composition on line intensity described above has been of great value in our laboratory for the determination of light elements in organic compounds, especially organic polymers where standards preparation is often difficult.
wavelength than the target line of the x-ray tube. This principle was used in the determination of chlorine and sulfur a t the 0 to 1% level in organic solvent mixtures of unknown composition. Phosphorus was added, as triethyl phosphate, to samples and standards. The ratio of chlorine to phosphorus and sulfur to phosphorus line intensities was used to calculate the amount of chlorine and sulfur in the samples, using chlorine and sulfur standards similarly spiked with the same amount of phosphorus as the samples. Since changes in matrix composition affect all three elements the same, the effects of changes in matrix are compensated. The data in Table 11 show how the described technique can be used to calculate the effect of a varying concentration of a light element on the line intensity of a light element. In this case, the calculated and measured intensities agree within experimental error. The data in Table I11 show how this technique fails when the matrix contains an element with an absorption edge of shorter wavelength than the target line. In general, the described technique always overestimates the effects of a heavy element. Similarly, the effect of a varying organic composition on an element whose absorption edge occurs at a higher energy than the target line cannot be accurately calculated. In these cases, the target line obviously does not
ACKNOWLEDGMENT The author acknowledges the work of Sarah Buchholz, B. H. Collins, and P. L. McConnell, who assisted in the experimental work. LITERATURE CITED (1) E. P Bertin, “Principles and Practice of X-Ray Spectrometric Analysis”, 2nd ed., Plenum Press, New York, N . Y , 1975 (2) J. V Gilfrich and L S. Birks. Anal Chem , 40, 1077-1080 (1968).
RECEIVED for review April 11, 1977. Accepted May 16,1977. Paper was presented at the Siemens Logic Controller Conference, Buck Hill Falls, Pa., October 27, 1976.
Propylene Incorporation in I-Butene Copolymers by Carbon- 13 Nuclear Magnetic Resonance Spectrometry Michael H. Fisch” Witco Chemical Corporation, P.O. Box 110, Oakland, New Jersey 07436
J. J. Dannenberg Department of Chemistry, Hunter College, City University of New York, 695 Park Avenue, New York, New York 10021
A method based on 13C nuclear magnetlc resonance spectrometry is described whereby standards can be obtained of known propylene content in copolymers wlth 1-butene. These standards can be used to calibrate the heated cell Infrared method for determining propylene content in polybutene.
Numerous methods have been applied to the analysis of 1-butene/a-olefin copolymers, including pyrolysis gas chromatography (1-3), differential thermal analysis ( 4 ) , x-ray crystallography ( 5 ) ,and melting-point fractionation (6). The most widely adopted technique is infrared spectrometry (5-9), either using a heated cell to eliminate the effects of crystallinity, or more simply by scanning a film of known thickness and comparing the absorbance to those of standards. For quality control work, infrared is the easiest method to run and the least demanding in equipment. I t requires, however, a set of standards for calibration of the instrument used. These standards have in the past been frequently obtained by copolymerization of 14C tagged monomer and radioassay (10, 11). This technique, which goes back to the early Italian work (12, 13) introduces additional manipulations and the possi-
bility of isotope effects, is time-consuming, and cannot economically be run on a scale approximating production. We wish now to report that satisfactory calibration standards can be drawn from actual production batches and analyzed by 13C NMR.
EXPERIMENTAL Copolymers were prepared at 65 “C and 150-200 psi in the presence of hydrogen using (C2H&A1C1/TiC13catalyst. During the reaction, makeup propylene was fed in to keep its concentration fixed. Conversion to copolymer was typically carried to 10-15%.
