Table I. Recoveries of Sodium Cyclamate and Calcium Cyclamate Using Cyclohexylamine as Standard Sodium cyclamate Calcium cyclamate Mg
taken 14.3 13.4 39.5 36.8 59.6 60.5
z
Recovery, 100.5 102.8 95.0 100.7 101.8 98.4 Av 99.9 =k 2 . 1
ME
taken 15.8 14.7 33.9 37.1 52.1
60.4
z
Recovery, 100.9 98.5 99.9 99.7 100.7 98.6 Av 99.7 f 0 . 8
There was very little difference between the hydrolysis rates obtained with the two acids. See Figure 1. Tests were made on 1.5 and 4N hydrochloric acid solutions to determine volatility of HCI in the sterilizer, Both solutions were left in the sterilizer for 15 hours, then titrated to determine whether the concentration had changed. N o significant change was found-i.e., a difference of less than 3 % was observed after heating. Effect of Heating Time at Constant Temperature and Acidity. The optimum time of hydrolysis was determined by analyzing several portions of sodium cyclamate (0.5 mg,/ml) keeping all conditions constant except the time of hydrolysis. The hydrolysis time was varied from 0.5 t o 15 hours, and the absorbance of the developed color as function of time is given in Figure 2. Analysis of the experimental data shows that the rate of
hydrolysis is first order with respect to sodium cyclamate and follows the integrated rate law, 2.303 log
=
-kt
where A t = absorbance of (I) a t time t and A , is the absorbance of (I) when all the sodium cyclamate has been hydrolyzed to cyclohexylamine. The half time for the hydrolysis reaction is 1.17 hours. On the basis of these results, it was decided to use a heating time of at least 7 hours at 125' C in the analytical procedure to assure quantitative hydrolysis of sodium cyclamate to cyclohexylamine. Varying amounts of sodium cyclamate and calcium cyclamate (15 to 60 mg) were analyzed according to the procedure given under Experimental. In addition, corresponding quantities of cyclohexylamine were carried through the color development procedure. Recoveries of sodium cyclamate and calcium cyclamate, referred to the cyclohexylamine standard, averaged 99.9 i 2.1 and 99.7 f 0.8 %, respectively, verifying the quantitative hydrolysis of both cyclamates. See Table I. The method developed in this paper is intended for application to foods containing cyclamates. It has been established that sodium cyclamate (0.5 mg/ml) can be quantitatively determined by our procedure in the presence of 3 0 z by weight sucrose or 2.5 by weight of saccharin. The method has also been successfully applied to canned pears. Procedures for specific foods are under development and will be reported elsewhere.
RECEIVED for review August 10, 1967. Accepted November 15,1967.
Monomer Sequence Distribution in Ethylene-Propylene Copolymers by Computer Analysis of Infrared Spectra Harry V. Drushel, J. S. Ellerbe, Robert C. Cox, and Lloyd H . Lane Esso Research Laboratories, Humble Oil & Refining Co., Baton Rouge, Louisiana The purpose of this study was to elucidate the microstructure of ethylene-propylene copolymers from infrared spectra in which the bands of interest were seriously overlapped. Spectra were digitized in the methyl and methylene rocking region (700-1000 cm-l) using a general-purpose instrument based on voltageto-frequency converters and an electronic gated totalizer with punched paper tape readout. Methylene group frequencies for 2, 3, or 4+ contiguous groups occur a t 750, 732, and 722 cm-1 with half-widths of about 12 to 20 cm-1 which do not permit their spectral resolution. Similarly, the methyl absorption for 1, 2, or 3+ contiguous propylene monomer units at 937, 960, and 972 cm-1 are not resolved. The digitized spectra were analyzed by an iterative least-squares procedure using a computer to provide band positions, intensities and half-widths for the overlapped bands in these regions. The contribution from each structural unit was calculated using band areas derived from computer-resolved band parameters. Results were treated in terms of the effect of composition (ethylene-propylene content) on the relative concentration of the measured structural features. The computer approach was also checked by evaluating the integrated 370
e
ANALYTICAL CHEMISTRY
70821
absorptivities for the symmetrical and asymmetrical C-H stretching frequencies for methyl and methylene groups in a series of n-alkanes.
THEPROPERTIES of ethylene-propylene copolymers are determined by such factors as the relative percentage of each monomer in the polymer, the distribution of monomer units along the polymer chain, and the way in which the monomer unit has entered the chain. A number of workers (1-8) have discussed the application of infrared spectrophotometry to the determination of ethylene(1) G. Bucci and T. Simonazzi, Chim.Ind. (Milan),44,262 (1962). (2) F. Ciampelli, G. Bucci, T. Simonazzi, and A. Santambrogio, Chim.Ind. (Milan), 44, 489 (1962). (3) H. V. Drushel and F. A. Iddings, ANAL.CHEM.,35, 28 (1963). (4) T. G o d , Makromol. Chem., 42, 1 (1960). (5) G . Natta, G. Mazzanti, A. Valvassori, and G. Pajoro, Chim. Ind. (Milan),39, 733 (1957). ( 6 ) W. E. Smith, R. L. Stoffer, and R. B. Hannan, J. Polymer Sci'., 61, 39 (1962). (7) R. L. Stoffer and W. E. Smith, ANAL.CHEM., 33, 1112 (1961). (8) P. E. Wei, Ibid., 215 (1961).
