Phonon Scattering in Polyethylene at Low Temperatures

An expression, valid below 4 ^∘{}K, for the phonon mean free path in polyethylene is derived through a consideration of the microscopic structure. Above 1 ^∘{}K, scattering of phonons occurs mainly within the amorphous regions and can be described by a structure scattering term. The amorphous-crystalline boundaries contribute a constant term to the mean free path above 1 ^∘{}K, but below this temperature, when the phonon wavelength is comparable to the size of the crystallites, it is suggested that the alternation of crystalline and amorphous material should be described by a second structure scattering term. This free path is shown to account for the anomalous temperature variation of the thermal conductivity recently observed below 1.5 ^∘{}K: No modification to the phonon density of states predicted by the Debye theory is required. A discussion of phonon resonant scattering is also presented.