NMR spectra were measured on representative materials from initial propylene levels of 1.97, 4.05, and 6.91 mol % (Figure 1). Samples were dissolved in deuterochloroform and the spectra measured on a JEOL model PSlOO spectrometer. Since the size of the propylene peaks depended on the level of incorporation, accumulations were arbitrarily continued until the signal to noise ratio was adequate. This required 31 000 scans at the lowest propylene level. NMR Conditions. T = 50 O C . The spectrum width was 5 kHz with 8K data points which corresponds to a computer resolution of 1.2 Hz. The internal lock was deuterium on CDCln and the internal standard, CDCls solvent. Integrations were performed using standard JEOL/Texas Instrument computer software. The ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1405
CH (Butene)
Butylene CH
Backbonm CHz (BB
Backbone CHZ (BP)
CDC1)
Backbone CHZ (PP)
Figure 1. I3C NMR spectrum of a propylene-1-butene copolymer
-~
Table I. Chemical Shiftsa for Propylene-Butene-1 Copolymer
Assignment
Diads and triads in head-to-tail polymer (cf. Fig. 2)
Propylene CH,
BPB, BPP, PPP
20.61
21.00
Backbone CH, Backbone CH,
PP BP
44.36 41.67
45.61 43.27
Propylene CH
BPB, BPP, PPP
28.38
28.90 28.62
Butylene CH,
BBB, BBP, PBP
11.36
11.89
Side Chain CH,
BBB, BBP, PBP
27.66
28.70
Backbone CH,
BB
38.98
40.93
Butylene CH
BBB, BBP, PBP
34.98
35.37 35.09 34.81 0.70
a =
a
Calc. (Head-to-Head) Propylene residues head-to-tail Lindquist Carman and Adams ( 1 4 ) et al. (16)b only ( 1 4 )
fiPmNq
All shifts in parts per million relative to TMS.
0.55
The epsilon correction (-0.03
13C frequency was 25.03 MHz. Exponential multiplication of the FID before Fourier Transform induced line broadening of 0.6 Hz. Normal spectra were taken with 8-gs pulse width (single pulse) corresponding to an approximately 30' flip angle; proton noise decoupled; acquisition time, 0.812 s; and 1.5-s repetition. Gated decoupled spectra were taken with 20-fis pulse width corresponding to an approximately 75O flip angle; 1-s interval, and 5-s repetition.
DISCUSSION NMR spectra of butene-propylene copolymers were interpreted based on the additivity relations of Lindeman and 1406
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
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17.13 20.12 17.62 41.42 34.97 32.03 28.84 34.99 30.45 32.92 11.36 11.85 27.66 24.72 27.41 36.04 38.98 34.98 43.66 37.05
Observed 21.4
43.1 28.2 10.9 27.5 39.6 34.4
0.04) was omitted.
Adams ( 1 4 ) ,see also ( 1 5 ) )and of Carman et al. (16) (Table I). If one assumes that polymerization is exclusively head-to-tail, there are 18 chemically different carbons, ignoring tacticity (Figure 2). Application of the additivity relationships reduces the number of predicted different chemical shifts to those in Table I(17). For comparison, the calculated shifts for polymer whose propylene component was incorporated in head-to-head fashion are also shown. The observed resonance at 43.1 6, due to the methylene of the diad BP, occurs slightly less than 2 ppm downfield from that calculated using the Lindeman-
Mads -
approximation in three different ways (Equations 1-3).
Mol 5% Butene
4 d 4-4 4 BB
BBB
BPB
BBP
BPP
BP
PP
PBP
PPP
3 each
CH, CHZ, CH3 (butene)
3 each
CH, CH3 (propylene) = 6 l i n e s
Total
= 9
+
6
+
3
-
= 9 lines
3 types of
C H z - 3 lines
18 l i n e s
Figure 2. Carbons in head-to-tail random propylene/butene copolymer
Table 11. Propylene Incorporation in Propylene-Butene-1 Copolymer Mol % C, in Copolymer Mol % C, in Feed By Equations 1-3 Correcteda 1.97 4.05 6.91
2.83 i 0.21 7.80 i 0.25 11.38 i 0.56
2.91 8.50 13.00
* * *
0.22 0.27 0.62
a Corrected for probabilistic corrections as outlined in text.