propylene copolymer composition. However, the choice of infrared bands for use in compositional analysis is influenced by effects related t o crystallinity, monomer sequence distribution or other microstructural features (3,9-14). Infrared spectrophotometric measurements on monomer distributions have been focused primarily on the methylene group rocking frequencies between 720 and 750 cm-l. For example, Veerkamp and Veermans (15) developed a unique differential method for measuring (CH& and (CH& units a t 745 and 730 cm-1, respectively, by use of a normal-alkane in the reference cell to compensate for absorption attributed t o longer methylene chains. The frequencies cited for the methylene sequences ranging from l to 4 or more contiguous units vary slightly from worker to worker (2,3,15-17). Bucci and Simonazzi (18) have reviewed and studied the use of this region of the spectrum. In addition to accurately assigning the bands in the region between 900 and 650 cm-' and evaluating their corresponding absorptivities, they developed a method for calculating the contribution from each of the methylene sequences using a relatively simple 3-point measurement (a series of 3 simultaneous equations) t o evaluate band intensities for the overlapped bands in this region. Digital computer techniques for curve fitting have been used t o evaluate band parameters in cases where bands are overlapped for several different spectral methods. For example, Stone (19) described a method for mathematical resolution of overlapped spectral bands in the near-infrared spectrum of benzene, Several groups of workers (20-22) have used leastsquares fitting procedures t o determine g-values and hyperfine coupling constants from electron paramagnetic resonance spectra. Rosenberg and Smith (23) described the application of computer techniques to resolve the overlapping bands in the C-H stretching region of the infrared spectra. Swalen and Reilly (24), among others, have used iterative methods for the analysis of complex nuclear magnetic resonance (NMR) spectra. Schaefer (25) presented a n extensive treatment of random monomer distributions in copolymers (ethylenevinyl chloride and ethylene-vinyl acetate) by a least-squares fit t o spin-decoupled high-resolution N M R spectra. Pitha and Jones (26) recently made a thorough comparison of seven numerical methods of fitting infrared absorption band envelopes with analytical functions using nonlinear least-squares approximations. The comparisons were made with respect (9) P. J. Corish, R. M. B. Small, and P. Wei, ANAL. CHEM.,1798 (1961). (10) P. J. Corish and M. E. Tunnicliffe, J . Polymer Sci., C7, 187 (1964). (11) V. L. Falt, J. T. Shipman, and S. Krimm, Ibid., 61, S17 (1962). (12) J. M. Lamonte, Ibid., B1, 645 (1963). (13) G. Natta, A. Valvassori, F. Ciampelli, and G. Mazzanti, Ibid., 3A, 1 (1965). (14) J. Van Schooten, E. W. Duck, and R. Berkenbosch, Polymer, 2, 357 (1961). (15) T. A. Veerkamp and A. Veermans, Makromol. Chem., 50, 147 (1961). (16) A. V. Iogansen, Zaacodskaya Lab., 25, 320 (1959). (17) H. L. McMurray and V. Thornton, ANAL. CHEM.,24, 318 (1952). (18) G. Bucci and T. Simonazzi, J . Polymer Sci., C7, 203 (1964). (19) H. Stone, J. O p f . Soc. Amer., 52,998 (1962). (20) J. A. Ibers and J. D. Swalen, Phys. Rec., 127, 1914 (1962). (21) T. S. Johnston and H. G. Hecht, J . Mol. Spect., 17,98 (1965). (22) D. W. Marquardt, R. G. Bennett, and E. J. Burrell, J . Mol. Spect., 7, 269 (1961). (23) A. S. Rosenberg and H. F. Smith, Pittsburgh Conf., Mar. 2-6, 1964, paper No. 221. (24) J. D. Swalen and C. A. Reilly, J . Chem. Phys., 37, 21 (1962). (25) J. Schaefer, J . Phys. Chem., 70, 1975 (1966). (26) J. Pitha and R. N. Jones, Can. J . Chem., 44, 3031 (1966).
