2320
Anal. Chem. 7904, 56,2320-2327
General Analysis of the Carbon- 13 Nuclear Magnetic Resonance Spectra of Vinyl Copolymers by the Spectral Simulation Approach H.N. Cheng* and M. A. Bennett Hercules Incorporated, Research Center, Wilmington, Delaware 19899
A general approach is developed for the characterization of vinyl and Vinylidene copolymers by lacNMR. The method involves the combined use of reaction probability models, Monte Carlo slmuiatlon, spectral prediction, and spectral stmulation. Empirical additivity relationships are devised for the 13C NMR chemical shifts of polymers, and substituent parameters proposed for the various comonomers. The entire computation is automated. The method enables simulated spectra to be obtained of homopolymers and binary and ternary copolymers of 21 common vinyl groups. The use and application of this approach are illustrated by suitable examples.
Table I. Vinyl and Vinylidene Functional Groups Recognizable by Program PSPEC Olefins ethylene propylene butylene 4-methyl-1-pentene
isobutylene
Acrylates/Methacrylates acrylic acid methyl acrylate acrylonitrile
methacrylic acid methyl methacrylate methacrylonitrile
acrylamide Haloal kenes
NMR spectroscopy is widely used as an analytical technique to characterize polymers (1-5). Much work has been I3C
done on homopolymers where information such as tacticity, regiospecificity, branching, and defect structures can be determined. In comparison, copolymer analysis is a less studied and perhaps slightly more difficult area. One application of 13CNMR is to identify unknown copolymers and to determine the overall copolymer compositions. More detailed analyses of copolymer spectra usually enable comonomer sequence distribution and reactivity ratios to be determined. Owing to the complexity of many copolymer spectra, complete assignments of the spectra are not necessarily a simple task. Nevertheless,because of the high information content of fully interpreted spectra, reports of copolymer spectral interpretation appear steadily in the literature (6-19). The bulk of NMR studies of copolymers usually involve synthesizing the copolymers, obtaining the spectra, and assigning the observed resonance lines to specific comonomer sequences. The reactivity ratios are then deduced from the sequence distribution. This "analytical" approach has been highly successful in many cases, but even for binary copolymers typically involves a lot of painstaking work (6-17). For ternary copolymers, complete analyses are very difficult and have been reported only in very few cases (18,19). For 21 common vinyl and vinylidene monomers (Table I), there could be a total of 210 binary copolymers and 1330 ternary copolymers. Only about 30 combinations have been characterized thus far by 13C NMR (4). Since each copolymer combination can be either blocky, random, or alternating (or a mixture of these), the total number of copolymer types is mindboggling. It is safe to say that within the next few years only a small fraction of all these possibilities will be studied by the "analytical" approach. In view of the complexity of this problem and ita importance in industrial analyses, we sought to find a general approach that is applicable to all these comonomer combinations. We call this the "synthetic" or spectral simulation approach. The idea is to take a given set of comonomer concentrations and reactivity ratios and then through mathematical and empirical methods simulate a 13C NMR spectrum for any vinyl CO0003-2700/S4/0356-2320$01.50/0
vinyl fluoride
vinylidene fluoride vinylidene chloride
vinyl chloride
Styrene styrene
a-methylstyrene Other Vinyl Monomer Units
vinyl alcohol vinyl acetate vinyl methyl ether polymer. An advantage of the approach is that this is a predictive method; no laboratory work is needed to get a simulated spectrum. Thus, even for copolymers that cannot easily be synthesized, one can obtain a 13C NMR spectrum that bears a reasonable resemblance to the real spectrum. In the process of carrying out this work, we found the substituent chemical shifts of the vinyl functional groups to be reasonably additive, and that a full list of parameters can be constructed to predict the 13C NMR shifts of polymers. In an earlier work (20),one of us had proposed an a priori approach for the spectral simulation of binary and ternary copolymers of ethylene, propylene, and butylene. A computer program (CALPO)was written for that purpose. The present work is a generalization of the earlier effort. With the present method (program PSPEC), one can simulate the binary and the ternary copolymers of any compositions and reactivity ratios and for any combinations of comonomers given in Table I.
