Quantifying Changes in the High-Frequency Dynamics of Mixtures by Dielectric Spectroscopy

Additives to polymeric materials can lead to appreciable changes in the rates of relaxation and reaction in these mixtures that can profoundly alter material properties and function. We develop a general theoretical framework for quantifying changes in the high-frequency relaxation dynamics of mixtures based on classical transition state theory, in conjunction with mathematical statements regarding the dependence of the entropy (S+) and enthalpy (E+) of activation of the high-frequency relaxation time on diluent mass fraction, x(w). Specifically, we deduce a general classification scheme for diluents based on a consideration of the sign of the differential change in S+ and E+ with x(w). Two of these classes of diluents exhibit a transition from plasticization to antiplasticization (defined specifically as a speeding up or slowing down of relaxation relative to the pure system, respectively) upon varying temperature through an antiplasticization temperature, T-anti. Extensive dielectric relaxation measurements on polycarbonate (PC) as a function of temperature and diluent (Aroclor) concentration are utilized to illustrate our theoretical model, and we focus particularly on the Arrhenius beta dielectric relaxation process of these mixtures. Many aspects of our scheme for quantifying changes in the high-frequency dynamics of mixtures are rationalized by our mixture model. In particular, we show that the dilution of PC by Aroclor is consistent with a theoretically predicted (one of the two antiplasticization mixture classes mentioned above) transition from antiplasticization to plasticization with decreasing temperature. We briefly compare our findings from dielectric measurements with those from elastic incoherent neutron scattering and dynamical-mechanical measurements, providing further evidence for the antiplasticization-to-plasticization transition phenomena that we observe in our high-frequency dielectric measurements.