t o degree of convergence and the computation time needed t o achieve an acceptable fit. Analog computers (27-29) have also been described. They are less time-consuming but require a certain degree of operator judgment. This paper describes the application of digital computer techniques for the evaluation of monomer sequence distributions from digitized infrared spectra. An iterative leastsquares method for calculating band parameters of overlapped bands is presented for both the methylene and methyl group rocking frequencies. This method provides information concerning the microstructural features related t o both ethylene and propylene monomer units in the polymer. EXPERIMENTAL
Sample Preparation. For studies in the 700-800 cm-' region thin films of the copolymer were prepared with a heated press as previously described (3). Weaker absorption in the 900-1000 cm-' region, particularly for copolymers having low propylene contents, required the use of thicker films of about 1 mm thickness. Infrared Spectrophotometer. A Beckman Model IR-9 infrared spectrophotometer was used t o obtain infrared spectra of the copolymer films in digital form. Spectra were presented in a linear absorbance vs. frequency (cm-1) format. Voltage signals corresponding to pen position and frequency (cm-l) were digitized by means of a general-purpose data acquisition system described in the section below. A voltage corresponding t o the frequency (cm-l) was obtained from a potentiometer linked mechanically t o the chart drive mechanism. A simple magnetic clutch was used to engage or disengage the system for starting or stopping the scan, resetting spectral positions, etc. The voltage signal corresponding to pen position was tapped directly from the IR-9 pen servo system (ca. 0 to 11 volts). In this way, spectra were digitized in terms of transmittance or absorbance depending upon the mode of operation selected on the spectrophotometer. Of course, conversion between transmittance and absorbance can be easily accomplished on the computer. Digitizing Equipment. Spectra were digitized by means of a general-purpose data acquisition system constructed from standard components. A simplified schematic diagram of the apparatus is presented in Figure 1. Analog to digital conversion was accomplished by a pair of voltage to frequency converters (one for each signal). The electrical pulses from the converters were counted by means of electronically gated totalizers. Gate intervals were determined by the timer and present controller. The raw digital data (counts) from each channel were converted to the proper binary code by the tape perforator adapter and then punched on paper tape by a Tally punch. Computer Techniques. The raw digitized spectral data were converted to proper units, treated by a smoothing routine, interpolated, and prepared for plotting by means of a n IBM-1620 computer. Similar techniques were described by Savitzky and Golay (30). Factors for converting to proper units were determined for each spectrum, Le., counts per absorbance unit and counts per crn-'. This intermediate program generated a deck of cards representing data points ( A , cm-I) at equal increments (e.g., at every 0.5 to 1.0 cm-') along the spectrum. An auxiliary program was also used to calculate first and second derivatives for use in locating peaks, shoulders, or inflection points. (27) F. W. Noble and J. E. Hayes, Jr., A m . N . Y . Acad. Sci., 115, 644 (1964). (28) E. D. Becker, Specfrochim. Acta, 17, 436 (1961). (29) Anon., Chem. Eng. News, 43, 50 (November 15, 1965). (30) A. Savitzky and M. J. E. Golay, ANAL. CHEM.,36, 1627 (1964). VOL. 40, NO. 2, FEBRUARY 1968
371
TAPE PERFORATOR
SIGNAL INPUT
TOTALIZER
TIMER AND
GATE OUTPUT
PRESET CONTROLLER
Figure 1. Block diagram of the digitizing apparatus
The digitized spectra described above were used on an IBM 7074 computer to mathematically resolve the overlapped bands in the methyl and methylene rocking region of the spectrum. The computer program which was used was a modification of the iterative least-squares method described by Stone (19) altered in such a way as to be similar to the method of Meiron
are the vectors of the parameters (Le,, band width, band position, etc.) and their current values, and H is the matrix whose i, jth element is [in = I c a I c d
* dIk c a l c d =2x---k =1
api
(31). .
(5)
aP5
+
I
In the computer program, a spectrum is assumed to be of the form
d z k calcd
This linear system of equations may be solved for p if the matrix, H , is nonsingular.
N
Z(V) =
QI
+ PV + YV' + ,Eajgj(v,
yjo,
J=1
Avj)
(1)
where the first three terms represent background absorption, aj is the peak intensity of band j , v j o is the band position, and Avi is the band width parameter (this is half of the band width a t half height). For all of these studies the function gj was of the Lorentzian form 1
g5 =
1
+ (T)'
*
although the Gaussian form was included as an option in the program. The method of least squares is used to find the values of the parameters in the above equations which give a minimum value of the least squares function rn
points
N
The minimum value of the function is found by setting the derivative (with respect to the parameters) equal to zero and solving for the values of the parameters. As pointed out by Stone (19) the resulting equations are not simple and must be solved by a series of successive approximations. If the resulting set of partial differential equations is expanded in a Taylors series about a set of initial values for the unknown parameters, p I o ,pz0, . . . . . . . . . . p0sn+3, the following equation is obtained, written in matrix form:
= g + (r, - Po>H
+ - +
0
-+
-+
+
(4) 4
-+
where g is the vector with components b F / d p p l op, and p o (31) J. Meiron, J. Opr. SOC.A m . , 55, 1105 (1965).
372
ANALYTICAL CHEMISTRY
The complete matrix, H , is often difficult to invert and Stone (19) used an approximation to circumvent this difficulty in which he let the i, jth element be zero unless i = j . In our program, we have retained all of the off-diagonal elements a t the risk of requiring more computer time for the inversion. More rapid convergence was achieved by using the entire matrix and its diagonal form in a manner similar to that described by Meiron (31). -
+
p = po
+
- g r ( H + O.OlB)-l
(7)
where H is the entire matrix and B is the diagonal form of the matrix. Meiron's approach probably yields more rapid convergence because the scalar is selected which gives the lowest value of F at each step (instead we used the fixed value 0.01). The step length factor, r (a multiplying factor of the matrix), is adjusted internally in the program so as to guarantee a decrease in the value of F. For spectra which cannot be fitted too well, considerable computer time is often used to going through the r routine on each iteration in order to reduce F. Any parameter may be held constant in the program. The value of bF/appkis set equal to zero just before phi is computed. The program was also modified to prevent peaks from becoming negative (an unrealistic situation) in an attempt to find the minimum value of F. Also, the program scales the frequency (cm-l) data to average zero (by subtracting the average value) in order to avoid large numbers in the matrix terms for the background. The output lists- the parameters after each iteration, the gradient vector ( g ) , and its norm (listed as GQT), the value of F (called the Loss), and the step length factor 7 . The final -t
results, when g is small (Le., < a set value) or when a given maximum number of iterations is reached, include the standard error of estimate.
