Theory of Normal Vibrations of Chain Molecules with Finite Length

Abstract

This paper is concerned in the end effects on the normal vibrations of a chain molecule with finite length. In Part I we study the mathematical problem of how to solve the eigenvalue problem of the GF matrix of the chain molecule with finite length. Making use of the fact that the force range can be regarded finite we reduce the problem to solving a determinantal equation usually of much lower order than that of the GF matrix through the introduction of auxiliary variables and transfer matrices. We obtain the simple formula for giving an admissible phase difference in which the end effect is taken into account. In Part II, using this formula we analyze the infrared data of Snyder on crystalline normal paraffins C3H8 through C30H62. Our analyses indicate that the formula is generally useful for making extrapolation, interpolation, assignment, and determination of frequency-phase relations from the experimental data of homologous series of chain molecules.