Shangguan Yonggang, Chen Feng, Jia Erwen, Lin Yu, Hu Jun, Zheng Qiang
MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China.
The Affiliated Stomatology Hospital, College of Medicine, Zhejiang University, Hangzhou 310006, China.
Polymers (Basel). 2017 Nov 2;9(11):567. doi: 10.3390/polym9110567.
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 (PP), 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--maleic anhydride) (PMMA/SMA) and PP/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.
对聚合物时间-温度叠加（TTS）中涉及的三个方程，即威廉姆斯-兰德尔-费里（WLF）方程、沃格尔-富尔彻-塔曼-黑塞（VFTH）方程和阿伦尼乌斯方程进行了重新审视，揭示了WLF形式与阿伦尼乌斯形式的数学等价性。结果，建立了一个改进的WLF（DWLF）方程来描述聚合物从次级松弛到末端流动的松弛性能的温度依赖性，并提出了其普遍应用的必要标准。DWLF方程在高温下很好地实现了包括等规聚丙烯（PP）、高密度聚乙烯（HDPE）、低密度聚乙烯（LDPE）和乙丙橡胶（EPR）在内的不同聚合物的粘弹性行为的TTS结果。通过研究聚（甲基丙烯酸甲酯）/聚（苯乙烯-马来酸酐）（PMMA/SMA）和PP/EPR共混物的相分离行为，发现DWLF方程可以很好地描述非晶/非晶共混物的相分离行为，而成核过程导致结晶/非晶共混物在熔融温度区域的位移因子较小。聚苯乙烯（PS）和PMMA的TTS以及PMMA和聚氯乙烯（PVC）的次级松弛均证实，由于表观活化能对温度的强烈依赖性，阿伦尼乌斯方程仅在高温区域有效，在玻璃化转变附近无效；而DWLF方程可用于包括次级松弛以及从玻璃化转变到末端松弛的整个温度区域。通过讨论自由体积和化学结构对聚合物松弛活化能的影响，还揭示了DWLF方程普遍应用的理论解释。