Computer-Evaluated Band Parameters and Integrated Absorptivities for n-Nonane in the C-H Stretching Region of the Spectrum Half width Integrated Band parameter,a absorptivity,* position, v (cm-1) Mode of vibration Intensity, ( A ) (Av) Area, (T Av A ) (cm mole-') X 10-6 0.391 8.38 10.28 6.4 2858.9 -CHr Sym. str. 0.143 4.63 2.08 1.3 2877.0 -CHa Sym. str. 0.051 11.12 1.78 1.1 Combinations and 2900.4 overtones of -CHscissoring and --CHI bending 0.063 12.44 2.46 1.5 2915.1 -CH,-Asym. str. 0.825 11.10 28.80 17.9 2932.2 -CH3 Asym. str. 0.441 8.20 11.52 1.2 2965.8 Table I.
t
This is the band width at the band height Cell path length was 0.055 mm and concn was 37.40 g/liter. The formula used was simply a = A/bc, where A is the area in cm-l, b is the path length in crn, and c is the concentration in moles/liter. Above values should be multiplied by 2.303 to convert to values obtained by integration according to the formula A,,,, = 2.303 Jf$' b
u =
[F/(M - N)]"2
(8)
and an error analysis (difference between actual and calculated values at all digitized points along the spectrum). DISCUSSION OF RESULTS
Application to the C-H Stretching Region of the Spectra. In order to test the performance of the digitizing equipment and the computer programs, the areas of the bands in the C-H stretching region of the infrared spectra of n-alkanes were evaluated. Band parameters obtained for n-nonane, a typical example, are presented in Table I. Band areas were calculated from the band parameters using the formula
Area
=
( ~ / 2 (band ) width) (band intensity)
(9)
Integrated absorptivities were calculated from the area, cell path length, and concentration. As shown in the table, the best fit to the experimental spectrum was obtained only if two small bands were assumed to be present near 2900 and 2915 cm-1 in addition to the 4 obvious asymmetric and symmetric C-H stretching bands for methyl and methylene groups. Examination of the error curve readily provided clues as to the presence of these small bands. Rosenberg and Smith (23) also found a small band near 2915 cm-1 in a similar study. These weak bands may be attributed to combinations and overtones of methylene scissoring and methyl group C-H bending modes. The success of the computer approach in resolving the overlapped bands is depicted in Figures 2 and 3 in which the integrated absorptivities are plotted against chain length. Assuming no specific interactions, the asymmetric and symmetric methylene C-H stretching absorptivities should be related linearly to the number of methylene groups in the molecule as shown in Figure 2. On the other hand, if resolution of the bands by the computer technique has been satisfactorily accomplished the absorptivities for the two methyl group bands should be independent of chain length as shown in Figure 3. These values agree fairly well with integrated absorptivities which were obtained by a graphical evaluation of overlapping for alkanes and alkanols (32). The values for integrated absorptivities per functional group as determined by the two methods are compared in Table 11. Differences (32) H. V. Drushel, W. L. Senn, Jr., and J. S. Ellerbe, Spectrochim. Acta, 19,1815 (1963).
Table 11. Comparison of Integrated Absorptivities for C-H Stretching Modes as Determined from Computer Evaluated Band Parameters and Mechanical Integration Functional Group Integrated Absorptivities (cm mole-') X le6 Computer Mechanical C-H Stretching Mode Method Integration Asyrn. -CHI 8.23 6.38 Asym. -CH2-5.89 4.95 Sym. -CHI 1.50 1.64 Sym. -CH22.10 1.85
I
l
l
l
1
1
1
1
1
l
I
I
I
I
NL'UBER OF METHYLESE GROLPS
Figure 2. Infrared absorptivities for the -CH2bands from computer-evaluatedband parameters
stretching
between the two methods may be attributed to such factors as differences in spectrophotometers, errors in evaluating cell path length, errors in graphical methods of correcting for overlap, errors in calculating area from band parameters, etc. The Methylene Rocking Region. An infrared spectrum of a polymer film in the methylene rocking region of the spectrum is shown in Figure 4. Four bands were clearly discernible and the number of contiguous methylene groups which each represents along with their approximate frequencies are included in the figure. Actually, the frequency for long methylene chains does not reach a constant value until 5 contiguous groups are involved. It should be pointed out that the frequency for 4 contiguous groups is slightly higher than that for 5 groups. Values from 724 to 728 cm-l VOL. 40, NO. 2, FEBRUARY 1968
373
HCMBER OF METHYLESE CROL'PS
Figure 3. Integrated absorptivities for -CHI bands from computer-evaluated band parameters
stretching I 8 SO
I 800
I
I 750
I
I 700
FREQUENCY (crn-')
have been quoted (14, 17, 18) for 4 contiguous groups but by means of the computer program no appreciable contributions at these frequencies have been observed. Therefore, the longer methylene chains in the ethylene-propylene copolymers probably represent 5 or more contiguous methylene groups. For simplicity we shall refer t o this grouping as four or more contiguous methylene groups, Le., (-CH2-)n 2 4. It is not difficult t o visualize the origin of 3 contiguous methylene groups in a structure where the monomer units alternate.
