The structure of chain molecules in the liquid state: Low-frequency Raman spectra of n-alkanes and perfluoro-n-alkanes

Publisher Website
Google Scholar
Abstract
A model, in which the random elements of the kinetic energy matrix are replaced by statistically weighted averages, is used to explain the principal features of the low‐frequency Raman spectra of a series of liquid n‐alkanes and perfluoro‐n‐alkanes. The spectra of the longer chains of the n‐alkanes are dominated by an intense band that is associated with the longitudinal‐acoustic mode observed in the crystalline state. For the liquid, the frequency ν and the number of carbon atoms n are found to be related as ν = ν0+B/n2. This relation, which can be derived from the weighted‐average model, implies that the vibration exhibits frequency dispersion and has the character of an optic mode. The dependence of the width of this band on the number of carbons can also be accounted for in terms of the model. The intercept frequency ν0 and the slope B are functions of the energy difference Eg between gauche and trans CC bond states. For the perfluoro‐n‐alkanes, Eg was estimated from the observed value of the slope. The value derived 1050 cal/mol is roughly twice that reported for the polymethylene chain and is near the value reported by Bates and Stockmayer [J. Chem. Phys. 45, 2321 (1966)] from dipole moment measurements.