Tatsuo Miyazawa

OPTICALLY ACTIVE LATTICE VIBRATIONS AS TREATED BY THE GF-MATRIX METHOD.

A general description has been given of an application of the Wilsons GF‐matrix method to the treatment of optically active lattice vibrations. As examples, formulas are derived for the calculation of the frequencies of the lattice vibrations of a one‐dimensional, the diamond, and CaF2 lattices.

Normal vibrations and force constants of polymethylene chain

Abstract Normal vibrations of an infinite polymethylene chain in the extended conformation have been treated. The G and F matrices of infinite order may be reduced to the G(δ) and F(δ) matrices of finite order corresponding to the phase difference (δ) between two adjacent methylene groups. The observed vibrational frequencies of long-chain n-paraffins and of polyethylene are compared with the frequencies of polymethylene chain calculated for various phase differences and their assignments have been discussed. A modification of the Urey-Bradley force field has been made in accordance with the present vibrational assignments.

Molecular Vibrations and Structure of High Polymers. III. Polarized Infrared Spectra, Normal Vibrations, and Helical Conformation of Polyethylene Glycol

The polarized infrared spectra of highly oriented crystalline films of polyethylene glycol were measured in the region 3500–400 cm—1. Five parallel bands and eleven perpendicular bands due to the fundamental vibrations were observed in the region 1500–600 cm—1. From the analysis of these bands, the polyethylene glycol chain was found to belong to the dihedral group and have twofold axes intersecting the helix axis at right angles. The structural models of polyethylene glycol were discussed by the use of the equations for the helical parameters (the second paper of this series). The most likely model (TGT) contains seven repeating units and two helical turns per fiber period of 19.25 A. The internal rotation angles for this model are calculated to be 60° for the C–C bond and 191.5° for the C–O bond. The A1, A2, and E(θ) normal vibrations of polyethylene glycol were calculated by the general method for treating helical polymers (the first paper of this series). The normal vibrations of p‐dioxane were also c...

Infra-red absorption spectra of inorganic co-ordination complexes—IX1: Infra-red spectra of oxalato complexes

Abstract The infra-red spectra of simple metal oxalates have been measured and the assignment of bands haa been based on the normal vibration calculation for the free oxalate ion. The infra-red spectra of oxalato complexes of Fe(III), Co(III), Cr(III), Al(III), Pd(II), and Cu(II) have been measured in the NaCl and CsBr regions. Assignment of bands has been made by the comparison of the spectra with those of alkali metal oxalates and dimethyl oxalate.

Infrared spectrum and normal vibrations of cyclohexane

The infrared spectra of cyclohexane have been studied in the region of 4000-150 cm−1 in the liquid and vapor states. The infrared band due to the Eu skeletal deformation vibration was found at 248 cm−1. The calculation of Coriolis coupling constants has also been carried out along with the normal coordinate treatment using a modified Urey-Bradley force field. The assignment of the infrared and Raman bands was made with reference to the results of this calculation.

Molecular Vibration and Structure of High Polymers. IV. A General Method of Treating Degenerate Normal Vibrations of Helical Polymers and Infrared‐Active Vibrations of Isotactic Polypropylene

Polarized infrared spectra of an oriented crystalline film of isotactic polypropylene have been measured in the region 600–300 cm—1. Two parallel bands and three perpendicular bands due to the skeletal deformation modes have been observed. A general method for treating the normal vibrations (with any given phase difference) of infinite helical chain polymers has been restudied. The method has been applied to the infrared active normal vibrations, A and E(⅔π), of isotactic polypropylene. The modified Urey—Bradley force field has been used and the potential constants have been transferred from aliphatic hydrocarbons. The calculated frequencies and potential energy distributions have been used as aids in assigning the infrared bands of isotactic polypropylene in the region 1500–300 cm—1.

Infrared and Raman spectra of polyethyleneglycol dimethylethers in the liquid state

Abstract Infrared spectra of ethylene- through heptaethyleneglycol dimethylethers and Raman spectra of ethylene- through tetraethyleneglycol dimethylethers have been measured in the liquid state. Assignments of the vibrational frequencies have been made and the effect of the chain length on the spectra has been discussed with reference to the nature of vibrational modes. The CH 2 rocking and the CO and CC stretching modes are appreciably coupled. In the liquid state the internal rotation angles ( trans and gauche ) about the CC and the CO bonds of the molecular chain are randomly distributed.

A refined treatment of normal vibrations of polymethylene chain

Abstract A refined treatment has been made for the torsional coordinate around the CC bond of a polymethylene chain. A coordinate (Δt) which is set up from the torsional internal coordinates around the CC bond and equals the change of the internal rotation angle has been introduced. On assuming the internal rotation potential of the type 1 2 Y( Δ t) 2 , an agreement between the observed and the calculated frequencies of the out-of-plane vibrations of a polymethylene chain has been obtained. Force constants have been refined.

Infrared spectra of poly(ethylene glycol) dimethyl ethers in the crystalline state

Abstract Infrared spectra of CH 3 O(-CH 2 CH 2 O-) p CH 3 ( p = 1–7) in the crystalline state have been measured in the region 4000-400 cm −1 . Assignments of absorption bands have been made with reference to the dispersion curves (wavenumber vs. phase difference) calculated for an infinite chain of poly(ethylene glycol). Normal coordinates have also been treated on some of these molecules in order to check the vibrational assignments. The band progression observed at 520–590 cm −1 has been analyzed on the basis of the coupled oscillator model. Chain conformation of these molecules in the crystalline state is similar to that of the high polymer.

Normal coordinate treatments of internal-rotation vibrations

Abstract The general formulas of the G-matrix elements associated with internal-rotation coordinates are tabulated. The normal vibrations of the trans and gauche isomers of dichloroethane were treated by the use of the internal-rotation potential.