Additive Size Controls the Temperature-Dependence of Relaxation in Bulk Polymers

We measure the dependence of bulk, coarse-grained polymer dynamics on the size of spherical additives from the small molecule to nanoparticle size scale. We consider two scenarios for the interactions between the additive and polymer.  In both cases, we find a characteristic additive size that is comparable to the monomer size, below which the alpha relaxation time τ of polymers drops sharply. For each additive size, we find that the Localization Model (LM) can relate the temperature dependence of τ to that of the pico-second dynamics quantified by the Debye-Waller factor〈u²〉.  We find that the parameters of the LM depend only on additive size, and are independent of the monomer-additive interactions, such that the shapes of the temperature dependencies of dynamic changes can be solely attributed to entropic effects associated with the additive size; interaction strength renormalizes the temperature scale of these dependencies. Further, we find that the LM fit parameters plateau for additives larger than a monomer diameter, suggesting that a ‘nanoparticle limit’ of the LM is reached at a surprisingly small additive size. We also consider how the collective motion is altered by additives, and how these changes are affected by confinement when we examine ultra-thin polymer films.