Normal mode analysis of the conformational fluctuation of polymethylene chains in their nearly extended states

Abstract

The conformational motion of a nearly stretched polymethylene molecule is studied by a normal mode analysis of the dihedral angle fluctuations. It is assumed that the conformation can be described by the dihedral angles only, the bond length, and the bond angle being fixed. The simplified model Hamiltonian consists of the intramolecular energy due to the dihedral angle distortions of the C–C bonds and the effective intermolecular energy which favors the stretched chain conformations. The Hamiltonian is expanded, around the transplanar state, in a quadratic form of the dihedral angles {τi}, and the normal modes of the dihedral angle fluctuations are obtained through diagonalization of the Hamiltonian. The normal modes are found to be classified into the in-phase and the out-of-phase modes; in the former modes the adjacent bonds make concerted rotations in the same direction resulting in the twisted chains, while in the latter modes they make counterrotations which give rise to the large out-of-plane bending of the chain. The power spectra of the dihedral angle fluctuations are calculated. They are found to be composed of the in-phase and the out-of-phase components; the spectra qualitatively reproduce those obtained in our previous computer simulation. A new variable, the curvature of the chain contour, is devised and is used throughout the discussion; it is found to be very useful in the description of the conformational fluctuations.