The Transfer Matrix Method in the Theory of Normal Vibrations of Chain Molecules

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Abstract
After reviewing the transfer matrix method introduced by Schmidt, and by Hori and Asahi for the problem of the vibration of a disordered linear chain, we discuss its extension by Yamamoto, Okada, and the present author to more complex systems. Classifying the frequency regions by the ‘s-value’, which is defined as half a number of eigenvalues with absolute value 1 of the transfer matrix, we study the general aspects of normal modes in each region. When s = 1, a ‘phase shift’ is shown to be a very useful quantity for expressing end effects on the frequency and intensity of the infrared absorption of a chain molecule. As an application we discuss the analysis of the experimental data on the rocking-twisting modes of normal paraffins, which indicates the practical importance of our theory.

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