Adams set, which parallels the case of polypropylene itself (observed 46 6 (18);calculated 44.4 6). As easily seen from the Table, agreement between the observed and predicted spectrum for head-to-tail polymer is quite good. Clearly, the head-to-tail random copolymer is consistent with the observed spectra, which is in accord with previous work (19,20). The simplicity of the spectrum, showing only a single peak for each carbon, suggests that the polymer is highly stereoregular (21, 22). Agreement between experiment and predicted values is satisfactory for either empirical method. The somewhat better fit to the Lindquist-Adams set as opposed to the Carman et al. parameters is not significant. Propylene residues in the copolymer with 1-butene are believed to be randomly distributed (19,20). The failure to observe the methylene resonance of the diad PP at -46 ppm under our conditions is consistent with this conclusion. Even a t our highest level of propylene incorporation, the PP diad methylene resonance is predicted to be only 6-7% of that due to the backbone methylene (BP) a t 43.1 6. Only the area of the methylene from the B P diad was suitable for calculating propylene content. It is the most sensitive to propylene incorporation, since each propylene in a BPB triad gives rise to two such signals, whereas only one propylene methine, and propylene methyl result. The relative methyl area is further reduced because of the nuclear Overhauser effect, and the methine cannot be accurately integrated except as part of the total area with butylene side chain CH2, from which it is incompletely resolved. Spectra were integrated and the mol 70 butene was calculated to a first
)
Butylene CH Butylene CH + / 2 Backbone CH2 (PB) Mol 5% Butene Propylene CH + Side Chain CH2 - l / 2 Backbone CH2 (PB) = 100 Propylene CH + Side Chain CH2 Mol 76 Butene =
100
(1)
(
Backbone CH (BB) + ' / 2 Backbone CH2 CH2 - (BB) . . + Backbone CH2 (PB)
\
/
By use of Equations 1-3, all the nonmethyl signals are used in the calculations. The results, which were invariably in reasonable agreement, were averaged from several analyses. Simply taking the relative areas from the carbon spectra and applying Equations 1-3 yields the direct data in Table I1 which assume all propylenes to be in BPB triads. The corrected propylene levels are then obtained from the following considerations. The polymer structure is taken to be random from the absence of a detectable methylene from the diad PP, and kinetic considerations (19,20). Let the (true) mole fraction of propylene be x . Then it can be shown that the proportion of the propylenes with two butenes as neighbors, the triad BPB, will be (1- x ) ~ those ; with two propylenes as neighbors, the triad PPP, will be x2; and those with one neighbor of each type, PPB will be the rest, 1- (1- x)' - x 2 = 2x - 2x2. Larger blocks are negligible at the levels of incorporation here. Each propylene in the environment BPB contributes two carbons to backbone methylene (PB), but the result is quite different for either of the other arrangements. Per propylene residue, P P B contributes one backbone CH2(PB) and backbone CH2(PP),whereas PPP adds 2 / 3 each of backbone CH2(PP) and backbone CH2(PB). Correction for the probabilistic considerations and the fact that contributions to the integrated intensity at 43.1 S are different for PPB, PPP, and BPB, raises the observed values for propylene incorporation to the corrected ones in the last column, the effect being greater as the levels of incorporation are raised. To estimate the importance of the nuclear Overhauser effect, spectra were run in both the normal Fourier Transform and gated-decoupled modes. Except for the methyl carbons, which were not used in the calculations, the