Thermorheological Complexity in Polystyrene Melt

Using the successful description of creep compliance$ J(t)$ of nearly monodisperse polystyrene melts$^{1}$ in terms of the extended reptation theory$^{2}$ (ERT) in the rubber(like)-fluid region as the\textit{ reference frame} in time, the analysis of the glassy-relaxation process$ A_{G}u_{G}(t)$ that occurs in the short-time region of $J(t)$ in terms of a stretched exponential form incorporated into ERT reveals that the temperature dependence of the $A_{G}u_{G}(t)$ process being stronger in a simple manner than that of the \textit{entropy-derived} ERT processes accounts fully for the uneven thermorheological complexity in the $J(t)$. The results being displayed in the modulus $G(t)$ form, it is shown that at $T_{g}$, the contribution from$ A_{G}u_{G}(t)$ to $G(t)$ at the time scale corresponding to 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 length scale of the polymer at $T_{g}$, giving 3 nm for polystyrene. Based on the obtained results, the basic mechanism for the thermorheological complexity is analysed, showing that the break-down of Stoke-Einstein relation in glass-forming liquids, such as OTP, should occur for a similar reason. Ref: (1) D. J. Plazek, \textit{J. Phys. Chem.} \textbf{1965}, $69$, 3480; \textit{J. Polym. Sci. A}-2 \textbf{1968}, $6$, 621. (2) Y.-H. Lin, \textit{Macromolecules} \textbf{1984}, $17$, 2846; \textbf{1986}, $19$, 159; 168; \textbf{1987}, $20$, 885; \textbf{1999}, $32$, 181; \textit{Polymer Viscoelasticity}:\textit{ Basics, Molecular Theories and Experiments}; World Scientific: Singapore, 2003.