EXPERIMENTAL SECTION Although the prototype program (CALPO)was written (20) in FORTRAN IV, this program (PSPEC) was rewritten in the BASIC language. This change should make the present program more adaptable to small computers. The present version of the program was written for a Nicolet 1280 computer associated with a Nicolet NT 360 WB spectrometer. The operational features of Nicolet BASIC are given in the Nicolet manual (21). The simulated spectra were produced on a Zeta plotter. The ethylene-propylene-butylene terpolymer given in Figure 9 was prepared with Ziegler-Natta stereoregular-type catalysts. It was run as a 20% (w/w) solution in 1,2,4-trichlorobenzenewith benzene-d6as the lock material. The spectrum was taken on a 0 1984 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984
SY NTHET I C
__.-
APPROACH
GENERATION OF POLYMER CHAIN
REACTION PROBABILITY MODEL
*
1, CALCULATION 2,
OF
2321
13C SHIFTS
PLOTTING OF SPECTRUM
*4-----+-
NMR SPECTRUM
1
I
I REACTIVITY
\TORS
I
REACT ION
ANALYTICAL APPROACH
DETERMI NATION OF R1AND R2
- CALCULATION
SEQUENCE
OF
1, ACQUISITION OF SPECTRUM ASSIGNMENT OF PEAKS
2,
Flgure 1. Logical steps in the “synthetic”approach toward NMR studies of copolymers. (The “analytical”approach Is also shown for comparison,
below.) Nicolet NT 360 WB spectrometer at 90.55 MHz and 120 “C. The free induction decays were stored in 8K memory addresses, zero-filled upon processing, with a spectral window of 6000 Hz. A pulse angle of 45” was used with 4-s delay.
RESULTS AND DISCUSSION The monomers included in this program are given in Table
I. For convenience they are classified into several types. The column on the left correspondsto the monosubstituted olefins; those on the right are the disubstituted olefins. Together they form the bulk of common vinyl and vinylidene comonomers. The basic logical flow of the “synthetic” approach is given in Figure 1. A study of Figure 1 indicates that the process of spectral simulation requires several distinct steps. First, a reaction probability model is used that approximates the copolymerization process. The reaction probabilities thus obtained are then used to build a polymer chain of predetermined size. The polymer chain can be visualized if needed and is then decoded and the lacchemical shifts computed for all the constituent carbons. Finally, the chemical shifts are rank ordered and plotted out as the simulated spectrum. For ease of discussion, these steps are described separately below. Reaction Probability Models. Many copolymerization schemes have been proposed in the literature (22,23)of which we shall only use the Bernoullian and the Markovian models. These models basically relate the reaction probabilities to the feed concentrations of the comonomers and the reactivity ratios. Depending on the particular models used and the number of comonomers, one can have six possible cases and up to 18 reaction probabilities. 1st order 2nd order Bernoullian Markolrian Markovian
binary copolymer terpolymer
1
2
2 6
4 18
For future reference, the equations involved in these models are given in the Appendix. Generation of Polymer Chain. A schematic diagram of program F%PEis given in Figure 2. To initiate the calculation,
one inputs the reactivity ratios and comonomer feed concentrations. The computer program then calculates the Markovian probabilities via eq Al-A5. The method can be applied to any one of the six cases described above. The reaction probabilities thus obtained are then used to determine the polymer sequence distribution. Several methods can be used. One can apply the continuous system modeling program (CSMP) reported by Harwood et al. (241, or carry out computations on the basis of known relationships between reaction probabilities and sequence distribution (5, 12,23,28). In this work we have chosen to construct a polymer chain with Monte Carlo simulation methods (26). The Monte Carlo method is easy to apply and is very versatile. Its application to polymer sequence determination has been established by Marconi 0, Harwood (28),and O’Driscoll(29). As an added benefit, one can visualize the exact sequence of comonomers in the entire polymer chain, as one is actually simulatingthe process of polymerization. Moreover, if needed, the compositional distribution as a function of conversion can also be monitored. The Monte Carlo method basically involves a random number generator producing a random number between 0 and 1. This is then compared with the reaction probabilities of the comonomers, and depending on the magnitude of the random number, different monomers may be added. This process is repeated until a polymer chain of predetermined size is reached. For the program PSPEC 425 units are used for fast turnaround. For more accurate results, especially in higher order Markovian models, longer chains may be needed.
