Knowledge Bank

“The lowest-frequency modes of chain molecules in a gas have zero frequency, corresponding to free rotation and translation. In liquids and solids, these modes are inhibited by intermolecular forces and become low-frequency vibrations. These vibrations have been analyzed both classically and quantum-mechanically, assuming for each degree of freedom a one-term potential function with arbitrary exponent. Even if the intermolecular forces are assumed to be linear, some of the vibrations are non-linear, so that the resulting bands have temperature-dependent frequencies and strong overtones. The temperature dependence determines the proper exponent in the appropriate term of the potential function, since the frequency varies as the (n-2)/2n power of the absolute temperature, where n is the exponent in the potential function and is not necessarily integral. For typical hydrogen-bonded polymers with one bond per repeating unit, the theory predicts infrared and Raman bands at frequencies below about $100cm-1$, some of which will have different temperature dependence than others, to aid in assignment. The greater the temperature dependence, the stronger the overtones, and the odd overtones should be particularly strong.”