Low temperature specific heat calculations for amorphous polystyrene

Numerous attempts have previously been made to explain low temperature specific heat anomalies in glasses. The potential value of low frequency Raman data in interpreting such results is demonstrated here: the density of states for the 60 cm^?1 side-group mode in amorphous polystyrene is calculated from Raman measurements. Using the harmonic approximation, the contribution to the specific heat from this side-group motion is calculated and added to the Debye term. The form of C/T³ between 1.5 and 4 K is shown to be reproduced, although the magnitude of C/T³ is only about 70% of experimental values. This discrepancy and the anomalous behaviour below 1.5 K is believed to the due to lower-lying vibrational states of the system, perhaps not accessible through Raman scattering experiments.