Strain rate and temperature dependence of the mechanical properties of polymers: A universal time-temperature superposition principle.

Establishing the Time-Temperature and Frequency-Temperature Superposition Principles (TTSP and FTSP) to describe the mechanical behavior of polymeric materials is always of paramount significance. In this work, by adopting the classic coarse-grained model, we investigate the validity of these superposition principles for a series of networks, such as the pure polymer network, interpenetrating polymer networks composed of stiff and flexible networks (IPNs-SF), interpenetrating polymer networks composed of different cross-linking networks (IPNs-DC), polymer nanocomposites (PNCs), and surface grafted modified PNCs. The study focuses on the three critical mechanical properties such as the stress relaxation, the storage modulus versus the frequency obtained from the dynamic periodic shear deformation, and the uniaxial tensile stress-strain. The glass transition temperature (T) is about 0.47 for the simulated polymer network (CL400), and a smooth master curve is obtained for the stress relaxation process by setting the reference temperature T = 0.6 via the horizontal shifting process, indicating the validity of TTSP. Furthermore, similar smooth master curves are also achieved for both dynamic periodic shear and uniaxial tensile deformation, which exhibit similar trends and share the identical linear viscoelastic regime in the temperature interval above T: 0.55<T<1.0. Importantly, the Williams-Landel-Ferry and Vogel-Fulcher-Tammann equations are both adopted to quantitatively analyze non-linear TTSP behavior when the temperature approaches T. For the three mechanical properties, we emphasize that the master curve from TTSP or FTSP is independent of the reference temperature if it is higher than T, and based on the linear relation of the shift factor versus the inverse of the temperature higher than T, we propose a universal framework for the description of the TTSP or FTSP on the various mechanical properties. Then, we verify that the TTSP seems to be valid for the IPNs-DC system, while it does not hold for both PNCs and IPNs-SF systems because of their structural and dynamic heterogeneity. Furthermore, for PNCs filled with NPs grafted with polymer chains, the TTSP recovers back to be valid because of the enhanced compatibility between polymer and NPs attributed to the grafted polymer chains.