Lin Y-H
Department of Applied Chemistry, National Chiao Tung University, Hsinchu, Taiwan.
J Phys Chem B. 2005 Sep 22;109(37):17654-69. doi: 10.1021/jp040568k.
The rubber(like)-to-fluid region of the creep compliance J(t) results reported by Plazek of two nearly monodisperse polystyrene melts in the entanglement region have been quantitatively analyzed in terms of the extended reptation theory (ERT), giving the frictional factor K (= zetab2kTpi2m2) in quantitative agreement with the values obtained previously from analyzing the relaxation modulus Gt line shapes as well as calculated from the viscosity and diffusion data-a quantity shown independent of molecular weight as expected from the theory. Using the successful description of Jt in terms of ERT in the rubber(like)-to-fluid region as the reference frame in time, the glassy-relaxation process microG(t) that occurs in the small-compliance short-time region of J(t) can be studied in perspective. As shown from the analysis in terms of a stretched exponential form for microG(t) incorporated into ERT, the temperature dependence of the energetic interactions-derived microG(t) process being stronger in a simple manner than that of the entropy-derived ERT processes accounts fully for the uneven thermorheological complexity occurring in J(t) as initially observed by Plazek. When the results of analysis being displayed in the G(t) form, the relative roles of the energetic interactions-derived dynamic process and the entropy-derived ones in polystyrene are clearly revealed. It is shown that at the calorimetric glass transition temperature (Tg) the contribution from energetic interactions among segments to G(t) at the time scale of the highest Rouse-Mooney normal mode greatly exceeds that derived from entropy, indicating vitrification at the Rouse-segmental level. At the same time the Rouse-Mooney normal modes provide an internal yardstick for estimating the characteristic length scale of a polymer at Tg, giving approximately 3 nm for polystyrene. On the basis of the obtained results, the basic mechanism for the thermorheological complexity occurring in polystyrene is analyzed. It is shown that this basic mechanism should be also responsible for the breakdown of the Stoke-Einstein equation in relating the translational diffusion constant and viscosity as observed in glass-forming liquids, such as OTP and TNB, in approaching Tg from above.
普拉泽克报道的关于两种几乎单分散的聚苯乙烯熔体在缠结区的蠕变柔量J(t)的橡胶态到流体态区域的结果，已根据扩展的reptation理论（ERT）进行了定量分析，得出的摩擦因子K（=ζb2kTπ2m2）与先前通过分析松弛模量G(t)线形以及根据粘度和扩散数据计算得到的值在定量上一致——正如理论预期的那样，该量与分子量无关。以橡胶态到流体态区域中ERT对J(t)的成功描述作为时间参考框架，可以从整体上研究J(t)的小柔量短时间区域中发生的玻璃态松弛过程μG(t)。如将μG(t)以拉伸指数形式纳入ERT进行分析所示，能量相互作用衍生的μG(t)过程的温度依赖性比熵衍生的ERT过程以一种简单的方式更强，这完全解释了普拉泽克最初观察到的J(t)中出现的不均匀热流变复杂性。当分析结果以G(t)形式展示时，能量相互作用衍生的动态过程和熵衍生的动态过程在聚苯乙烯中的相对作用就清晰地显现出来。结果表明，在量热玻璃化转变温度（Tg）下，在最高的Rouse-Mooney正常模式时间尺度上，链段间能量相互作用对G(t)的贡献大大超过了熵衍生的贡献，这表明在Rouse链段水平上发生了玻璃化转变。同时，Rouse-Mooney正常模式为估算聚合物在Tg时的特征长度尺度提供了一个内部标准，对于聚苯乙烯约为3纳米。基于所获得的结果，分析了聚苯乙烯中发生热流变复杂性的基本机制。结果表明，这种基本机制也应该是玻璃形成液体（如OTP和TNB）在从高于Tg的温度接近Tg时，斯托克斯-爱因斯坦方程在关联平移扩散常数和粘度方面失效的原因。