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984
Table 11. Proposed Empirical Additive Parameters for the "C NMR Shifts of Vinyl Polymers no.
compd
1 2
13 14 15 16
ethylene propylene butylene 4-methyl-1-pentene acrylic acid methyl acrylate acrylonitrile acrylamide vinyl fluoride vinyl chloride styrene vinyl alcohol vinyl acetate vinyl methyl ether isobutylene methacrylic acid
17
3
A
B
C
D
E
X1
3.8 9.7 6.0
8.0
-2.5
0.3 0.5 0.5 0.3 0.3 -0.4
0.03 0.03 0.03 0.03 0.03 0.03 0.03
21.0
-2.2 -2.2 -2.4
2.7
5.2 6.1 3.3 2.6 4.5 3.6 7.3 8.4 6.8 8.0 6.0 4.8 14.3
26.8
12.1
-2.4 -3.0 -3.2 -4.0 -3.7 -2.4 -4.6 -3.4 -4.0 -5.0 -4.9
methyl methacrylate
24.1
11.8
-4.9
0.9
0.06
18
methacrylonitrile
12.7
10.4
-5.3
-0.3
0.06
19 20
vinylidene fluoride vinylidene chloride a-methylstyrene
99.2 68.0 22.4
7.1 17.0 14.3
-8.0 -4.3 -4.8
0.6 -0.7 0.9
0 0
4
5 6 7
8 9 10 11 12
21
21.2
17.0 4.2
18.9 70.0 33.5 17.0 45.0 45.0 54.0
-0.4
0.3 -0.3 0.4 0.2 0.3 0.6 1.3
0.03 0.05
0.1
x3
XZ
x 4
0
10.74 25.9
27.14
45.48 182.2 173.9 120.3 180.8
0 0
23.66a
0
51.5
0 0 0
0 0
0.03
145.1
0 0
0.06
0.06
Q
0 0
127.6"
128.4O
169.5 56.3
20.9
125.6
0.8
0
30.7a 179.6 20.8 176.6 18.8 123.5 25.5
0 0 8.0
0
51.7
0
0 0
147.5 23.0
125.7"
126.4'
123.8
-2.7 0
uThere are two equivalent carbons at this chemical shift. This can be readily accommodated (up to 1000 units) with a simple change in one program statement. Needless to say, the longer the chain, the longer is the computation time. Additivity Rules for 13CShifts of Polymers. The next step is to go through the polymer chain one carbon at a time, calculate, and then make a list of 13C NMR chemical shifts. The basis of the calculation is an empirical additive rule first proposed by Grant and Paul (30)for hydrocarbons. This rule assumes that the observed chemical shifts can be approximated by the linear combination of additive terms related to the neighboring carbons &bsd
= -2.3
+ naSa + nsSB+ n,S,+
n6S,
+ n,S, + S, (1)
where ni refers to the number of i neighboring carbons (i = a , /3, y, 6, and e). Si is a constant characteristic of the ith carbon, and S, represents steric corrective terms to be used for contiguous secondary, tertiary, and quaternary carbons. This hydrocarbon rule was subsequently modified and refined by other workers (31, 32). Similar additive rules have also been reported for alcohols (33,34),amines (35,361,carboxylic acids and esters (37-401, amino acids (37-401, nitroalkanes (41),and others (45). Wehrli and Wirthlin (42),Clerc and Pretsch (43),and Cheng and Ellingsen (45) have proposed additive rules for many functional groups. Computer approaches have been proposed (44,45),including one by the present author (45). In applying these rules for polymers, one problem that occurs is the steric correction term (8,in eq 1). In our earlier work on computerizing the additive rules (45),the computer program remembers whether each carbon being considered is primary, secondary, tertiary, or quaternary. A test of the neighboring carbons then produces the appropriate steric correction terms. For polymer chains with a large number of carbons, this bookkeeping device slows down the computation considerably. In reviewing the reported chemical shift values for homopolymers and copolymers, we discovered that for regular (head-to-tail) polymer structures, a set of empirical additive rules can be devised that obviate the use of steric correction terms altogether. Our proposed substituent parameters are listed in Table 11.
The letters A , B, C, D, and E in Table I1 refer respectively to the substituent chemical shift effect of a functional group that is a,8, y, 6, and c to the carbon in question. In the case of disubstituted olefins (e.g., monomers 15-21 in Table 11), the effecta of both substituents are included in the parameters A, B, C, D, and E so that one needs to add the parameter values only once. The letters, Xi (i = 1, 2, 3, and 4),refer to the chemical shifts of the carbons on the substituents themselves (vide infra). In reviewing published copolymer NMR data (6-1 7), and carrying out simulations, we found that the 13C shifts of the backbone methylene carbons (Cp below) are reasonably additive. The substituents are either /3 away (Rl, Rz, R