ratios of the integrated carbon resonances were the same within experimental error for both the gated-decoupled and normal modes. Our chosen repetition rate of 5 s meets Levy's recommendation (23) that pulse intervals be at least 4-5 times TI, known to be typically less than 1 s (24, 25). Although 13C NOES for solutions of polymers near room temperature are often less than theoretically maximal values (24),Schaefer has observed that they are generally invariable from one type of carbon to another within the same polymer (26, 27). Observation of an analogous phenomenon for our system obviated the necessity to record the spectra a t a temperature sufficiently elevated to render the NOES (presumably) maximal and equal. Therefore, we believe that areas obtained from normal noise decoupled spectra a t room temperature are adequate for the computations. A least-square linear plot of mol % C3 in the feed vs. that in the polymer (corrected) yields a slope of 1.95 f 0.68 and a correlation coefficient of 0.994 (F statistic 153.7, a 99.35% ANALYTICAL CHEMISTRY, VOL. 49,
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AUGUST 1977
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*
value). The derived reactivity ratio for butene, i.e., the reciprocal of the slope, 0.51, is quite reasonable in comparison with the literature value of 0.50 (28) reported for a related catalyst system, Et3A1/TiC13. However, much more data would be required for a satisfactory measure of this parameter. These materials were then used in the heated cell infrared method of Tosi et al. (8). The absorbances were recorded together with those obtained for a number of blends of polybutene and polypropylene homopolymers. The blends and the standards generate two different lines (Equations 4 and 5 respectively) which, by t test, have significantly different slopes ( t = 2.10; t0.06, 16 = 2.12). Thus, calibrated standards are necessary to carry out the method accurately. Presumably, this is the reason that blends were not used in earlier work on the infrared methods.
y(absorbance ratio) = 1.015~(molar ratio P/B) + 0.244 (4) y = 0.798~ + 0.240 (5) Coincidentally, the line generated in our work is not statistically different from that obtained by Tosi, et al. (81, (Equation 6) whereas that for the blends is strikingly so.
y = 0.705~ + 0.244
(6)
where t for slopes of Equations 5 and 6 = 0.89, to.o5,33 = 2.04, t for slopes of 4 and 6 = 4.49, to.001, 35 = 3.60.
CONCLUSION 13C NMR is a simple and effective method for determination of propylene incorporation into butene-propylene copolymers. Standards calibrated by this method are suitable for use in simpler plant methods, e.g., IR or DSC. ACKNOWLEDGMENT We thank Henry P. Katstra who painstakingly made the infrared measurements, Walter T. Young who prepared the copolymers, and Robert L. Lichter for useful discussions.
LITERATURE CITED (1) J. C. Verdler and A. Guyot, Macromol. Chem., 175, 1543 (1974). (2) E. W. Neumann and H. G. Nadeau, Anal. Chem., 35, 1454 (1963). (3) E. M. Barrall, R. S. Porter, and J. F. Johnson, J. Chromafogr.,11, 177 (1963). (4) E. M. Barrall, R. S. Porter, and J. F. Johnson, J . Appl. folym. Sci., 9, 3061 (1965). (5) A. Turner Jones, J. folym. Scl., folym. Left. Ed., 3, 591 (1965). (6) D. F. Slonaker, R. L. Combs, and H. W. Coover, Jr., J . Macromol. Scl., Chem., 1, 539 (1967). (7) T. Huff, C. J. Bushman, and J. W. Cavender, J. Appl. folyrn. Scl., 8 , 825 (1964). (8) C. Tosl, M. P. Lachl, and A. Pinto, Macromol. Chem., 120, 225 (1968). (9) N. J. Wegemer, J. Appl. Polym. Scl., 14, 573 (1970). (10) J. Lomonte, J. Polymer Sci., Polym. Left. Ed., I , 645 (1963). (11) J. E. Brown, M. Tryon, and J. Mandel, Anal. Chem., 35, 2172 (1963). (12) A. Valvassorl and G. Sartorl, Chlm. Ind. (Mian),44, 