8 J. Chem. In$ Comput. Sci. 1987, 27, 8-13 Computerized Model Fitting Approach for the NMR Analysis of Polymerst H. N. CHENG Research Center, Hercules Incorporated, Wilmington, Delaware 19894 Received May 21, 1986; Revised Manuscript Received October 29, 1986 A computer program (called FITCO) was developed for the general analysis of the NMR spectra of polymers through the (analytical) model-fitting approach. The method attempts to optimize the amount of information available from each spectrum and is especially useful for spectra with overlapping resonances and for studies of polymerization mechanisms. Examples are shown of the use of the program for the analysis of copolymer composition in ethyl acrylate-methyl methacrylate copolymers and for the studies of tacticity in polypropylene. INTRODUCTION NMR spectroscopy has been widely used for studies of polymer microstructure. Information available includes homopolymer tacticity, copolymer sequence determination, and polymer chain branching. Over the years numerous papers and texts’-5 have appeared on this subject. The analysis of polymer N M R spectra usually follows fa- miliar patterns. A schematic is given in Figure 1 showing the logical steps needed. In general, NMR analysis of the polymer spectrum can be carried out at several levels. At the simplest level, one can treat the polymer spectrum as a fingerprint pattern and use it, for example, for the identification of un- known samples. If more information is needed about the polymer, then the spectrum must be interpreted. This process may be aided by model components or analogous polymers. Recently many advanced (e&, polarization transfer, spectral editing, and two-dimensional NMR) have been developed and increasingly used in polymer NMR.9 Assuming that all the significant resonances can be properly assigned, one must then devise computational schemes to obtain polymer compositions and sequence distributions. This general method of analysis can be referred to as the “analytical approach”. (An alternative method, called the “synthetic approach”, has also been developedlOJ1 recently). A more refined analytical approach is to approximate the copolymerization reaction with a statistical model (Figure 1).l2 One can then associate every spectral intensity with a theo- retical expression involving reaction probability parameters. The observed and the theoretical intensities for all the spectral lines are then compared, and optimization is carried out to obtain the best-fit values of the reaction probability parameters. Depending on the goodness of fit, these probability parameters then fully describe the structure of the polymer system in question. This model-fitting approach has been successfully applied to a number of specific polymer system^.'^-^^^*^ In this work a general computer program has been developed that is capable of rapidly and conveniently applying this model-fitting approach to a variety of polymer systems. Two examples are shown that illustrate this approach: composi- tional analysis of ethyl acrylate-methyl methacrylate co- polymers and determination of polypropylene tacticity by 13C NMR. This is the first time that the I3C NMR spectra of ethyl acrylate-methyl methacrylate copolymers have been assigned and analyzed. PROGRAM FITCO The program is organized into eight sections. The rela- tionships among the various sections are summarized in Figure 2. These sections are described as follows: Presented at the 190th National Meeting of the American Chemical Society. Chicago, IL, September 1985 (Paper CINF 26). (1) The first section involves input of observed spectral intensities. It also produces a header in the output. (2) In the second section, the user may wish to devise computational schemes to calculate polymer composition and sequence distribution. (3) The format of the input data (in section 1) is specified in this section. One method is to use DATA-READ state- ments; corrections on the input can be easily made (e.g., lines 200-420, Figure 3). (4) The expressions for reaction probability parameters are coded in this section. The common statistical models are (a) Bernoullian, (b) first-order Markov, (c) second-order Markov, (d) Coleman-Fox, and (e) enantiomorphic models. Other models have also been proposed. For the common statistical models the theoretical expressions for many stereosequences have been given in the Expressions that are not available may be derived if needed. (5) The simplex algorithm is contained here. The purpose is to compare the observed vs. the calculated intensities and to provide a fast and logical means to obtain the optimal values of the reaction probability parameters. (6) This section provides the output, viz., final reaction probabilities, optimal values for polymer’ composition and sequence distribution, and reactivity ratios product. (7) This section provides additional opportunities for com- putations. (8) Termination occurs last with provision for looping back to carry out other computations. It is clear that sections 2, 3, 4, and 7 must be inserted by the user. The other sections need no user input. EXAMPLES Program FITCO in its present form is very versatile. It can be used for the compositional analysis and sequence distri- bution of copolymers and also for the tacticity of homo- polymers. Examples are given here to illustrate these cases. 1. Compositional Analysis. The I3C NMR spectrum of a copolymer of ethyl acrylate (EA) and methyl methacrylate (MMA) is shown in Figure 4. The complex pattern indicates the combined effects of copolymer sequence placements and tacticity on the I3C shifts. In polymers of such complexity, complete interpretation of all resolvable resonances is very difficult and has been accomplished in very few cases. For EA-MMA copolymers, the interpretation of 13C NMR spectra has not been previously reported. A close scrutiny of Figure 4, however, indicates that the backbone carbons (cy and 0) all resonate in the 33-55 ppm region. Except for this region, all other resonances can be assigned with some effort. The as- signments were aided by comparing copolymer samples with different compositions. The results are shown in Table I and Figure 4. Of particular interest are the assignments of the methyl region (1 5-23 ppm) and the carbonyl region (1 73-1 80 ppm), where the effects of comonomer sequence placements 0095-2338/87/1627-0008$01.50/0 0 1987 American Chemical Society