On the effect of Molecular weight and Frequency dependence of Tg on the interpretation of Dynamic viscosity data

In this work, we re-plot dynamic data for a series of monodispersed Polystyrene melts, and their blends, obtained at constant temperature and variable frequency $\omega$, to enable a new analysis at constant (T-Tg) instead, where Tg is made a function of Mn and $\omega$. Tg ($\omega)$ is determined by DMA, from the shift of the max of E'' with $\omega $. Tg increases rapidly with $\omega $ and levels off at higher $\omega$. The Mn dependence of Tg varies in a similar way, quickly plateaus off at approximately M=2 Me, consistent with a free volume interpretation. It is shown that correction for the Tg dependence on Mn and $\omega$ does play an important role in the determination of the scaling parameters exponents, such as the molecular weight dependence exponent for M$<$ 2 Me data, or the low frequency tail representative of the terminal behavior for blends of monodispersed samples. The paper concludes that a true separation of the variables to determine the independent effect of structural (local) and molecular weight (scaling) factors, can only be done at constant (T-Tg). The incidence of Tg($\omega $, ${\rm M})$ on the superposition at low $\omega$, is also reviewed.