1091 (1962); Chem. Absfr., 57, 16824f (1962). (13) G. Natta, Q. Mazzantl, A. Valvassorl, and G. Pajaro, Chlm. Ind. (Milan), 30, 733 (1957); Chem. Abstr., 52, 3729c (1958). (14) L. P. Lindeman and J. Q. Adams, Anal. Chem., 43, 1245 (1971). (15) D. M. Grant and E. G. Paul, J. Am. Chem. Soc., 86, 2984 (1964). (18) C. J. Carman, A. R. Tarpley, Jr., and J. H. Goldstein, Macromolecules, 8, 719 (1973). (17) J. G. Murray, J. Zymonas, E. R. Santee, Jr., and H. J. Harwood, folym. Prepr., Am. Chem. Soc., Div. folym. Chem., 14, 1157 (1973). (18) L. F. Johnson, F. Heatley, and F. A. Bovey, Mscromkuks, 3, 175 (1970). (19) I. D. Rubin, “Poly(l-Butene),” Gordon and Breach, New York, 1968, Chap. 8. (20) C. A. Lukach and H. M. Spurlln In “Copolymerization,” Vol. 18 of “High Polymers”, 0. E. Ham, Ed., Intersclence, New York, 1964, Chap. I V A. (21) A. Zambelli, P. Locatelll, G. Bajo, and F. A. Bovey, Macromolecules, 8, 6819 (1975). (22) A. Zambelil, D. E. Dorman, A. I. R. Brewster, and F. A. Bovey, Macromolecules, 6, 925 (1973). (23) J. R. Lyerla, Jr., and G. C. Levy in “Topics In NMR Spectroscopy”, Vol. 1, G. C. Levy, Ed., Wlley, New York, 1974, p 79. (24) J. Schaefer and D. F. S. Natusch, Macromolecules, 5, 416 (1972). (25) J. Schaefer, Macromolecules, 5, 427 (1972). (26) Identity of NOE for methlne and methylene protons at 35 ‘C has been reported for three homopolymers by J. Schaefer, Macromolecules, 8, 882 (1073). (27) J. Schaefer In “Topics In NMR Spectroscopy,” Vol. 1, G. Levy, Ed., Wliey, New York, 1974, p 149. (26) I. Hyashl and K. Ono, Kobunshl Kagaku, 22, 446 (1965); Chem. Absfr., 64, 21740 (1966).
RECEIVED for review October 15,1976. Accepted May 20,1977. The funds for the spectrometer were provided in part by NSF Grant No. GP 37025.
Computerized Curve-Fitting to Determine the Equivalence Point in Spectrophotometric Titrations Scott R. Goode Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208
A nonllnear least-squares curve-fit Is used to determlne the equivalence polnt In spectrophotometrlctltratlons. Tltratlon curves, wlth a maximum absorbance of 0.4 to 0.8, are calculated under condltlons of dllferent equlllbrlum constants, and slgnal-to-noise ratios and then flt to a two-parameter model. The equlvalence polnt found Is wlthln 2 % of the true value as long as the noise Is less than 0.008 absorbance unlt, even when the tltratlon curve Is sufflclently smooth to show no change in slope at the equlvalence polnt. More favorable condltlons yleld an equlvalence polnt wlthln a few tenths of a percent of the true value.
Volumetric methods are among the most widely-used techniques of chemical analysis. Their popularity is a consequence of their precision, accuracy, and simplicity. The 1408
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
analytical result (location of the equivalence point) is based on a rapid concentration change; thus only relative concentrations need be measured. This makes titrations inherently more accurate than methods which require an absolute knowledge of concentration. The titration curve is a plot of some signal, proportional to analyte concentration as a function of the amount of titrant added. Titration curves have two general forms, sigmoidal and segmented ( I ) . An example of the former is the classical, sigmoid-shaped curve which resulta when pH is plotted during the titration of an acid with a base. The segmented curve is obtained when a parameter which is related linearly to analyte concentration, e.g. absorbance, is corrected for dilution and plotted as a function of titrant added. The accuracy and precision of the chemical analysis are directly related to the error in locating the equivalence point. When a sigmoidal titration curve is obtained, the inflection
