A linear relationship was established for several polymers between the pre-exponential factor and the activation energy of a modified form of the standard Arrhenius equation. In addition, the energy term itself was modified such that the alpha and beta absorptions were related to the number of carbon atoms available for segmental motion. At large activation energies the modified Arrhenius relationship suggested upper limits of 495.5K and 321K for the alpha and beta transition temperatures, respectively.