A model is presented that characterizes the temperature dependence of the specific heat of amorphous polymers. The model utilizes a density of vibrational states given by ρ(ω)∝ωd̃-1, where d̃ is the fracton, or spectral, dimension. This density of vibrational states, when introduced into the standard Debye model, leads to a specific heat temperature dependence of the form C(T)∝(T/⊖d̃) d̃, where ⊖d̃ is a characteristic temperature. This model fits the data well for the temperature region ∼4 to ∼40 K. A key feature of the model is the prediction of a crossover of the polymer scaling properties that causes a crossover from T2 to T 5/3 of the specific heat temperature dependence. In addition, this model allows a simple estimate of the specific heat for a wide range of polymers using only the formula weight.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry