Measurements of the specific heat of polymethyl methacrylate and polystyrene have been performed using the heat pulse method between 0.5 and 4.3deg;K. Above 2deg;K the specific heat is about double that expected on the basis of the Debye theory and acoustic measurements. Below 2deg;K the experimental data approach the Debye value. The excess specific heat can be fit by two Einstein modes. For polymethyl methacrylate the Einstein temperatures are 4.9 and 17.5deg;K containing 0.014percnt; and 1.0percnt; of all modes, respectively. For polystyrene the corresponding modes are 5.5 and 16deg;K with strengths of 0.038percnt; and 1.8percnt; respectively. The data support a model of pendant side groups near voids capable of independent low frequency torsional oscillations. The barrier to internal rotation of the pendant group is estimated.
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