What length scales control the dynamics of miscible polymer blends?

The segmental dynamics of miscible polymer blends have been the focus of much recent research since the two constituents typically appear to experience different average dynamic environments. It has been suggested that these results can be attributed to concentration fluctuations coupled to chain connectivity effects. However, the relative importance of these two factors in determining chain dynamics is unresolved. Here we assess the importance of concentration fluctuations and also the magnitude of self-concentrations experienced by a test segment by analyzing literature values of the mean segmental relaxation times of the components of several miscible polymer blends and a disordered tetrablock copolymer. The self-composition derived in this manner is used to estimate the cooperative length scale which controls segmental dynamics, a quantity for which no first principles theory exists. Using a Taylor series expansion, we show that concentration fluctuations can strongly affect the mean relaxation time of the blend constituents in the immediate vicinity of the blend glass transition temperature, with this effect being significant even 50 K higher. We then consider the size scale of cooperative motion. For the blend component with the lower glass transition, the self-concentration is apparently independent of temperature and blend composition and consistent with a cooperative length scale of the order of one Kuhn length. This result is in good agreement with the recent conjecture of Lodge and McLeish. The results for the other blend component are quite different. At high temperatures, apparently above the glass transition of this component, the Kuhn length is still the controlling length scale for dynamics. However, the size of the cooperative volume is found to increase monotonically with decreasing temperature, in qualitative accord with the previous work of Donth