Molecular Vibrations and Structures of High Polymers. I. General Method of Normal Coordinate Treatment by Internal Coordinates and Infrared Frequencies and Conformations of (—CH2—)n, (—CH2–O—)n, and (—CH2–O–CH2—)n

Abstract

The normal coordinate treatment of the (—A—)_n chain was made in terms of internal symmetry coordinates and optically active frequencies of (—CH₂—)_n were calculated for various chain conformations. The calculated frequencies of polyethylene and cyclopentane agreed with the observed values. The low infrared frequency was found to be structure sensitive. The infrared band of polytetrafluoroethylene at approx 100 cm^—1 may be primarily due to this mode. The low infrared frequencies of polyoxymethylene were compared with the corresponding frequencies of (—A—)_n calculated for various conformations and were found to be in accord with Huggins' model but not with the planar zigzag structure. The normal coordinate treatment of (—A—B—)_n was made taking into account the torsional potential as well as the stretching and bending potentials, and vibrational assignments of polyoxymethylene were made. For poly‐(ethylene glycol) a structure model was proposed. This model is made up of only the gauche configuration throughout the helical chain and contains seven chemical units and five turns of the helix per fiber period. The polarized infrared spectra of this polymer were measured in the region 800–400 cm^—1 and the observed skeletal frequencies were compared with the corresponding frequencies of (—A—)_n calculated for various conformations. The infrared spectra were found to be in accord with the model proposed here. The infrared spectra in the rocksalt region were also reasonably assigned. Finally a general method of treating any infinite helical chain belonging to dihedral group is presented in terms of real internal symmetry coordinates. The G or F matrix of an infinite order is factored into the set of matrices G(δ) or F(δ) associated with the phase difference δ. The method is explained for the cases of polyoxymethylene and poly‐(ethylene glycol).