The vibron model and long molecular chains: Algebraic polyethylene and its first CH stretching overtone |
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| Affiliation: | 1. KTH Royal Institute of Technology, School of Chemical Science and Engineering, Fibre and Polymer Technology, SE-100 44 Stockholm, Sweden;2. Laboratory of Innovation Technology, Dept. of Electrical, Electronic and Information Engineering, University of Bologna, Italy;1. Van ''t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands;2. Dutch Polymer Institute DPI, PO Box 902, 5600 AX Eindhoven, The Netherlands;1. Research Division of Green Function Materials and Equipment, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, PR China;2. Institute of Plastics Machinery and Plastics Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China;1. Univ Rennes, CNRS, Institut des Sciences Chimiques de Rennes (ISCR), UMR 6226, F-35042 Rennes, France;2. Total Research & Technology Feluy, Zone Industrielle Feluy C, B-7181 Seneffe, Belgium;3. Université de Toulouse, CNRS, INSA, UPS, LPCNO, UMR 5215, 135 avenue de Rangueil, F-31077 Toulouse Cedex 4, France;1. School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff, CF10 3AT, UK;2. Department of Chemistry, College of Science, University of Basrah, Basrah, Iraq;3. Cornea Research Chair, Department of Optometry, College of Applied Medical Science, King Saud University, P. O. Box 10219, Riyadh 11443, Saudi Arabia;1. School of Materials and Chemical Engineering, Hubei University of Technology, Wuhan, 430068, China;2. Hubei Provincial Key Laboratory of Green Materials for Light Industry, Hubei University of Technology, Wuhan, 430068, China |
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| Abstract: | We apply the algebraic (vibron) model to very long molecular chains, starting from n-alkanes molecules up to polyethylene. The infrared spectrum of CH stretches is computed in an algebraic basis and we obtain analytical formulas for both energy values and intensities of vibrational modes in the ν=2 overtone. We provide a simple, yet confident explanation of the main features of the IR spectrum of the polyethylene molecule in this energy range. |
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