Two contiguous methylenes might be formed from two adjacent propylene units in which the second unit enters opposite to its normal configuration. Alternatively, an ethylene unit may enter between 2 propylene units in the configuration shown near the center of structure 111. The fact that 4 contiguous methylene groups have not been observed t o be pres-
Similarly, a random copolymer should give rise to isolated methylene groups and segments containing 5 contiguous groups as well as 3 contiguous groups.
ent t o a significant extent implies that the structure for PEP segments as shown on the right side of structure I11 occurs infrequently along the polymer chain.
-CH-CHZ-
E
I I CH3 l i 1 -CH-CH2I I I
P
I
I I I -CH2-CH2I I
E
Only by invoking a polymerization mechanism giving rise t o head-to-head and tail-to-tail propylene units can groupings of 2 or 4 contiguous methylene groups occur.
374
0
Figure 4. Infrared spectrum of an ethylene-propylene coC?)in the methylene rocking region of polymer (54.3 wt the spectrum
ANALYTICAL CHEMISTRY
Portions of a typical computer printout from the analysis of the methylene rocking region of an ethylene-propylene copolymer are shown in Table 111. As seen in this table it was
Table 111. Portions of a Typical Printout for the Methylene Rocking Region of an Ethylene-Propylene Copolymer (54 wt Ethylene)
6 BANDS, 3 2 7 9 A T A PTS, O.OOlOOO#S 2 RACKGKPUQD TEi?YS 9 14 I T E R A T I O M S T
J@P.
TOL,
9
2 F I X E D PARAMS.
f I X E D PARAMETERS
RAND NO
PARAM Ng
4 5
2 2
.
INTFNSI J Y I) 3 ~ 1 c 0 ~ 0.2C933CC
0.08n')nQ 0.053900 0 03 O G O C o.ol'tOc'3 -O.Oh'3000
GRAD1 ENT V E C T O R
-
1 98099 - 0 . '31 1 7 0 -0.0 7 3 4 7
-2.65ri56 0. o c o 1 7 -0.33514 343.79168
-6.14138
-2.45995
-1 9 2 2 8 5 0.00179
0.00319
0.15290
-0.14768 0.00056
o.oecc5
-17. Q 1 3 4 9
-0.O0632
-0.09097
-0. OG C O O
-n. PO691 -2. ~ 7 r 3 0 C l -0.ODc)04
-0.00556 1).OO\?OL -0. no09 L
(31)1 3 5 C!.O0DOL -0.ci)coo
0.233474 O..QOCO 1 -0.liOC30
INFORMAT ION V E C T f l R
GR A !I IEN T V E C r.9R
-0 .')040.7 -0.300o1 -0.00Gl9 -0.3LSlL
-G.00556 4. i.!COU 1 -0.OCJQC7 1.78799
(1!.
INFnRMATInY VECTOR
GOT#
~ a s s f i ! o.
1.7R:+OR91
0016353
fTEII.4TION YO.
8
T4\1# C. 75CG00
FINAL RESULTS STD.
ERROR#
OeC023344
INTENSITY PEAK P7SITIOY* 0 366457 7 2 3 F!416?0 0-124531 736.74542n 0.063196 75 5 . a 1 2 6 7 ~
0.019107 0.0393347 CsG19873 -0.Q39570.
770
cT)ccoo
R17.119130 858. C q O G Q O
O.C3017h
HALF ! J 1 9 T H 7.777146 9.552904
9.5399Gl
6.333227 12.503523 4 4 . 4 3 1 4r)4 0. C B O O r 3 0
(Continued)
Table 111. (Continued)
709.53928 7 11 4 1 4 6 4 7 13 3 7468 715.29147 717.22312 719.16643 721.1331 6 7 2 3 . C582 8 7 2 5 . 0 3 176 726.98176 729.09143 731.05653 733.061 3 9 735.12947 737.03973 739. r5479 741.14235 743.02823 7 4 5 . ~ 1 9 ~ ~ 3 746.95173 748.8 7 6 3 5 7 5 0 . Ah938 752.75529 754.80C 3 1 7 5 6 . 9 5 1 87 758.99314 761 03329 763.01674 765.09297 7 6 6 9 56 75 768.84541 770.94833 17 3 Q 4 496 775.17831
.
. . .
