Time-Temperature and Time-Concentration Superposition of Nanofilled Elastomers: A Molecular Dynamics Study

We systematically investigated the structural and dynamic properties of nanofilled elastomer on the basis of the idealized model of elastomer and nanoparticle. The Simulated results indicate that the introduced nanoparticles induce more efficient chain packing. Meanwhile, a mobility gradient of polymer chains is found to exist approaching the nanoparticles. For the dynamic properties, we find for the first time that both the time-concentration and time-temperature superposition principles (TCSP and TTSP) are applicable at the chain length scale, while both break down at the segmental length scale for the filled system. However, the TTSP still holds at the segmental length scale for the pure system. Furthermore, the time-temperature-concentration superposition principle (TTCSP) applies well for the terminal relaxation of polymer nanocomposites. This scaling behavior has the underlying implication that the rheological properties (i.e., steady-state shear viscosity) of polymer nanocomposites possess thermorheological simplicity. In addition, interestingly, the characteristic relaxation time as a function of filler concentration exhibits an Arrhenius temperature dependence, if the concentration variation is regarded as an inverse of temperature variation. We suggest the introduced nanoparticles exert the similar effect to the thermodynamic variables (e.g., pressure and temperature) on the polymer dynamics. Lastly the stress relaxation of the model system is also examined. The decay of the bond orientation of polymer chains during the relaxation process is studied by changing the draw ratio, the filler loadings and the affinity between the nanoparticle and polymer. In order to equivalently investigate the stress relxation, we propose a new approach named conformational relaxation. It is observed that the conformational relaxation can be approximately fitted well by an exponential function for the pure and filled systems, similar to the stress relaxation. The TTSP is also applicable for the conformational relaxation of the pure system, while breaks down for that of the filled system. The relaxation time extracted by fitting the conformational relaxation curves with an exponential function at different temperatures, exhibits an Arrhenius relationship with the temperature for the pure and filled systems. Moreover, contrary to the isotropic dynamics during the creep process of the polymer from the simulated results of de Pablo, our simulated result shows an anistropic polymer dynamics with an accelerated relxation in the predeformed direction during the stress relaxation process.