New Insight into Time-Temperature Correlation for Polymer Relaxations Ranging from Secondary Relaxation to Terminal Flow: Application of a Universal and Developed WLF Equation

The three equations involved in the time-temperature superposition (TTS) of a polymer, i.e., Williams–Landel–Ferry (WLF), Vogel–Fulcher–Tammann–Hesse (VFTH) and the Arrhenius equation, were re-examined, and the mathematical equivalence of the WLF form to the Arrhenius form was revealed. As a result, a developed WLF (DWLF) equation was established to describe the temperature dependence of relaxation property for the polymer ranging from secondary relaxation to terminal flow, and its necessary criteria for universal application were proposed. TTS results of viscoelastic behavior for different polymers including isotactic polypropylene (iPP), high density polyethylene (HDPE), low density polyethylene (LDPE) and ethylene-propylene rubber (EPR) were well achieved by the DWLF equation at high temperatures. Through investigating the phase-separation behavior of poly(methyl methacrylate)/poly(styrene-co-maleic anhydride) (PMMA/SMA) and iPP/EPR blends, it was found that the DWLF equation can describe the phase separation behavior of the amorphous/amorphous blend well, while the nucleation process leads to a smaller shift factor for the crystalline/amorphous blend in the melting temperature region. Either the TTS of polystyrene (PS) and PMMA or the secondary relaxations of PMMA and polyvinyl chloride (PVC) confirmed that the Arrhenius equation can be valid only in the high temperature region and invalid in the vicinity of glass transition due to the strong dependence of apparent activation energy on temperature; while the DWLF equation can be employed in the whole temperature region including secondary relaxation and from glass transition to terminal relaxation. The theoretical explanation for the universal application of the DWLF equation was also revealed through discussing the influences of free volume and chemical structure on the activation energy of polymer relaxations