A versatile approach for modeling and simulating the tacticity of polymers

Authors: MIRI, MASSOUD - Rochester Institute Of Technology; PRITCHARD, BENJAMIN - Rochester Institute Of Technology; Cheng, Huai

Submitted to: Journal of Molecular Modeling
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/15/2010
Publication Date: 7/1/2011
Citation: Miri, M.J., Pritchard, B.P., Cheng, H.N. 2011. A versatile approach for modeling and simulating the tacticity of polymers. Journal of Molecular Modeling. 17:1767-1780.

Interpretive Summary: NMR is a premiere technique to study polymer structures and reaction mechanisms. An advantage of NMR is the wealth of information available in a given spectrum. Depending on the nature of the sample involved, a spectrum may contain such information as main polymer structure (including homopolymer tacticity and copolymer sequence distribution), structural heterogeneity, branching, defect structures, chain ends, additives, and impurities. All the spectral lines and their intensities can potentially provide detailed information about the reaction mechanisms for initiation, propagation, chain transfer and termination. A challenge is to properly interpret the NMR spectrum and to maximize the information available. To facilitate NMR spectral analysis, statistical models are often used to provide a suitable interpretive framework. Many common polymerization mechanisms can be approximated by statistical models. As new catalysts or new methods of polymerization are devised, new polymerization models need to be devised. Through these models, the NMR spectral intensities can be predicted and compared with observed values. The calculations involved are often tedious and sometimes fairly complex. In this work, we have devised a computer-assisted approach, whereby seven most common statistical models are encoded in an Excel spreadsheet. With appropriate input of model parameters, the computer program quickly and easily calculates the requisite information on polymer tacticity. One of the models is actually new and pertains to the polymers made by certain types of metallocene catalysts. The computer program is currently written to analyze and simulate homopolymer tacticity. Tacticity is a fundamental structural property of a polymer. Thus, a highly isotactic or syndiotactic polymer is crystalline, but an atactic polymer is usually amorphous. NMR is a good method to identify and quantify tacticity. Through the use of the methods given in this work, a prospective user can more easily understand NMR spectra and interpret NMR data with statistical models.

Technical Abstract: We are introducing a versatile computerized approach to model and simulate polymer tacticities using seven single-stage statistical models. The theory behind the models, e.g., Bovey's versus Price's, Bernoullian, 1st or 2nd order Markovian, enantiomeric types, and combinations thereof is explained. One of the models, "E-B gen", which can be used to produce four types of enantiomerically controlled tacticities, and the pentad distribution for the model "E-M1" are reported here for the first time. The relations of chain end controlled models to binary copolymerizations are discussed in detail and equations for the conversion of tacticity based probabilities to reactivity ratios to obtain related n-ad distributions are presented. The models were applied to twenty polymers with exemplary tacticities found in the literature. A software program based on Microsoft's Excel has been designed with the objective to calculate all relevant characteristics of the polymer tacticity and to present them in graphical form in a user-friendly manner using Macros. One of the main intended uses of the program is for comparing the computed n-ad distributions to those of experimental polymers obtained from NMR spectroscopy, and to gain insight into the polymerization mechanisms.