A model for dynamic relaxations in amorphous polymers. II. Extensions and generalizations of formalism and application to poly(methacrylates)

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Abstract
Extensions and generalizations of a new model for the dynamic relaxations in amorphous polymers, and its application to the poly(methacrylates), will be presented. The sizes of moving subunits will be extrapolated for the β and γ relaxations in several poly(methacrylates), by working backward from the relaxation temperatures (Tr) observed at frequencies of 1 to 100 Hz to subunits giving Tcs comparable to those Trs. A general form will be proposed for activation energy distributions; and used to derive relaxation time distributions satisfying the experimental trends. The good agreement between the calculated Tc and the Tr observed dynamically at frequencies of 1 to 100 Hz will be shown to result from the nature of these distributions. The loss peak observed at very low temperatures by isochronal sweeps at very low frequencies is therefore caused by the dissipation of applied energy in localized domains. At sweep frequencies of 1 to 100 Hz, Tr ≈ Tc, and energy dissipation begins to take place over regions spanning the entire polymer. This delocalization of the energy dissipation is relevant to the effects of molecular level factors on many mechanical and thermodynamic properties of amorphous polymers. The effects of activation entropy and of dynamic excess entropy will be shown to be small in magnitude but important in terms of fully understanding relaxation behavior. Physical aging will be shown to result in a slight increase in the calculated characteristic temperatures. Finally, it will be shown that the relaxation behavior of the moduli and the compliances share some important common features with many other physical phenomena of seemingly very different nature.