71G.15275 712.11551 716.0L934 715 , 9 6 3 9 5 7 17.89972 719.83597 721.77586 723.72557 725.73235 777.66447 7 7 9. 7S't 1 7 731 715 9 9 733.69235 735.67296 737.67452 739.69471 741.72279 743.653507 745.65233 747.616q4 749.53956 751.43983 7 5 3.43 1 4 6 755.49738 757,55455 759.65445 761.75C57 753.65972 765.68616 767.61762 769.59272 771.58312 773.7h690 775.92910
necessary to add bands at 770 cm-1 and 858 cm-1 (in addition to the bands of interest at 723,735,753, and 818 cm-1) in order to obtain the best fit to the experimental spectrum. To prevent these two bands from assuming the position of the bands of interest their positions were fixed in the program. If this was not done, occasionally the parameters would assume unreasonable values (as would the background terms also), The weak band near 770 cm-l (in most cases it was fixed at 767 cm-l) appeared in all of the spectra. Also, in most cases its band width parameter was also fixed at 10 cm-'. Absorption at these frequencies is often attributed to pendant ethyl groups. It is possible that such structures exist and their origin could be conceived as the insertion of a butene molecule derived from dimerization of ethylene. We have, in fact, identified a wide variety of dimers, trimers, and tetramers involving ethylene and propylene in the recovered diluent. Some typical band parameters obtained by means of the computer program are listed in Table IV. The mole methylene groups in each sequence category were calculated from areas (using the parameters) normalized as shown in Table IV. Absorptivities for a number of pure hydrocarbons as models were determined but wide variations in methylene group absorptivities from compound to compound were ob376
ANALYTICAL CHEMISTRY
0.30038 C.01364
C'oOO452 G. 0 6 4 2 9 -0.30256 -Q.C)0578
0 002YP 0.00157 -0.002 5 6 -9 0 0 1 6 1
.
3.00253 O.OnGR7 -9 0 0 1 1 4 -0 0 0 3 Q 1
.
0.00c27
-0 0 0 17 9 0.00192 -0.0$104ij -0.n0074 0.03216 Q.30124 0.90054 0. 013967 -9 0 C09 1 -3oQ5r)27 3.30027 9.30185 0.30 1 1 5 0.3005P -3.9or377 -0.00101 -0.00073 i).OG;225 3.0020a
.
710.781 7 2 712.79310 714r67502 7 1 6 6 0 0 16 7 18 . 5 2 6 9 3 72'7.44209 722.43853 724.36G44 726 36206 728.38039 732.39381 732- 3721 8 734,40702 736.32402 73a.37210 740.44689 742.35Q64 744.34338 746,32387 743.2 5393 7543 2 1 3 9 0 752.09743 754.16876 756.17570 75R.24907 760.30249 762.39379 754.38953 766.30240 755.17108 7713.26401 772.29742 774.4440 1 776.61017
0.00328
O.OCG91 O.OZ445 O.CC437 -0. PC464 -0 0 0 3 2 9 O.CG449 0*?@C21 -0. GC 2 1 3 -0.0cc57 0.OC130 0 0 Ci 14 4 - 0 .nCO 7 6 -0 C 0 1 7 3 6 0 0 15 6 -0, G G C h R 0oOC053 -0 09 1 3 3 -0s 0 0 2 0 5 0eOOC76
.
. .
.
9,COC53 -0. C 3 L 9 9 -Q. Oi)C'4 1 - 0 ;? 0 2 8 3 -C. '3C C 5 6 3.0OC 5 6 0.09184 0. O O C 8 2 0000099 -0 000 109 -0 0 0 0 9 7 -C o O C C 3 8 0.06295 c)oco149
.
served. Therefore, for the calculation of the relative concentrations of methylene groups in the different categories, it was assumed that the integrated absorptivities were the same for all categories. This assumption was made for convenience because of the lack of consistent data regarding the absorptivity per methylene group in different methylene sequence lengths in selected hydrocarbons. The data suggest, in fact, that the absorptivity increases as n, the number of contiguous methylenes, decreases, Relative areas were converted to percentages by normalizing as follows. It was assumed that ethylene units (C,) contribute two methylene groups and propylene units (C,) contribute one methylene and one methyl group. All results were normalized to the sum of all methylene and methyl groups in the polymer (the methine groups were not included in the calculations). The distributions of methylene groups in 1, 2, 3, or 4 or more contiguous units as a function of composition are presented graphically in Figure 5 . The shape of these curves and the quantitative distributions of the structures agree rather well with the data presented by Natta and coworkers (33) and Bucci and Simonazzi (18). (33) G. Natta, G. Mazzanti, A. Valvassori, G. Sartori, and D. Morero, Chim. Znd. (Milan), 42, 125 (1960).
FOUR OR MORE CONTIGUOUS GROUPS
THREE CONTIGUOUS GROUPS
II \
MOL. '3 C z
(751 CM-l)
UI
B
B
P
P
= CHZ
(ETHYLESE (PROPYLESE TERMIN4TION) TERMIN.ATIOH)
% Cg=
I S O L A T E D METHYLEHE GROUPS
TWO CONTIGUOUS GROUPS
I I I
4om MOL.
