Normal Vibrations of Chains of Similar and Similarly Situated Dynamical Systems and the Infra-Red Spectrum of Undecane

Theory indicates that the normal modes of vibration of chain molecules fall into two classes; end vibrations in which the amplitude falls off exponentially from the ends towards the middle, and chain vibrations in which it varies harmonically as in a standing wave. The transition from one class to the other takes place via chain vibrations with a small number of nodes of amplitude along the chain. For a long chain we expect only those chain vibrations to show up in the infra-red spectrum for which the phase of the electric moment is constant along the chain. These considerations have been applied to predict the vibration spectra of the straight chain paraffins, assumed to consist of a zigzag chain of carbon atoms each carrying two hydrogen atoms in a plane perpendicular to the chain and alternately above and below it. The infra-red spectrum of undecane has been measured from 1 to 15μ on a prism spectrometer, the positions of 31 bands being determined. Accepted values of the interatomic distances and angles were assumed and force constants were adjusted to fit four of the fundamental frequencies to observed bands. Bands were observed near all the other fundamental frequencies predicted certainly to occur (as chain vibrations) and near one out of three that should possibly occur (as end vibrations near chain vibrations with few nodes). All but three of the observed bands could be accounted for as fundamentals, harmonics, or simple combination frequencies.