A model for the specific heat of amorphous polymers

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)∝ω^d̃-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.