,C '
- C H = CH2
E 0
20
LE
i
P
0
50
100
MOL. % C g =
MOL. % C 3 =
Figure 5. Methylene group sequence distribution as calculated from computer-resolved band parameters
(3 OR MORE CONTIGUOUS UNITS)
1000
C 3 UNlTS
ISOLATED PROPYLENE
UNITS
9 50
900
FREQUENCY (CM -')
The Methyl Rocking Region. Examination of the infrared spectra of a large number of copolymers covering a wide range in composition led to the conclusion that the behavior of the methyl rocking region paralleled, in a sense, the methylene region. In fact, Natta and coworkers (13) also recently observed that this region may give clues as to the distribution of propylene sequences. Whereas the position of the 1155 cm-1 methyl absorption is not appreciably affected,
Figure 6. Infrared spectra of ethylene-propylene copolymers in the methyl rocking region of the spectrum the position of the band near 970 cm-l is influenced by the number of methylene groups separating the methine groups to which the methyl groups are attached. For example, copolymers containing low concentrations of propylene show relatively more absorption at 937 cm-* as compared to 972
Table IV. Some Typical Computer-Resolved Band Parameters from Infrared Spectra of the Methylene Rocking Region Normalized* Sample Mol Z Ca vmsx (cm-9 Av (cm- I) A Av A Mol -CHs1 68.3 723. l a 7.11 0.175 1.246 11.9 733.5" 7.66 0.174 1.332 12.7 751.5 9.89 0.147 1.451 13.9 767. Oo 10.00= 0.005 0.046 ... 817.0a 17.00" 0.191 3.239 31 .O __ 65.9 0.359 2.253 40.1 6.56 721.3" 2 34.5 0.139 1.358 23.1 9.77 731.9" 0.055 0.511 8.7 9.25 751.4 10.00" 0.013 0.125 ... 767. O' 0.038 0.638 1.09 815.0° 17.00. 82.8 721.34 6.81 0.546 3.718 27.8 3 46.8 731 .4a 9.65 0.289 2.791 20.9 750.7 11.33 0.138 1.567 11.7 767.00 10.005 0.003 0.033 ... 814.4" 17.00 0.127 2.166 * 16.2 76.6 3, Strippede 46.8 730.8 9.31 0.273 2.542 19.5 750.8 7.58 0.120 0.910 7.0 812.P 17.000 0.167 2.836 21.7 from 721.3 6.81 0.546 3.718 28.5 above 76.6 Parameters fixed. * Normalized to mol. C mol. G/2. c After subtracting the spectrum of n-hexadecane. ~
~
0
+
VOL. 40, NO. 2, FEBRUARY 1968
377
THREE OR MORE CONTIGUOUS C UNITS (PROPYLENE B?OCKS) 50
ISOUTED PROPYLESE CXITS TWO CONTIGUOUS UNITS
,
(OR ALTERSATISG STRL'CTURE) 20 I
Q
0 50
100
0
MOL. F CJ=
100
50
MOL. W Cg=
MOL. % C3=
Figure 7. Propylene unit (methyl group) sequence distribution as calculated from computer-resolved band parameters cm-1 than at higher propylene levels. At these low levels of propylene, more structures involving isolated propylene units or involving alternating ethylene and propylene units should be expected. It is not surprising, then, that a band near 937 cm-' should also be observed for squalane (2, 6, 10, 15, 19,23-hexamethyltetracosane) and hydrogenated polyisoprene which contain the sequences shown in structure (I). In fact, after the study described herein was completed, Ciampelli and Valvassori (34) proposed a propylene distribution index based on the ratio of absorbances at 972 and 937 cm-1 which are, respectively, proportional to the number of propylene units in sequences of two or more units and to isolated propylene units. Compounds in which only two (rather than 3) methylene groups appear between the methyl-methine groupings absorb at somewhat higher frequencies, from 955 to 960 cm-'. Koenig, Wolfram, and Grasselli (35) have observed that the 972 cm-1 band in polypropylene becomes asymmetric toward lower frequencies as atactic content increases. All ethylene (34) F. Ciampelli and A. Valvassori, J . Polymer Sci.; C ; (Abstr.) Polymer Previews, 2, 398 (1966). (35) J. L. Koenig, L. E. Wolfram, and J. G. Grasselli, Specfrochim. Acta, 22, 1233 (1966).
propylene copolymers show this asymmetry suggesting the presence of a band near 960 ern-'. In fact, we have shown that an atactic polypropylene fraction has a definite band at 964 cm-l by means of the computer program. It may also be possible that 2 contiguous propylene units with ethylene units on each side could produce absorption near 960 cm-' as shown below.
1
-CH2-CH2-
1 TH3
[ -CH-CHz-
I E
I
P
I I CHI I / I -CH-CHr I I
I -CHz-CHzI I
I
I
P
I
I I
E
(W Three or more (blocks) of propylene obviously absorb at 972crn-'. Figure 6 shows some typical infrared spectra in the methyl group rocking region of the spectrum. Band assignments according to the discussion above are shown in the figure. The enhanced relative concentration of isolated propylene
Table V. Some Typical Computer-Resolved Band Parameters from Infrared Spectra of the Methyl Rocking Region Normalized* Mol X C3 vmax (cm-9 Av (cm-1) A Av A Mol -CHa Sample 100 962.0" 1.15 0.005 0.006 0.1 Heptane Insol. 972.0 3.75 0.796 2.985 49.9 Polypropylene 50.0 100 ? 939.0. 3.72 0.009 0.032 0.3 Ether Extract 964.2 9.52 0.254 2.417 23.5 of Atactic 973.0 5.10 0.530 2,702 26.2 Polypropylene __ 50.0 ? 0.830 5.9 14.27 0.058 68.5 939.50 1 0.175 1.718 12.1 9.83 960.00 0.367 2.300 16.3 970.7 6.26 34.3 0.224 3.919 8.0 17.53 44.5 937.5 a 4 0.356 4.425 9.0 12.43 960.9 0.394 2.615 5.3 6.64 971.l a 22.3 0.153 2.702 4.2 17.62 15.0 937.s a 5 0.148 1.900 2.9 12.87 961.5a 0.051 0.270 0.4 972.Oa 5.25 ~
7.5
Parameter fixed. b Normalized to mol % (32. Q
~
378
ANALYTICAL CHEMISTRY
units is obvious in the polymer containing only 12.5 wt% propylene. Examples of the application of the computer program to the 900-1000 cm-* region of the spectrum are given in Table V. Because the bands were badly overlapped in this region the band position parameter, v, was fixed in most cases. The 964 cm-l band for the atactic propylene was a well-defined shoulder and, rather than fixing V , the computer program defined its value. Band areas and other calculations were similar to that described for the methylene rocking region. Plots of the contributions for the different microstructures against composition are presented in Figure 7. From these curves it is obvious that the behavior in the methyl rocking region is rather analogous to the behavior in the methylene rocking region of the spectrum. Spectral Stripping Using the Computer. An attempt was made to subtract the spectrum of a n-alkane from the spectrum of a copolymer in the 700-800 cm-' region. In effect, this is simulating the differential technique of Veerkamp and Veer-
mans (15). For the spectral stripping, the amount of the n-alkane spectrum to be subtracted was determined from the computer-resolved band parameters in a preliminary application of the computer program described herein. The results, which were included in Table IV are nearly the same as results when the computer program was applied alone. More significantly, the stripping technique eliminated the weak absorption at 770 cm-' which was also present in the n-alkane, making it unnecessary to include this band in the second application of the program following the stripping operation. ACKNOWLEDGMENT
The authors thank Esso Research Laboratories for permission to publish this material. We also wish to thank H. Stone of Shell Development Company for supplying information on the computer program. RECEIVEDfor review July 27, 1967. Accepted November 27, 1967. Presented at the Eight Annual Eastern Analytical Symposium in New York, N. Y . November 16-18,1966.
Indirect Ultraviolet Spectrophotometric and Atomic Absorption Spectrometric Methods for Determination of Phosphorus and Silicon by Heteropoly Chemistry of Molybdate Thomas R . Hurfordl and D. F. Boltz Department of Chemistry, Wayne State Unicersity, Detroit, Mich. The feasibility of effecting a selective extraction separation of molybdophosphoric and molybdosilicic acid followed by quantitation either by ultraviolet spectrophotometry and/or atomic absorption spectrometry has been investigated. The molybdophosphoric and molybdosilicic acids are formed in acidic solution by the addition of an excess of molybdate. Molybdophosphoric acid i s extracted with diethyl ether from an aqueous solution which is approximately 1M i n hydrochloric acid. After adjusting the hydrochToric acid concentration of the aqueous phase to approximately 2M, the molybdosilicic acid i s extracted with a 5: 1 diethyl ether-pentanol solution. The extracts of molybdophosphoric acid and molybdosilicic acid are subjected t o acidic washings to remove excess molybdate. Each extract i s then contacted with a basic buffer solution to strip the heteropoly acid f r o m the organic phase. The molybdate resulting from the decomposition of the heteropoly acid in the basic solution i s then determined either by measurement of the absorbance at 230 mccusing an ultraviolet spectrophotometer or by measurement of the absorbance at 313.3-mp resonance line of molybdenum using an atomic absorption spectrometer. The optimum concentration ranges are approximately 0.1-0.4 ppm of phosphorus or silicon for the indirect ultraviolet spectrophotometric method and 0.1-1.2 ppm for the indirect atomic absorption spectrometric method.
BOTHPHOSPHATE and silicate ions react with molybdate ions in acidic solution to form heteropoly adds. Therefore, methods based on the formation of a heteropoly acid report l Present address, E. I. du Pont de Nemours & Co., Inc., Plastic Dept., Polyolefins Division, Orange, Texas.
phosphate and silicate as mutual interferences. This paper is concerned with the development of a method in which molybdophosphoric acid and molybdosilicic acid are formed, individually separated, and the amount of nonmetal determined indirectly by measuring the amount of molybdenum present in each heteropoly complex. Indirect ultraviolet spectrophotometric methods for phosphorus and silicon have been reported (1,2), but these methods did not eliminate the interference due to the other constituents presence. DeSesa and Rogers ( 3 ) determined phosphate in the presence of silicate by measuring the absorbance at 330 mp of the molybdophosphoric acid extracted with isoamyl acetate. The silicon was determined indirectly by correcting the absorbance at 332 mp of the combined molybdophosphoric acid and molybdosilicic acid in aqueous solution (prior to extraction) by using the previously determined absorptivity of molybdophosphoric acid in aqueous solution. They observed the trend of higher results for increasing amounts of phosphorus and a corresponding decrease in silicon and indicated that this separation needed further study. An indirect atomic absorption spectrometric method for phosphorus has been reported while this work was in progress. Zaugg and Knox ( 4 ) extracted molybdophosphoric acid in 2octanol and used citrate to suppress the effects of the
(1) C. H. Lueck and D. F. Boltz, ANAL.CHEM., 30,183 (1958). (2) L. Trudell and D. F. Boltz, Ibid., 35, 2122 (1963). (3) M. A. DeSesa and L. B. Rogers, Ibid., 26, 1381 (1954). (4) W. S. Zaugg and R. J. Knox, Ibid., 38, 1759 (1966). VOL 40, NO. 2, FEBRUARY 1968
379
