Self-Concentrations and Effective Glass Transition Temperatures in Polymer Blends

In a miscible polymer blend the local environment of a monomer of type A will, on average, be rich in A compared to the bulk composition, φ, and similarly for B; this is a direct consequence of chain connectivity. As a result, the local dynamics of the two chains may exhibit different dependences on temperature and overall composition. By assigning a length scale (or volume) to particular dynamic mode, the relevant “self-concentration” φ<INF>s</INF> can be estimated. For example, we associate the Kuhn length of the chain, l<INF>K</INF>, with the monomeric friction factor, ζ, and thus the composition and temperature dependences of ζ should be influenced by φ<INF>s</INF> calculated for a volume V ~ l<INF>K</INF>³. An effective local composition, φ<INF>eff</INF>, can then be calculated from φ<INF>s</INF> and φ. As lower T<INF>g</INF> polymers are generally more flexible, the associated φ<INF> s</INF> is larger, and the local dynamics in the mixture may be quite similar to the pure material. The higher T<INF>g</INF> component, on the other hand, may have a smaller φ<INF>s</INF>, and thus its dynamics in the mixture would be more representative of the average blend composition. An effective glass transition temperature for each component, T<INF>g</INF>^eff, can be estimated from the composition-dependent bulk average T<INF>g</INF> as T<INF>g</INF>(φ<INF>eff</INF>). This analysis provides a direct estimate of the difference in the apparent T<INF>g</INF>'s for the two components in miscible blends, in reasonable agreement with those reported in the literature for four different systems. Furthermore, this approach can reconcile other features of miscible blend dynamics, including the asymmetric broadening of the calorimetric T<INF>g</INF>, the differing effects of blending on the segmental relaxation times of the two components, and the failure of time−temperature superposition.