The Vibration Frequencies and Thermodynamic Functions of Long Chain Hydrocarbons

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Abstract
A method is developed for calculating thermodynamic functions for long chain molecules with particular attention to normal paraffins. In this connection the infinite chain approximation method for calculating vibration frequencies is considered. Starting with the results of Kirkwood, a modification is made which improves the agreement with the exact values for the simpler cases. In addition this method of attack is extended to out of plane motions. This vibrational analysis shows that all skeletal frequencies for molecules of the normal paraffin type can be put into two groups, one fairly narrow band near 1000 cm—1, and a broader band extending from 0 to 460 cm—1. The partition function is then set up on the assumption that motions in the low frequency group can be treated classically, and that the high frequency band can be replaced by a suitable number of 1000 cm—1 frequencies. Contributions from hydrogen atom vibrations are added on later. A formula is finally obtained which is quite simple, considering the complexity of the molecules. The calculated entropies can be brought into agreement with experimental values on the basis of very reasonable internal rotation restricting barriers.

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